 

   
 
  

W
LIBRARY 1

menu“ State
University

 

1‘

PLACE IN RETURN BOX to remove this checkout from your record.
TO AVOID FINES return on or before date due.

 

‘u

 

DATE DUE DATE DUE DATE DUE H

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

MSU Is An Affirmative Action/Equal Opportunity Institution
cmmwt

. , ,

INTERFACE CIRCUIT
FOR
PIEZORESISTIVE PRESSURE SENSORS
By

Muhammad Akbar

A DISSERTATION

Submitted to
Michigan State University
in partial fulﬁllment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Electrical Engineering

1991

 

g 77- 75'5” 5

ABSTRACT

INTERFACE CIRCUIT
FOR
PIEZORESISTIVE PRESSURE SENSORS

By

Muhammad Akbar

A major problem associated with piezoresistive pressure sensors is their cross-
sensitivity to temperature. Moreover, in batch fabrication, minor process variations
change the temperature characteristics for individual units. An important economic
implication for the success of smart sensors is the use of batch fabrication techniques
to bring down the cost of individual units. This research fulﬁlls this need by develop-
ing a new temperature compensation technique suitable for batch fabricated sensors for
a temperature range of -40°C to 130°C over a pressure range of O to 45 psi. Hardware

for the implementation of the technique and digitization of sensor output is also

developed.

The sensor model is developed from the viewpoint of simulating the sensor I/O
characteristics as a function of pressure, temperature, and processing variations. The
model includes the effects of temperature, resistor mismatch, and appropriate structural
details. The simulation results provide the worst case error band for sensors coming
from the same wafer or different wafers. All sensor parameters are functions of tem-

perature and the tracking errors.

The temperature compensation technique is implemented in two parts, using a

compensation bridge and a temperature half bridge. The zero pressure offset is reduced

ii

below the measurement precision limit for the entire pressure and temperature range.
For the sensor output, the technique is very effective for the pressure values below
35psi and provides reasonable results for higher pressures. The possible use of a

software approach to implement part of the compensation technique is also discussed.

The hardware for the ampliﬁcation, temperature compensation, and the digitiza-
tion of the sensor output has been designed and verﬁed. A dual slope AID conversion
has been identiﬁed as a simple and precise conversion technique, suitable and compati-
ble for on-chip integration with the sensor. The bipolar dual slope ADC with a word
length of 10-bits and the clock frequency of SOKHz has been designed and verﬁed.

The temperature compensation technique is suitable for batch fabrication. More-
over, it does not require compensation of individual units under sensor operating con-
ditions. The resulting interface circuit is simple, requiring modest chip area. It can be

implemented using standard IC fabrication techniques.

iii

To my mother and my father

iv

Acknowledgements

First of all I would'thank Allah (SWT), the creator and sustainer, of this universe
for providing me with the abilities and opportunity to complete this work.

I am grateful to the government of Pakistan for supporting me ﬁnancially during

my studies. Without this support, this research effort would not have been possible.

I would like to express my deepest gratitude to my advisor Dr. Michael A. Shan-
blatt for his continuous moral and professional support and guidance throughout my
doctoral program. It was a profound learning experience to work under his able gui-
dance. It has greatly enhanced my academic and professional growth. He was very
helpful and understanding throughout my work.

I owe my thanks to Dr. Donnie K. Reinhard for serving on my committee and
providing me with his valuable suggestions and helpful comments about my research
work. I also express my gratitude to Dr. Chin-Long Wey, Dr. Abdol H. Esfahanian,
and Dr. Roy V. Erickson for serving on my guidance committee and evaluating and
reviewing this research work. I express my sincere appreciation for Dr. Mohammad
Aslam for his encouragement during my work and help in obtaining the software for

my research.

I am indebted to many friends for their encouragement and support during this
work. I owe my thanks to my family and my wife’s family for their continued prayers,
encouragement, and patient wait for the successful completion of this work. My wife
Tahira and children Ammar, Aaisha, Aamina, and Safaa deserve a special thanks for

their support and understanding through out this research effort.

Table of Contents

List of Tables ............................................................................................................ xi
List of Figures ..... xii
Chapter 1. Introduction ......................................................................................... 1
1.1 Problem Statement ........................................................................................ 4
1.2 Approach ....................................................................................................... 5
1.3 Organization of Dissertation ......................................................................... 7
Chapter 2. Background .......................................................................................... 10
2.1 Deﬁnitions .................................................................................................... 11
2.2 Integrated Smart Sensors ............................................................................. 11
2.2.1 Development Stages .......................................................................... 12

2.2.2 Salient Features ................................................................................. 12

2.2.3 Application Areas ............................................................................. 13

2.3 Silicon Sensors ............................................................................................. 13
2.3.1 Design Principles .............................................................................. 14

2.3.2 Silicon Bulk Properties ..................................................................... 15

2.3.3 Electronic Transducer Devices ......................................................... 15

2.3.4 Fabrication Considerations ............................................................... 17

2.3.5 Mechanical Structures for Silicon .................................................... 19

2.3.5.1 Manufacturing Methods ...................................................... 19

2.3.5.2 Mechanical Structures ......................................................... 20

2.3.5.3 The Cutting Edge ................................................................ 21

2.4 Smart Sensor Interface Electronics ............................................................. 22
2.4.1 Interface Considerations ................................................................... 23

2.4.2 Speciﬁc Components ........................................................................ 25

2.4.3 High Temperature Microelectronics ................................................. 28

vi

2.5 Silicon Pressure Sensors .............................................................................. 29

2.5.1 Capacitive Pressure Sensors ............................................................. 30
2.5.2 Piezoresistive Pressure Sensors ........................................................ 32

2.5.3 Other Types ....................................................................................... 35

2.6 Temperature Compensation of Piezoresistive Pressure Sensors ................ 35
2.6.1 Temperature Characteristics ............................................................. 36
82.6.1.1 Temperamre Coefﬁcient of Pressure Sensitivity ................ 37

2.6.1.2 Temperature Coefﬁcient of Offset ...................................... 37

2.6.2 Temperature Compensation Techniques .' ......................................... 38
2.6.2.1 Laser Trimming ................................................................... 38

2.6.2.2 Matching Temperature Coefﬁcients ................................... 40

2.6.2.3 Mathematical Compensation ............................................... 42

2.7 Modeling and Simulation of Piezoresistive Pressure Sensors ................... 44
2.8 Summary ...................................................................................................... 46
Chapter 3. Sensor Modeling ......................................................................... 47
3.1 Introduction ................................................................................................... 47
3.2 Objectives ...................................................................................................... 47
3.3 Approach ....................................................................................................... 49
3.4 The Simulator ................................................................................................ 49
3.4.1 Overview of the Program .................................................................. 50
3.4.2 Program Veriﬁcation .......................................................................... 51
3.4.3 Revalidation ........................................................................................ 51

3.5 The Sensor Model ......................................................................................... 53
3.6 Simulation Methodology and Results ........................................................... 56
3.6.1 Methodology and Organization ......................................................... 57
3.6.2 Simulation Results: Ideal Sensor ....................................................... 57
3.6.3 Simulation Results: Batch Fabrication .............................................. 60
3.6.3.1 Batch Fabrication Model ...................................................... 61

3.6.3.2 Simulation Organization ....................................................... 62

3.6.3.3 Simulation Results ................................................................ 63

vii

3.7 Summary ........................................................................................................ 66
Chapter 4. Temperature Compensation .............................................................. 68
4.1 Introduction ................................................................................................... 68
4.2 Temperature Characteristics .......................................................................... 68
4.2.1 Review ................................................................................................ 69
4.2.2 Temperature Errors ............................................................................ 69

4.3 Objectives ...................................................................................................... 71
4.4 Approach ....................................................................................................... 71
4.5 Compensation Technique .............................................................................. 72
4.5.1 Compensation: Same Wafer Variations ............................................ 73
4.5.1.1 The Double Bridge Technique ............................................. 73

4.5.1.2 Results ................................................................................... 76

4.5.2 Compensation: Wafer-to-Wafer Variations ....................................... 79
4.5.2.1 Approach ............................................................................... 79

4.5.2.2 The Half Bridge Technique ................................................. 80

4.5.2.3 Results ................................................................................... . 82

4.5.2.4 Discussion ............................................................................. 86

4.6 Summary ........................................................................................................ 88
Chapter 5. Interface Hardware ............................................................................. 90
5.1 Introduction .................................................................................................. 90
5.2 Design Objectives and Philosophy ............................................................ 91
5.3 Design Speciﬁcations ................................................................................... 92
5.4 Ampliﬁcation ................................................................................................ 93
5.4.1 Design Approach for the Op-amp .................................................... 94

5.4.2 The Op-amp Circuit .......................................................................... 94

5.4.3 The Ampliﬁer Circuit ....................................................................... 97

5.5 Analog Subtraction ...................................................................................... 98
5.6 Analog to Digital Conversion ..................................................................... 99
5.6.1 Types of ADCs ................................................................................. 101

viii

5.6.1.1 Successive Approximation .................................................. 101

5.6.1.2 Flash or Parallel .................................................................. 102

5.6.1.3 Ramp or Integration ............................................................ 102

5.6.1.4 Tracking or Servo ............................................................... 104

5.6.2 Selection of the Analog to Digital Conversion Technique ............. 104

5.6.3 The Dual Slope ADC ....................................................................... 105

5.6.4 Designof the Dual Slope ADC ....................................................... 108

5.6.4.1 Design Speciﬁcations .......................................................... 110

5.6.4.2 Analog Circuit for the ADC ............................................... 113

5.6.4.2.1 Sign Detector ...................................................... 115

5.6.4.2.2 Integration Control .............................................. 115

5.6.4.2.3 The Integrator Circuit ......................................... 117

5.6.4.2.4 Zero Crossing Detector ....................................... 118

5.6.4.2.5 Performance of the Analog Circuit ..................... 118

5.6.4.3 Digital Circuit for the ADC ................................................ 119

5.6.4.3.1 Timing Pulse Generator ...................................... 119

5.6.4.3.2 The ADC Counter and Register ......................... 12]

56.4.3.3 Control Circuit .................................................... 122

5.7 The Half Bridge Compensation Hardware ................................................. 123

5.8 Summary ...................................................................................................... 125
Chapter 6. Conclusion ............................................................................................ 127
6.1 Summary and Contributions ........................................................................ 127

6.2 Future Research ........................................................................................... 131
Appendix A. SENSIM Simulations ....................................................................... 133
Al Sensor Structures and Model Parameters ................................................... 133
A2 The Simulation Code for the Sensor with no Tracking Errors ................. 134
A3 The Simulator Output for the Sensor with no Tracking Errors ................ 135
Appendix B. Simulation Results ........................................................................... 141

ix

B.l Piezoresistive Bridge Outputs ..................................................................... 141

B2 Compensation Bridge Outputs .................................................................... 153
3.3 The Compensated Outputs .......................................................................... 156
3.4 The Half Bridge Outputs ............................................................................ 162
3.5 The Final Temperature Compensated Outputs ........................................... 163
Appendix C. PSpice Simulation Code .................................................................. 167
' C.1 'nte Op-amp Circuit .................................................................................... 167
C2 The Analog Circuit for the ADC ............................................................... 168
Appendix D. VHDL Simulation Code ................................................................... 170
Bibliography .............................................................................................................. 177

2.1
2.2
3.1
4.1
5.1
5.2

5.3

List of Tables

Physical effects for sensors in silicon [4].

 

Silicon devices that can be used for sensing [91].

Characteristics of various piezoresistor layouts.

Piezoresistor tracking error values.

 

 

 

Characteristics of the op-amp [137].

 

ADC characteristics as functions of word length,

 

frequency, and reference voltage.
Characteristics of the Bipolar Dual Slope ADC.

xi

 

14
18
59
77
96

112
113

2.1
2.2
2.3
2.4
2.5
2.6
2.7
3.1
3.2
3.3
3.4

3.5
3.6
3.7
3.8
3.9
4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8
4.9

4.10 The compensated output for the sensor with 20% tracking errors. ...................

4.11 The pressure sensitivity for the sensor with -20% tracking errors. ...................

List of Figures

Diaphragm types [101,102].

 

 

Smart sensor technology temperature range and cost [122].

 

Typical silicon pressure sensing structures.
Pressure-voltage characteristic for the sensor described in [7].

Temperature response of the sensor with 10% tracking errors.

 

 

 

Zero pressure offset of the sensor with 10% tracking errors.

Typical calibration/compensation circuit [5].

 

The measured and simulated diaphragm center deﬂection [17].

Stress distribution over the diaphragm.

 

 

The sensor structure.

 

Piezoresistor layouts on a diaphragm and their Cartesian
coordinates in micrometers (Not to scale).

 

Pressure sensitivity for the three layouts.

 

Output voltage for the three layouts.

 

The sensor response as a function of pressure and temperature.

 

 

Pressure sensitivity for various tracking errors.

 

The zero pressure offset for various tracking errors.

 

The error voltages for the sensor.

 

The double bridge temperature compensation technique.

The improved double bridge temperature compensation technique. ....................

 

The compensated zero pressure offset voltage.

The compensated output voltage.

 

The half bridge temperature compensation technique.

 

Flow chart for the half bridge temperature compensation technique. .................
The compensated sensor response as a function of the temperature. ..................

The compensated output for the sensor with no tracking errors.

xiii

 

21
29
3 1
34
39
39
41
52
53
54

58
6O
61
64
65
66
70
74
76
78
79
81
83
84
84
85
86

CHAPTER 1

INTRODUCTION

Sensors are used to acquire physical information in a usable form, usually electri-
cal. Historically, sensors were mechanical components which used physical means to
convey their responses. The next generation of sensors were solid-state. Currently, a
new generation of sensors is evolving by integrating the interface circuitry on the sen-
sor chip. The prime advantage of such a sensor is the proximity of transducer and
associated electronics. For many smart sensors, the performance of the overall device
depends more on the interface electronics rather than on the transduction element. An
important economic implication for the success of smart sensors is the use of batch

fabrication techniques to bring down the cost of individual units.

One such sensor of current interest is the piezoresistive pressure sensor. Presently
this is the most common pressure sensing technique followed by capacitive pressure
sensors. For both techniques a thin diaphragm is etched from the silicon as the basic
sensing element. The capacitive pressure sensor uses the ﬂexible diaphragm as one
plate of a variable air-gap capacitor. Capacitive pressure sensors have higher sensitivity
and are less vulnerable to temperature but introduction of any electronics with the
sensing device is a difﬁcult process [1]. For the piezoresistive pressure sensors the
stress sensing resistors are generally formed in a wheatstone bridge conﬁguration on
the thin diaphragm. The piezoresistive sensors are easier to manufacture and, as a
result, cost less. Additionally the response is more linear so the output requires less

signal conditioning. The major problem of piezoresistive pressure sensors is their

cross-sensitivity to temperature. Moreover, in batch fabrication, minor process varia-

tions change the temperature characteristics for individual units.

The primary aim of this research is to develop an interface circuit for the
piezoresistive pressure sensors to provide a compensated digital output over a wide
pressure and temperature range. The sensor is intended to be used in a temperature
range of -40°C to 130°C over a pressure range of 0 to 45 psi. This pressure and tem-
perature range is sufﬁcient to cover the automotive [2,3] and other general applications
[4-6]. The interface should also take care of the processing variations, eliminating the
need for temperature compensation of individual units. The interface circuit should be
simple and suitable for the batch fabrication of such sensors. This aspect is very
important for the economical development of the integrated sensors since batch fabri-

cation is the key factor in lowering the costs of these devices.

As stated earlier, the major problem associated with piezoresistive pressure sen-
sors is their cross-sensitivity to temperature. Recognizing this difﬁculty many research-
ers have devoted considerable effort in developing new hardware and software tech-
niques for temperature compensation of piezoresistive pressure sensors. Temperature
compensation techniques have been reported using laser trimming, external resistors,
mathematical compensation, and clever use of material properties [7-16]. Generally
these techniques are for limited temperature and pressure ranges, and in many cases
for speciﬁc applications such as biomedical devices. Moreover, these techniques
involve additional processing steps performed under sensor operating conditions which
add time and cost to the device fabrication process. Therefore, these techniques may
not have an immediate large user base because of their high cost. Such cost require-
ments are best matched by a technique which is suitable for batch fabrication and still

utilizes standard IC fabrication techniques.

 

Temperature affects the transducer and measurand in a variety of ways. The
inﬂuence of temperature is manifested as a change in the span and offset of the sensor
response. The errors in the piezoresistive sensor response are mainly caused by three
sources: on-chip tracking errors, wafer-to-wafer tracking errors, and the temperature
dependency of the coefﬁcient of piezoresistivity. A new temperature compensation
technique is developed in two parts in this work. The ﬁrst part employing an identical
compensation bridge, takes care of the zero pressure offset and the errors caused by
on-chip tracking errors. The second part of the technique uses a temperature half
bridge and companion digital circuit to remove the remaining temperature dependence
from the sensor output. Both the techniques are simple, use standard IC technologies,
and are suitable for batch fabrication. The use of this technique make the sensor
response temperature independent. The only variation left in the output of the sensor is
caused by wafer-to-wafer tracking errors. This can be taken care of during the calibra-

tion of the sensors.

Piezoresistive pressure sensors are modeled from the viewpoint of batch fabrica-
tion. Sensim, a simulation program for the piezoresistive and capacitive pressure sen-
sors [17] is used to. simulate the sensor I/O characteristics as a function of pressure,
temperature, and processing variations. The simulation program requires a low level
physical model and produces diaphragm deﬂection, stress distribution over the
diaphragm, average stress over the piezoresistors, node voltages, changes in resistance
due to stress, and capacitance changes with pressure. The analog output of the com-
pensation circuit is digitized by a dual slope analog to digital converter. The conver-
sion technique is simple, precise, and compatible with on-chip integration with the sen-
sor [18]. The design for the bipolar dual slope analog to digital converter is presented.

The analog portion of the interface circuit is veriﬁed by PSpice 4.03, the de facto

standard for analog circuit simulation. The digital portion is tested by VHDL, the IEEE
standard hardware description language (HDL).

1.1 Problem Statement

Ongoing advancement of IC fabrication, micromachining, and packaging techno-
logies have given rise to the concept of integrated smart sensors in the form of monol-
ithic silicon chips containing both sensors and circuitry. Though some very convincing
advantages are attached to smart sensors, only a few such devices are commercially
available at present. Some of the obvious concerns in achieving the integration are the
possible drop in yield, package design, and the need for process compatibility between

the sensing element and the associated electronics.

Pressure sensors are one of the most developed type of sensors at present. Of
these, piezoresistive pressure sensors show better process compatibility for the integra-
tion of on-chip electronics [1]. Piezoresistive pressure sensors offer good linearity
over a wide dynamic range, moderately high pressure sensitivity, and freedom from
hysteresis, however they have experience a high degree of temperature sensitivity.
Their pressure sensitivity as well as zero pressure offset are a function of temperature.
The temperature dependence is determined by the transducer structure and the bridge
resistors tracking errors. Therefore the temperature characteristics for individual units
differ slightly because of minor processing variations. As a result of this, temperature
compensation of individual units must be used at the present time. Techniques like
precise laser trimming of individual units [5,8,9,11,13,16,19-22] are used but are

expensive and time consuming processes.

One possible way to address this problem is the development of temperature com-
pensation techniques which are not speciﬁc to individual units. Some of these tech-
niques have been developed, but for a limited temperature range and for speciﬁc appli-
cations such as certain biomedical devices [23-25]. This limits the application variety
for pressure sensors, especially for the applications requiring operation over a wide

temperature range. One of the urgent needs is the development of a simple but

generalized temperature compensating circuit which covers a wide temperature range
and does not have to be adjusted for individual units. To fulﬁll the smartness concept
the sensor output must be compatible with the digital world. Therefore the output has
to be ampliﬁed and converted to digital form. In response to these needs, the aim of
this research is to develop an interface circuit which takes the sensor output and pro-
duces a corresponding temperature compensated digital number for -40°C to 130°C

over a pressure range of 0 to 45 psi.

1.2 Approach

The general approach of this research is to 1) review the design, architecture, and
existing temperature compensation techniques for the piezoresistive pressure sensors;
2) develop a realistic model for the sensor and generate sensor performance data over
the desired pressure and temperature range; 3) deve10p a temperature compensation
technique for the sensor; and 4) design and verify the temperature compensation and
the digitization circuitry.

The ﬁrst task, an in-depth review of existing piezoresistive pressure sensors and
their associated electronics, serves four purposes. First, it provides an understanding of
the physical structure of the sensor and its effects and demands on the interface elec-
tronics. Second, the more advanced and useful techniques can be adopted as part of the
new design. Third, critiques on previous approaches enable the avoidance of known
pitfalls in the design decisions. Fourth, the research areas which need urgent attention
but are not covered by this research may be identiﬁed. The review is focused on four
key areas: silicon mechanical structures, the associated interface electronics, tempera-
ture compensation techniques, and modeling and simulation of piezoresistive pressure
sensors. An understanding gained ﬁom this study will help in developing a better sen-

sor model and interface circuit.

For the second task, the sensor model is developed from the viewpoint of simulat-
ing the sensor I/O characteristics as a function of pressure, temperature, and process
variations. The model lays a foundation for further work. It enables functional simula-
tion of the sensor and provides an input source for the interface circuit. The model is
also used to study the temperature characteristics of the sensor. The model includes the
effects of temperature, resistor mismatch, and structural details of the sensor. Sensim,
the piezoresistive and capacitive sensor simulation program is used for the simulation.
The simulator is validated and used to generate data over the desired pressure and tem-

perature range.

The third task is to develop a compensation technique to remove the effects of
temperature and processing variation for a temperature range of -40°C to 130°C overia
pressure range of 0 to 45 psi. Temperature dependence of the sensor output and mro
pressure offset are the major drawbacks of piezoresistive pressure sensors. The effects
of temperature are studied with respect to these two parameters, using the data gen-
erated in the second task. The temperature compensation technique has been developed
in two parts. The ﬁrst part makes use of two bridges: a piezoresistive bridge fabri-
cated on the diaphragm and an identical compensation bridge located on the bulk part
of sensor chip. Output of the ﬁrst bridge is a function of pressure, temperature, and
processing variations whereas the compensation bridge response is dependent on tem-
perature and processing variations only. The difference of the two bridge outputs
removes the zero pressure offset and the variations caused by on-chip tracking errors.
The second part of the technique uses a temperature half bridge located on the bulk
part of the chip to generate the temperature signal. This signal and some digital circui-

try is used to remove the remaining temperature dependency from the sensor output.

The fourth task is the speciﬁcation of a circuit design for ampliﬁcation, tempera-
ture compensation, and digitization of the sensor output. This task will produce the

hardware for interface circuit. The ampliﬁcation of the bridge signals is implemented

using an op-amp based ampliﬁer circuit. The ampliﬁer also serves the purpose of con-
verting the double ended bridge outputs to the single ended signals. The difference of
the piezoresistive bridge and the compensation bridge outputs is obtained from an op-
arnp based analog subtractor circuit. Use of analog subtraction results in considerable

savings of chip area.

One of the key requirements for expanding microtransducers into smart sensors is
simple, and process compatible analog-to-digital conversion. To cope with the process-
ing variations, the technique should not require precise components. To fulﬁll these
requirements the dual slope conversion technique is selected for the interface circuit.
The design of the bipolar dual slope analog to digital converter is carried out in

bottom-up fashion.

The ﬁnal task involves interface hardware behavioral modeling to ﬁne tune and
verify the design. The sensor model developed in second task is used as the input
source for the simulations. The design and testing of the circuit is carried out in bot-
tom up fashion. Initially small blocks, such as op-amp, comparator, counter, and
decoder are simulated to ensure desired behavior. Then these blocks are integrated to
form the complete circuit. Finally the complete analog and digital portions of the cir-
cuit are simulated and tested. PSpice, the de facto standard for analog circuit simula-
. tion is used for the analog portion of the circuit and VHDL, the IEEE standard
hardware description language is used for digital simulations. The necessary
reﬁnements, modiﬁcations, and parameter and component selection is documented in

the design process.

1.3 Organization of the Dissertation

In Chapter 2 an overview of smart integrated sensors and their associated inter-

faces is presented. First, a set of deﬁnitions used in this dissertation is presented. Then

 

 

silicon based sensors are reviewed with two issues highlighted: the use of silicon bulk
properties, and micromachining techniques used to create three dimensional intricate
structures in silicon. With this background the smart sensor interface electronics are
reviewed from the viewpoint of understanding possible interface functions and
approaches taken to implement these functions for the fulﬁllment of the smart sensor
concept. Then various approaches to implement smart pressure sensors are discussed
and a review of the temperature characteristics of the piezoresistive pressure sensors is
presented. Previous efforts for temperature compensation are reviewed and reassessed
from the viewpoint of their usefulness for a generalized, low cost interface, suitable for
batch fabrication. Finally previous efforts in modeling and simulation of piezoresistive
pressure sensors are reviewed in order to gain an understanding of the existing design
aids.

In chapter 3 the sensor is modeled and simulated to provide data for the develop-
ment of temperature compensation circuitry. Sensim, the piezoresistive and capacitive
sensor simulation program is described and tested for its correctness. A realistic sensor
structural model is developed and used to generate the sensor response for the desired
pressure and temperature range. The results of the simulations are organized and stu-
died. With this background, the sensor is modeled from the viewpoint of batch fabrica-
tion and simulations are run again to include the effects of processing variations.
Again the results are organized and used to gain a better understanding of the inﬂuence

of processing variations on the temperature characteristics of the sensor.

In Chapter 4 the temperature compensation technique for the offset and sensor
output is described. Sensor responses from the previous chapter are evaluated and the
compensation technique is developed in two parts. In the ﬁrst part the double bridge
technique is proposed for temperature compensation. Sensirn and PSpice are used to
test the effectiveness of the technique. The compensation effectively removes the zero

pressure offset and errors caused by on-chip processing variations but the sensor output

is still a function of temperature. The second part of the technique employs a tempera-
ture half bridge and some digital circuin to eliminate the remaining temperature

dependency. The resulting response is independent of temperature variations.

In Chapter 5 the interface hardware is described. The analog portion of the circuit
is simulated with PSpice 4.03 and the digital portion with VHDL. The design of the
interface circuit went through numerous reﬁnements during its course. Desirable as it
may be, documenting all the changes is itself a formidable task. The objective is to
discuss and document the important design decisions. First, the design objectives, phi-
1030phy, and speciﬁcations are set. Then the implementation details for the ampliﬁer
and the subtractor circuit are presented. This is followed by the description of the
selection and retroﬁtting of the analog to digital conversion circuit. Basic analog to
digital conversion techniques are reviewed from the standpoint of selecting the one
best suited for the interface circuit. The dual slope technique is selected and the design
for a dual slope analog to digital converter is presented. Finally, the proposed digital

circuit for the implementation of the half bridge temperature compensation technique is

described

In Chapter 6, a summary of major results and contributions of this research is

presented. Further research issues are identiﬁed and discussed.

CHAPTER 2

BACKGROUND

In this chapter an overview of integrated smart sensors and their associated inter-
faces is presented. First, a set of deﬁnitions used in this dissertation is presented. This is
followed by a brief review of integrated smart sensors. Silicon based sensors are then
reviewed from the perspective of understanding how silicon can be used to fabricate
integrated smart sensors. Two issues are specially addressed: the use of silicon bulk pro-
perties, and micromachining techniques used to create three dimensional intricate struc-
tures in silicon. Then the smart sensor interface electronics are reviewed from the
viewpoint of understanding possible interface functions and approaches taken to imple-
ment these functions for the fulﬁllment of the smart sensor concept. Then various
approaches to implement smart pressure sensors are discussed. This is followed by a
review of the temperature characteristics of piezoresistive pressure sensors. Previous
efforts for the temperature compensation are reviewed and reassessed from the viewpoint
of their usefulness for a generalized, low cost interface suitable for batch fabrication.
Finally previous efforts in modeling and simulation of piezoresistive pressure sensors are
reviewed in order to gain an understanding of the existing design aids for piezoresistive

pressure sensors.

10

11

2.1 Deﬁnitions

Numerous permutations of some basic deﬁnitions of sensors and related devices can
be found in the current literature. Since the purpose of this chapter is primarily to sum-
marize the background work in this area, it is appropriate at this point to put forth a stan-

dard set of deﬁnitions as will be used throughout this dissertation.

In the most general sense, a sensor can be anything from the most simplistic trans-
ducer, like a bi-metal strip, to an intelligent device, like a digital fever thermometer. It
takes one form of energy (a sensed input) and converts it to another form of energy, often
an electrical signal or some other form which is useful for interpreting or processing. The
terms sensor and transducer are used interchangabily. If the sensor is integrated onto sili-
con or some other substrate material then, for the purpose of this dissertation, it is

referred to as an integrated sensor.

A smart sensor is a device which, in addition to containing a transducer, also con-
tains some degree of additional circuitry such as signal conditioning and/or interface cir-
cuits. If these devices all reside on the same substrate then, again for the purpose of this

dissertation, they are referred to as integrated smart sensors.

A hybrid smart sensor is a device in which more than one sensor and their associ-
ated smart circuin are incorporated into one conglomerate functional unit. If the device
resides on a single, or sometimes in a closely related package of multiple chips, it is

referred to as an integrated hybrid smart sensor.

2.2 Integrated Smart Sensors

Sensors are used to acquire physical information in a usable form, usually electrical.
They are the input to all control and monitoring systems and, therefore, form a very
important class of devices. A review of development stages, advantages, and application

areas for these modern sensing devices is presented in this section.

 

 

 

12

2.2.1 Development Stages

Historically all sensors were mechanical components, which used physical means to
convey their responses. Consequently, when electronic sensors were developed they used
analog signals to transmit their responses. The sensing element was still mechanical,
which was specially designed to take care of all abnormalities such as nonlinearity,
cross-sensitivities, compensation, etc. This resulted in complex bulky sensors. The next
generation of sensors were solid-state. The sensor and analog signal conditioning circuits
were implemented in. a discrete or hybrid module amplifying the sensor output and com-
pensating for some secondary parameters. This output was hardwired to a remote
analog-to-digital converter over a one way analog line. Currently, a new generation of
sensors is evolving by integrating the interface circuitry on the sensor chip. Thus, the
semiconductor sensor research and application efforts encompass not only the design of
silicon-based transducers but also the on-chip incorporation of additional circuitry for
signal processing and conditioning. Additionally, micromachining techniques, which
involve the production of mechanical components in and on silicon, have opened new

vistas in the area of silicon-based sensing of mechanical functions.

2.2.2 Salient Features

Integrated sensors have the inherent advantages of small size, light weight, high
performance, low cost, and high reliability. These sensors provide a better signal-to-
noise ratio, improve sensitivity, and provide a digital output which is less prone to noise.
The sensor design is simpliﬁed and the electronics and the processor take the burden of
correcting parameters and removing cross-sensitivity effects. The on-chip electronics
include ampliﬁcation, calibration, and digitization of the sensor output signal. The effects
to be corrected may include non-linearity, cross-sensitivity, hysteresis, stability, repeata-
bility, and excitation voltage variations. Apart from this, communication and interface

electronics are also necessary to make the smart sensor chip addressable and capable of

 

 

 

 

 

 

13

communicating with a central processor and, in some cases, other sensors or actuators.

2.2.3 Application Areas

The integrated smart sensors have wide ranging applications in a variety of ﬁelds.
Integrated sensors currently available or under development include pressure
[6,7,9,12,25-43], temperature [4,26,28,44,45], chemical (ion concentration)
[27,29,44,46-49], optical [4.28.50], magnetic ﬁeld [4,51-56], motion and acceleration
[57-63], vibration and frequency [61,64,65], force [66-71], gas composition [72-79], and
humidity sensors [33,80,81]. Integrated sensors have been used in the automobile indus-
try, robotics, biomedical applications, hydraulics control, the marine and aeronautical

engineering, industry, and the semiconductor industry itself.

2.3 Silicon Sensors

Nearly all present integrated sensors are silicon based. Silicon as a sensor material
is very promising because it shows sensitivity to many physical parameters, makes batch
fabrication possible, and permits the integration of sensing elements and electronic circu-
itry on the same chip (providing, of course, that the processing requirements are compati-
ble). Effects shown by silicon for various types of physical signals are summarized in

Table 2.1 [4].

' Fabrication technology of silicon is very mature and can be used for creating very
precise patterns on the wafer. The ease of forming silicon dioxide and its effective use as
a mask to deﬁne various regions enables the creation of ﬁne three dimensional
geometries in silicon. The art of doing so is called micromachining. To obtain some
insight into this new technology the basics of silicon bulk properties and micromachining
techniques are reviewed in this section. The use of these concepts in fabricating

microsensors as well as other novel miniature devices and structures is summarized.

14

Table 2.1. Physical effects for sensors in silicon [4].

 

Physical Signal Effect

 

Radiant Signals photovoltaic effect, photoelectric effect,
photoconductivity, photomagneto-electric effect

 

Mechanical Signals piezoresistivity, piezoelectric
effect, piezojunction effect

 

Thermal Signals Seebeck effect, temperature dependence of
conductivity and junctions, Nemst effect

 

Magnetic signals Hall effect, magnetoresistance, Suhl effect

 

 

 

Chemical signals ion-sensitive ﬁeld effect

 

 

2.3.1 Design Principles

Silicon can be employed in three basic ways to produce a microsensing element.
Firstly its bulk properties can be exploited. Secondly it can be used as substrate to deposit
ﬁlms of other materials. Finally micromachining can be used to fabricate intricate
mechanical structures such as thin diaphragms, cavities, apertures and cantilevered

beams. Sensors are being developed using all these approaches.

Magnetic and optical sensors make use of the bulk properties of silicon. Chemical
and humidity sensors employ chemically sensitive semiconductor devices (CS SD). These
devices are special types of ﬁeld-effect transistors (FETs) with an overlay of chemically
sensitive or selective materials over their gate electrode. Flow and temperature sensors
make use of micromachined structures. Some form of heating of the ﬂuid at two dif-
ferent points is employed for ﬂow sensors. Finally both types sense/measure the tempera-

ture.

Pressure, tactile force, motion, acceleration, vibration, and frequency sensors use

micromachining to fabricate diaphragms, cantilever beams or bridges on which ﬁlms are

15

deposited. An alternate approach uses diffusion or ion implantation to create electronic
components in these structures. The sensing element may be a variable capacitor, a sin-
gle resistor, a resistor bridge, or a transistor/diode. Capacitance change, piezoresistive
effect, piezoelectric effect, or piezojunction effect is used to convert motion or stress into

an electrical signal.

2.3.2 Silicon Bulk Properties

The silicon wafers used for smart sensors are the same as those used for integrated
circuits. They are composed of single crystal silicon, extremely pure except for the trace
presence of elements intentionally introduced to provide excess charge carriers. Because
of the purity and single crystal structure, there are few slip planes and dislocation sites to
allow for the plastic deformation common in metals. Hence, silicon based mechanical
devices have less creep and hysteresis than metal or plastic based devices. Silicon is, in
fact, about three times stronger than stainless steel [82]. In general silicon has very
impressive mechanical properties. Silicon also has good temperature characteristics, with
electronic devices constructed using a silicon basis capable of functioning up to 200°C or

higher with modiﬁcations to the substrate and packaging.

Bulk silicon is sensitive to ﬁve basic properties [53]. First, it demonstrates a sensi-
tivity to electric ﬁelds which modify the ﬂow of carriers. Second, magnetic ﬁelds can
create a potential difference due to the redistribution of charge (Hall effect) or a
deﬂection of charge carriers [55]. Third, radiation striking the material can generate car-
riers. Fourth, strain changes the resistivity and junction potentials. Fifth, temperature

variations also affect both the resistivity and junction potentials.

2.3.3 Electronic Transducer Devices

Various electronic devices are being used to transduce physical parameters into

electrical signals. These devices are usually standard electronic building blocks that have

16

been modiﬁed in their material and/or construction to make them sensitive to the desired

phenomenon.

Modiﬁcations to MOS ﬁeld effect uansistors form an important area of sensor
research [83]. The threshold voltage of a MOSFET is a function of the gate-to-
semiconductor work function, charges in the silicon and the insulator, the insulator capa-
citance, and the Fermi work function. One of the keys to using the MOSFET structure as
a transducer is to modify its threshold voltage by the physical or environmental parame-
ter to be measured. This can be accomplished by one of several methods. First, the gate
can be constructed of a material sensitive to the parameter being measured [74,84—87].
Second, the gate can be separated from the insulator with an electrolyte [87,88]. This
produces the ion sensitive FET (ISFET). In order to increase sensitivity to particular
ions, a thin membrane may be placed on the insulator to produce a chemically sensitive
FET (CI-IEMFET). If the environment is hostile to silicon dioxide, the insulator may be
coated with other oxides. Third, the gate can be eliminated entirely, producing the open
gate FET (OGFET) for detecting gases. Undercutting the gate of a MOSFET to expose
the insulator yields the surface accessible FET (SAFET).

Bipolar transistors are also being used to implement sensors. Because they are junc-
tion devices, they ﬁnd usage detecting the bulk sensitivities of silicon. One example is
the sensitivity to magnetic ﬁelds. A two dimensional and a three dimensional magnetic

ﬁeld detector has been constructed by splitting the collector [55,56].

Diodes can also be modiﬁed to sense physical parameters. Like MOSFETs, one of

the electrodes is made of a material or metal sensitive to the physical parameter. Thus,
the V-I characteristics of the diode are modiﬁed in response to variations in the desired
physical parameter. This provides information about the parameter being sensed. Chemi-

cal and gas sensors have been implemented using this technique [87,89].

Many transducers use the piezoresistance effect to convert strain into resistance

[7,8,30,58]. This effect utilizes the change in resistance of bulk silicon when

l7

mechanically stressed. The piezoresistors can be created in the silicon by diffusion or ion
implantation. These resistors changes anisotropically under stress due to the crystalline
nature of silicon, resulting in sensitivities based on orientation as well as construction

parameters.

The piezoresistors can also be formed over silicon using ﬁlm deposition techniques.
In this case silicon dioxide is used as a dielectric isolation between the polysilicon resis—
tor and the silicon substrate. This construction has the advantages of being isotropic and
also makes possible on-chip laser trimming of piezoresistors [8,16,22,90]. Possible disad-
vantages include the capacitive coupling of the substrate td the resistor and a lower pres-
sure sensitivity.

The devices which can be fabricated in and on silicon which give an electric output
are summarized in Table 2.2 [91]. Most of these devices are already being used for the

implementation of integrated sensors.

2.3.4 Fabrication Considerations

For most of the manufacturing of the sensors discussed above, the fabrication tech-
niques are the same as are usually required for standard VLSI constructions [44]. One of
the difﬁculties that still exists in the mass production of microsensors, however, is that
techniques used to optimize the transducer manufacturing tend to compromise the elec-

tronics manufacturing and vice-versa.

The same techniques that traditionally have been used for deposition can still be
applied to sensor manufacturing. Metals can be sputtered [73,76,92] or vacuum eva-
porated [75-77,93,94]. Metal oxides are deposited by sputtering [74,79], low power
chemical vapor deposition [89], or by exposing the metal to an oxygen atmosphere at an
elevated temperature after it has been deposited [75,79]. Spin casting, used for deposit-
ing masking materials, can be used to place parameter sensitive polymer ﬁlms on the

chip [95,33]. Ion implantation is available to drive chemicals into existing materials

[49].

18

Table 2.2. Silicon devices that can be used for sensing [91].

 

 

 

 

 

 

 

 

Domain Silicon device
Radiant Photodiode, Solar cell, Phototransistor
Photoconductor, MIS diode, Strip detector
Mechanical Piezoresistor, Piezojunction, Piezo-MOSFET ‘
Thermal Therrrristor, Therrnodiode, Thermotransistor
Magnetic Hall plate, Magnetoresistor
Magnetodiode, Magnetotransistor
Chemical ISFET, Pd- gate MOSFET, Chemdiode
Chemcapacitor, Chemresistor

 

In addition, some new methods not used for traditional IC fabrication have also
been developed One technique is the Langmuir-Blodgett ﬁlm transfer technique used to
deposit a lipid sheet, one molecule thick, on the chip [96,97]. Another very important

technique developed for sensors is the micromachining of mechanical structures into sili-

COII.

 

19

2.3.5 Mechanical Structures for Silicon

Because bulk silicon has such good mechanical properties, it is well suited for pro-
viding physical structures for sensors. The advantages of making micromechanical trans-
ducers include small size, the ability to include on chip electronics, and a resistance to
creep and hysteresis common in larger structures. Manufacturing methods, mechanical
structures for silicon sensors, and recent expansion of micromachining techniques into

other research areas are reviewed in this section.

2.3.5.1 Manufacturing Methods

Silicon can be machined to form three dimensional shapes through the use of chem-
ical and plasma etching techniques. The process of micromachining is used to create
mechanical structures on a silicon wafer using anisotropic and isotropic etching of silicon
[82]. Micromachining was initially developed for the fabrication of microsensors but

now it is being used to create a variety of structures in silicon.

In addition to micromachining, several additional manufacturing techniques for sup-
porting mechanical structures are necessary. The ﬁrst is the ability to accurately align
masks on either side of the silicon wafer for double-sided or back etching. Alignment
can be achieved with infrared optics or by placing alignment marks on both sides of the
wafer at the ﬁrst production step [98].

Another technique for supporting the fabrication of mechanical structures is the use
of anodic glass bonding to silicon. The glass produces a supporting structure with about
the same thermal expansion coefﬁcient as silicon [82]. A pyrex plate and the silicon
wafer are placed in contact, raised to 400 °C, and a high voltage is applied across them.

This yields a strong, long lasting, low stress bond [46].

A new silicon/silicon bonding technique, silicon fusion bonding (SFD), has been
developed for diaphragm based sensors [99]. Using this technique, single crystal silicon

wafers can be reliably bonded with near-perfect interfaces without the use of

20

intermediate layers. This technique makes it possible to fabricate ultraminiature
diaphragm based structures. It has also been used to fabricate high pressure sensors suit-

able for pressure ranges from 1000psi to 10,000psi [99].

2.3.5.2 Mechanical Structures

In recent literature, the most popular mechanical structure has been the thin
diaphragm [7,8,,15,16,19,22,24,30,34,68,100-103]. Initially, circular or annular
diaphragms were used [20,24,42,104-107] but currently, the square diaphragms are pre-
ferred for most applications [7,19,22,34,35]. Rectangular diaphragms have also been
used in some designs [8,108,109]. The popularity of square diaphragm stems from case
of fabrication and higher pressure sensitivity [98]. The principal physical parameter for a
diaphragm is the pressure sensitivity, which is inversely proportional to the square of the
thickness and proportional to the area of the diaphragm [25,101]. This implies that the
thinner diaphragms provide higher pressure sensitivity.

There are two leading methods for manufacturing diaphragms, examples of which
appear in Figure 2.1. In the ﬁrst method, shown in Figure 2.1(a) the silicon is back
etched from the opposite side that will contain the logic circuitry. After the logic
manufacturing is done, the chip is bonded to glass as described above. Diaphragms as

thin as 20 um i 2 um have been produced using this method [101].

A new method, shown in Figure 2.1(b), does not require back etching and, there-
fore, dispenses with the need for anodic glass bonding and mask alignment. This tech-
nique uses a channel through etch-resistant masks to laterally etch a v-groove. Because
the etch process is self stopping, very accurate devices can be made. A 1.4 um thick, 80
um x 80 um square diaphragm has been produced [34,68,102]. SFB can also be used to
create the same type of structure. A v-groove is etched ﬁrst, followed by the bonding of a
thin p-type silicon wafer with n-type epi-layer on top [99]. The thickness of the epi-layer
corresponds to the required thickness of the ﬁnal diaphragm for the sensor.

21

 

    

Metal -:zir::€:3:é:223:3:3:::3:5::.3532355332.:3v:3r2r-::§:é:?:3:?3-::5:':=::::r;:i:§:3'3’5.3:§-§-‘:3ra-::1'
Si 0 2

      

    

       
 
   
    

If: ¥ .

 

Diffused
piezoresistor

  

Silicon

 

 

m Si 02

a) Back etched diaphragm.

     

m
lllllllllllllllllllllll

 

 
  

~ L—— nitride I oxide

seal

 

polysilicon plate—2

 

 

 

‘
‘7

 

cavity
etch channel Si

(100)

 

 

b) Laterally etched diaphragm.

Figure 2.1. Diaphragm types [101,102].

2.3.5.3 The Cutting Edge

Besides diaphragms, many other structures have been micromachined. One exam-
ple is a 1.5 m long channel etched in a spiral pattern on a 5 cm diameter chip. This chan-
nel serves as the capillary column for a gas chromatograph [77]. Another example is the
silicon ink jet nozzle for printers with an oriﬁce of about 20 um in diameter [82]. Other

structures implemented utilizing micromachining techniques include cavities, nozzles,

22

trenches, and bridges [90].

Apart from integrated smart sensors, micromachining is opening new avenues in
other areas of solid-state research. For example, a new generation of vacuum microelec-
tronic valves is evolving through the use of innovative micromachining techniques.
These devices offer the advantages of small size, faster speed, extended operating tem-
perature range, and better immunity to radiations. Miniature, vacuum diodes and triodes
have been sculpted in silicon [110,111]. These micrometer sized devices employ ﬁeld
emission instead of thermionic emission. These are specially suited for use in electronics
in the hazardous environments. It has been reported that all the processing steps are
completely compatible with the existing integrated circuit fabrication techniques [110].
On—chip microcoolers have also been developed for superconducting junctions and for

closely packed high-speed integrated circuits [82].

A new generation of miniature control devices is also emerging. These ﬂeas-sized
mechanical structures might well transform the control of mechanical elephants like air
crafts and automobiles. Intricate structures like motors, gear-trains, turbines with a rotor
blade, a pair of tongs, ﬁxed-axle pin joints, springs, cranks, slider and spring combina-
tions, and miniature valves and pumps have been fabricated through the micromachining

of single and polycrystalline silicon [90,112,113].

2.4 Smart Sensor Interface Electronics

The prime advantage of integrated sensors is the proximity of their associated elec-
tronics. For many smart sensors, the performance of the overall device depends more on
the interface electronics rather than on the transduction element itself. Typical circuit
functions for signal conditioning are signal ampliﬁcation, multiplexing, analog-to-digital
conversion, buffering, cross-sensitivity compensation, offset reduction, non-linearity
correction, drift reduction, auto-calibration, impedance matching, output formatting, and

communication with other sensors and the central processing unit.

23

This section contains a background discussion of the major considerations in the
signal conditioning and practical interfacing of integrated smart sensors. First a broad
overview of signal conditioning tasks and interfacing considerations is presented fol-
lowed by a discussion of salient individual issues. Finally, efforts in the ﬁeld of high tem-

perature microelectronics are reviewed brieﬂy.

2.4.1 Interface Considerations

Signal processing and conditioning issues deal with getting the signal from the sen-
sor to the decision making logic. One central issue is the type of analog-to-digital (AID)
conversion used. Particularly for a smart integrated sensor, the choice of an A/D scheme
can have secondary impact on design considerations such as chip area, accuracy, sensor
interrogation time, and manufacturing. Another primary issue is the method used to solve
the problems of cross-sensitivity and offset reduction. This includes the use of auxiliary
"dummy" sensors sensitive only to the cross parameter, dedicated cross parameter sen-

sors, table look-up compensation, and algorithmic techniques.

Decision making logic enables the smart sensor to come to some conclusion about
the condition of the measured system. This represents the highest level of sophistication
attainable in a sensor. Possible decision algorithms range from simple static thresholding
to artiﬁcial intelligence applied to the time and frequency statistics of the system
changes. Thoughtful use of sensor-distributed decision making logic has become manda-

tory in many large, real-time control systems.

Also critical are communication and system issues. These deal with the bidirec-
tional transfer of information between sensors and central processing units, and the
integration and control of distributed processing sensors. A key in the mass usage of
smart sensors will be the development of standard connection schemes, protocols, and

central control and analysis algorithms.

24

Integration of some or all of these functions on the chip is determined by the
speciﬁc needs of a particular sensor. For example, piezoresistive pressure sensors have a
linear output but need temperature compensation. On the other hand, the case is reversed
for capacitive pressure sensors which need little temperature compensation but have
highly nonlinear outputs. Apart from performance, the economic considerations are also

an important factor for on-chip integration.

The integration of on-chip circuits for many sensors only adds a few extra masks
since these sensors already utilize a rather broad spectrum of IC techniques. The circuit
process need only be accommodated in the existing passive sensor process (or vice
versa). For example, piezoresistive pressure sensors rely for their operation on the opera-
tion of an electronic circuit anyway and incorporating additional circuitry does not
greatly complicate the process. However, fabrication steps for some sensors, such as
capacitive pressure sensors, make the introduction of any electronics very difﬁcult [1].
Therefore, the question of whether circuitry should be integrated on-chip' not only
becomes dependent on the performance, but also on how complicated the ﬁnal process

becomes and how this complication effects the yield and cost of the ﬁnal device.

It should also be noted that with all the signal conditioning and digital means one
can never get more measurement information from a sensor or a group of sensors than
originally produced by those sensors. So, it remains essential to design primary sensors
with a high precision and a high signal-to-noise ratio. And, a prerequisite to signal condi-
tioning is that it must not deteriorate the accuracy of the sensor, but must sufﬁciently
preserve the measurement accuracy. The ﬁrst important consideration in this regard is
that the impedance levels of sensor, circuit and load are properly adapted. The second
consideration is that signal operations must be determined by the least number of accu-
rate components. Both of these considerations can be handled with the concept of opera-

tional ampliﬁers [18].

25

2.4.2 Speciﬁc Components

Sensitivity: The sensitivity of a sensor is deﬁned as the ratio of change in the output
magnitude to the change in the input after a steady state has been reached. It is expressed
as a ratio with the units of measurement of the quantities stated. The. ratio is constant
over the range of a linear device representing the slope of the input-output characteristic.

For a nonlinear device, the applicable input level must be stated.

The sensitivity is one of the most important characteristics of a sensor. On-chip
ampliﬁcation of the sensor output is the most general solution to achieve the highest pos-
sible sensitivity. But for some transducers, on-chip ampliﬁcation is a necessity forced by
the extremely small transducer variations in the primary variable to be measured [57]. In
capacitive pressure sensors, for example, capacitance variations of a few femto-farads

may need to be resolved [29].

Cross-sensitivity: Cross sensitivity is deﬁned as the sensitivity of a sensor to param-
eters other than the primary variable under measurement. Techniques employed to
correct these effects include structural compensation, table look-up, computational and

mathematical methods, use of sensor arrays, and the addition of compensation circuitry.

Temperature is the prime culprit as a cross-sensitive parameter. Many sensor chips
employ a separate temperature sensor to take care of this cross-sensitivity
[27,45,52,53,61,81]. Temperature affects the transducer and measurand in a variety of

ways. For example, six possible sources of temperature drift have been identiﬁed for a

piezoresistive pressure sensor in [19].

Structural compensation is achieved by creating design symmetry or by matching
material properties. The aim here is to cancel out the offending parameter. The simplest
form of this compensation is the adoption of bridge structures [7,34]. In some cases spe-
cial analog electronic circuits are included on the chip to take care of cross-sensitivities
[28,114,115]. Laser trimming can also be used for adjustment of ﬁlm resistors to reduce

cross-sensitivity to temperature [84,116,117]. Use of a separate temperature sensor to

26

measure the temperature and then use of this information to compensate the cross-
sensitivity is also employed in some cases. Computational or mathematical compensation
of cross-sensitivities is one of the major advantages of smart sensors. In this approach,
the offending parameter, most commonly the temperature, is measured separately and
compensation is applied via a known algorithm or some mathematical model used to
compute corrections [26,114,118]. The compensation approaches take the burden off the

the designer to produce sensors as insensitive as possible to cross parameters.

Drift: Drift is deﬁned as a slow change in the offset or gain over time [53]. The
drift may contain both systematic and random components [118]. If the majority of the
drift is due to systematic components, it can be calculated as a function of time. An on-
chip clock can be used to keep track of the time since the last calibration. The drift can

then be estimated and subtracted from the sensor output.

If the majority of the drift is random, several different approaches are possible.
First, the transducer can be redesigned to minimize the drift. Second, a method can be
provided for periodically presenting the sensor with a reference input with which the sen-
sor could calibrate itself (autocalibration). Third, an array of identical sensors could be
exposed to the same environment, with any transducer’s output value lying outside of a
speciﬁed difference from the average value being discarded, and that sensor being recali-

brated using the average.

Calibration: Due to variations in fabrication, two transducer parameters usually
need to be adjusted: the offset and the gain. The offset represents the difference between
the actual output and the desired output at the minimum input value. The gain sets the

output difference between the minimum and maximum input values (the span).

The u’aditional method for calibration is to include laser trimmable resistors in the
transducer circuit [9,16,22]. These are usually placed in series with the sensing element.
This method has two drawbacks. First, the laser trimming adds an additional manufac-

turing step that must be performed under the sensor operating conditions. Second, if the

———-—

27

reference voltage is not increased, the additional series resistance results in a loss of span
[119]. Another approach towards calibration is to digitize the sensor output and correct

the signal computationally [57,119].

Power Supply: The power supply is an integral part of all electronic circuits. Spe-
cial circuits are used to regulate and stabilize the power supply outputs. Stability of
power supply is especially important for microtransducers because in some cases even
minute variations in supply voltage may alter the weak output signals of the transducer.

Thus it is very important to have a stable power source.

AID Conversion: One of the key components for expanding microtransducers into
integrated smart sensors is the AID converter. In addition to the requirements normally
placed on an AID converter, namely accuracy, reliability and repeatability, there are spe-

cial requirements that may be imposed on a design used for integrated smart sensors.

A very precise AID converter requires a large and complex amount of circuitry and
may occupy more chip area than available. Thus a simple AID converter is desired
which will accomplish the task and is compatible with the sensor integration process.
Frequency ratio measurement, sigma-delta modulator [120], and the well known dual
slope AID converter have been identiﬁed as AID converter candidates for on-chip
integration with the sensor [18]. These AID converters offer good precision as well.
Other types of AID converters, such as successive approximation, cascade, or ﬂash A/D
converters, require accurate element matching, sample-and-hold circuits, or a complexity
that limits their accuracy when integrated together with a sensor on a single chip [18].

However, these methods generally allow higher conversion rates.

The normal AID conversion technique converts the analog transducer output vol-
tage or current into a digital number. Some new techniques have also been developed
that directly convert the sensed parameter into a discrete value. The ﬁrst of these new
techniques is based on an array of similar binary transducers tuned to different parameter

values. A second new technique, based on the power-up unpredictability of a ﬂip-ﬂop,

28

can be used with resistive transducers [116]. A third technique, based on the exponential
RC time constant, can be used with capacitive transducers [45]. The circuit uses a thres-
hold detector to start or stop a counter. This method, however, exhibits strong tempera-

ture dependencies that are difﬁcult to compensate for.

Communications: A sensor should not be considered as an isolated, independent
element. In most cases it forms part of an organization within which it interacts with
other sensors, computational elements, and actuators. Robots, automobiles, industrial
process control, and biomedical applications are common examples of such environ-
ments [26,66,121]. It is inherent in the smart sensor concept that the sensor be address-
able and capable of communicating with a central processor and other sensors
[26,45,57,121]. If the sensor is addressable, the capability of remote testing and/or cali-

bration by the processor also becomes possible [114].

Presently there are no communication standards for sensors but on the basis of
economy, reliability, and convenience, adherence to serial communication over a bus

using ASCII characters has most often been suggested [52.53.114.121].

2.4.3 High Temperature Microelectronics

In many cases, sensing requirements call for ambient temperatures which are higher
than what the electronics can tolerate. Thus new circuit approaches and materials are
being investigated which can operate reliably at elevated temperatures. Circuit

approaches to raise the operating temperature of silicon CMOS circuitry to 300°C have

been presented in [122,123].

Silicon on insulator (SOI), wider bandgap materials (gallium arsenide, silicon car-
bide, and diamond, etc.), and miniature vacuum devices using ﬁeld or thermionic emis-
sion, are some of the alternatives for high temperature electronics. Development of these
approaches ranges from unproven principles, to working but expensive large scale

integration models. Cost and ease of processing are the major determining factors for

29

adoption of a technique. Thus, for high temperature smart sensors, SOI, epi-CMOS, and
conventional bulk CMOS are the preferred technologies. The choice among these is
based upon cost trade-offs between the various strategies (technology, layout rules, and
circuits) which could be used to achieve the required temperature and reliability level.

The cost versus operating temperature trade-off for the three technologies is shown in

 

 

 

 

 

 

 

 

Figure 2.2 [122].
5 ___________________________________
I" " “I
i s o I I
4_ :. ____________________________________ J
Relative T
Cost
2 _ .................................................................
epi—CMOS
1 _ ................ B. ulkClVIOHS .................................
0 r T l I I
O 50 100 150 200 250 300
Temperature (°C)

Figure 2.2. Smart sensor technology temperature range and cost [122].

2.5 Silicon Pressure Sensors

Pressure sensors are transducers that convert a measure of pressure into an electrical
signal. Pressure sensors at present are one of the most highly developed types of sensors

and account for a major portion of commercial market.

The pressure sensors are available in two forms that permit measurements of abso-
lute, differential, and gauge pressure. Absolute pressure, such as barometric pressure, is

measured with respect to a built-in vacuum reference. A pressure differential, such as the

30

pressure drop across a damper or ﬁlter in an air duct, is measured by applying pressure to
opposite sides of the sensor simultaneously. Gauge pressure, as in blood pressure meas-
urement, is a special case of differential pressure, where atmospheric pressure is used as

a reference.

The sensing element for integrated pressure sensors is usually one of two types:
varying capacitance or piezoresistive. Both techniques employ micromachining to fabri-
cate a thin diaphragm to implement the silicon pressure sensor. Typical structures for the
two types are shown in Figure 2.3. The thickness of the diaphragm, its surface area, and
the geometrical arrangement of the resistor on the diaphragm, determine the pressure
range. Although at the wafer level silicon is brittle, at chip level it has a strength on the
order of stainless steel. This fact, combined with their extreme low mass, enables silicon

sensors to measure pressures in excess of 10,000psi [28].

Presently the piezoresistive sensors are more commonly used. These are easier to
manufacture and, as a result, cost less. Since they also have a more linear response than
the capacitive type, the output requires less signal conditioning. On the other hand, the
capacitive sensor is an order of magnitude more stable, has higher sensitivity, and is less

vulnerable to temperature changes.

Many piezoresistive and capacitive pressure sensors are presently in use. Variations
of these two approaches and some other techniques have also been developed. A brief

review of available types of pressure sensing techniques is presented in this section.

2.5.1 Capacitive Pressure Sensors

The capacitive pressure sensor has a ﬂexible diaphragm that acts as one plate of a
variable air-gap capacitor [29,31]. Pressure on the diaphragm causes a proportional

change in capacitance value, which can be converted to a voltage or frequency output.

31

Pad Si QZ Piezoresistor
./ / Diffused

 

 

 

(a) Piezoresistive

Metalized Plate On-chip Circuits
Seal

Reference Plate
\ J LBJ—

Silicon

 

 

 

 

 

 

 

 

Diaphragm |
External Pressure

(b) Capacitive [124]

Figure 2.3. Typical silicon pressure sensing structures.

The capacitive pressure sensor’s stability gives it the edge for use in harsh environ-
ments, such as an automobile engine. Some capacitive pressure sensors work by detect-
ing minute capacitance changes, and the signal conditioning electronics must be at least
as stable as the sensing element. For example, capacitive pressure sensors build for such
biomedical applications as measuring blood and spinal-ﬂuid pressure must show capaci-

tance changes on the order of 2 to 3 pF only [29]. Thus, on-chip signal ampliﬁcation and

32

conditioning is the only choice. In this technique a pressure sensitive capacitor is charged
against a reference capacitor through an on—chip switching bridge circuit composed of
CMOS transmission gates. A sensor of this type has been developed which measures
90x150 mils with a diaphragm thickness of about 27 um. Experimental results have indi-
cated a typical sensitivity of 56 uV/mmHg-V in the range from 0 to 300 mmHg. This
sensitivity is approximately ﬁve times the typical value of a piezoresistive sensor of simi-

lar size.

Another capacitive sensor developed by the Center for Industrial Research, Norway,
provides a frequency modulated output with a reported sensitivity of 1000 ppm/m Bar
[31]. The sensor uses two separate chips, one for the pressure sensor diaphragm and
another for the detection circuitry. A third silicon chip is used for support. The three
chips along with a tiny glass tube are sealed together to form the complete integrated
hybrid smart sensor. The sensor performance is adversely effected by the stray capaci-
tances and is being modiﬁed to reduce the stray capacitance and improve other sensor

characteristics.

2.5.2 Piezoresistive Pressure Sensors

In a piezoresistive pressure sensor, the diaphragm is etched from the silicon as the
basic sensing element. Thick or thin ﬁlm metal or polysilicon stress sensing resistors are
then deposited on the diaphragm in a wheatstone-bridge conﬁguration. Stress on the
diaphragm causes a current imbalance in the bridge, indicative of pressure. Laser trim-
ming is sometimes used to adjust ﬁlm resistors to achieve linearity and temperature com-

pensation.

The wheatstone-bridge resistors can also be diffused into the silicon diaphragm or
they can be ion-implanted for more immunity from stress-induced instabilities. An alter-
native to the wheatstone-bridge conﬁguration is to form a single piezoresistive element in

or on the silicon diaphragm. Applying pressure to the diaphragm results in a resistance

33

change, causing a change in output voltage in direct proportion to the applied pressure.

NEC Corporation, Japan, has developed an intelligent CMOS pressure sensor,
which employs a four arm piezoresistive bridge circuit, an ampliﬁer and a bridge excita-
tion circuit to suppress supply voltage and temperature variations on the same chip [7].
The piezoresistors are fabricated using boron ion implantation. The sensor provides a
voltage output with less than 10.50% sensitivity and offset voltage temperature shifts for
0—70°C range. The sensor response is linear over the entire temperature and pressure

range. The pressure-voltage characteristic for the sensor is shown in Figure 2.4.

Use of polysilicon ﬁlm resistors increases the operating temperature range of the
sensor and also permits the on-chip adjustment of resistor values by laser trimming. Toy-
ota Research Labs., Japan, have used polysilicon ﬁlm piezoresistors over a silicon nitride
diaphragm to implement their pressure sensor with a sealed cavity to measure absolute
pressure [34]. The output sensitivity obtained is more than 100 uV/V with respect to a
pressure of 100 KPa. The temperature coefﬁcient of the sensitivity is approximately
-O.13%I°C at the temperature range between -50°C and 150°C. Polysilicon resistors over
a rectangular diaphragm have also been used by Fraunhofer-Institute, W. Germany, to

implement the pressure sensor for an extended temperature range of -60°C to 200°C [8].

34

 

2.1

1.4 --
Output

Voltage

(V)
0.7 -

 

 

 

I I I
0 0.5 1 1.5 2

Pressure (kg/cmz)

Figure 2.4. Pressure-voltage characteristic for the sensor described in [7].

Unlike conventional pressure sensors which use a wheatstone bridge conﬁguration,
the Motorola MPX series uses a single four terminal shear stress sensitive piezoresistive
strain gauge [9,28]. A transverse voltage strain gauge is placed at the midpoint of the
edge of a square diaphragm at an angle of 45° with the edge in order to maximize sensi-
tivity to shear stress and minimize non-linearity effects. A detailed study of the theory of
piezoresistivity in semiconductors has lead to this speciﬁc design. The Motorola MPX-
100D silicon pressure sensor uses this technique. It is an uncompensated, uncalibrated

differential pressure sensor, which covers the pressure range from 0 to 100 KPa.

35

2.5.3 Other Types

A resonant diaphragm pressure sensor has been developed at Twente University,
Netherlands [30]. The excitation of the diaphragm is accomplished by means of a dif-
fused resistor acting as a thermal exciter. A pressure over the diaphragm changes the
resonant frequency by 0.5 Hz/Pa. The diaphragm resonance is detected by a piezoresis-

tive wheatstone-bridge.

Another approach has been adopted in [32] to implement the pressure sensor using a
ring oscillator. The change of carrier mobility in silicon under mechanical stress has been
utilized to vary the drain current of the transistor. Two ring oscillators are used to provide

a differential frequency output, which greatly reduces the effect of temperature.

Use of I 2L oscillators to detect pressure has been reported in [36]. The sensor uses
two oscillators which are located on the silicon diaphragm such that with the application
of pressure the frequency of one oscillator increases while the other’s frequency
decreases. The differential frequency output has been used to remove ﬁrst order tempera-

ture effects.

2.6 Temperature Compensation of Piezoresistive Pressure Sensors

As stated before the major problem with silicon is its strong cross-sensitivity to tem-
perature. Many sensor chips employ a separate temperature sensor to take care of this
offending parameter [27,45,52,53,81]. Temperature affects the transducer and measurand
in a variety of ways. For example, six possible sources of temperature drift have been
identiﬁed for a piezoresistive pressure sensor [19]: 1) temperature dependence of the
piezoresistive coefﬁcient, 2) resistor tracking errors, 3) gas expansion in the reference
cavity (if present), 4) junction leakage currents, 5) thermally-induced stress at silicon-

silicon dioxide interface, and 6) packaging effects.

The temperature characteristics of the piezoresistive pressure sensors are described

ﬁrst in this section. Then the previous efforts for temperature compensation are presented

36

and evaluated for their usefulness for a generalized, low cost interface circuit.

2.6.1 Temperature Characteristics

The inﬂuence of temperature changes on a sensor is exhibited by a change of zero

pressure offset and span. A typical piezoresistive pressure transducer was shown in Fig-

ure 2.3(b). Arrangement of resistors in a full bridge cancels the temperature coefﬁcients

of the individual resistors to the degree the resistors track each other. This is called struc-

tural compensation. For a full bridge of nominally identical diffused resistors, the bridge

output voltage [19] is given by

V0 1 _.A_R_ __A_’i _ _
-——[1 II. t W

where
V0 = output voltage,
Vcc = bridge supply voltage,
R = nominal value of resistors,
AR = fractional change in R due to applied stress,

0. = pressure induced stress (perpendicular to resistor),

o. I = pressure induced stress (parallel to resistor),
or = differential stress arising from thermal or non-pressure sources,
rt = piezoresistive coefﬁcient,

[3 = sum of any additional nonstress related offsets.

(2.1)

37

2.6.1.1 Temperature Coefﬁcient of Pressure Sensitivity

Pressure sensitivity of the sensor is given by [19]

_ 1 3V0._ _a_[c -0 )+6]
S—Vcc aP —1taP (l n r. (2.2)

Temperature coefﬁcient of the pressure sensitivity (TCS) is deﬁned as the deviation

of the pressure sensitivity with temperature. Mathematically it is given by [19]

The pressure sensitivity and its temperature coefﬁcient are primarily determined by
the behavior of piezoresistive coefﬁcient for a given structure. It has been shown in [125]
that piezoresistive coefﬁcient decreases with increasing surface concentration of diffused
layers and it is independent of diffused layer thickness. Iris also inﬂuenced by the resis-
tor tracking errors. It has been reported in [19] that for an absolute deviation of 2 percent
in the resistors from their nominal values, the value of 1: will shift by about 1.2 percent
and its temperature coefﬁcient will change by about 25 ppm/°C. The effect of a 10 per-
cent mismatch of bridge resistors on the output voltage as a function of temperature is

shown in Figure 2.5.

2.6.1.2 Temperature Coefﬁcient of Offset

The offset error is deﬁned by the maximum deviation of the offset voltage from its

speciﬁed value. Temperature sensitivity of the offset (T 80) is given by

8V 3
TSO=——1- 0 an(Ol-Cll)+g—;Cf+ﬂﬂ+gg

VCC in = 5? ar 37" (2'4)

T80 is affected by all the six sources mentioned above. Expansion of gas with tem-
perature in the sealed cavity makes a signiﬁcant contribution to TSO, but the bridge

offset voltage is most strongly inﬂuenced by the resistor mismatch. Moreover errors

38

produced by resistor mismatch are random for individual units. Zero pressure offset for a
piezoresistive sensor with 10% tracking errors is shown in Figure 2.6. The contribution
of junction leakage currents, oxide stress and packaging effects to the T80 are relatively

small.

2.6.2 Temperature Compensation Techniques

The most common problem associated with piezoresistive pressure sensors is their
sensitivity to temperature. It has been suggested in [114] that if the temperature
coefﬁcient (TC) of the sensor is linear and reproducible, design of the interface circuitry
for an equal and opposite TC may be a practical solution. However, if either the trans-
ducer or the circuit TC is nonlinear with temperature it may be more practical to bring
temperature out as a separate parameter and compensate via a microcomputer algorithm
or look-up table. If either is unpredictable, the only solution may be the laser trimming

on a unit-by-unit basis, which is both slow and expensive.

In this section previous work in the ﬁeld of temperature compensation of piezoresis-
tive pressure sensors is reviewed. Laser trimming, matching temperature coefﬁcients, and
mathematical compensation techniques are presented and evaluated from the viewpoint
of on-chip integration, cost, compatibility with IC technology, and temperature range
covered.

2.6.2.1 Laser Trimming

As mentioned in previous section the major contribution in TCS and T80 comes
from resistor mismatch. The most common temperature compensation methods
employed presently is laser trimming of ﬁlm resistors for individual devices
[5,8,9,1l,13,l6,19,20-23,28]. In some cases external temperature-stable resistors are also
used to achieve this [10,13,21,115].

39

0.8

 

 

 

 

 

 

 

 

Vout
(V)
0 I I I I ﬂ I I I
-40 -20 0 20 40 60 80 100 120
Temperature (°C)
Figure 2.5. Temperature response of the sensor with 10% tracking errors.
0.4
10% Tracking Errors ............
No Tracking Errors
0.2 —
Offset
Voltage 0
(V)
-0.2 -
'04 I I I I I

 

 

 

I I I
-40 -20 0 20 40 60 80 100 120
Temperature (°C) ,

Figure 2.6. Zero pressure offset of the sensor with 10% tracking errors.

40

A separate signal conditioning IC using three types of resistors has been designed in
[11]. It uses diffused as well as two types of thin ﬁlm metal resistors and the compensa-
tion is achieved through laser trimming. The IC is analog and uses bipolar technology. In
another effort eight polysilicon resistors have been used for temperature compensation of
pressure sensitivity and offset [16]. Sensor bridge resistors are implanted while the com-
pensation resistors are deposited using thin-ﬁlm techniques to allow laser trimming.
Seven of these have a roughly zero temperature coefﬁcient of resistivity (TCR) while the
eighth one has a large negative TCR. The offset voltage and the TCO must be measured
for each unit to select the two resistors from a group of four, to determine the resistors to

be laser trimmed for the offset compensation.

A typical calibration/compensation circuit for disposable blood pressure sensor
using laser trimming is shown in Figure 2.7. The calibration/trimming process is not as
straight forward as it sounds, because there is signiﬁcant interaction between different
components. For example, trimming the offset by changing the value of R4 will also
change the pressure sensitivity. It will also affect, to a certain degree, the temperature
coefﬁcient of offset, symmetry of output voltage in reference to excitation voltage, the
output impedance, and the input impedance. Not only is the laser trimming expensive
and time consuming, but it also adds an additional manufacturing step which must be
performed under the sensor operating conditions. Another drawback of laser trimrnin g
comes from the fact that the compensation circuit design must use the ﬁlm resistors.
Moreover, laser trimming resistors are added in series with the sensing element, thus the
sensitivity of the transducer goes down. To achieve the same sensitivity it is necessary to

increase the power supply voltage.

2.6.2.2 Matching Temperature Coefﬁcients

The temperature coefﬁcient of piezoresistivity is negative. Therefore, in some

designs this is matched with the positive temperature coefﬁcient of a single or a

41

combination of resistors. Different variations of this basic principle are applied. The
major drawback of this technique lies in the fact that the accuracy of compensation is
determined by the precision of the control of the impurity concentration for compensa-

tion resistors.

 

 

 

 

 

 

 

 

0+
R6
Ou ut
R2 tP
+ 0 IF 4W»
R
8
R7
Excitation
O _
R1

 

 

 

 

Figure 2.7. Typical calibration/compensation circuit [5].

A temperature-sensitive integrated feedback resistor R0 (T) has been used for tem-
perature compensation in [7,10]. Both circuits make use of NMOS technology and pri-
marily reduce TCS over a temperature range of 0-70°C. RG(T) is used in the ampliﬁer
feedback loop in [10] whereas in [7] it varies the bridge excitation voltage. Both circuits
use an external resistor and bias voltage to set the gain and offset of the sensor. The per-
formance of these circuits is dependent on the Ra’s resistance temperature coefﬁcient

which in turn is dependent on its impurity concentration. A similar technique using two

42

resistors and an operational ampliﬁer has been reported in [108]. The ion-implanted
resistors used for the feedback circuit of the operational ampliﬁer have different impurity

concentrations to give them an opposite temperature coefﬁcient.

Temperature compensation circuits for biomedical applications to be used in a
catheter have been presented in [23,24]. These designs were aimed at a small size, low
power consumption, long term stability, and a temperature range of 25-45°C. A separate
interface circuit, employing a double bridge active compensation technique, has been
developed in [23]. The pressure transducer bridge is used as one leg of a second bridge
which is used to derive a temperature dependent signal. This signal along with the pres-
sure dependent output is used for temperature compensation. Bipolar technology has
been used for interface circuitry in [24]. Positive TCR of diffused resistors is used to
compensate the negative TCS of transducer bridge. The interface circuit provides a
high-frequency FM analog signal output on two leads. This technique allows mounting of

several sensors on two leads, running through the catheter.

2.6.2.3 Mathematical Compensation

This technique uses a mixture of computation and table look-up. The microproces-
sor power is utilized to mathematically model the sensor and the table look-up is used to
obtain the calibration coefﬁcients stored in an on-chip PROM. The corrected response is
computed based on the measured information and calibration coefﬁcients. This technique
is complex in terms of hardware and software and requires memory to store the calibra-
tion coefﬁcients, which may have to determined for individual units under sensor operat-
ing conditions.

The two chip package, with signal conditioning on a separate chip, uses mathemati-
cal modeling to digitally trim the gain, offset, and other sensor parameters [14]. No
implementation details for the technique are given. Two mathematical compensation

techniques for the multichannel Electronically Scanned Pressure module have also been

43

reported [15]. In the ﬁrst technique, three or more known reference pressures are applied
to the pressure sensor and the electronic outputs are recorded. Curve ﬁtting this data to a
second order polynomial equation generates three coefﬁcients for offset, pressure sensi-
tivity, and non-linearity. These coefﬁcients are used later to calculate the applied pres-
sure. The method is stated to be very accurate but extremely expensive and difﬁcult to
implement in terms of hardware and software. The second technique, improving these
shortcomings is presented in the same paper. The new technique makes use of an 8-bit
microprocessor with on-chip serial communication and memory management. The inter-
face also includes 16K RAM, 136K EPROM, an AID converter, and a real time clock.
The interface measures the output of pressure sensor, its excitation voltage, and the tem-
perature signal from the internal temperature thermometer. The stored calibration
coefﬁcients are used to mathematically compute the corrected pressure. This interface
chip can be used with other sensors having analog outputs. The complete system consists
of two printed circuit boards housed in a 10.16cm long enclosure. Thus, the size and

complexity of the interface make it unsuitable for integration with the sensor.

A generalized interface design for the bus-organized sensors has been reported in
[126]. A host computer, acting as the system controller, interfaces with up to 256 nodes
over a bus. The standards for the bus have also been proposed. The interface circuit per-
forms the functions of multiplexing, ampliﬁcation, and digitization under the control of
an on-chip microprocessor. Actual compensation is carried out by the host system, where
much greater processing power is assumed. The compensation is based on the stored
compensation coefﬁcients and statistical computations. The interface circuit and the sen-
sor array are located on two separate chips. An off-chip commercial PROM, encoded at

sensor test time, is used to hold the information about the features of the sensor.

44

2.7 Modeling and Simulation of Piezoresistive Pressure Sensors

The implementation of silicon IC technology and elaborate micromachining tech-
niques for preparation of thin silicon diaphragms have made the pressure sensor fabrica-
tion a relatively high-yield batch process. Until recently most design work has been
intuitive and no detailed design aids exist with which to optimize the design of advanced
structures. In recent years some effort has gone into the modeling and simulation of
piezoresistive pressure sensors [10,17,125,127-129]. Progress in this area would lead to
computer aided-design (CAD) of pressure sensors. The modeling and simulation also
provides an accurate means of characterizing sensor performance which can lead to the
optimized design of sensors. It also provides a means to study the effect of various cross
parameters and design compensation and interface circuitry without having in depth

knowledge of physics and mechanics of the sensor structure.

SENSIM, a simulation program for piezoresistive and capacitive pressure sensors
has been developed at the University of Michigan [17,125]. It provides the output
response as a function of pressure and temperature for both types of sensors. Both analyt-
ical and ﬁnite difference solution methods are available, depending on the sensor struc-
ture. Diaphragm thickness taper, oxide and package stress, and rim effects are simulated
The user-speciﬁed outputs available are diaphragm deﬂection, stress distribution over the
diaphragm, average stress over piezoresistors, node voltages, changes in resistance due to
stress, capacitance changes with pressure and thermally induced bending moments and/or
stress. The simulation program consists of about 7000 Fortran statements. Excellent

agreement between simulation results and experimental data has been reported

A similar simulation program called Silicon Pressure Sensors Simulation Program
(SIPSES) has been reported in [128]. It has been developed on the same lines and uses
the 'experimental data from [125] for its veriﬁcation. It places somewhat more emphasis

on the simulation of sensors with a single four-terminal piezoresistor.

45

The Pressure/Transducer Simulator (PRESENTS) has been developed and used for
the simulation and analysis of MOS integrated silicon pressure sensor developed at NBC

Japan [10]. The simulation program is based on the ﬁnite-element method.

Analog and digital modeling techniques for piezoresistive pressure sensors have
been described in [119]. The application areas for these models include calculation of
temperature compensation components based on sensor test results and direct pressure
calculation based on a stored numerical sensor model and measured sensor outputs. The
four model elements are derived from the results of measurements performed with a con-
stant current source for sensor excitation. The procedure is repeated for each test tem-
perature and for each test current as well as for each additional pressure needed to model
pressure nonlinearity. For digital modeling, single segment and polynomial based numer-
ical models are used to model and store the constants for the sensor on a one-time basis.
Later the corrected pressure can be calculated based on the stored model constants, the

output voltage, and the bridge voltage.

The ﬁnite element analysis packages may also be used to model the sensor struc-
tures. GRAFEMIIFAD package of the Applicon BRAVO! CAD system has been used to
model silicon based aerospace pressure sensors [129]. The square diaphragm and the
complete sensor package were modeled separately. The diaphragm model provided the
stress distribution proﬁle. A post processor may be used to achieve a clear view of the
deformation pattern and stress contours of the structure. For the package model, the sili-
con structure is supported by a glass base and housed in a steel case. The ﬁnite element
model provides insight into the effects of packaging on the performance of the sensor.
The data was used to design a rugged and compact package with negligible effects on the
performance of the silicon diaphragm. The same ﬁnite element package was also used to
simulate a circular diaphragm and a beam [127]. The stress values computed from the
analysis were converted to strain and the voltage response for the wheatstone bridge

conﬁguration was calculated. The data compared well with the measured results from

46

thirteen prototype sensors.

2.8 Summary

Recent advances in silicon sensor technology have been reviewed. Issues concern-
ing fabrication and interface electronics for integrated smart sensors have been discussed
Various pressure sensing techniques and some of their recent implementations were
described Temperature characteristics of piezoresistive pressure sensors were discussed
and various temperature compensation techniques were surveyed. The pressure sensi-
tivity as well as the zero pressure offset for piezoresistive pressure sensors are functions
of temperature. Moreover, the temperature characteristics for individual units differ
slightly because of processing variations. Laser trimming, matching temperature
coefﬁcients, and table look-up or mathematical compensation are the prevalent tempera-
ture compensation techniques. These approaches are expensive, time consuming, com-
plex and based on the compensation of the individual units. In some cases processes used
are complicated and/or not directly compatible with standard IC technology. There is a
need for temperature compensation technique which is cost effective, covers a wide tem-

perature range and readily lends itself to compatible batch fabrication.

CHAPTER 3

SENSOR MODELING

3.1 Introduction

In this chapter the simulation results for the piezoresistive pressure sensors are
presented for a temperature range of -40°C to 130°C over a pressure range of 0 to 45 psi.
The sensor is modeled from the viewpoint of batch fabrication. First, the modeling and
simulation objectives are outlined followed by the description of the approach adopted to
fulﬁll these objectives. Then the simulation program is described from the viewpoint of
functionality, accuracy, and the computational errors. Next the structural, processing,
and control parameters are discussed and speciﬁed for the sensor model. The remainder
of the chapter describes the simulation results for the sensor. First, the simulation results
for the ideal sensor with no tracking errors are presented. Then the sensor model is
enhanced to include the batch fabrication effects. Simulation results are presented and

discussed in the last section.

32 Objectives

The ultimate aim for the modeling and simulation is to study the sensor I/O charac-
teristics as functions of pressure, temperature, and tracking errors. The simulation objec-
tives and modeling decisions are primarily governed by this aim. With this understand-
ing, the important issues are discussed and the objectives for the modeling and simulation

are set in this section.

47

 

48

The simulation results are studied to develop a new temperature compensation tech-
nique. The simulation data will be used as an input source to exercise the interface circuit
models. The interface circuit and the sensor are intended to be integrated on the same
chip and batch fabricated. The aim here will be to produce a realistic and generalized
sensor model. So that the simulation results can be utilized to produce an effective inter-
face circuit and the same results are also extendible to the similar structures and other

sensors using piezoresistive effect for their operation.

The characteristics of piezoresistive pressure sensors are determined by their struc—
ture. Moreover, the stress distribution over the diaphragm is not uniform. Therefore, the
sensor response is dependent on the shape, size, value, and location of the piezoresistors.
To account for this, the sensor model should include all the structural, processing, and

electrical details for the sensor.

A major problem associated with piezoresistive pressure sensors is their inherent
cross-sensitivity to the temperature. Temperature affects the transducer and measurand in
a variety of ways. The inﬂuence of temperature on a piezoresistive pressure sensor is
exhibited by a change in the span and offset of the sensor output. Moreover, minor pro-
cess variations give rise to piezoresistive tracking errors, which in turn change the tem-
perature characteristics for individual units. These variations are more realistically
modeled from the viewpoint of the batch fabrication. This requires modeling of the same

wafer as well as the wafer-to-wafer processing variations.

To summarize, the simulations should generate data for the sensor response as a
function of pressure and temperature for the same wafer as well as the wafer-to-wafer
processing variations. The data will be used to evaluate the effect of these factors on the

sensor output, pressure sensitivity, and zero pressure offset.

49

3.3 Approach

The accuracy of the simulation data produced is primarily determined by two fac-
tors, the quality of the model and the capabilities of the simulation program. The basic
sensing element to be modeled is the piezoresistor diffused in a thin diaphragm.
Piezoresistive effect is not new and many researchers have studied its characteristics
since its discovery in 1954 [130-132]. Similarly the fabrication and characteristics of the
diffused resistors are also well documented [133-136]. Therefore, a careful study of the
books and the literature was carried out to deduce the electrical and structural parameters
for the sensor model. These parameters were used to produce a very accurate model for

the sensor structure, piezoresistors, and the processing variations.

The second factor determining the accuracy of the simulation results is the simula-
tion program. SENSIM, a simulation program for capacitive and piezoresistive pressure
sensors, is useful for modeling and simulating both types of sensing elements under vari-
ation of physical and electrical parameters. The program has been veriﬁed through com-
parison with data from the actual sensing structures [17]. Minor changes were made to
upgrade the program to Fortran 77, compatible with the computing environment used for
this research. After these changes the program was veriﬁed again to ensure correct opera

tion. The procedure is documented in the next section.

3.4 The Simulator

SEN SIM, a simulation program developed at the University of Michigan was used
to obtain the sensor response [17]. First, a brief overview of the functionality of the pro-
gram is presented from the viewpoint of simulating piezoresistive pressure sensors. Then
the approach adopted for the program veriﬁcation and the errors associated with the pro-
gram are described Finally the changes made and the revalidation of the program is

presented.

50

3.4.1 Overview of the Program

SENSIM is a simulation program for silicon pressure sensors with a thin square
diaphragm. It provides the output response as a function of pressure and temperature for
piezoresistive and capacitive pressure sensors. The user can specify structural, process-
ing, electrical, and control parameters for the sensor and the simulation program. Both
analytical and ﬁnite difference solution methods are available, depending on the sensor
Structure. Diaphragm thickness taper, oxide and package stress, and rim effects are simu-
lated Available outputs are diaphragm deﬂection, stress distribution over the diaphragm,
average stress over piezoresistors, node voltages, changes in resistance due to stress, and

capacitance changes with pressure.

The geometry, dimensions, processing parameters, and the arrangement of
piezoresistors are speciﬁed by the user. The piezoresistors are speciﬁed in terms of their
locations on the diaphragm, processing parameters, electrical circuit node numbers, and
resistance values. The piezoresistor location (center of resistor) on the diaphragm is
speciﬁed using the standard two dimensional X-Y coordinate system with the origin
placed at the center of the diaphragm. The diaphragm deﬂection for the piezoresistive
and the capacitive sensors is found by solving the governing differential equations. For
the piezoresistive sensors, the deﬂection is used to determine the stress proﬁle over the
diaphragm. The stress distribution is used to calculate the average stress over the
piezoresistors. The sensor structure is deﬁned through the speciﬁcation of geometrical
dimensions and the material parameters for the diaphragm and the structural layers. The
calculated stress and the piezoresistive coefﬁcients are used to determine the fractional
change in the piezoresistor values. Finally nodal analysis is used to compute the electri-

cal response of the sensor.

51

3.4.2 Program Veriﬁcation

The validity of SENSIM has been assessed by comparing experimental data from
actual device structures with the simulation results. The experimental measurements
involved diaphragm deﬂection and the associated output from capacitive and piezoresis-
tive pressure sensors [17]. Figure 3.1 shows the measured diaphragm center deﬂection
and compares it with the simulated response. The dotted curve is for the ideal straight
diaphragm edges and the solid curve for the sloped edges. Complete details of experi-
mental set up can be found in [17]. Accuracy of deﬂection is very important because it
forms the basis for the determination of the stress distribution over the diaphragm, which
in turn is used to compute the sensor response. The major numerical errors in SENSIM
are associated with the grid size used for the ﬁnite-difference method. Other numerical
errors (round-off or truncation errors) are relatively small, and experiments have shown
that overall computational accuracy is good up to ﬁve signiﬁcant digits using double pre-
cision representation (64 bits). This overall accuracy is satisfactory except for the errors
introduced by the ﬁnite grid size. A detailed analysis was carried out for these errors and
it was concluded that the errors associated with the ﬁnite-difference method are very
small, and the simulated diaphragm deﬂection is accurate enough to be used in the design

and analysis of silicon pressure sensors [17].

3.4.3 Revalidation

SENSIM consists of 90 subroutines and functions. Moreover, these routines are
nested in a complex fashion. More than 200 global variables and arrays are deﬁned for
passing parameters. It is very difﬁcult to make any analytical changes in the program.
However, some syntax changes were necessary to upgrade the program so as to be com-
patible with the local computing environment. Few other errors were also observed and
corrected. In order to ensure that no change was made in the functioning of the program

the sample simulation program given in the user guide and the structures used in the

52

original veriﬁcation process [17] were simulated. A perfect match was observed for all

 

 

 

 

simulation results.
10
Experiment e '
Sloped edge
8 7 Built-in edge ............
Maximum 6 T
Deﬂection
(micron) 4 _ .33.”.
2 _
0 I I I I
O 150 300 450 600 750
Applied Pressure (mmHg)

Figure 3.1. The measured and simulated diaphragm center deﬂection [17].

An effort was also made to simulate some sensor structures using data from the
research literature. Unfortunately, almost all of the published data does not provide
enough information about the physical structure of the sensors. SENSIM needs physical
details for the diaphragm (dimensions, shape, bulk thickness, edges, layers, etc.) and
piezoresistors (location, dimensions, impurity concentrations, junction depth, etc.). Two
structures however, were found suitable and simulated. Firstly the 27pm thick, 1mm x
1mm square diaphragm structure reported in [35] was simulated and the normal stress

distribution 0,, and oy reported in the paper was obtained. The resultant stress

53

distribution for 14.5psi (1kg/cm2) is shown in Figure 3.2. The simulation and reported
experimental results compare favorably. Secondly the physical details of another sensor
were extracted form two papers written by the same authors [7,35]. Simulation showed
similar results but an exact comparison was not possible since the results presented in the

papers were for the complete device which included the signal conditioning circuits.

 

 

Ox
......... o ,
4 J ............. y Y = 0 ‘
X = 0.5 .......
Normal 2 _
Stress
(X108 dancmz)

 

o-

 

 

 

 

I I I
0 100 200 300 400 500

XIY Distance (micron)

Figure 3.2. Stress distribution Over the diaphragm.

3.5 The Sensor Model

After conﬁrming the correct functionality of SENSIM, the ﬁrst major task was to
develop a suitable sensor structure for the study of the temperature and pressure charac-
teristics of the piezoresistive pressure sensors. Some structural constraints are placed
(shape, orientation, silicon, etc.) by the simulation program while others were chosen to
obtain a model as close as possible to reality. The structure used for the evaluation of the
simulation program provides a good practical example. This was used as the starting

structure and some parameters were kept same while others were modiﬁed to suit the

54

goals of this research.

The sensor is composed of three layers: the thin silicon diaphragm, 1mm thick layer
of silicon dioxide grown over the diaphragm at 850°C, and the package (Corning glass
support plate) sealed at 450°C with a hole for the applied pressure. The piezoresistors are
diffused in a wheatstone bridge conﬁguration in the thin silicon diaphragm. The sensor
structure is shown in Figure 3.3. This structure is the same as is used for the original

veriﬁcation of the simulation program [17]. It also takes care of packaging effects.

SiO2 Piezoresistor

 

 

Silicon Diaphragm

 

 

 

 

 

W \\\\\\\\\\\\\\\\\\\N<— Package

Pressure Hole

 

 

 

Figure 3.3. The sensor structure.

Diaphragm thickness determines pressure sensitivity since the stresses caused by
applied pressure are inversely proportional to the square of diaphragm thickness. The
effect of process induced thickness variation can be made smaller by increasing the nom-
inal thickness but at a cost of pressure sensitivity. Therefore a trade-off based on the per-
formance of available and expected processing technology emerged. The size of

diaphragm also effects the pressure sensitivity. The larger diaphragm is more sensitive

55

and the stress increases from the center to the diaphragm edge. Therefore a piezoresistor
placed close to the edge is more sensitive but its sensitivity is more vulnerable to process
variations in diaphragm size, alignment and piezoresistor location. Based on the con-
siderations discussed above, the diaphragm is assumed to be square with side length of
1000um and a uniform thickness of 10m. All piezoresistors are placed 20pm from the
diaphragm edge.

There also is a trade-off between pressure sensitivity and reproducibility for the
piezoresistors. Speciﬁcally, an increase in resistor size improves device reproducibility
but decreases the sensitivity because of the stress averaging effect. A smaller size (width)
also implies increased tracking errors. A decrease in resistor width from 15m to 5pm
results in an increase of design tolerance from i20% to 140% [133]. The piezoresistor
width for our model has been set to 10am to strike a balance. The sheet resistance is
chosen to be 2009/square with a junction depth of 2.7um. It is a good compromise for
producing resistors since the sheet resistance is convenient and the tolerances and tem-
perature coefﬁcients are acceptable [133,135]. Typical measured sheet resistance values
plotted in [133] show that the temperature coefﬁcient for a 2009/square value is fairly
linear over the desired temperature range. Moreover, these are typical values for the base
diffusion [133,135,136] and may save a diffusion step if BJTs are included elsewhere in
the circuit. The piezoresistor values obtained for our dimensions are 2K9. Piezoresistor

values in the range of 500 to 500052 have been reported by the manufacturers and in the
literature [10,13,35,133].

The temperature coefﬁcient of the piezoresistors is another important model param-
eter. One of the most critical factors affecting the value of the temperature coefﬁcient is
the impurity surface concentration of the resistor surface. Therefore, the temperature
coefﬁcient of diffused resistors is determined to a great extent by the sheet resistance.
The temperature coefﬁcient is positive for the diffused resistors and it increases with the

sheet resistance. The temperature coefﬁcient of resistivity for the piezoresistor model was

56

set to l900ppm/°C. The same value of temperature coefﬁcient has been reported in [135]

for 2000/square sheet resistance.

The pressure sensitivity for a given structure is primarily determined by the value of
the piezoresistive coefﬁcients. The piezoresistive coefﬁcients in silicon have been inves-
tigated and documented by many researchers since the discovery of piezoresistive effect
in 1954 [130,132]. For the diffused layers the coefﬁcient values increase with a decrease
in the surface concentration. The coefﬁcient value is independent of the junction depth of
the piezoresistor. The temperature coefﬁcient of piezoresistivity (TCPI) is negative. For
the simulation purposes, TCPI can be speciﬁed directly or the program can compute it
from either the substrate doping, junction depth, and sheet resistance, or from the surface
concentration and the junction depth. If the surface doping is not speciﬁed, the needed
concentration is found from Irvin’s model for diffused layers (Gaussian impurity d0ping
proﬁle) [17]. For the sensor model the substrate doping concentration of 101°Icm3, sheet
resistance of 2009/square and a junction depth of 2.7um were provided to the program.
The TCPI value computed by SEN SIM for these parameters is -2308.29ppm/°C.

3.6 Simulation Methodology and Results

This section describes the simulation methodology and the results for the piezoresis-
tive pressure sensors. First, the methodology and the organizational details for the con-
duct of the simulations are outlined. Then the ideal sensor with no tracking errors is
simulated. Various piezoresistive layouts are tried and their performance results are dis-
cussed. The remainder of the section presents the simulation results for the batch fabri-
cated sensors. First, the model for the batch fabrication of the piezoresistive sensors is
presented. Then the organizational details for the simulations utilizing this model are
described Finally the simulation results are presented and the effects of the temperature
and the tracking errors on the pressure sensitivity, sensor output, and zero pressure offset

are discussed.

57

3.6.1 Methodology and Organization

The sensor performance data is required for a temperature range of -40°C to 130°C
over a pressure range of 0 to 45 psi. The effects of processing variations for the batch
fabrication are also to be incorporated in the simulations. For the purposes of simulation,
the temperature range is divided into 10°C steps and the pressure range into 5psi steps.
The program can not handle the entire temperature and pressure range in one simulation
run (too many analysis points). Thus each simulation was subdivided into four tempera-
ture and pressure subranges and four simulations were run for each sensor structure. Each
simulation produced a volume of data. The redundant data was removed and the results i

from four sub-simulations were combined into one ﬁle for each structure.

SENSIM allows the user to specify control parameters setting the accuracy for the
analysis. For all simulations the analysis level (LEVEL) is set to the highest value of 3.
This is required because of the three layered structure and to include thermal effects due
to package and thermal rrrismatch. The diaphragm grid is set to 25pm (GSIZE). Since the
diaphragm is square with uniform thickness the symmetry (SYM) is set to four-fold. This
saves considerable computational effort because only a quarter of the diaphragm region
is analyzed

As a ﬁrst step, the ideal sensor with no tracking errors, was simulated. Various
piezoresistor layouts were tried and the conﬁguration with highest pressure sensitivity
and minimum nonlinearity was selected for further analysis. The sensor model for this
structure was modiﬁed to include the tracking errors caused by processing variations.

This model was simulated to generate data for the interface circuit.

3.6.2 Simulation Results: Ideal Sensor

Various piezoresistor layouts on a diaphragm are possible. Moreover, pressure sen-

sitivity and linearity are a function of piezoresistor locations. A number of layouts with

58

differing locations and arrangements, some gleaned from the previous literature [125,35],
were simulated as an initial step. Three of these layouts were evaluated further. These
layouts are shown in Figure 3.4. Cartesian coordinates for the. piezoresistor center, using
the diaphragm center as the origin, are also shown in the ﬁgure. Some of the characteris-

tics for these layouts are summarized in Table 3.1.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Layout 1 Layout 2 Layout 3
:;RP1 t:.":IRP1 EDUUUE
RTll RT21 RP11 RTllgRT21 RP21
R“ Rm [3 [3 RP12 RT12§RT22 m2
r——1 7 ..... f f
t____. C] i I: .
: RT12 RT22
L:§:I RP2 I::I RP2 ,
RP1(0, 475) RP1(0, 475) RP11(-95,475) RP12(-95,445)
RP2(0,-475) RP2(0,-475) RP21( 95,475) RP22( 95,445)
arm-430,0) RT11(-455,15) RT12(-455,15) RT11(-45,455) RTl2(—15,455)
am 430,0) RT21( 455,15) RT22(455,-15) RT21( 15,455) RT22( 45,455)

Figure 3.4. Piezoresistor layouts on a diaphragm and their Cartesian coordinates in

micrometers (Not to scale).

59

Table 3.1. Characteristics of various piezoresistor layouts.

 

 

 

 

Characteristic Layout 1 Layout 2 Layout 3
Pressure Sensitivity 33.25 35.65 31.62
(mV/psi)
% Nonlinearity 1.023 0.242 -0.419
Temperature Coefﬁcient 78.66 81.98 70.94
of Pressure Sensitivity
mV/psi-°C)

 

 

 

 

 

 

Layout 1 has two parallel and two transverse piezoresistors. Each resistor is 100um
long and 10pm wide. The resistors are placed near the four edges of the diaphragm. This
layout provides a pressure sensitivity of 33.25mv/psi. The second layout provides an
improvement over the ﬁrst one. In this case the transverse resistors were broken into two
identical legs to increase the average stress over the piezoresistors. Now each transverse
resistor is 50m long but with the same width of 10m. This increased the sensitivity to
35.65mv/psi. A third layout places all resistors close by and near one diaphragm edge to
reduce the tracking errors. In this third case, all the piezoresistors are broken into two
parts to improve the average stress over the piezoresistors. The pressure sensitivity for

this layout is 31.62mv/psi.

Pressure sensitivity as a function of temperature is plotted in Figure 3.5. Layout 2
has the highest pressure sensitivity. For all three layouts the pressure sensitivity
decreases with temperature because the temperature coefﬁcient of piezoresistivity is

negative.

6O

 

45
Layout 1 -----
Layout 2 __
40 —- Layout 3 ............
Pressure
Sensitivity
(mV/psi)

 

 

 

20 I I

 

I I I I I I
-40 -20 0 20 40 60 80 100 120

Temperature (°C)

Figure 3.5. Pressure sensitivity for the three layouts.

Figure 3.6 shows the output voltage for the three layouts for applied pressures of 15
and 45 psi. Again layout 2 produces the maximum output with the least nonlinearity.
Zero pressure offset for all three layouts is nil since the bridge is composed of matching
resistors. Moreover, the offset remains zero over the entire temperature range because
temperature changes for individual piezoresistors are cancelled due to the bridge struc-

IUI‘C.

3.6.3 Simulation Results: Batch Fabrication

In this section the piezoresistive sensors are analyzed from the viewpoint of batch
fabrication. First, the model of Section 3.5 is enhanced to include the effects of batch
fabrication. Then the organizational details to run the simulations using this model are

described. Finally the simulation results are presented and discussed

61

 

 

 

 

2
1.6 --
Output 1,2 _
Voltage
(V) 0.8 -
0.4 -4
0 I I I I I I I I

 

Temperature (°C)

Figure 3.6. Output voltage for the three layouts.

3.6.3.1 Batch Fabrication Model

Based on the results of the previous section, layout 2 is chosen for further analysis.
In this section a model will be developed from the viewpoint of batch fabrication of the
piezoresistive pressure sensors. As discussed earlier, batch fabrication gives rise to track-
ing errors. Tracking errors are caused by variations in temperature, time period, impurity
concentration, mask alignment and other environmental changes seen by different silicon
wafers processed in a batch. There is no cost-effective technique for monitoring resis-
tance while the diffusion is taking place; in fact, at the temperatures used, silicon is no
longer a semiconductor. Thus the effect of diffusion can be measured only after the wafer
has been cooled when a subsequent correction is difﬁcult and expensive. The end result
is a variation in resistance values. These variations need to be modeled and handled in

two different ways: wafer-to-wafer variations and variations on the same wafer.

62

Wafer-to—wafer variations are large compared to the variations seen on the same
wafer. Variations of 10% to 25% from the nominal values have been reported for dif-
ferent wafers [133-136]. Variations on the same wafer are caused by temperature gra-
dients, uneven ﬂow of (10th gas within the furnace, shape and size of resistors, and
mask accuracy. Variations on the order of 1% to 3% have been reported for IOum wide

resistors [133-136].

To model the two types of tracking errors, rather large ﬁgures of :l:20% and i2.5%
were chosen for wafer-to-wafer and same wafer variations, respectively. It may be noted
here that the same wafer variations in actuality are same chip variations which are
expected to be even smaller than i2.5%. Simulations were run by introducing errors in
various possible combinations of four piezoresistors. It was concluded that the worst case
errors in the output voltage are obtained by introducing total error in either the parallel or
transverse resistor pair. Thus to represent wafer-to-wafer variations, all the piezoresistors
are changed by i20% of their nominal values. To add the effect of variations on the
same wafer, the 120% wafer-to—wafer variation for transverse resistors was modulated by
a :l:2.5% variation. Appropriate changes were also made in the sheet resistance and the
temperature coefﬁcient of resistivity. Thus the individual units have piezoresistor values

within 12.5% whereas values for the batch fall within i22.5% of the nominal values.

3.6.3.2 Simulation Organization

To include the effects of wafer-to-wafer variations three sensor structures with 0%,
20%, and -20% tracking errors were simulated. To modulate the effects of the same
wafer variations (32.5%) on the wafer-to wafer tracking errors a total of 9 sensor struc-
tures are possible. The list of these 9 sensor structures and their corresponding processing
parameters are given in Appendix A]. 36 simulations were run to cover all these struc-
tures and the complete pressure and temperature range. A sample input ﬁle for the SEN-

SIM code for the sensor with no tracking errors is given in Appendix A.2. Simulation

63

code for other structures is same with parameters changed to the values given in Appen-
dix A.1. The sample output for the sensor with no tracking errors for a temperature range
of -40°C to 0°C and pressure range of 10 to 20psi is given in Appendix A.3. Data from
all the simulations were organized and tabulated according to various temperature and
pressure values. This summarized data is given in Appendix B.l. The data in Appendix
BI is the output voltage of piezoresistive bridge produced as a function of pressure, tem-
perature, and tracking errors. Appendix B.1 also includes the modiﬁed piezoresistor
values for the desired pressure and temperature range. This organization of data pro-
vides some insight into the sensor characteristics but to gain a full understanding the sen-
sor response, plots provide a convenient tool. The plots and performance evaluation of

the sensor is presented in the next section.

3.6.3.3 Simulation Results

A large number of simulations were run to obtain sensor performance data for the
desired pressure and temperature range as a function of tracking errors. Results of these
simulations provide a worst case error band for various characteristics of the batch fabri-
cated piezoresistive pressure sensors. It was noted that all the Sensor parameters are
functions of temperature and tracking errors. The sensor response as a function of pres-
sure and temperature is shown in Figure 3.7. The plots are for the sensor with 20%
wafer-to-wafer tracking error and 2.5% same chip variations. The zero pressure offset
voltage of 56.8 to 68.7mV is caused by the same chip tracking errors. Moreover, the
offset is also a function of temperature. Higher outputs are obtained for the lower tem-
peratures because the temperature coefﬁcient of piezoresistivity is negative. The error
caused by temperature is near zero for low pressures and it increases linearly with pres-
sure. The maximum variation of 0.642V iS observed between the temperature values of

-40°C and 130°C.

64

 

 

 

 

 

2
1.5 —
Output
Voltage 1 —
(V)
0.5 —
0 . ' Zero pressure offset
l l
0 15 30 45

Pressure (psi)

Figure 3.7. The sensor response as a function of pressure and temperature.

The error bands for the pressure sensitivity are shown in Figure 3.8. The narrow
bands result from the tracking variations on the same wafer. At room temperature a max-
imum variation of 0.105 mV/psi is observed for the sensors located on the same wafer.
The wider band extending from 39.45 mV/psi to 42.60 mV/psi at -40°C indicates the
error band for the whole batch. At room temperature a maximum variation of 1.35
mV/psi is observed for the batch. It is also observed that higher pressure sensitivity is
obtained with larger bridge resistance values and for the units with negative tracking
errors. The pressure sensitivity is a function of temperature even for the sensor with the
perfectly matched piezoresistors, although the variation is linear. For the structure with
no tracking errors of any type, the pressure sensitivity decreases ﬁ'om 41.13 mV/psi to
27.20 mV/psi as the temperature rises from -40°C to 130°C. The error band is much
smaller for on-chip variations compared to the wafer-to-wafer variations. Moreover, the

error band is wider for lower temperatures.

65

 

20:1;2.S% Tracking Errors ............
“it“: 012.5% Tracking Errors
"it. . -2o:2.5% Tracking Errors —————

39.5 —

Pressure
Sensitivity 35 —

(mV/psi)

30.5 -

 

26—

 

 

 

I I I I I I I I
-40 -20 0 20 40 60 80 100 120

Temperature (°C)

Figure 3.8. Pressure sensitivity for various tracking errors.

Another error voltage, the zero pressure offset, contributed mainly by the same chip
tracking errors, is shown in Figure 3.9. Offset values of 56.8 to 68.7mV are observed for
12.5% tracking errors for the temperature range of -40°C to 130°C. The temperature
dependency of the zero pressure offset also shows a nonlinearity of 1.30% for positive
tracking errors and 1.26% for negative tracking errors. The offset voltage for the positive

and negative tracking errors is almost of the same magnitude.

66

 

 

 

 

100
25 % Tracking Errors
50 — ————————

Offset

Voltage 0
' (mV)

-50 — ......................... -2.5% TI'aCking Emrs
-100 l l l l I

 

I I r
-40 -20 0 20 40 60 80 100 120

Temperature (°C)

Figure 3.9. The zero pressure offset for various tracking errors.

3.7 Summary

The simulation details and results for the piezoresistive pressure sensors have been
presented in this chapter. Sensor performance data from these] Simulations will be used to
develop a new temperature compensation technique. The data will also be used as the
input for the interface circuit simulation. Simulation objectives have been discussed with
a goal to produce a generalized and realistic sensor model. SENSIM, the sensor simula-
tion program for the piezoresistive and capacitive pressure sensors was used to run the
simulations. The program has been validated through comparison with the experimental
data from the actual devices. The program allows the user to choose structural, process-
ing, electrical, and control parameters. Each model parameter was discussed with refer-
ence to the previous literature. The values for the model parameters were deduced from
these discussions and reviews. Various piezoresistors layouts on the diaphragm were dis-

cussed and Simulation results for the ideal sensor, with no tracking errors, were

67

presented The sensor model was enhanced to include the batch fabrication effects. :l:20%
variations in the piezoresistors values were modulated with :t2.5% variations to represent
the wafer-to-wafer and same wafer variations, respectively. 36 simulations were run to
cover the entire pressure and temperature range and the tracking errors caused by the pro-
cessing variations. The Simulation results provide the worst case error band for the sen-
sors coming from the same wafer or different wafers. The simulation results have been
used to study the temperature response of the sensor as function of tracking errors. All
sensor parameters are functions of temperature and the tracking errors. The worst case
nonlinearity for the sensor output is only 0.24%. The sensor output is a function of tem-
perature even for the sensors with no tracking errors. The zero pressure offset is also tem-
perature dependent. It varies from 56.8 to 68.9mV over the desired temperature range.
Moreover, the temperature dependency shows a maximum nonlinearity of 1.30%. The
simulation results are, in general, in agreement with other reported results. The simula-
tion results have provided a better understanding of the temperature characteristics of the
piezoresistive sensors as a function of tracking errors. The sensor performance data will
be very useful for devising a new temperature compensation technique and for the

designing and testing of the interface hardware.

CHAPTER 4

TEMPERATURE COMPENSATION

4.1 Introduction

In this chapter a new temperature compensation technique for piezoresistive pres-
sure sensors is presented for a temperature range of -40°C to 130°C over a pressure range
of 0 to 45 psi. The technique has been implemented in two parts. First, the double bridge
compensation removes the errors caused by the same wafer variations and then a tem-
perature half bridge is used to compensate temperature errors for wafer-to-wafer varia-
tions. First, the temperature characteristics and Simulation results for the piezoresistive
pressure sensors are discussed from the viewpoint of understanding the errors caused by
the temperature variations and the tracking errors. Then, the two parts of the temperature
compensation technique are presented. Each part is described and the Simulation results

are presented and discussed.

4.2 Temperature Characteristics

The major problem associated with piezoresistive pressure sensors is their inherent
cross-sensitivity to temperature. In this section the behavior of a piezoresistive pressure
sensor as a function of temperature is explained. First, a brief review of the temperature
characteristics of a batch fabricated sensor is presented. Then, an analysis of the Speciﬁc

temperature errors deduced from the simulation results of the last chapter is presented.

68

69

4‘.2.1 Review

The inﬂuence of temperature on a piezoresistive pressure sensor is exhibited by a
change in the Span and the offset of the sensor output. Moreover, process variations,
which are random, give rise to piezoresistive tracking errors, which in turn change the
temperature characteristics for the individual units. The processing variations cause two
types of piezoresistive tracking errors: those on the same wafer and those which may
vary from wafer-to-wafer. Zero pressure offset and the sensor output are functions of the
tracking errors as well as the temperature. The zero pressure offset is not encountered for
a sensor with matching piezoresistors but the sensor output is a function of temperature
even for the sensors with no tracking errors. This results from the temperature depen-
dency of the piezoresistive coefﬁcients. Temperature compensation techniques have been
reported using laser trimming, external resistors, and clever use of material properties
[10,11,23]. Generally these techniques are for limited temperature and pressure ranges,
and in most cases for Speciﬁc applications such as biomedical devices. Moreover, these
techniques involve additional processing steps performed under sensor operating condi-

tions which add time and cost to the device fabrication process.

4.2.2 Temperature Errors

The sensor model for the batch fabrication of piezoresistive pressure sensors has
been presented in the last chapter. The sensor was Simulated and the required data pro-
duced over the desired pressure and temperature range including the effects of processing

variations. The error analysis of the simulation results is presented in this section.

The errors caused by tracking errors and temperature can be subdivided into three

partsas

eTotal = eoffset + etc + etemp-

70

eaﬁgm is the zero pressure offset voltage mainly caused by the on-chip tracking
errors, which cause an imbalance in the piezoresistive bridge. The offset error is also a
function of temperature. em is the error caused by wafer-to-wafer and same wafer track-
ing errors. These errors only shift the sensor response curve as a function of the magni-
tude of the tracking errors. camp are the errors solely due to the temperature, Since the
piezoresistive coefﬁcients are a function of the temperature. These errors are present
even in a sensor with perfectly matched piezoresistors. The good thing about the tem-
perature dependency is that the relation is linear. The magnitude of these errors as a func-
tion of temperature is Shown in Figure 4.1 for the sensor with positive tracking errors.
Room temperature is taken as the reference for the emmp error plot. Thus, the error is zero

at 27°C and increases linearly on either Side.

 

 

 

 

400
300 —
Error
e
Voltage 200 ._ .. temp
(mV)
e
100 — Le
.-_-_-_-_-_-— -—-—.,.t'.— ________________
. eoﬁset
0 I l I I I I I l

 

Temperature (°C)

Figure 4.1. The error voltages for the sensor.

71

4.3 Objectives

The compensation circuit and the sensor are intended to be integrated on the same
chip and batch fabricated. A proposed hardware design for implementation of the tech-
nique will be developed in the next chapter. The ultimate objective is to produce a low
cost interface circuit. The key to reducing the cost of any integrated circuit is batch fabri-
cation. Moreover, reduction in design time is also a must for achieving a lower cost. To
meet this end, the resulting hardware should be structurally simple to reduce the area
consumed by the compensation circuit on the chip. The technique should be implement-
able using the standard integrated circuit fabrication technologies. Moreover, temperature
compensation of the individual. units under the sensor operating conditions must be
avoided. The technique should result in a ﬂexible design with possible extensions to

other sensors utilizing the piezoresistive effect and batch fabrication.

To summarize, the temperature compensation technique should be structurally sim-
ple, cost effective, use Standard IC fabrication techniques, and suitable for batch fabrica-
tion. It should not require handling of the individual units for the trimming of their tem-

perature characteristics under sensor operating conditions.

4.4 Approach

The sensing element consists of four piezoresistors in a wheatstone bridge
conﬁguration diffused in the thin diaphragm. The sensor and the interface circuit is to be
batch fabricated which will result in tracking errors for the piezoresistors. Moreover, the
sensor is to operate over a wide pressure and temperature range. To ensure Similar pro-
cessing, pressure, and temperature variations, the temperature compensation techniques
developed are based on the bridge conﬁgurations. The diffused compensation bridge
resistors have the same mask patterns and values as the piezoresistors. This is the key to
eliminating the need for the compensation of the individual units because the sensing

bridge and the compensation resistors undergo exactly the same processing conditions.

72

Moreover, during Operation the two share the same temperature environment.

The compensation bridge resistors are located on the bulk part of the chip, away
from the effects of the pressure induced stress, to differentiate the pressure effects from
the temperature variations. The resistors are modeled using the parameters discussed in
Sections 3.5 and 3.6.3.1. Two approaches were considered for obtaining the temperature
response of the resistors. The simplest option was to use piezoresistive bridge output for
the zero applied pressure. This output is available as part of the piezoresistive bridge
simulations but may not be realistic since the piezoresistors are located on the thin
diaphragm. Moreover, the Simulator used, SENSIM, is primarily for the pressure simula-
tion and also includes other effects such as package Stress, and thermal mismatch. The
second option was to use PSpice for the simulations as this program is also used for the
simulation of the analog portion of the interface circuit. Therefore, the second option was

adopted for Simulating the compensation bridge and the temperature half bridge.

The double ended bridge output is ampliﬁed and converted to a single ended Signal
through the use of an op—amp based ampliﬁer circuit. The circuit is identical to the
ampliﬁer for the piezoresistive bridge output. The overall behavior of this circuit is deter-
mined by the ratio of the resistors, thus making the circuit insensitive to processing varia-

tions and temperature changes.

4.5 Compensation Technique

In this section a new temperature compensation technique for the piezoresistive
pressure sensors is presented. Same wafer and wafer-to-wafer variations are handled in
two parts. First, the zero pressure Offset and same wafer variations are compensated, pro-
ducing an output free of variations caused by same wafer tracking errors. The resulting
output is Still a function Of the temperature. Then in the second part, the technique to
remove this dependency is developed. The technique developed utilizes a temperature

half bridge as the primary compensation element.

73

In this section the two parts of the new temperature compensation technique are

described and the simulation results are presented and discussed.

4.5.1 Compensation: Same Wafer Variations

In this section the double bridge technique for the temperature compensation Of
errors caused by same wafer tracking errors is described Initially the technique was
developed and simulated. Later, on the basis of the simulation results, the hardware
implementation of the technique was improved to reduce the chip area. First, the double
bridge technique and its improvements are described. Then the simulation results for the

technique are presented and discussed.

4.5.1.1 The Double Bridge Technique

Based on the results of Chapter 3 a new temperature compensation technique using
two bridges is developed. The block diagram Of this technique is shown in Figure 4.2. A
piezoresistive bridge is located on the thin diaphragm and its output is a function of pres-
sure and temperature. The compensation bridge is located on the bulk part of the chip;
thus its response is dependent on the temperature only. The Shape and Size of the com-
pensation bridge resistors are identical to the corresponding resistors of the pressure sen-
sitive bridge. Physically, the corresponding arms of the two bridges are located as close
as possible to each other. To prevent the effects of induced stress in the diaphragm, a safe
distance of 100nm from the diaphragm edge has been suggested for the peripheral cir-
cuits [35]. These physical considerations and the close proxirrrity of resistors eliminates
the factors contributing to the tracking errors on the same chip rendering the variations
between the corresponding bridge arms negligible [133]. Therefore, the effect of same
wafer tracking errors can be eliminated by taking the difference of the two bridge out-
puts. Differential ampliﬁers are used to amplify and convert the double-ended bridge out-

put to a Single-ended Signal. Two analog to digital converters are used to digitize the

74

pressure and the temperature outputs. A digital subtractor is employed to obtain the
difference of the two bridge signals. The digital temperature Signal is available and may

be used else where in the circuit and/or provided as temperature output for the chip.

I
VB AID
: V (RT) Converter __
T ,

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Di 'tal

Piezoresistive Bridge gr . VG”)
Compensation .—>

1 Circuit
V __
B A / D
: vm Converter
Temperature Bridge

Figure 4.2. The double bridge temperature compensation technique.

To see the effectiveness of the technique, the temperature bridge was Simulated and
its output subtracted from the piezoresistive bridge output. The results indicate that the
temperature bridge output is not dependent on temperature alone, as initially presumed.
Rather the temperature bridge response is dependent on the temperature as well as the
on-chip tracking errors. Thus, if there are no tracking errors present for a particular sen-

sor unit, the bridge is balanced and its output remains zero for the entire temperature

75

range. These observations led to two conclusions. First, the double bridge technique will
only compensate the errors contributed by the same wafer tracking errors. Therefore, the
technique will only compensate for the zero pressure Offset and the differences in the out-
putsof the devices fabricated on the same wafer. The second observation was that the so
called temperature bridge output does not provide a true temperature signal. Thus, the
temperature bridge output does not provide enough real information about the tempera-
ture to be utilized in the digital part of the temperature compensation circuit or elsewhere
on the chip. Therefore, digitizing this Signal is not of much use. Instead it was
discovered to be more advantageous to subtract it from the piezoresistive bridge output in
analog form. The resulting signal then may be digitized. The improved block diagram

implementing this change is shown in Figure 4.3.

In the improved circuit, an analog subtractor circuit is used to generate the differ-
ence of the two bridge outputs. The use Of the subtractor eliminates the need for two AID
converters. Moreover, the output of the subtractor is a unipolar signal which doubles the
resolution of the AID converter. The output of the subtractor is digitized for further pro-

cessing to produce a temperature compensated digital output.

The improved implementation offers a number of advantages. First and foremost is
the savings of the chip area taken by the AID converter, register, and the digital subtrac-
tor circuit for the temperature bridge. Secondly the output of the subtractor circuit, which
is the difference of the outputs of the two bridges, is unipolar over the entire temperature
and pressure range. Therefore, the analog input to the A/D converter is a unipolar signal
for a particular sensor unit. This doubles the resolution of a carefully designed AID con-
verter because the analog voltage range of 10V (iSV) has been reduced to 5V (either
+5V or -5V). Moreover, if there are any differences in the Operation of the A/D con-
verter for the two polarities of the input signal it will not effect the individual units.
These differences just Shift the response curve and can be resolved during the calibration

of the sensors.

76

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

— Differential
Ampliﬁer
I . Digital
Piezoresistive Bridge A I D __ Compensation __,
Converter Circuit v(p)
Subtractor
VB :
Differential
Ampliﬁer
Compensation Bridge

Figure 4.3 The improved double bridge temperature compensation technique.

4.5.1.2 Results

' To Simulate the double bridge technique rather large ﬁgures were chosen to model

the tracking errors. The tracking error values are summarized in Table 4.1. The data in
0

Appendix B2 is the output voltage of the compensation bridge for same wafer tracking

errors. The data is organized according to the appropriate temperature ranges.

77

Table 4.1. Piezoresistor tracking error values.

 

 

 

 

Conﬁguration Component Tracking Error
Wafer to wafer Compensation bridge :l:20%
Piezoresistive bridge i20%
Same wafer/chip Compensation bridge :l:2.5%
Piezoresistive Bridge i2.5%
Same chip Corresponding bridge arms Negligible

 

 

 

 

 

Simulations for the double bridge compensation technique for a temperature range
of -40°C to 130°C show encouraging results for the temperature compensation of the
zero pressure offset and the errors caused by the processing variations on the same chip.
The simulation results showing the compensated output are given in Appendix B.3. The,

data is organized according to the appropriate pressure and temperature ranges.

Zero pressure offset, which is a function of tracking errors and temperature, Shows a
maximum nonlinearity Of 1.30% with a worst case error band of 3:68 mV over the desired
temperature range. It is reduced to a fraction of a microvolt for the compensated sensor,
which is below the measurement precision limit. Zero pressure offset curves for the com-
pensated and uncompensated sensors with i2.5% tracking errors are Shown in Figure 4.4.
The curve in the middle, centered around zero, Shows the compensated zero pressure
offset for all types of tracking errors. The curves on the top and bottom represent the

offset values for positive and negative tracking errors, respectively.

78

 

 

100
Uncompensated (+2.5 % Tracking Errors)
L __________________________________
50 —
Offset
Compensated (All Tracking Errors)
Voltage 0
(mV)
-50 _D ....................... uncompensated (-2.5% TraCKing Errors)
‘100 I r I I I

 

 

 

l j l
-40 -20 0 20 40 60 80 100 120

Temperature (°C)

Figure 4.4. The compensated zero pressure Offset voltage.

The sensor output is also a function of the temperature and the tracking errors. Sen-
sors with 32.5% tracking errors Show a worst case error band of i3.04% of the full scale
output at 45psi. The error band is reduced to i0.24% of the full scale output for the com-

pensated sensor. A plot of the sensor response for both cases is shown in Figure 4.5.

The double bridge technique eliminates the zero pressure offset and compensates
for the output variations caused by the same wafer tracking errors. The technique is not
effective for wafer-to-wafer tracking errors and the errors contributed by the temperature

dependency Of the piezoresistance.

79

 

   
    

2
. g ‘ 2.5% Tracking Errors -----
I ..... : No Tracking Errors __
......... -2.5% Tracking Errors ............
1.75 — ., -
., . Compensated
Output .. .,
Voltage 1.5 - .
(V) - .........
1.25 -— ...........
1 l | l I l I I

 

 

 

I
-40 -20 0 20 4O 60 80 100 120

Temperature (°C)

Figure 4.5. The compensated output voltage.

4.5.2 Compensation: Wafer-to-Wafer Variations

The double bridge compensation technique effectively removes the zero pressure
offset and the errors caused by same wafer tracking errors. Thus the task of temperature
compensation is reduced to the compensation of the wafer-to-wafer processing variations
only. Although the resistors are matChed, the sensor output is still a function of tempera-
ture. In this section a new temperature compensation technique is developed to remove

the remaining temperature errors from the output of the double bridge technique.

4.5.2.1 Approach

It is observed that the piezoresistive pressure sensor response with the matched
resistors is also a function of the temperature. This dependence is caused by the tempera-
ture sensitivity of piezoresistive coefﬁcients. Moreover, the wafer-to-wafer tracking

errors also vary the values Of the piezoresistive coefﬁcients. camp, the error solely caused

45

nit
tio

pr:

bu
sir
of:
sur‘
Hm
rest

CHI

80

by the temperature was shown in Figure 4.1. The magnitude of the error voltage
increases linearly with the temperature on the either Side of the reference temperature. To
compensate for this error, a diffused resistor which has a positive temperature coefﬁcient
of resistivity, is used to derive a temperature Signal of the corresponding magnitude. The

magnitude Of this Signal is not a function of the applied pressure.

The sensor outputs as functions of pressure and temperature were shown in Figures
3.6 and 3.7. The Slope Of the output signals is negative for all pressure values. Moreover,
the error magnitude increases with the applied pressure. This implies that the temperature
signal can not be used directly for all pressure values. To overcome this difﬁculty the
temperature signal is scaled digitally to take care of various pressure ranges. The scaled
temperature Signal is then added to the pressure output. The temperature signal may be

positive or negative depending on the pattern of tracking errors.

4.5.2.2 The Half Bridge Technique

Based on the Observations of Section 4.5.1.1, a new temperature compensation tech-
nique is developed. This technique processes the results of the double bridge compensa-
tion technique to produce the ﬁnal temperature compensated output for the piezoresistive

pressure sensors. A proposed circuit to implement the technique is shown in Figure 4.6.

The temperature half bridge, driven by a constant current source, is located on the
bulk part of the sensor chip. Its response is dependent on the temperature alone. Even a
Single resistor is sufﬁcient to obtain the temperature Signal but R1 has been added to
Offer a higher load resistance to the current source. Any value may be chosen for R1 to
suit the design of the current source Since it does nOt effect the operation of the tempera-
ture compensation technique. The Shape, Size, and value of R2 is identical to the parallel
resistors on the piezoresistive bridge. This is to ensure same wafer-to-wafer tracking

errors forRz and the piezoresistors.

in

15 Sin

81

Figure 4.6. The half bridge temperature compensation technique.

The current source provides a constant current of 1.25mA. This value has been
chosen as the center of the tracking errors and the temperature range. The output for the
compensation resistor with no tracking error at the room temperature for this current is
2.5V. The current value is used to set a reference for the design with respect to the sensor
structure and the temperature range. The variations in the reference temperature do not
alter the effectiveness of the technique. With another reference, the sensor response will
still be insensitive to temperature, but a corresponding shift will result in the compen-

sated output which may be calibrated out.

The voltage across R2 is subtracted from a 2.5V reference to obtain the temperature
signal. The resulting temperature Signal is unipolar or bipolar depending on the value of
the tracking error for a particular sensor unit. Theoutput voltages for the 0%, 20%, and
-20% tracking errors are given in Appendix B4. The temperatrue signal is ampliﬁed,
digitized, and Stored in a register. The response of the double bridge compensation circuit

is Simultaneously available in a second register. The temperature bridge output is scaled

82

down for various ranges of applied pressure and added to the compensation bridge out-
put. The temperature signal may be positive Or negative. The ﬂow chart for the compen-

sation algorithm is shown in Figure 4.7. The hardware and the implementation details for

the technique are given in Chapter 5.

4.5.2.3 Results

Three sensor Structures with 0%, 20%, and -20% were Simulated. A large number of
simulations were run to obtain sensor performance data for the desired pressure and tem-
perature range. The ﬁnal compensated output voltages for the sensor are given in Appen-
dix B5. The data in the appendix is organized according to appropriate pressure and tem-

perature ranges.

The compensated and the uncompensated sensor response as a function Of tempera-
ture for the sensor with no tracking errors is Shown in Figure 4.8. The uncompensated
output shows a large sensitivity to the temperature variations. This is caused by the tem-
perature dependence of the piezoresistive coefﬁcients. The compensated output for lower
Pressure values is Slightly overcompensated. The uncompensated output for 30psi shows
a temperature coefﬁcient of -2.44mV/°C. The temperature coefﬁcient of the compensated
Ontput for the same applied pressure is reduced to a modest value of 74.9uV/°C. The

Compensated response as a function of pressure for the same sensor structure is shown in

Figure 4.9.

83

C )
l

Read pressure
and
temperature

 

 

 

 

 

No Yes

Pressure > 22.5psi

No

 

 

 
 

Pressure < 11.25psi

 

   

 

I

Divide temperature Divide temperature Divide temperature
output by 8 output by 4 output by 2

i

Add temperature
and pressure
outputs

l
< >

Figure 4.7. Flow chart for the half bridge temperature compensation technique.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

84

 

Compensated ............
Uncompensated

 

 

 

 

I
-40 0 40 80 120

Temperature (°C)

Figure 4.8. The compensated sensor response as a function of the temperature.

 

 

 

 

 

2
1.6 -
Output 12 ._
Voltage
(v) 0.8 — -
0.4 —
0 I I I
5 15 25 35 45
Pressure (psi)

Figure 4.9 The compensated output for the sensor with no tracking errors.

85

The plots provide the worst case error band for the extreme temperature values of
-40°C and 130°C over the entire pressure range. The solid curve in the middle shows the
response at the room temperature. The sensor response at the intermediate temperature
values will lie inside the error band. The compensation becomes less effective for the
pressure values higher than 35psi. It is noted that the reduction in the effectiveness is
more pronounced for the extreme temperature values. For the temperature range of 0°C
to 80°C, the worst case error band is reduced to less than half the value shown in the
ﬁgure. The maximum error voltages observed for -40°C and 130°C are less than one
tenth of a volt with the full scale output of 1.69V. The compensated response Of the sen-
sor with 20% tracking errors is shown in Figure 4.10.

 

 

 

 

 

 

2
-40°C -------- .I
30°C ”xv". , ’
1.6— 130°C ............ ,..-°'°"
Output 12 _
Voltage
(v) 0.8 -
0.4 —
0 I I I
5 15 25 35 45
Pressure (psi)

Figure 4.10 The compensated output for the sensor with 20% tracking errors.

The response is Similar to that of the sensor structure with no tracking errors. The
maximum output in this case iS 2.0V. The error voltage for the pressure values below

35psi is less than 0.025V. The error band expands above this pressure to a maximum

86

value Of 0.1V for 45psi at 130°C.

The pressure sensitivity for the compensated and the uncompensated sensor with

-20% tracking errors is Shown in Figure 4.11.

45

 

Compensated ............
Uncompensated

Pressure
Sensitivity

(mV/psi)

 

 

 

 

Temperature (°C)

Figure 4.11 The pressure sensitivity for the sensor with -20% tracking errors.

Again the effectiveness of the technique is reduced for 45 psi. The pressure sensi-
tivity for the uncompensated sensor is 77.67uV/psi-°C. It improves to 35.4uV/psi-°C for
a pressure range of 45psi and becomes almost independent of the temperature for the

pressure range of 25psi with an insigniﬁcant value of 1.05uVIpsi-°C.

4.5.2.4 Discussion

The temperature compensation technique presented above has been developed for
the large tracking errors values of i20%. The technique also covers a wide temperature
and pressure range. The balancing of these three parameters to minimize the compensa-

tion errors is a very complicated task. The half bridge technique provides very accurate

87

results for the pressure values below 35psi over the entire temperature range of -40°C to
130°C. The accuracy is reduced for higher pressure values at extreme temperatures. The
technique is suitable for the applications requiring reasonable accuracies such as automo-
biles. For more precision applications, the higher pressure range may need further

reﬁnement.

The temperature outputs are ﬁxed for a particular tracking error pattern. The tem-
perature output is divided by powers Of 2 to obtain corrections for various pressure
ranges. The division by 2 (Shift right) is conveniently handled by the digital circuit. The
response for the lower pressure values is trimmed well by sealing the temperature values
by factors of 4 and 8 but for higher pressure values the correction step of divide by 2 pro-
vides a rather coarse trimming. This expands the error band for the pressure values above
35psi. The output for the higher pressure values can be reﬁned and errors reduced by
using a scale factor between 0.5 and l (non-power of 2)..This will require a large amount
of compensation and control circuitry and may defeat the goal of the structural simpli-
city.

The temperature bridge output and the partially compensated pressure outputs may
also be processed using software. This approach assumes the availability of a micropro-
cessor or a microcomputer. The register contents for the pressure and the temperature are
read and manipulated by the processor. The temperature bridge response in this case may
be scaled down to any desired value and added/subtracted to the pressure output. This
approach may be developed to produce very precise compensation results, but at a lower
speed. Moreover, the availability of a processor is a must for this alternate approach.
Hardware processing is faster and doesn’t consume much in chip area as well. The only
circuits required are the 2-tO-3 multiplexers and a controlled adder circuit. The exact
choice of the approach will be determined by the need for the required accuracy, and the

temperature and pressure ranges to be covered for a speciﬁc application.

88

4.6 Summary

The temperature compensation technique for the piezoresistive pressure sensors has
been presented. The technique has been implemented in two parts, using a compensation
bridge and a temperature half bridge. The double bridge technique is very effective for
the zero pressure offset and the temperature errors caused by the same wafer processing
variations. The zero pressure offset is reduced below the measurement precision limit for
the entire pressure and the temperature range. The output errors for the sensor, caused by
the same wafer variations, are reduced by a factor of 100. The output of the double
bridge technique compensates sufﬁciently for same wafer variations but still shows tem-
perature dependency caused by the temperature sensitivity of the piezoresistive
coefﬁcients. Anyhow, the task Of temperature compensation is reduced to the compensa-

tion of wafer-to—wafer variations only.

The remaining temperature errors for the sensor output are removed by the second
part of the compensation technique. A temperature half bridge has been employed to
implement this technique. The technique is very effective for the pressure values below
35psi and provides reasonable results for the higher pressure values at extreme tempera-
tures. The causes of this degradation of accuracy have been discussed and the irnprove-
ment techniques have been suggested. The possible use of software approach to irnple-
ment part of the compensation technique has also been out lined and discussed. The sen-
sor output becomes temperature independent, showing only a Shift in the output for vari-
ous tracking errors. These shifts can be resolved during the calibration of the sensors car-

ried out at room temperature.

The temperature compensation technique presented in this chapter has very cOn-
vincing advantages. The compensation circuitry is structurally simple and suitable for
batch fabrication. It is implementable using the available IC fabrication technologies.
The technique does not require the compensation of the individual units under sensor

operating conditions. Moreover, no external components are required for the

89

implementation of the technique. All these features make the technique very cost effec-

tive, the ultimate Objective for the design of the interface circuit.

CHAPTER 5

INTERFACE HARDWARE

5.1 Introduction

The analog portion of the circuit was Simulated with PSpice 4.03 and the digital
portion was simulated in VHDL (VHSIC (V ery High Speed Integrated Circuit) Hardware
Description Language. The design and simulation were carried out in a bottom-up
fashion. Analog and digital building block circuits including op-amp, comparator, sub-
tractor, switch, zero crossing detector, integrator, ﬂip ﬂop, decoder, counter, register, and
various gates were tested ﬁrst. The testing and reﬁnement of analog circuits involved pro-
vision of typical inputs and then comparison of the outputs to the expected responses. In
many cases the analog components were adjusted and/or changed to tailor the response to
the desired values. For the digital blocks, a typical set of data was provided as input to
the modules (VHDL programs). The simulated responses of the output signals were then

compared to what was expected from the truth tables to verify correctness.

The design of the interface circuit went tluough numerous reﬁnements during its
course. Desirable as it may be, documenting all the changes is itself a formidable task.
But even if it can be done, documentation alone is not a substitute for the understanding,
which is what this work sets out to accomplish in the development of an interface circuit

for the piezoresistive pressure sensors.

In this chapter the interface hardware for piezoresistive pressure sensors is
presented. First, the design objectives, philosophy, and speciﬁcations are for the
hardware design. Then the implementation details for the ampliﬁer and the subtractor cir-

cuit are presented. The remainder of the chapter describes the selection and designing of

91

the analog to digital converter circuit. Basic analog to digital conversion techniques are
studied with a goal to select the one best suited for the interface circuit. The dual slope
analog to digital conversion technique is selected and complete details for its design are
presented. In the end the hardware for the implementation of the half bridge temperature

compensation technique is described.

5.2 Design Objectives and Philosophy

The clear understanding of the design objective and philosophy is an integral part of
the decision making process, because these are the ultimate justiﬁcations of the
designer’s decision. With this understanding, the objectives for the interface design are
outlined ﬁrst, followed by a discussion of the bearing of these objeCtives on the design of
the circuit.

The interface circuit is intended to be integrated on the same chip as the piezoresis-
tive sensing element. Moreover, the complete device is to be batch fabricated for mass
production. The sensor should be operable over a temperature range of 440°C to 130°C to
make its application area wider. An effort was made to come up with a design as close as
possible to these objectives. In some cases it was possible, while in others a compromise
was required as will be described.

The circuit is to be batch fabricated {thus the problem of tracking errors for
piezoresistors as well as other circuit resistors and components becomes important. The
best remedy for this problem is to design for resistive ratios instead of absolute values for
the resistors. Also it is better to choose design techniques in which the overall behavior is

less sensitive to component tolerances. These principles were applied in all the designs.

The integration of the sensOr and the interface circuit leads to two conclusions.
Firstly the circuit should be structurally simple so that it consumes a minimum of real
estate on the chip. Secondly the fabrication process should be, as far as possible, compa-

tible with the sensor processing steps. Because of the broader temperature range. the

92

design should be such that its output is least dependent on the temperature. Again the use

of ratios instead of absolute values reduces the effect of temperature.

The lowest level of design is at the transistor level whereas the highest level consti-
tutes a design at the block level. The design approach adopted here was to take the mid-
dle path, that is, use small blocks such as a comparators or ﬂip ﬂops. Analog circuits
were Simulated at transistor level while digital circuits were simulated at gate and/or
block level. The designs were not geared towards a particular technology but fabrication
and implementation details were kept in mind. Literature and books were searched when
setting design parameters to obtain Simulation models close to reality. Extremes were
examined and parameters were set to a reasonable value somewhere in the middle. The
same approach was used for making some assumptions about the circuit operation and/or
its characteristics. Moreover it is not the objective here to specify the implementation
technology at the lowest level, but of course such details were kept in mind while making
design decisions. These objectives provided guidelines to streamline the design approach.
It was not possible to fulﬁll these requirements completely in all cases. In many cases

there were a trade-off necessitated to balance certain requirements.

5.3 Des'gn Speciﬁcations

The input to the circuit comes from the piezoresistive bridge and the compensation
bridge. The output signal is double ended in both cases. Moreover, the voltage variations
caused by temperature and/or pressure ride over a common mode signal. The magnitude
of the differential mode Signal varies ﬁ-om 0 to 1.962V. The signal is low frequency, or to
be more speciﬁc, it is a slow varying DC signal. The polarity of the signal is random
which is determined by the pattern of tracking errors. In some cases the signal is positive
or negative over the entire temperature and pressure range while in other cases it may
switch polarity over the temperature and pressure range. The interface circuit is operable

from a dual power supply of :tSV.

93

The interface circuit is to provide a 10-bit digital output. Ideally the output should
be linear and independent of the temperature and tracking errors. This output could be
calibrated for the individual units (not part of this work) for the desired pressure range.
Linearity, as was described, in Chapters 2 and 3 is not a major concern for piezoresistive

pressure sensors.

5.4 Amplification

The ﬁrst task of the interface circuit is to convert the double ended bridge outputs to
Single ended outputs. Secondly the outputs must be ampliﬁed to cover the entire analog
input range of the ADC. The natural choice to accomplish both these tasks was an opera-
tional ampliﬁer (op-amp). The same op-amp could be used in the subtractor and for the

integrator in the ADC circuit.

Op-amps are ampliﬁers (controlled sources) that have sufﬁciently high forward gain
so that when negative feedback is applied, the closed-loop transfer function is practically
independent of the gain of the op-amp. Ideally, an op-amp has inﬁnite differential-
voltage gain, inﬁnite input impedance, and zero output impedance. In reality an op-amp
only approaches these values.

In this section the design approach and the op-amp circuits are described ﬁrst. Then

the details of the op-amp based ampliﬁer, used for the interface circuit, are presented.

94
5.4.1 Design Approach for the Op-amp

For the interface circuit, the op-amp could be designed from the scratch, that is from
transistor level. On the other hand, a Short cut could be taken to simply model and simu- '
late it as a voltage controlled voltage source. These two approaches represent two
extremes. A compromise was made to follow the middle path to have realistic simula-
tions without wasting undue effort. Thus the op-amp was not designed from scratch
instead the available circuits were surveyed and simulated. A number of circuits ﬁ'om
various books [137-139] were tried. The aim here was to ﬁnd a circuit with high open
lOOp gain, large common-mode rejection ratio, high power supply rejection ratio, and a
low offset voltage. Slew rate, bandwidth, and frequency response were not major con-
cerns since it was to be used for a low frequency application. A symmetric voltage swing
with saturation voltages approaching the power supply was also desired. Simulations

were run to pick the op-amp with a linear output over the the entire output range of iSV.

5.4.2 The Op-amp Circuit

The op-amp circuit shown in Figure 5.1 was selected for the interface. This is a two
stage op-amp with an MOS/BJT output stage consisting of emitter-follower Q1 and MN9
[137]. Except for these devices, the circuit is a two stage op-amp. The BJT in the output
reduces the output resistance of the op-amp without adding complex circuitry. This
characteristic allows the op-amp to drive the large capacitive and the small resistive

loads.

All devices, except Q1, used in the circuit are enhancement mode NMOS and
PMOS transistors. The BJT used is a Special type called substrate BJT. The fabrication
process for this transistor is compatible with the basic sin gle-well CMOS fabrication pro-
cess even though the collector terminal is constrained to V4,, (or V”). The emitter is the
source or drain diffusion of the NMOS device, the base is the P-well and the n“ substrate

is the collector. The primary advantage of a BJT in the output stage is a low resistive

95

output impedance. The major disadvantage is the requirement for a base current causing

a Slew rate limitation.

 

 

 

MP8 ‘ MP5 3
T MP7
- l

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

12 L13 Vdd 8 Q1
_ + — MNII
Vin , Vin 11
V‘l MP1 MP2 +0 Vss 5
2 ‘ 1 I vdd
| V Vout
MPlO dd
6 11 L MP12
—I_
7 Vss
tﬂ MN3 ' ‘ MN4

 

MN13 . 4

L t], -9

 

 

r——T
1L

Figure 5.1. The op-amp circuit [137].

96

The complete design details and the calculations are contained in [137]. The sum-

mary of the relevant performance characteristics of the op-amp is given in Table 5.1.

Table 5.1. Characteristics of the op-amp [137].

 

 

 

Parameter Value

Open loop low frequency gain 12,000 (81.6dB)
Power consumption 4mW
Output resistance 4.5K
Output voltage swing

No load -5 to 4.4V

1K load -3.8 to 4V
Common mode rejection ratio

0V input 88.9dB

1V input 63dB
Power supply rejection ratio

Negative 97dB

Positive 89.5dB
Unity Gain bandwidth 1.3MI-lz
Slew rate 6/-15V/us
1%Settling time with 100pF load Sits

 

 

 

The node numbers for the PSpice simulation program are also shown in Figure 5.1.
The simulation program for the circuit is included in Appendix C. 1. The op-amp circuit
was included in the PSpice library to be used as a subcircuit block for other circuit simu-

lations.

I3”

t‘

97

5.4.3 The Ampliﬁer Circuit

The op-amp is used as an inverting ampliﬁer in a closed loop conﬁguration with
negative feedback. Since the output of the bridges is double ended, the balanced
conﬁguration was used for the ampliﬁer circuit. The ampliﬁer circuit is shown in Figure
5.2. The bridge is isolated from the ground, and the two conductors are used to connect it
to the ampliﬁer. Each conductor has the same resistance (R1 + Rp) to ground. The bal-
anced input also has the added advantage of cancelling any noise pickup along the signal
paths since it is common to both the inputs. To compute the circuit response it is assumed
that half the input Signal is connected to each input and the principle of superposition is

used. The circuit response is given by

RF
Vout = VB ('5?)- . (4-1)

 

 

Figure 5.2. The ampliﬁer circuit.

98

The maximum output from the bridges is 1.96V. Thus the gain for the circuit is set
to 2.25 with R]: as 5K and R1 being 2.2K. The linear transfer function for an input of
:l:2V is Shown in Figure 5.3. The gain of the ampliﬁer circuit is not dependent on the
absolute values of the components but rather is determined by the ratio of RF and R1.
Thus the output of the ampliﬁer is insensitive to component tolerance caused by process-

in g variations.

 

2.5 — /

OUtpllI I ’
Voltage 0 — /
(V) , . ’

-2.5 — / ’

 

 

 

‘
_

I I I I I
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2

Input Voltage (V)

Figure 5.3. The DC transfer characteristics of the ampliﬁer.

5.5 Analog Subtraction

The subtractor circuit is built using the op-amp circuit discussed in Section 5.4.2.
The subtractor circuit is shown in Figure 5.4. The circuit was Simulated using different
resistor values. Various resistor values were tried to minimize the conversion error.
Based on these results 2K resistors were selected for the circuit. Increasing the resistor
value above this does not improve the accuracy whereas going below this value intro-

duces signiﬁcant conversion error.

99

 

 

. O
V01“: VA" VB

a 1

Figure 5.4. The subtractor circuit.

The inputs to the subtractor are from the piezoresistive and the compensation
bridges. The inputs may have either polarity but simulations have shown that the subtrac-
tor circuit works ﬁne for all combinations. The piezoresistive and compensation bridge
output data from Chapters 3 and 4 has indicated that the nature of bridge outputs is such
that the output of the subtractor circuit would always be of the same polarity for a partic-

ular sensor unit.

5.6 Analog to Digital Conversion

The temperature half bridge response and the difference of piezoresistive and com-
pensation bridge outputs are analog signals. Conversion of these signals to the digital
form, using an ADC, is a salient step towards building a digital interface circuit. An ADC
is a device which converts a continuous range of input amplitude levels into a discrete,
ﬁnite set Of digital words. Therefore, there is an inherent quantization uncertainty of i1/2

LSB in the conversion process. In addition, an ADC is characterized by offset, scale

100

factor or gain, integral linearity, and differential linearity errors. Typically, Offset and
gain errors are calibrated out, in either hardware or software. Linearity errors are harder
to handle requiring special hardware or software linearizing techniques for correction. In

many ADC designs a Digital to Analog Converter (DAC) is also part of the design.

Figure 5.5 shows block diagram of a representative ADC circuit. Analog input is
sampled and held for a prespeciﬁed time by a sample-and-hold circuit. The output of the.
sample-and-hold circuit is connected to the comparator. This input along with me is
used to determine the digital word that best represents the analog input signal, Va. The
means by which conversion is accomplished is dependent on the speciﬁc ADC design.

 

 

 

 

 

 

 

 

 

 

 

 

 

Analog . Comparator
rnput Sample and | Digital
’ hold circuit ' '
Va , Switch I::I>—> output >213“?
u u
v ref circuit tp
A l '
Timing and
control logic

 

 

Figure 5.5. Block digram of a representative ADC.

In this section the four basic AID conversion techniques are surveyed from the
viewpoint of their suitability for use in this interface circuit. The dual slope technique is

selected and the design for the bipolar dual slope ADC is presented.

101
5.6.1 Types of ADCS

A vast number of circuit designs for ADCS exist and are being developed for vari-
ous applications especially for fast data acquisition circuits. Selection of an ADC for
integrated sensor use has been discussed in detail in [18]. Most designs are extensions of
the basic conversion techniques. As an initial step a study was carried out to review the
available analog to digital conversion techniques and pick the one best suited for the
interface circuit design. There are four basic classes of ADCS; successive approximation,

ﬂash or parallel, counter-ramp or series, and tracking or servo type.

5.6.1.1 Successive Approximation

This conversion technique consists of comparing the analog signal against a precise
voltage or current generated by a digital to analog converter (DAC). To start the conver-
sion the DAC’S MSB output (0.5V,,f) is compared with the sampled input signal. If the
input is greater than the DAC’S MSB output, the MSB remains set (HIGH) and the next
signiﬁcant bit is tried. If the analog input is less than the DAC’S MSB output, the MSB is
reset (LOW) and the next bit is tried. The process continues in order of descending bit
weights until the last bit (the LSB) has been tried. The bit pattern formed by the com-
parisons gives the equivalent digital word. In an alternate design a precise resistor net-

work is used in place of the DAC.

Successive approximation converters are classiﬁed as medium speed ADCS with
conversion times ranging from 1 to 100|rs [140]. An analog input is converted to an n-bit
digital word in approximately n clock cycles. Thus the conversion time is constant and it
is independent of the magnitude of the input voltage. The circuit takes up more chip area
because the DAC is an integral part of the converter. Moreover, rather complex timing
and control circuitry is required. Accuracy, linearity, and speed are primarily affected by
the properties of the DAC, and the comparator. In general, the settling time of the DAC

and the response time of the comparator are considerably slower than the switching time

102

of the digital elements. Bipolar analog to digital conversion can be achieved by using a

Sign bit to choose either V",- or - ,4.

5.6.1.2 Flash or Parallel

Flash converters use parallel techniques to achieve very short conversion times of
less than 100ns [140]. The ultimate conversion speed is one clock cycle, which would
typically consist of set-up and convert phases. Some high-speed architectures comprom-
ise speed with area and require more than one clock cycle but less than 11 cycles. Flash

converters are used for high speed data acquisition and signal processing applications.

For a ﬂash converter W4 is divided into 2"-l levels (1 LSB apart), using a resistive
voltage divider network. These reference levels and the analog input is applied simul-
taneously to the two inputs of 2"—1 latched comparators. The outputs of the comparators
are taken to a digital decoding network that determines the digital output word from the
comparator outputs. Many versions of this basic concept exist. For example, the number
of voltage levels may be increased or the voltage divider resistor string could be con-

nected between wa and - ,4 to achieve bipolar conversion.

Unfortunately, the number of elements (comparators, resistors, and decoding logic
network) increases geometrically with resolution. For n greater than 6, too much chip
area is required. Moreover, the technique requires precision resistors which may not be

fabricated using a process compatible with the sensor fabrication.

5.6.1.3 Ramp or Integration

This family of converters is popular for the low frequency applications. Its
members perform an indirect conversion by ﬁrst converting to a function of time and
then converting from the time function to a digital number using a counter. Relatively

longer conversion times result in noise reduction through signal averaging.

103

A Single slope ADC consists of a ramp generator, an interval counter, a comparator,
and a counter that generates the output digital word. At the beginning of the conversion
cycle, the analog input is applied to the noninverting terminal of the comparator. The
counter is reset and the ramp generator begins to integrate the reference voltage, which is
applied to the inverting terminal of the comparator. The counter counts until the refer-
ence voltage equals the analog input. At this instant the comparator ﬁres and the counter
is frozen. The binary number representing the state of the counter is converted to the
desired digital word format. Single slope ADC is Simple in operation but it is very sensi-
tive to any types of errors in the ramp generator and any variations in the clock fre-

quency.

An improvement over the single slope design is implemented by adding a discharge
cycle for the integrator capacitor, which gives rise to the dual Slope ADC. The basic
advantage of this architecture is that it eliminates the dependence of the conversion pro-
cess on the linearity and the accuracy of the ramp slope. Initially the analog input is
integrated for a speciﬁed number of clock pulses. As a second step, a reference voltage of
the opposite polarity is applied to the integrator circuit, and now it integrates oppositely A
with a constant Slope, because the reference voltage is constant. Counter is stopped when
the output reaches zero or a prespeciﬁed level, and the binary count of the clock pulses
gives the digital word.

The dual slope conversion technique offers a number of advantages, foremost being
the independence of the resolution of both the capacitance and the clock frequency. This
is because they affect both the up-slope and the down-slope in the same ratio. The dual
slope technique also offers excellent noise rejection. Since the input voltage is integrated
over a period of time, any high-frequency noise riding over the input Signal is cancelled
out. Thus, good resolution is relatively easy to obtain and can be varied by adjusting the
size of the internal counter and the clock frequency. The dual-slope converters are slow

but generally quite adequate for the low frequency applications. Bipolar operation

104

requires the polarity sensing and the reference polarity-switching.

5.6.1.4 Tracking or Servo

This class of ADCS is faster than the dual slope converters. The conversion tech-
nique in this case uses an internal signal to hack the analog input signal. Again a DAC is
used to convert the binary (digital) output from the counter to an analog voltage. The
counter starts counting up and the DAC output increases in a staircase fashion, each vol-
tage Step corresponding to a particular binary count. When the Staircase voltage exceeds
the analog input Signal, the comparator ﬁres and the counter is frozen giving the

equivalent digital number.

A variation of the above technique is the "servo" type converter which employs an
up-down counter. If the output of DAC is less than the analog input, the counter counts
up. On the other hand if the DAC output is greater than the analog input, the counter
counts down. Its small signal frequency response is good, because it can follow small
bidirectional input changes within one clock period. However its slew capability is very
poor.

The conversion time for this technique is proportional to the magnitude of the ana-
log voltage. The DAC requirement increases chip area. Moreover, the converter charac-

teristics are dependent on the DAC. For bipolar operation a bipolar DAC is required.

5.6.2 Selection of the Analog to Digital Conversion Technique

Four basic classes of the ADCS have been discussed above. Each class has charac-
teristics that make it most useful for a speciﬁc application, based on the speed, accuracy.
cost, size, and versatility. Upon careful examination of the performance of the ADCS and
the speciﬁc requirements of interface circuit, the dual-lepe integration technique comes

out to be the best choice for the following reasons:

105

The major disadvantage of the dual-Slope ADC is its low conversion rate but it is
not important because the interface circuit needs only 10 to 40 conversions per

second which can easily be handled by a dual slope ADC.

The dual Slope technique is very accurate and versatile. It is independent of both the
clock frequency and the integrator component values, because they affect both the
integration and the de-integration process in the same ratio. This advantage makes it

more suitable for batch fabrication and operation over a wider temperature range.

The circuit is simple and does not employ a DAC as its integral part, thus econom-
izing on chip area. This makes it suitable for on-chip integration.
There is no need for a separate sample-and-hold circuit because the ﬁrst operation

step integrates the analog input signal for a predetermined amount of time. This also

saves on chip area.

The ADC can be made bipolar simply by switching the polarity of the reference

voltage.

The integration provides rejection of the high-frequency noise and the averaging of

the changes that occur during the sample period.

The resolution and speed of the ADC can be varied by adjusting the size of the
internal counter and the clock frequency. This makes the converter design very
ﬂexible.

5.6.3 The Dual Slope ADC

This section describes the theoretical details of the dual slope conversion technique.

A block diagram of a basic dual slope ADC and its waveforms are shown in Figure 5.6.

To start the conversion, the integrator capacitor is discharged (not shown) and the output

of the integrator V,- is 0 or some predetermined value V0,. At this instant the counter is

reset and the analog input, Va is applied through the switch to the integrator circuit. Va is

106

integrated for an number of clock pulses. At the end of the integration interval the accu-
mulated charge on the integrator capacitor is proportional to the average value of the ana-
log signal over the interval. Figure 5.6(b) illustrates the conversion process. It is seen that
the slope of the voltage V,- is proportional to the magnitude of Va.

The voltage V,-(t) during the integration is given by

‘1

mo =K [Vadt + V,-(0) for to < t < t1. (4.2)
‘0

Assuming Va is constant during this interval, V,- at :1 is given by
Vi(t 1) = KVaNrechlk + V”! (4.3)

where
i K = a constant,
Va = analog input voltage,
Tc”, = time period of the clock,
N",- = number of reference clock pulses,

V”, = comparator threshold.

At t1 the counter is reset and the input to the integrator is switched to - ,4. Now
the integrator proceeds with a downward constant slope, because V"; is constant. When
V,- becomes less than the value of V”, the counter is stopped and the binary number is
converted to a digital word. During this interval, V; is given by

‘2

V,-(t2)=V,-(t1)+K j(—V,,,)dt for r, < r < t2. (4.4)
‘1

107

 

 

Vref

Reference
mput

   

 

 

Counter Binary
output

 

 

 

 

 

 

 

(a) Block diagram.

 

 

 

 

 

 

 

 

 

 

Vi( t) A
Va”
Va” > Va’ > Va
va’
Va
th
f"— Nref Tclk +‘ Nout Tclk —>'

(b) Waveforms.

Figure 5.6. The dual slope ADC and its waveforms.

108

At t = t2, V; is gIVCI'l by
vt(r2>= [KI/amber” Va] -Kv,.,~,,,r,,,. (4.5)

Since V;(t2) = V0,, it can be Simpliﬁed to

KVaNrechIk = KVre/NoutTclk: (4-6)
01'
V
Nora = ref—0° (4.7)
Vref

Thus, Now, the number of output pulses, is a fraction of N, , the number of refer-
ence pulses. Moreover, the output of the converter (Now), is not a function of the thres-
hold of the comparator, the Slope of integrator, or the clock frequency. It is also obvious
that W4 is inversely proportional to the converter output. W4 is derived from the bridge
excitation voltage. Thus any change in the excitation voltage causes a variation in the
same direction for the pressure and the temperature bridge outputs. Therefore, variations

in the excitation voltage are counteracted by the dual slope conversion technique.

5.6.4 Design of the Dual Slope ADC

The bipolar dual SIOpe ADC for digitization of the temperature half bridge output
and the difference of piezoresistive and compensation bridge outputs was built using an
op-amp, comparators, voltage controlled switches, and passive components. The block
diagram along with necessary waveforms and control signals for the circuit is Shown in
Figure 5.7. The complete circuit can be partitioned into distinct analog and digital parts.
The analog portion was Simulated using PSpice while VHDL was used for the simulation
of the digital part.

109

Initially each block was designed and simulated separately to ascertain the correct

operation. Subsequently the small portions were integrated to form the complete design.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

- +
Va Va Vrcr Vrer
Sign . Integration “—3 Charge
detector 813“ + control
d— Discharge
Si f‘
gn ._J
Convert
* Integrator + Start
Control —> Reset
“mu" —> Start i +
I . I crossing
Charge Discharge detector
1
Clock —> Clock
Timing
pulse
generator
Clock
* J—L Timing pulse

 

l Counter and register ’d— Reset

Ii. . . . .Ii

Figure 5.7. Block diagram of the bipolar dual slope ADC.

110

The conversion process starts with a convert pulse from an external source. The
integration control connects the analog input to the integrator for a ﬁxed time interval.
This generates a ramp in positive or negative direction depending on the polarity of the
input Signal. At the end of the interval, the Sign detector selects the reference voltage of
the opposing polarity and connects it to the integrator. The integrator output now follows
a ramp in the opposite direction. The integrator output is connected to the zero crossing
detector whose output is complemented when its input crosses the zero volt reference

from either direction.

The timing pulse circuit receives its input from the analog circuit. The circuit gen-
erates a tinting pulse whose width is proportional to the magnitude of the analog input
signal. This pulse is used to gate the clock signal to the counter, which produces an

equivalent 10-bit digital word and Stores it in the register.

The counter is a lO-bit synchronous counter which Operates during the charge as
well as the discharge phase of the integrator circuit. The counter output is transferred to a
10-bit register at the completion of the conversion cycle. Inputs to the control circuit are
the convert pulse and the second most signiﬁcant bit from the counter. The convert pulse
remains high for a time sufﬁcient to reset the counter and other control circuit blocks.
The control circuit produces start pulse, charge pulse, discharge pulse, and reset pulse for

the ADC counter and the integrator capacitor.

In this section, ﬁrst the design speciﬁcations are set for the dual slope ADC. Then,

architectures for the analog and digital parts of the’ ADC circuit are described.

5.6.4.1 Design Speciﬁcations

The bipolar dual SIOpe ADC was designed for an analog input range of 0 to 5V or 0
to -5V. The analog input represents a pressure range of 0 to 45psi. As a ﬁrst step, a Study

was done to select various parameters of the ADC and to deﬁne its speciﬁcations.

111

The major portion of conversion time is taken by the integrator circuit. This time is
determined by the clock frequency, digital word Size, and the reference voltage. The
maximum value of the input voltage is 5V. Initially the reference voltage was set to 5V
but later it was lowered to 2.5V. The lowering of the reference voltage cuts the integra-
tion time in half while maintaining the same resolution. The reference voltage of 5V
needs 2048 clock pulses while 1536 pulses are required for the reference voltage of 2.5V.

The waveforms for the two cases are shown in Figure 5.8.

 

 

 

7

 

° I
0 512 1024 1536 2048
Number of Clock Pulses

Figure 5.8. The charge and the discharge time for an = 5V and 2.5V.

The next Step was to select the clock frequency and the word size. These two
parameters determine the speed and resolution of the converter, respectively. ADCS with
word lengths of 8 to 12 bits have been reported in the literature [2,126]. The conversion
speed of 1 to 100 conversion/second has been reported for the existing dual slope ADCS
[140]. Increasing the frequency for a given design (integration time) reduces the resolu-
tion of the ADC. To keep the same resolution a higher charging current is needed which
may introduce nonlinearity in the ramp. Another factor in selecting the frequency is the

noise frequency, if known. To average out noise, the integration time should be a

112

multiple of the noise frequency period. With this understanding word lengths of 8, 10,
and 12-bits and clock frequencies of 50KHz and 60 KHz were considered initially. Table
5.2 summarizes results of various combinations of these two parameters and the refer-

ence voltage.

Table 5.2. ADC characteristics as functions Of word length, frequency, and reference

 

 

 

 

 

 

 

 

voltage.
Number , Number of Conversions per Second
Resolution
of
bits 50KI-Iz 60KI-lz
mV psi V,,f=5V V,4=2.5V V,4=5V V,,f=2.5V
8 19.53 0.1758 97.66 130.21 117.19 156.25
10 4.88 0.0439 24.41 32.55 29.30 39.06
12 1.22 0.0109 6.10 8.14 7.32 9.77

 

 

 

 

 

 

 

It may be noted that the conversions/sec are approximate since they do not include
the time taken by digital circuit which is negligible compared to the-time taken by the

integrator circuit.

To obtain a reasonable resolution and conversion Speed, a ﬁequency of 50KHz and
a word length of lO-bits was selected for the interface circuit. It provides 32
conversion/second with a resolution of 4.88mV. The design is very ﬂexible and any ﬁe-
quency or word length may be selected to suit a particular application without making
any changes in the basic design. The only modiﬁcation required to the circuit will be the
change of clock frequency and change the length (number of ﬂip ﬂops) of the counter and

the register. The resulting ADC characteristics for the selected reference voltage.

113

frequency, and word length are summarized in Table 5.3.

Table 5.3. Characteristics of the bipolar dual slope ADC.

 

 

Parameter Value
Analog input voltage 0 to 5V or 0 to -5V
Digital output word 10 bits
Reference voltage i2.5V
Voltage resolution 4.88mV
Pressure resolution 0.0439psi
0.0029 atmosphere
2.8millibar
Oscillator frequency 50KI-Iz
Number of conversions 32.55/sec
Integration time 512 pulses
10.24ms
Maximum de-integration time 1024 pulses
20.48ms

 

 

 

 

5.6.4.2 Analog Circuit for the ADC

The heart of the analog portion of the ADC circuit is the integrator. An array of vol-
tage controlled switches selects various voltages. Two zero crossing detectors determine
the polarity of the analog input signal and the polarity switching of the integrator output.
The PSpice code for the complete analog circuit is included in Appendix C2. The analog
portion of the bipolar dual slope ADC is shown in Figure 5.9. The architectural and func-

tional details for this circuit are described in this section.

114

.Oo< 8% sec 585 be toe ease moses 2:. a.“ some

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

vm.
. _
_ /
CAM mm .H mm_ ﬂemma
ll owes—Lemma
om .Il mm w 6 K</\Io|\</\|o
#38 N; :e a>
/ =me
+
50> I
NM :— U M
as tl— Em
0am / o a>
2 mm / I 8%
embezu
Co + >

 

1 15
5.6.4.2.] Sign Detector

A Sign detector was implemented using the LM139 comparator and some passive
components; the circuit being extracted from a library [141]. The comparator operates
from a single 5V supply. The output of the detector is close to 5V for an input greater
than 0 and near zero otherwise. The transfer characteristic for the detector circuit is
shown in Figure 5.10. The detector is being used to sense the polarity of the input signal.
The output of the detector is used to select the polarity of the reference voltage. The out-

put is also used by the timing pulse circuit in the digital portion of the circuit.

 

 

 

 

 

 

5
4— ‘.
Output 3 _ 1
Voltage I.
(V) 2 - :
1— a
g
0 I I l
-0.1 -0.05 0 0.05 0.1

Input Voltage (V)

Figure 5.10. The transfer characteristics of the zero crossing detector.

5.6.4.2.2 Integration Control

The integration control consists of four voltage controlled switches arranged to
select the analog input signal or the reference voltage of either polarity. The ON and OFF
resistance of the switches is 4009 and 1012!), respectively. The resistance varies con-

tinuously in this range. The ON voltage for S4 is 1V and the OFF voltage is 3V. For the

116

other switches the ON voltage is 3V and the OFF voltage is IV.

81 and 82 are controlled by the positive going charge and discharge control pulses
provided by the control circuit. 83 and S4 are operated by the output of the Sign detector.
The switches are complement of each other, thus only one of these is closed at any one
time. The transfer characteristics of the switch are shown in Figure 5.11. Initially the ana-

log input voltage is connected to the integrator for 512 clock pulses and then the refer-

ence voltage of opposing polarity is connected for the duration of the cycle.

 

 

 

 

5 r
. 'I
4 _ I
I
Output 3 _ :
Voltage 'I
(V) 2 - ;
1 — I
t'
I
O I [J I I
2 3 4 5

Input Voltage (V)

Figure 5.11. The transfer characteristics of the switch.

117

5.6.4.2.3 The Integrator Circuit

The integrator is composed of the op-amp, a resistor, a capacitor and a voltage con-
trolled switch. The op-amp is same as discussed in Section 4.4.2. At the start of a new
conversion cycle the capacitor is quickly discharged by closing 85 by the start pulse from
the control circuit. Then, the analog input is integrated for 10.24ms, which is followed by
integration of the reference voltage of the opposing polarity. This generates a ramp in the
opposite direction. The time taken by the integrator output to become zero again will
depend on the magnitude of the analog input with a maximum value of 20.48ms. Since
the reference voltage is constant, the slope of the discharge ramp is also constant. Thus
the time taken to completely discharge the capacitor is proportional to the magnitude of
the capacitor voltage which in turn is determined by the magnitude of the analog input

signal.

The ramp generated by the integrator is given by

=—, 4.8
V0 RC! ( )

The maximum value for VC, the integrator capacitor voltage, is 5V and the max-
imum value for t is 10.24ms. For a maximum output of 5 volts the overall value of the
time constant is 10.24ms. Various combinations of R and C were tried to obtain better
charging and discharging characteristics for the integrator (linear ramp). Based on the

results, R1 is set to 1.3M!) and C 1 to 8.3nF.

The integrator waveforms and the start pulse for the integrator capacitor are shown
in Figure 5.12. The waveforms in Figure 5.12 are for a sample input of -3.5V with a

reference voltage of 2.5V.

118

 

 
     

 

 

 

 

 

 

5 r
Integrator
input
2.5 t
I
Voltage
o ..................... .,
(V) I
I
-25 —
'5 I I
0 0.009 0.018 0.027

Time (sec.)

Figure 5.12. The integrator waveforms.

5.6.4.2.4 Zero Crossing Detector

The zero crossing detector at the output of the integrator detects the completion of
the discharging of the integrator capacitor (integrator output = 0). This point may be
approached from either direction depending on the polarity of the input signal. In either
case, the output of the detector is complemented at the completion of the discharge
phase. The zero crossing detector circuit is same as the Sign detector described in Sec-

tion 4.6.4.2.1.

5.6.4.2.5 Performance of the Analog Circuit

The analog portion of the ADC was simulated and tested separately by applying
voltages from -4.99V to +4.99V in 0.5V increments. The Start, charge, and discharge
control pulses for the integrator circuit were set to 40p.s, 10.24ms, and 20.48ms, respec-

tively. The timing diagram (waveforms) for an analog input of -3.5V is as shown in

119

Figure 5.12. The variation of the discharge time and the maximum voltage across the
integrating capacitor with analog input voltage is shown in Figure 5.13 and Figure 5.14,
respectively.

The discharge time represents the magnitude of the analog input signal. As indi-
cated in the Figure 5.13, the time varies linearly with the analog voltage. The discharge
time is converted to a timing pulse which is fed to the digital portion of the converter cir-

cuit for conversion to a corresponding digital word.

5.6.4.3 Digital Circuit for the ADC

The function of the digital part of the circuit is to convert the timing pulse to a
corresponding 10—bit digital word. It is also responsible for generating the tinting and
control Signals for the entire circuit. The circuit diagram for the digital section of the
ADC is shown in Figure 5.15. The VHDL code for the circuit is Shown in Appendix D.

The architectural details for this circuit are presented in this section.

5.6.4.3.1 Timing Pulse Generator

The timing pulse generator Simply consists of three gates. The XOR gate is used as
a controlled complementer for the zero crossing detector output. The Signal is comple-
mented only if the analog input is negative, otherwise it is passed as is. The ﬁrst gate is
used for ANDing the XOR gate output and the discharge control Signal. The output of
this gate is a positive pulse of 5V, irrespective of the polarity of the analog input signal.
The duration of this pulse is proportional to the magnitude of the analog input signal.
Even if the input voltage polarity switches for some pressure or temperature values, the
ADC operation will be unchanged. The OR gate is used to provide the clock signal to the

counter during the charge and the discharge phases.

120

 

 

 

 

 

25
Positive input .....
Negative input
20 —
15 —
Time
(m8)
10 1
5 _
0 I I I I
0.5 1.5 2.5 3.5 4.5
Magnitude of the analog input voltage (V)
Figure 5.13. The discharge time.
5
Positive input .....
Negative input
Output
(V)

 

 

 

I I I I
0.5 1.5 2.5 3.5 4.5

Magnitude of the analog input voltage (V)

Figure 5.14. The maximum integrating capacitor voltage.

 

121

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

One Ch
arge
Q9 Control 2 X 4 Shot
counter Decoder
Tic Disch e
Convert T iIL OR arg
Preset
Start
‘0’ D Q
ﬂip-ﬂop
OR Sign
Reset From
_ analog
. section
ADC Counter ,
Q10Q9° " ' 'Q2Q1
Load
Register

Q10 Q9 Q2 Q1
Figure 5.15. The digital section of the ADC.

5.6.4.3.2 The ADC Counter and Register

The clock produces a SOKHz Signal for the circuit. The ADC counter is used to con-
vert the timing pulse into a lO-bit digital word. The ADC counter is synchronous made

up of JK ﬂip-ﬂops and AND gates. The register is composed of the D ﬂip-ﬂops with a

122

parallel-in-parallel out facility. The output of the timing pulse generator is used to gate
the clock Signal to the counter. The counter is used in the charge as well as the discharge
phase. In the charge phase it counts to 512 and then is reset by a pulse form the control
circuit. During the charge phase the control circuit also produces the positive pulse to
connect the analog input signal to the integrator. At the end of the charge phase, a posi-
tive pulse switches the integrator input to the reference voltage of the appropriate polar-
ity. The counter is reset and it starts counting again. The discharge phase is completed
when the output of the zero crossing detector is complemented. The count for this phase
depends on the magnitude of the analog signal being converted, with a maximum value
of 1024. At the end of this phase, a pulse from the control circuit inhibits the clock to the
counter thus freezing the count. At this instant the counter output is loaded, in parallel,
into the lO—bit register. The falling edge of the clock inhibition pulse is used to control

this action.

5.6.4.3.3 Control Circuit

The control circuit is responsible for timing the events of the ADC circuit. The con-
trol circuit is composed of a 2-bit counter, a D ﬂip-ﬂop, a 2x4 decoder, a one shot and
some glue logic. The conversion cycle is started by the positive going convert pulse. The
duration of the pulse should be sufﬁcient to discharge the integrator capacitor. For an
8.3nF capacitor and 4009 ON resistance of the switch, the pulse width should at least be
17115. The convert pulse sets the D ﬂip-ﬂop which normally is kept in the reset State. The
positive pulse produced by the D ﬂip-ﬂop is used to discharge the capacitor and reset the

two counters and the decoder.

The second most signiﬁcant bit from the ADC counter is used as a clock signal for
the 2-bit control counter. The negative edge triggered control counter is composed of two
JK ﬂip-ﬂops. The counter output is used to select the outputs of the 2x4 decoder. For the
ﬁrst 512 clock pulses, 01 remains high and provides the charge pulse. The falling edge

123

of this pulse triggers a one Shot which provides a positive going pulse of 40ns duration.
This pulse is used to reset the ADC counter which starts counting again for the discharge
phase. For the next 1024 pulses (control counter = 01 and 10), 02 and 03 go high during
the ﬁrst and the second half of the counting, respectively. These outputs provide a posi-
tive pulse for the discharge phase. Note that this phase will be interrupted by a pulse
from the timing pulse circuit before it reaches the maximum count. This is done by inhi-
biting the clock pulses to the ADC counter. The falling edge of the timing pulse is also

used to parallel load the frozen count into the output register.

5.7 The Half Bridge Compensation Hardware

The digital circuit for the implementation of the half bridge temperature compensa-
tion technique is shown in Figure 5.15. The function of the circuit is to shift the output of
the temperature half bridge and then add it to the pressure output derived from the differ-
ence of the compensation and the piezoresistive bridges. The pressure output is always
positive whereas the temperature output may either be positive or negative. Moreover,
the magnitude of the temperature output is smaller than half the pressure output and thus

it can ﬁt in a 9 bit register.

At the end of the conversion cycle the output of the two ADCS is stored in the pres-
sure and the temperature registers. The temperature output is divided by two by ignoring
the LSB and hardwiring the remaining 8 bits to the shifting circuit. The shifting of the
temperature register contents is implemented by an array of 8, 2-to-3 multiplexers. Zeros
are hardwired to M7 and M8, to pad the high order bits of the temperature signal for 2
. and 3-bit shifts. The control inputs (number of shifts), co and CI, to the multiplexers are
determined by the three higher order bits of the pressure output. A simpliﬁcation of the
Boolean function yields co and (:1 as p10 and 510 p9, respectively. The Sign bit of the

temperature bridge output is stored in the MSB of the temperature register.

124

 

 

 

 

 

 

FromADC FromADC
Pressure register . l Temperature register I
II.'....II- 41.....11
91099 P2 P1 51%“ T9 ' T2 T1

‘0’ ‘0' T9 ‘0’ T9 r3 r9 r8 r7

      

 

 

t8 t7 t6
Pro‘O’ P9 ‘0’ P8 ‘8 P2 t2 P1 t1
I 10-Bit controlled adder I17 Sign
311 s10 . s2 81

Figure 5.16. Hardware for the half bridge temperature compensation technique.

The shifted temperature output and the pressure output are added by a 10-bit con-
trolled adder circuit to produce a temperature compensated output for the sensor. Zeros
are hardwired in the t9 and (10 bit positions of the adder to make the temperature signal a
10-bit number. 1’s complement or 2’s complement implementations may be used for the
controlled adder circuit. The hardware and the time delay requirements for the two
approaches are similar. In both cases the Sign bit and an array of XOR gates is used to

obtain the controlled complementation of the shifted temperature output. For, the 2’s

125

complement approach the sign bit is also used as the carry input to the adder.

5.8 Summary

The interface hardware for the piezoresistive pressure sensors has been described.
The major design decisions for the circuit have been documented. First, the design
objectives and the philosophy were outlined followed by a description of the architectural

and functional details of the circuit.

The outputs of the piezoresistive bridge and the compensation bridge are ampliﬁed
and converted to a single ended Signal. The ampliﬁed signals from the two bridges are
subtracted using an op-amp based analog subtraction circuit. The output of the subtractor
circuit is a 0 to 5V or 0 to -5V signal. The use of analog subtraction has eliminated the
need for a separate bipolar ADC, the digital subtractor circuit, and the additional digital

control circuitry. This yields a substantial saving in the chip area.

The dual slope AID conversion has been identiﬁed as a Simple and precise conver-
sion technique, suitable and compatible for on-chip integration with the sensor. The con-
verter response is not a function of the slope of the integrator and the clock frequency.
The converter design is ﬂexible to allow changes in Speed, and accuracy to suit a particu-
lar application. The bipolar dual Slope ADC with a word length of 10-bits and the clock
frequency of 50KI-lz has been designed and tested. The Sign bit is stripped off at the ﬁrst
stage and the ADC essentially converts the magnitude of the analog voltage to the digital
word. The Sign bit is used for the operation of the ADC and the half bridge temperature
compensation technique. It is also available as a 0/5V signal which may be used else-
where. The 10-bit ADC design actually provides an 11 bits of resolution. In terms of

pressure, the resolution is 0.439psi (4.88mV).

Two ADCS have been used for the digitization of the half bridge output and the
difference of the piezoresistive and compensation bridge outputs. The digital output is

Stored in the registers and processed further by digital circuit to generate the temperature

126

compensated output signal.

The circuit is simple requiring modest chip area. It can be implemented using stan-
dard IC techniques. Use of ratios instead of absolute values and the dual slope AID
conversion technique reduces the circuit sensitivity to the temperature and the processing
variations. The design is ﬂexible and modular. Thus, it can very easily be modiﬁed to suit

the accuracy and other requirements for a speciﬁc application.

CHAPTER 6

CONCLUSION

The objective of is research was to develop an interface circuit for the
ampliﬁcation, temperature compensation, and digitization of the piezoresistive pressure
sensors for a temperature range of -40°C to 130°C over a pressure range of 0 to 45
psi. The objective has been accomplished. The sensor is modeled form from the
viewpoint of batch fabrication and its performance Simulated over the desired pressure
and temperature range. A new temperature compensation technique has been developed
and its effectiveness evaluated over the desired pressure and temperature range as a
function of the tracking errors. The hardware for the ampliﬁcation temperature com-
pensation, and the digitization hardware of the sensor has been designed and veriﬁed.
The next section summarizes the major results of this research and outlines the contri-
butions made in the ﬁeld of smart integrated piezoresistive pressure sensors. This is

followed by the identiﬁcation of the issues for further research in this ﬁeld.

6.1 Summary and Contributions

To provide an understanding of the physical structure and its effects and demands
on the interface electronics, an in-depth review of existing piezoresistive pressure sen-
sors and their associated electronics has been carried out. The review focused on four
key areas: silicon mechanical structures, the associated interface electronics, tempera-
ture compensation techniques, and modeling and simulation of piezoresistive pressure

SCIISOI'S.

127

128

The sensor model has been developed from the viewpoint of simulating the sensor
I/O characteristics as a function of pressure, temperature, and processing variations. The
model includes the effects of temperature, resistor mismatch, and structural details of the
sensor. The model parameters have been discussed with reference to the previous litera-
ture. The values for the model parameters were deduced from these discussions and
reviews. Various piezoresistors layouts on the diaphragm were discussed and simulation
results for the ideal sensor, with no tracking errors, were presented. The sensor model
was enhanced to include the batch fabrication effects. :l:20% variations in the piezoresis-
tors values were modulated with i2.5% variations to represent the wafer-to-wafer and

same wafer variations, respectively.

SENSIM, the sensor simulation program for piezoresistive and capacitive pressure
sensors was used to run the simulations. The program has been validated through com-
parison with the experimental data from actual devices. The simulation results provide
the worst case error band for sensors coming from the same wafer or different wafers.
The simulation results have been used to Study the temperature response of the sensor as
a function of tracking errors. All sensor parameters are functions of temperature and the
tracking errors. The sensor output is a function of temperature even for the sensors with

no tracking errors. The zero pressure offset is also temperature dependent.

A new temperature compensation technique for the piezoresistive pressure sensors
was presented The technique has been implemented in two parts, using a compensation
bridge and a temperature half bridge. The ﬁrst part makes use of two bridges: a
piezoresistive bridge fabricated on the thin diaphragm and an identical compensation
bridge located on the bulk part of the sensor chip. Output of the ﬁrst bridge is a function
of pressure, temperature, and processing variations whereas the compensation bridge
response is dependent on temperature and processing variations only. The difference of
the two bridge outputs removes the zero pressure offset and the variations caused by the

on-chip tracking errors. The second part of the technique uses a temperature half bridge

129

located on the bulk part of the chip to generate the temperature signal. This signal and
some digital circuitry is used to remove the remaining temperature dependency ﬁom the

sensor output.

The double bridge technique is very effective for the zero pressure offset and the
temperature errors caused by the same wafer processing variations. The zero pressure
offset is reduced below the measurement precision limit for the entire pressure and tem-
perature range. The output errors for the sensor, caused by the same wafer variations, are
reduced by a factor of 100. The output of the double bridge technique compensates
sufﬁciently for same wafer variations but still shows temperature dependency caused by
the temperature sensitivity of the piezoresistive coefﬁcients. The remaining temperature
errors for the sensor output are removed by the second part of the compensation tech-
nique. The technique is very effective for the pressure values below ,35psi and provides
reasonable results for the higher pressure values. The possible use of software approach

to implement part of the compensation technique has also been outlined and discussed.

The new temperature compensation technique has very convincing advantages. The
compensation circuitry is structurally simple and suitable for batch fabrication. It is
implementable using the available IC fabrication technologies. The technique does not
require the compensation of the individual units under sensor operating conditions.

Moreover, no external components are required for the implementation of the technique.

The hardware for the ampliﬁcation, temperature compensation, and the digitization
of the sensor output has been designed and simulated. The simulations of these com-
ponents, however, have been carried out at the room temperature. The analog portion of
the circuit was Simulated with PSpice 4.03 and the digital portion with the VHDL. Final
component level design of this hardware must ensure the correct operation of the circuit

over the desired temperature range.

The outputs of the piezoresistive bridge and the compensation bridge are ampliﬁed

and converted to a single ended signal. The ampliﬁed signals from the two bridges are

130

subtracted using an op-amp based analog subtraction circuit. The operation of these cir-
cuits is determined by the ratio of the resistors rather than the absolute values. Thus their
output is less sensitive to temperature changes and the component tolerances caused by
the processing variations. The use of analog subtraction has eliminated the need for a
separate bipolar ADC, the digital subtractor circuit, and the additional digital control cir-
cuitry. This yields a substantial saving in the chip area.

The dual slope AID conversion has been identiﬁed as a simple and precise conver-
sion technique, suitable and compatible for on-chip integration with the sensor. The con-
verter response is not a function of the slope of the integrator and the clock frequency.
The converter design is ﬂexible to allow changes in speed, and accuracy to suit a particu-
lar application. The bipolar dual Slope ADC with a word length of 10-bits and the clock
frequency of 50KHz has been designed. The Sign bit is stripped off at the ﬁrst stage and
the ADC essentially converts the magnitude of the analog voltage to the digital word.
The Sign bit is used for the Operation of the ADC and the half bridge temperature com- '
pensation technique. It is also available as a 0/5V signal which may be used elsewhere.
Thus the 10-bit ADC design actually provides 11 bits of resolution. In terms of pressure,
the resolution is 0.439psi (4.88mV). Two ADCS have been uSed for the digitization of
the half bridge output and the difference of the piezoresistive and compensation bridge
outputs. The digital output is Stored in the registers and processed further by the digital
circuitry to generate the temperature compensated output signal. The digital circuit is

composed of two registers, a controlled adder circuit, and a shifting mechanism.

The temperature compensation technique is structurally simple and suitable for
batch fabrication. The resulting interface circuit is simple, requiring modest chip area. It
can be implemented using standard IC fabrication techniques. Use of the dual slope AID
conversion technique and the resistor ratios instead of absolute values reduces the circuit
sensitivity to temperature and the processing variations. The design is ﬂexible and modu-

lar. Thus, it can be easily modiﬁed to suit the accuracy and other requirements for a

131

speciﬁc application. The complete or part of the interface circuit may be integrated with
the sensor. In the later case, the compensation bridge, the temperature half bridge, and
the ampliﬁcation circuits may be placed on the sensor chip and rest of the circuit fabri-
cated on a separate chip. All these features make the interface circuit very cost effective,

the ultimate objective for the design of the interface.

6.2 Future Research

Piezoresistive pressure sensors are being successfully used for the measurement of
many physical parameters such as pressure, force, motion and acceleration, and vibration
and frequency. With the advancement in the integrated circuit and the micromachining
technologies, silicon based smart sensors can be miniaturized and have a great potential
as a low cost, high performance devices for many applications. This section outlines
some of the issues that must be addressed in order to ensure the continued advancement
of the smart sensors, focusing on those concerns of special interest to the computer
engineers.

The ﬁrst issue is the continuation of this research and advancing the work which has
been accomplished in this research. To complete the interface design, the ﬁrst step is the
fabrication of , the interface circuit and comparison of experimental results with the simu-
lation results. As a second step the sensor and the interface circuit may be integrated on
the same chip and their performance evaluated over the desired pressure and the tempera-
ture range.

The digital part of the compensation circuitry is structurally simple, utilizing regis-
ters, a controlled adder and multiplexers to implement the shifting. This part may also be
implemented in the software as outlined in Section 4.5.2.4. The digitized output of the
temperature half bridge and the difference of compensation and piezoresistive bridge out-
puts may be read and processed by a microcomputer. The performance of the hardware

and the software approaches may be compared and the application areas for the two may

132

be further speciﬁed.

Although the major part of the interfacing has been accomplished, fulﬁllment of the
complete smart sensor concept requires integration of more electronic functions into the
interface circuit. The ﬁrst being the calibration of the sensor output. Digital calibration
implemented through hardware and software techniques requires further exploration. The
autocalibration of the sensor may be used by subjecting the sensor to the known pressure

values and storing the sensor output in a EEPROM.

It is inherent in the smart sensor concept that the sensor be addressable and capable
of communicating with a central processor and other sensors. The minimum requirement
is to add the address decoding logic to allow the sensor to be part of a bus architecture.
Depending on a Speciﬁc application and the available resources, more hardware and/or
software may be used to add the intelligence to the sensor unit. Moreover, presently there
are no communication Standards and protocols for the sensors. A key in the mass usage
of the smart sensors will be the development of standard connection schemes, protocols,

and central control and analysis algorithms.

A ﬁnal issue is the investigation of the new materials and techniques for raising the
operating temperature of the sensor and the companion electronics above 300°C for the
high temperature applications. Wider band gap materials (diamond, gallium arsenide, and
silicon carbide) and miniature vacuum devices are some of the candidates being investi-
gated for the high temperature applications. With the deveIOpment of these new tech-
niques there will be a need for the development of the design automation tools for these
techniques. New models and simulation techniques will be required to analyze the pro-
cessing and operating characteristics of these new devices, and identify the parameters to
be compensated and corrected. The existing simulation programs, sensor models, and
compensation techniques may be used as the parallel examples for the future work on the

new devices.

APPENDICIES

APPENDIX A

SENSIM SIMULATIONS

APPENDIX A
SENSIM SIMULATIONS

A.l Sensor Structures and Model Parameters

SNSS: Structure-2, No tracking errors.
RP = 2K RST = 200 TCR = 1.9E-3
RT = 1K RST = 200 TCR = 1.9E-3

SNSSl: Structure-2, +2.5% tracking errors.
RP = 2K RST = 200 TCR = 1.9E-3
RT = 1.025K RST = 205 TCR = 1.925E-3

SNSSZ: Structure-2, -2.5% tracking errors.
RP = 2K RST = 200 TCR = 1.9E-3
RT = 0.975K RST = 195 TCR = 1.875E-3

SNSSa: Structure-2, +20% tracking errors.
RP = 2.4K RST = 240 TCR = 2.1E-3
RT = 1.2K RST = 240 TCR = 2.1E-3

SNSSa1:Structure-2, +2.5% tracking errors from snSSa (20%)
RP = 2.4K RST = 240 TCR = 2.1E-3
RT = 1.23K RST = 246 TCR = 2.125E-3

SNSSa2:Structure-2, -2.5% tracking errors from snSSa (20%)
RP = 2.4K RST = 240 TCR = 2.1E-3
RT = 1.17K RST = 234 TCR = 2.075E-3

SNSSb: Structure-2, -20% tracking errors.
RP = 1.6K RST = 160 TCR = 1.7E-3
RT = 0.8K RST = 160 TCR = 1.7E-3

SNSSb1:Structure-2, +2.5% tracking errors from snSSb (-20%)
RP = 1.6K RST = 160 TCR = 1.7E-3
RT = 0.82K RST = 164 TCR = 1.725E-3

SNSSb2:Structure-2, -2.5% tracking errors from snsSb (-20%)
RP = 1.6K RST = 160 TCR = 1.7E-3
RT = 0.78K RST = 156 TCR = 1.675E-3

133

134

A.2 The Simulation Code for the Sensor with no Tracking Errors

* PRPS-snsS Structure-2 No tracking errors *
.PARAM LEVEL=3 SYM=4 GSIZE=25U
* PIEZORESISTORS *
RPl 2 3 2K PAR W=10U L=100U YCNT=475U XCNT=0
RP2 5 0 2K PAR W=10U L=100U YCNT=475U XCNT=0
RTll 1 2 1K PAR W=10U L=50U XCNT=455U YCNT=15U
RT12 l 0 1K PAR W=10U L=50U XCNT=455U YC =-15U
RT21 3 4 1K PAR W=10U L=50U XCNT=455U YCNT=15U
RT22 4 5 1K PAR W=10U L=50U XCNT=455U YCNT=-15U
* INDEPENDENT VOLTAGE SOURCE *
VDD 3 0 DC 5 RS=0.0001
* STRUCTURAL ELEMENTS *
DIAPH 3 SILICON UNIFORM L=1000U ANGLE=45
LSIOZ 4 OXIDE TYPE=1 H0=1U T=800
LPYREX 5 PYREX TYPE=2 H0=200U H1=200U T=450
* MODEL CARDS *
.MODEL PAR PIEZOR(NSUB=1.0E16 XJ=2.7U RST=200 TCR=1.9E-3)
.MODEL SILICON M (81 1=.764P 812=-.214P S44=1.256P ALPHA=2.65E-6)
.MODEL OXIDE M (E=6.6E11 G=l.188E11 PO=0.18 ALPHA=0.5E-6)
.MODEL PYREX M(E=6.1E10 G=2.67E10,PO=0.1,ALPHA=4.3E-6)
.MODEL UNIFORM DIAPH(HO=10U H1=200U)
* TEMPERATURE LOOP *
.TEMP -40 40 10
***.TEMP 50 130 10*“
* PRESSURE LOOP *
PRESSURE 0 20 5 PSI
***.PRESSURE 25 45 5 PSI***
* OUTPUT *
.PRINT .P RPl RTll
.PRINT .P VOUT(2,5)
.END

135

A.3 The Simulator Output for the Sensor with no Tracking Errors

*****************************t********#**********************#*t********

* PRPS-snSS Structure-2 No tracking errors *
13:26:35 10-15-1991
(SENSIM 4. OCT. .1981)

#***********************************************************************

* LIST OF SOURCE PROGRAM *

* PRPS-snSS Structure-2 No tracking errors *
.PARAM LEVEL=3 SYMﬂ GSIZE=25U
* PIEZORESISTORS *
RPl 2 3 2K PAR W=10U 1:100U YCNT=475U XCNT=0
RP2 5 0 2K PAR W=10U L=100U YCNT=475U XCNT=0
RTll 1 2 1K PAR W=10U L=50U XCNT=455U YCNT=15U
RT12 1 0 1K PAR W=10U L=50U XCNT=455U YCNT=-15U
RT21 3 4 1K PAR W=10U L=50U XCNT=455U YCNT=15U
RT22 4 5 1K PAR W=10U L=50U XCNT=455U YCNT=-15U
* INDEPENDENT VOLTAGE SOURCE *
VDD 3 0 DC 5 RS=0.0(X)1
* STRUCTURAL ELEMENTS *
DIAPH 3 SILICON UNIFORM L=1000U ANGLE=45
LSIOZ 4 OXIDE TYPE=1 H0=1U T=800
LPYREX 5 PYREX TYPE=2 H0=200U H1=200U T=450
* MODEL CARDS *
.MODEL PAR PIEZOR(NSUB=1.0E16 XJ=2.7U RST=200 TCR=1.9E-3)
.MODEL SILICON M (81 1=.764P 812=-.214P S44=1.256P ALPHA=2.65E-6)
.MODEL OXIDE M (E=6.6E11 G=1.188E11 PO=0.18 ALPHA=0.5E-6)
.MODEL PYREX M(E=6.1E10 G=2.67E10,PO=0.1,ALPHA=4.3E-6) .
.MODEL UNIFORM DIAPH(H0=10U H1=200U)
* TEMPERATURE LOOP *
.TEMP -40 0 10
***.TEMP 50 130 10*"
* PRESSURE LOOP *
.PRESSURE 10 20 5 PSI
***.PRESSURE 25 45 5 PSI***
* OUTPUT *
.PRINT .P RPl RTll
.PRINT .P VOUT(2,5)
.END

****************tit************************t*****#***********************

* PRPS-snsS Structure-2 No tracking errors *

136

13:26:35 10-15-1991

(SENSIM 4. OCT. .1981)

*************************************************************************

m INPUT DATA SUMMARY m

* RESIST ORS *
NODEl NODEZ VALUE TCR W (MICRON) L (MICRON)
RPl 2 3 0.20000d+04 0. 19000d-02 10.00 100.00
RP2 5 0 0.20000d+04 0.19000d-02 10.00 100.00
RT] 1 1 2 0.10000d+04 0.19000d-02 1011) 50.00
RT12 1 0 0.10000d+04 0.19000d-02 10.(X) 50.00
RT21 3 4 0.10000d+04 0.19000d-02 101]) 50.00
RT22 4 5 0.10000d-I-04 0. 19000d-02 10.00 50.00
VDD 3 0 05le RS OR G0 = 0.10000d-03
CENTER(X,Y)

( 0.00, 475.00) ; PRESSURE SENSITIVE R.
( 0.00,-475.00) : PRESSURE SENSITIVE R.
( 455.00, 15.00) ; PRESSURE SENSITIVE R.
( 455.00, -15.00) ; PRESSURE SENSITIVE R.
(455.00, 15.00) ; PRESSURE SENSITIVE R.
(455.00, -15.00) ; PRESSURE SENSITIVE R.

* PIEZO-RESISTIVE COEFFICIENTS FOR P-TYPE DIFFUSED LAYER
( X 1.0E-12 CM**2/DYNE ) AT T = 27.00 C
P111, P112, P144 * COEFF. ALONG THE CRYSTALOGRAPHIC AXIS
P(L) : COEF. FOR NORMAL STRESS (PARALLEL TO CURRENT )
P(T) : COEF. FOR NORMAL STRESS (TRANSVERSE TO CURRENT)
P(SHEAR) : COEF. FOR SHEAR STRESS IN X-Y PLANE

R-NAME MOD. NAME PI(L)

PI(T) PI(SHEAR) TCPI(PPM)
RPl PAR

57.47 -51.97 0.00 -2308.29
RP2 PAR 57.47 -5 1.97 0.00 -2308.29
RT] 1 PAR 57.47 -51.97 0.00 -2308.29
RT12 PAR 57.47 -5 1.97 0.00 -2308.29
RT21 PAR 57.47 -5 1.97 0.00 -2308.29
RT22 PAR 57.47 -5 1.97 0.00 -2308.29
P11 1 P112 P144
6.60 -1. 10 109.43
6.60 -1.10 109.43
6.60 -1.10 109.43
6.60 -1.10 109.43

137

6.60 -l.10 109.43
6.60 -1.10 109.43

* STRUCTURAL ELEMENTS *
DIAPHRAGM ; LENGTH = 1000.00 MICRON
EDGE DIRECTION = 45.00 DEGREE
EDGE CONDITION = 0.00000d+00
THICKNESS MODEL = UNIFORM (TYPE = 0)

NAME MATERIAL H (MICRON) TEMP. YOUNG“S MODULUS
DIAPH SILICON 10.00 0.00 0.1697 8d+13
4 1.8102 OXIDE 1.00 800.00 0.66m0d-i-l2

U)

POISSON’S RATIO SHEAR MODULUS ALPHA
0.66214d-01 0.62267d+12 0.26500d-05
0.18000d+00 0.1 l880d+12 0.500(0d-06

NAME MATERIAL H (MICRON) TEMP. YOUNG’S MODULUS
3 DIAPH SILICON 200.00 0.00 0.16978d+13
5 LPYREX PYREX 200.00 450.00 0.6 roood+1 l

POISSON'S RATIO SHEAR MODULUS ALPHA
0.66214d-01 0.62267d+12 0.26500d-05
0.10000d+00 0.26700d-I-l l 0.430(XJd-05

* SENSOR ANALYSIS METHOD "'

FOR INSIDE DIAPHRAGM ANALYSIS ; DEFLECTION/STRESS
LEVEL = 3 : FINITE DIFFERENCE METHOD (DMS)
MULTI-LAYERED DIAPHRAGM.
GRID SIZE = 26.32 MICRON

* ANALYSIS TYPE *
PRESSURE = 0.10000d+01 0.2(XDOd+02 0.50000d+01 PSI

************************************#*****tit******#********#***************

* PRPS-snSS Structure-2 No tracking errors *
13:26:35 10-15-1991
(SENSIM 4. OCT. . 1981)

****************************************************************************

138

TRANSFER FUNCTION: INPUT (PRESSURE = 0.10d+10 0.200d-I-02 0.5(XJd+01 PSI

* PRESSURE SENSITIVE RESISTORS *

TEMPERATURE = 40.000 DEGREE (C)

PRESSURE PSI RPl RTll
0.1m00d+02 0.1599742d+04 0.9419248d+03
0.15000d+02 0.1526553d+04 0.9763570d+03
0.20000d+02 0.1453364d+04 0.1010789d+04

* PRESSURE SENSITIVE RESISTORS *

TEMPERATURE = -30.000 DEGREE (C)

PRESSURE PSI RPl RTll
. 0.1(D00d+02 0.1637500d-IO4 0.9610387d+03
0.15000d+02 0.156419ld+04 0.9955285d+03
0.2m00d+02 0.1490882d+04 0.1030018d-I-04

* PRESSURE SENSITIVE RESISTORS *

TEMPERATURE = -20.000 DEGREE (C)

PRESSURE PSI RPl RTll
0.10000d+02 0.1675384d+04 0.9800924d-I-03
0.15000d+02 0.1602019d+04 0.1014610d+04
0.2m00d+02 0.1528654d+04 0.1049127d+04

* PRESSURE SENSTTIVE RESISTORS *

TEMPERATURE = -10.000 DEGREE (C)

PRESSURE PSI RPl RTll
0.1(XIOOd-I-02 0.1713396d+04 0.9990857d+03
0.15000d+02 0.1640038d+04 0.1033601d+04

0.2(XJ00d+02 0.1566680d+04 0.10681 16d+04

139

* PRESSURE SENSTTIVE RESIST ORS *

TEMPERATURE =

PRESSURE PSI
0. 1m00d+02
0. 15000d+02
0.2(XJOOd+02

0.000 DEGREE (C)

RPl RTll

0.1751534d-I-04 0.1018019d+04
0.1678247d+04 0.1052501d+04
0.160496ld+04 0.1086984d-I-04

* OUTPUT VOLTAGE AT NODE (1,1) *

TEMPERATURE = 40.000 DEGREE (C)

PRESSURE PSI

0. 1m00d+02
0. 15000d+02
0.2(X)00d+02

VOUT
(2. 5) (
0.4077790d+00
0.6124288d+00
0.8175880d+00

* OUTPUT VOLTAGE AT NODE (l,J) *

TEMPERATURE = -30.000 DEGREE (C)

PRESSURE PSI

, 0.10000d+02
0. 15000d+02
0.2(D00d+02

VOUT
(2. 5) (
0.3997346d+00
0.6003321d+00
0.8014188d+00

* OUTPUT VOLTAGE AT NODE (1,1) *

TEMPERATURE = —20.000 DEGREE (C)

PRESSURE PSI

0. 1m00d+02
0. 15000d+02
0.2(XXXId-t-02

VOUT
(2. 5) (
0.3916859d+00
0.5882296d+00
0.7852426d-I00

140

* OUTPUT VOLTAGE AT NODE (I,J) *

TEMPERATURE = -10.000 DEGREE (C)

PRESSURE PSI VOUT
(2. 5) (
0.1m00d+02 0.3836329d-I-00
0.15000d+02 0.5761211d+00
0.2m00d+02 0.7690593d-I-00

* OUTPUT VOLTAGE AT NODE (I,J) *

TEMPERATURE = 0.000 DEGREE (C)

PRESSURE PSI VOUT
(2. 5) (
0. lm00d+02 0.375575 6d+00
0. 15000d+02 ‘ 0.5640068d+00
0.2m00d+02 0.7528690d+00

* Job Concluded *
* Job Finished at 13:51:24 on 10-15-1991

APPENDIX B

SIMULATION RESULTS

APPENDIX B
SIMULATION RESULTS

B.l Piezoresistive Bridge Outputs

*******************************#**it*************************t********48*4!

snSS(No tracking errors-structure 2)

Sensitivity (mv/psi)

41.1353760 40.3167343 39.4979362 38.6790009 37.8599129370406876
36.2213326 35.401821] 34.5821571 33.7623558 32.9424019 32.1223106
31.3020687 30.4816666 29.6611328 28.8404446 28.0195999 27.1986008

V(2,5) for T=27 "C

0.0000000 0.1767098 0.3537990 0.5312686 0.7091199
0.8873542 1.065973 1.244977 1.424367 1.604146
0.7981891

V(2,5) for T=30 "C

0.0000000 0.1755017 0.3513774 0.5276283 0.7042557
0.8812607 1.058645 1.236409 1.414554 1.593082
0.7927110

V(2,5) for T=-40 "C

0.0000000 0.2036367 0.4077790 0.6124288 0.8175880
1.023258 1.229442 1.436141 1.643357 1.851092
0.9203592

V(2,5) for T=0 "C

0.0000000 0.1875738 0.3755756 0.5640068 0.7528690
0.9421636 1.131892d 1.322056 1.512657 1.03696
0.8839256

V(2,5) for T=40 "C

0.0000000 0.1714729 0.3433026 0.5154903 0.6880371
0.8609441 1.034213 1.207843 1.381838 1.556197
0.7744455

V(2,5) for T=80 "C

0.0000000 0.1553339 0.3109599 0.4668790 0.6230918
0.7795994 0.9364024 1.093502 1.250898 1.408593
0.7013087

V(2,5) for T=120 "C

141

142

0.0000000 0.1391567 0.2785473 0.4181725 0.5580327
0.6981287 0.8384610 0.9790303 1.119837 1.260882
0.6280512

V(2,5) for P=15psi

0.6124288 0.6003321 0.5882296 0.5761211 0.5640068 0.5518866
0.5397604 0.5276283 0.5154903 0.5033464 0.4911965 0.4790407
0.4668790 0.4547113 0.4425376 0.4303580 0.4181725 0.4059809
0.5312686

V(2,5) for P=30psi

1.229442 1.205067 1.180683 1.156292 1.131892 1.107484
1.083069 1.058645 1.034213 1.009772 0.9853238 0.9608672
0.9364024 0.9119294 0.8874482 0.8629587 0.8384610 0.8139551
1.065973

V(2,5) for P=45psi

1.851092 1.814253 1.777407 1.740555 1.703696 1.666831
1.629960 1.593082 1.556197 1.519306 1.482408 1.445504
1.408593 1.371675 1.334751 1.297820 1.260882 1.223937
1.604146

III#41411“:********##1##!!!**************#*********#*****************************
snsSl (2.5% tracking errors-structure 2)

Sensitivity (mv/psi)

41.0128365 40.1976929 39.3825493 38.5673256 37.7520599 36.9367027
36.1212234 35.3056259 34.4899139 33.6740227 32.8579559 32.0417099
31.2252789 30.4086285 29.5917778 28.7746849 27.9573765 27.1397953

V(2,5) for T=27 "C
0.06172839 0.2386797 0.4158303 0.5931805 0.7707307
0.9484812 1.126432 1.304585 1.482938 1.661493

V(2,5) for T=-40 "C
0.0569264 0.2608638 0.4650815 0.6695802 0.8743604
1.079423 1.284768 1.490396 1.696308 1.902504

V(2,5) for T=0 "C
0.05994938 0.2477881 0.4358562 0.6241542 0.8126824
1.001441 1.190431 1.379653 1.569106 1.758792

V(2,5) for T=30 "C
0.06191478 0.2376553 0.4135920 0.5897252 0.7660551
0.9425822 1.119307 1.296229 1.473349 1.650668

V(2,5) for T=40 "C

143

0.06252101 0.2342242 0.4061132 0.5781884 0.7504501
0.9228986 1.095534 1.268357 1.441368 1.614567

V(2,5) for T=80 "C
0.06473535 0.2202652 0.3759438 0.5317711 0.6877475
0.8438732 1.000148 1.156573 1.313148 1.469873

V(2,5) for T=120 "C
0.06666202 0.2059803 0.3454154 0.4849675 0.6246366
0.7644229 0.9043266 1.044348 1.184487 1.324744

V(2,5) in mVs for OFFSET(P=0psi)

56.92640 57.73082 58.50142 59.24030 59.94938 60.63042
61.28505 61.91478 62.52101 63.10502 63.66802 64.21111
64.73535 65.24168 65.73102 66.20420 66.66202 67.10520
61.72839

V(2,5) for P=15psi

0.6695802 0.6582803 0.6469413 0.6355654 0.6241542 0.6127094
0.6012326 0.5897252 0.5781884 0.5666235 0.5550317 0.5434139
0.5317711 0.5201043 0.5084142 0.4967017 0.4849675 0.4732122
0.5931805

V(2,5) for P=30psi

1.284768 1.261241 1.237675 1.214071 1.190431 1.166756
1.143048 1.119307 1.095534 1.071731 1.047899 1.024038
1.000148 0.9762321 0.9522893 0.9283206 0.9043266 0.8803080
1.126432 -

V(2,5) for P=45psi

1.902504 1.866627 1.830716 1.794770 1.758792 1.722782
1.686740 1.650668 1.614567 1.578436 1.542276 1.506088
1.469873 1.433630 1.397361 1.361065 1.324744 1.288396
1.661493

****************************************:1:********************************
snS52(-2.5% tracking errors-structure 2)

Sensitivity (mv/psi)

41.2521858 40.4297333 39.6070290 38.7840996 37.9610100 37.1377029
36.3142624 35.4906769 34.6669579 33.8431244 33.0191841 32.1951408
31.3710365 30.5468502 29.7226009 28.8983078 28.0739651 27.2495880

V(2,5) for T=27 "C
-0.06329ll4 0.1131233 0.2901001 0.4676417 0.6457510
0.8244307 1.003684 1.183512 1.363920 1.544908

144

V(2,5) for T=40 ”C
0.0584984] 0.1447851 0.3488036 0.5535610 0.7590613
0.9653087 1.172307 1.380061 1.588574 1.797850

V(2,5) for T=O "C
0.06151341 0.1257416 0.3136266 0.5021448 0.6912993
0.8810935 1.071530 1.262614 1.454346 1.646732

V(2,5) for T=30 "C
0.06347754 0.1117314 0.2874952 0.4638166 0.6406981
0.8181425 0.9961524 1.174731 1.353880 1.533603

V(2,5) for T=40 "C
0.06408399 0.1071049 0.2788245 0.4510771 0.6238654
0.7971918 0.9710588 1.145469 1.320425 1.495929

V(2,5) for T=80 "C
0.06630168 0.08878392 0.2443075 0.4002710 0.5566763
0.7135251 0.8708195 1.028561 1.186752 1.345395

V(2,5) for T=120 "C
0.06823446 0.07071084 0.2100091 0.3496617 0.4896699
0.6300352 0.7707588 0.9118422 1.053287 1.195094

V(2,5) in mVs for OFFSET(P=0psi)

-58.49841 -59.29999 -60.06837 -60.80555 -61.51341 -62.19366
-62.84788 -63.47754 -64.08399 -64.66851 -65.23225 -65.77630
-66.30168 -66.80933 -67.30014 -67.77492 -68.23446 -68.67947
-63.29114

V(2,5) for P=15psi

0.5535610 0.5406684 0.5278027 0.5149621 0.5021448 0.4893490
0.4765734 0.4638166 0.4510771 0.4383539 0.4256459 0.4129519
0.4002710 0.3876024 0.3749451 0.3622985 0.3496617 0.3370340

0.4676417

V(2,5) for P=30psi
1.172307 1.147079 1.121875 1.096693 1.071530 1.046387
1.021262 0.9961524 0.9710588 0.9459795 0.9209138 0.8958607

0.8708195 0.8457894 0.8207697 0.7957597 0.7707588 0.7457665

1.003684

V(2,5) for P=45psi

1.797850 1.760038 1.722248 1.684479 1.646732 1.609003
1.571294 1.533603 1.495929 1.458272 1.420631 1.383005
1.345395 1.307799 1.270217 1.232649 1.195094 1.157552
1.544908

145

t******************************i**********#**************t***************

1990 sns5a(20% tracking errors-structure 2)

"H“ Sensitivity (mv/psi)

42.4687347 41.6130028 40.7571564 399011765 39.0451126 38.1889343
37.3326416 36.4762230 35.6197128 34.7630653 33.9063110 33.0494461
32.1924667 31.3353558 30.4781322 29.6208019 28.7633553 27.9057770

***** V(2,5) for T=27 "C
0.0000000 0.1819579 0.3643392 0.5471456 0.7303784
0.9140392 1.098129 1.282651 1.467604 1.652992

****** V(2,5) for T=-40 "C

0.000000 0.2100561 0.4206787 0.6318701 0.8436326
1.055968 1.268880 1.482370 1.696440 1.911093
0.9497287

"in" V(2,5) for r=o "C

0.000000 0.1932943 0.3870672 0.5813206 0.7760561
0.9712757 1.166981 1.363174 1.559856 1.757030
0.8736053

“we V(2,5) for r=30 "C

0.0000000 0.1806971 0.3618119 0.5433456 0.7252999
0.9076761 1.090476 1.273700 1.457351 1.641430
0.8164352

****** V(2,5) for T=40 "C

0.0000000 0.1764932 0.3533845 0.5306753 0.7083671
0.8864610 1.064959 1.243861 1.423170 1.602887
0.7973637

****** V(2,5) for T=80 "C

0.0000000 0.1596526 0.3196303 0.4799341 0.6405649
0.8015239 0.9628119 1.124430 1.286379 1.448661
0.7210033

"H" V(2,5) for T=120 "C

0.0000000 0.1427725 0.2858044 0.4290964 0.5726492
0.7164636 0.8605402 1.004880 1.149483 1.294351
0.6445237

****** V(2,5) for OFFSE'T(P=0psi)
Offset is ZERO for all cases .........

****** V(2,5) for P=15psi
0.6318701 0.6192417 0.6066073 0.5939669 0.5813206 0.5686683

146

0.5560099 0.5433456 0.5306753 0.5179990 0.5053167 0.4926284
0.4799341 0.4672337 0.4545273 0.4418149 0.4290964 0.4163719
0.5471456 '

"M" V(2,5) for P=30psi

1.268880 1.243417 1.217946 1.192467 1.166981 1.141487
1.115985 1.090476 1.064959 1.039434 1.013901 0.9883603
0.9628119 0.9372557 0.9116917 0.8861199 0.8605402 0.8349527
1.098129

"N" V(2,5) for P=45psi

1.911093 1.872585 1.834072 1.795553 1.7570301.718502
1.679969 16414301602887 1.564338 1.525784 1.487225
1.448661 1.410091 1.371516 13329361294351 1.255760
1.652992

***********#**********************4!**************************************

1990 snsSal (2.5% tracking enor from snSSa {20%} )

******* Sensitivity (luv/psi)

42.3339005 41.4820442 40.6302071 39.7783699 38.9265289 38.0746536
37.2227020 36.3706741 35.5185356 34.6662636 33.8138618 32.9613190
32.1085854 31.2556973 30.4025917 29.5492878 28.6957722 27.8420391

V(2,5) for T=27 "C

****** V(2,5) for T=-40 "C
005685142 0.2672009 0.4778787 0.6888854 0.9002218
1.111889 1.323887 1.536217 1.748880 1.961877

“in" V(2,5) for r=0 "C
0.05993919 0.2534920 0.4473134 0.6414040 0.8357645
1.030395 1.225297 1.420470 1.615915 1.811633

****** V(2,5) for r=30 "C
0.06191467 0.2428450 0.4240050 0.6053952 0.7870160
0.9688679 1.150951 1.333267 1.515814 1.698595

****** V(2,5) for T=40 "C
0.06251901 0.2392370 0.4161727 0.5933265 0.7706989
0.9482902 1.126101 1.304131 1.482382 1.660853

****** V(2,5) for T=80 "C
0.06470669 0.2245509 0.3845692 0.5447618 0.7051289
0.8656709 1.026388 1.187281 1.348349 1.509593

****** V(2,5) for T=120 "C

147

0.06658534 0.2095162 0.3525835 0.4957877 0.6391288
0.7826070 0.9262226 1.069976 1.213867 1.357895

"In" V(2,5) in mVs for OFFSET(P=0psi)

56.85142 57.67899 58.46773 59.22032 59.93919 60.62654
6128442 61.91467 62.51901 63.09899 63.65606 64.19155
64.70669 65.20263 65.68040 66.14100 66.58534 67.01425
61.72839

Mu" V(2,5) for P=15psi

0.6888854 0.6770785 0.6652276 0.6533354 0.6414040 0.6294356
0.6174321 0.6053952 0.5933265 0.5812275 0.5690996 0.5569440
0.5447618 0.5325541 0.5203219 0.5080662 0.4957877 0.4834873
0.6090097

****** V(2,5) for P=30psi

1.323887 1.299303 1.274675 1.250([16 1.225297 1.200551
1.175768 1.150951 1.126101 1.101218 1.076305 1.051361
1.026388 1.001387 0.9763587 0.9513036 0.9262226 0.9011162
1.158400

"H“ V(2,5) for P=45psi
1.961877 1.924371 1.886827 1.849247 1.811633 1.773986
1.736306 1.698595 1.660853 1.623081 1.585280 1.547451

1.509593 1.471709 1.433797 1.395859 1.357895 1.319906
1.709911

***********************4!*************************************************

1990 snSSa2 (-2.5% tracking error from sns5a (20%} )

****** Sensitivity (mv/psi)

42.5979729 41.7380295 40.8778610 40.0175056 39.1569405 38.2962418
37.4353828 36.5744286 35.7133789 34.8522301 33.9910278 33.1297493
32.2684441 31.4070930 30.5457439 29.6843662 28.8229656 27.9616032

V(2,5) for T=27 "C
0.3917051 0.5687816 0.7451061 0.9206833 1.095518
1.269615 1.442979 1.615614 1.787525 1.958717

Hun V(2,5) for T=~40 ”C
005842372 0.1512851 0.3618031 0.5731350 0.7852854
0.9982592 1.212061 1.426696 1.642169 1.858485

****** V(2,5) for r=0 "C
006150323 0.1314772 0.3251499 0.5195186 0.7145871
0.9103591 1.106838 1.304029 1.501935 1.700559

148

"H" V(2,5) for r=30 "C
0.06347743 0.1169312 0.2979484 0.4795773 0.6618210
0.8446827 1.028165 1.212273 1.397007 1.582372

an" V(2,5) for T=40 ”C
0.06408199 0.1121312 0.2889259 0.4663052 0.6442720
0.8228290 1.001979 1.181726 1.362072 1.543020

"H" V(2,5) for T=80 "C
0.06627295 009313437 0.2530203 0.4133871 0.5742368
0.7355717 0.8973939 1.059706 1.222509 1.385807

****** V(2,5) for T=120 "C
0.06815748 0.07440578 0.2173533 0.3606866 0.5044073
0.6485169 0.7930170 0.9379092 1.083195 1.228876

****** V(2,5) in mVs for OFFSE'T(P=0psi)

08.42372 09.24833 00.03476 00.78561 01.50323 02.18978
02.84725 03.47743 04.08199 04.66247 05.22027 05.75669
06.27295 06.77016 07.24936 07.71150 08.15748 08.58813

“u" V(2,5) for P=15psi

0.5731350 0.5596857 0.5462682 0.5328799 0.5195186 0.5061824
0.4928692 0.4795773 0.4663052 0.4530515 0.4398147 0.4265936
0.4133871 0.4001941 0.3870136 0.3738447 0.3606866 0.3475384

****** V(2,5) for P=30psi

1.212061 1.185715 1.159397 1.133106 1.106838 1.080594
1.054370 1.028165 1.001979 0.9758103 0.9496570 0.9235185
0.8973939 0.8712823 0.8451827 0.8190946 0.7930170 0.7669494

****** V(2,5) for P=45psi

1.858485 1.818963 1.779469 1.740002 1.700559 1.661141
1.621745 1.582372 1.543020 1.503688 1.464376 1.425082
1.385807 1.346549 1.307309 1.268085 1.228876 1.189684

*****************************************************4!*************

1990 sns5b(-20% tracking errors-Structure 2)

******* Sensitivity (mv/psi)

39.5721130 38.7968674 38.0214195 37.2458229 36.4700203 35.6940651
34.9179306 34.1415977 33.3651123 32.5884438 31.8115788 31.0345535
30.2573547 29.4799557 28.7023773 27.9246216 27.1466885 26.3685780

V(2,5) for T=27 "C
0.5555555 0.3830373 0.2086031 0.03222066 0.1461428
0.3265208 0.5089476 0.6934585 0.8800893 1.068877

149

mm V(2,5) for T=-40 "c
0.0000000 0.1960958 0.3926294 0.5896022 0.7870157
0.9848713 1.183171 1.381915 1.581106 1.780745

****** V(2,5) for T=0 "C
0.0000000 0.1808537 0.3620787 0.5436764 0.7256478
0.9079941 1.090716 1.273816 1.457294 1.641151

we" V(2,5) for r=30 "C
0.0000000 0.1693982 0.3391216 0.5091712 0.6795480
0.8502529 1.021287 1.192651 1.364346 1.536372

****** V(2,5) for T=40 "C
0.0000000 0.1655751 0.3314608 0.4976579 0.6641673
0.8309899 0.9981266 1.165578 1.333346 1.501430

****** V(2,5) for T=80 "C
0.0000000 0.1502601 0.3007753 0.4515463 0.6025737
0.7538583 0.9054006 1.057201 1.209261 1.361581

"we V(2,5) for T=120 ”C
0.0000000 0.1349085 0.2700221 0.4053413 0.5408667
0.6765986 0.8125375 0.9486840 1.085038 1.221601

tsetse V(2,5) for OFFSET(P=OPSI)
Offset for all cases is ZERO.

****** V(2,5) for P=15psi

0.5896022 0.5781294 0.5666509 0.5551665 0.5436764 0.5321805
0.5206788 0.5091712 0.4976579 0.4861387 0.4746137 0.4630829
0.4515463 0.4400038 0.4284555 0.4169013 0.4053413 0.3937754

an“ V(2,5) for P=30psi

1.183171 1.160070 1.136960 1.113843 1.090716 1.067582
1.044438 1.021287 0.9981266 0.9749579 0.9517807 0.9285949
0.9054006 0.8821977 0.8589862 0.8357662 0.8125375 0.7893003

****** V(2,5) for P=45psi

1.780745 1.745859 1.710964 1.676062 1.641151 1.606233
1.571307 1.536372 1.501430 1.466480 1.431521 1.396555
1.361581 1.326598 1.291607 1.256608 1.221601 1.186586

#*******#*******#**********4!*14!******************************************

1990 sns5b1 (2.5% tracking enor from sns5b {-20%} )

****** Sensitivity (luv/psi)
39.4541969 38.6821709 37.9100800 37.1379128 36.3656120 35.593193]

150

34.820629] 34.0479126 33.2750206 32.501953] 31.7286854 30.9552212
30.1815434 29.4076309 28.6334877 27.8590832 27.0844402 26.3095493

V(2,5) for T=27 "C
0.4945055 0.3213255 0.1463911 0.03032433 0.2088483
0.3892086 0.5714337 0.7555528 0.9415955 1.129592

****** V(2,5) for T=-40 "C
0.05699906 0.2533336 0.4499013 0.6467025 0.8437377
1.041007 1.238512 1.436251 1.634226 1.832438

"H" V(2,5) for r=0 "C
005995944 0.2410227 0.4222764 0.6037209 0.7853566
0.9671836 1.149202 1.331413 1.513816 1.696412

****** V(2,5) for r=30 "C
006191489 0.2315014 0.4012507 0.5711628 0.7412382
0.9114770 1.081879 1.252446 1.423176 1.594071

****** V(2,5) for T=40 "C
006252303 0.2282795 0.3941901 0.5602552 0.7264748
0.8928492 1.059379 1.226063 1.392904 1.559899

****** V(2,5) for T=80 "C
0.06476459 0.2151782 0.3657151 0.5163752 0.6671587
0.8180659 0.9690969 1.120252 1.271531 1.422934

****** V(2,5) for T=120 "C
006674122 0.2017754 0.3369064 0.4721342 0.6074590
0.7428809 0.8783999 1.014016 1.149730 1.285541

****** V(2,5) in mVs for OFFSET(P=0psi)

56.99906 57.78130 58.53439 59.25995 59.95944 60.63426
61.28567 61.91489 62.52303 63.11112 63.68015 64.23102
64.76459 65.28167 65.78300 66.26929 66.74122 67.19940

"H" V(2,5) for P=15psi

0.6467025 0.6360071 0.6252774 0.6145149 0.6037209 0.5928968
0.5820437 0.5711628 0.5602552 0.5493217 0.5383633 0.5273809
0.5163752 0.5053470 0.4942970 0.4832259 0.4721342 0.4610226

"H" V(2,5) for P=30psi

1.238512 1.216236 1.193926 1.171581 1.149202 1.126792
1.104351 1.081879 1.059379 1.036849 1.014292 0.9917077
0.9690969 0.9464601 0.9237980 0.9011111 0.8783999 0.8556648

"H" V(2,5) for P=45psi

15]

1.832438 1.798479 1.764488 1.730466 1.696412 1.662328
1.628214 1.594071 1.559899 1.525699 1.491471 1.457216
1.422934 1.388625 1.354290 1.319928 1.285541 1.251129

***************************************************************#*********

snsSbZ (-2.5% tracking error from sme {-20%} )

Sensitivity (mv/psi)

39.6843948 38.9056053 38.126583] 37.3473129 36.567810] 35.7881203
35.008232] 34.2281685 33.4479332 32.6675453 31.8870087 31.1063614
30.3255558 29.5446548 28.7636280 27.9825153 27.2012863 26.4200020

V(2,5) for T=27 "C
0.6179775 0.4461827 0.2723089 0.09631825 0.08182824
0.2621704 0.4447490 0.6296061 0.8167844 1.0)6328

******* V(2,5) for T=-40 "C
0.05857079 0.1372357 0.3336886 0.5307909 0.7285460
0.9269571 1.126027 1.325760 1.526159 1.727227

******* V(2,5) for r=0 "C
0.06152346 0.1190688 0.3002167 0.4819228 0.6641897
0.8470201 1.030417 1.214382 1.398918 1.584028

******* V(2,5) for r=30 "C
0.06347765 0.1056802 0.2753288 0.4454702 0.6161066
0.7872402 0.9588732 1.131008 1.303646 1.476790

******* V(2,5) for T=40 "C
0.06408602 0.1012559 0.2670676 0.4333509 0.6001081
0.7673410 0.9350517 1.103242 1.271915 1.441071

******* V(2,5) for T=80 "C
006633099 008372492 0.2341702 0.3850065 0.5362352
0.6878578 0.8398760 0.9922913 1.145105 1.298319

******* V(2,5) for T=120 "C
006831398 006642039 0.2014702 0.3368365 0.4725205
0.6085232 0.7448458 0.8814895 1.018455 1.155744

***** V(2,5) in mVs for OFFSET(P=0psi)

-58.57079 -59.35031 00.10125 00.82515 01.52346 02.19749
02.84850 03.47765 04.08602 04.67462 05.24440 05.79624
06.33099 06.84943 07.35228 07.84025 08.31398 08.77408

**"'**** V(2,5) for P=15psi
0.5307909 0.5185416 0.5063147 0.4941089 0.4819228 0.4697551

152

0.4576046 0.4454702 0.4333509 0.4212458 0.4091539 0.3970744
0.3850065 0.3729494 0.3609025 0.3488651 0.3368365 0.3248162

******* V(2,5) for P=30psi

1.126027 1.102098 1.078187 1.054294 1.030417 1.006555
0.9827072 0.9588732 0.9350517 0.9112419 0.8874432 0.8636548
0.8398760 0.8161063 0.7923451 0.7685917 0.7448458 0.7211068

******* V(2,5) for P=45psi

1.727227 1.691402 1.655595 1.619804 1.584028 1.548268
1.512522 1.476790 1.441071 1.405365 1.369671 1.333990
1.298319 1.262660 1.227011 1.191373 1.155744 1.120126

**************************4333**4!*1!*Itllnlnt*4“!********************************

153

8.2 Compensation Bridge Outputs
*************************************************************************

SNSS], 2.5%tracking enors from $1185 (Structur-Z)

Rpl 2 3 R‘I'EMP 2K

Rt] 0 2 RTEMP12.05K

MODEL RTEMP RES(R=1 TC]=0.00]9 TC2=0)
MODEL R'I'EMP] RES(R=1 TC1=0.001925 TC2=0)

RT (-40 to 130 C) P=0

1786 1825 1865 1904 1943 1983 2022 2062 2101
2141 2180 2220 2259 2299 2338 2378 2417 2456
2000

V(2,5) for (-40 to 130 C) P=0

0.0569263 0.0577307 0.0585012 0.0592403 0.0599494 0.0606303
0.0612850 0.0619149 0.0625210 0.0631051 0.0636683 0.0642114
0.0647354 0.0652418 0.0657310 0.0662045 0.0666623 0.0671058

***************t**********************$***************

SNSSZ, -2.5%tracking errors from snsS (Stmctur—Z)

Rp] 2 3 RTEMP 2K

Rt] 0 2 RTEMP] 1.95K

MODEL RTEMP RES(R=1 TC]=0.0019 TC2=0)
MODEL RTEMP] RES(R=] TC1=0.001875 TC2=0)

RT (-40 to 130 C) P=0

1705 1742 1778 1815 185] 1888 1924 1961 1998
2034 2071 2107 2144 2180 2217 2253 2290 2327
2000

V(2,5) for (-40 to 130 C) P=0

0.0584984 0.0592999 0.0600681 0.0608053 0.0615134 0.0621934
0.0628476 0.0634775 0.0640841 0.0646687 0.0652323 0.0657763
0.0663018 0.0668097 0.0673003 0.0677752 0.0682349 0.0686798

******t**********************************************it

SNSSal, 2.5%tracking cums from snsSa:20% (Structur-Z)

Rpl 2 3 RTEMP 2.4K

Rt] 0 2 RTEMP12.46K

MODEL RTEMP RES(R=1 TC1=0.0021 TC2=0)
MODEL RTEMP] RES(R=1 TC1=0.002]25 TC2=0)

154

RT (-40 to 130 C) P=0

2110 2162 2214 2267 2319 237] 2423 2476 2528
2580 2633 2685 2737 2789 2842 2894 2946 2998
2460

V(2,5) for (40.10 130 C) P=0

0.0568514 0.0576787 0.0584674 0.0592203 0.0599389 0.0606265
0.0612845 0.0619144 0.0625191 0.0630989 0.0636563 0.0641918
0.0647068 0.0652027 0.0656805 0.0661416 0.0665860 0.0670147
0.0617284

***********tt******************************************

SNSSaZ, -2.5%tracking enors from snsSa:20% (Structur-Z)

Rpl 2 3 R'I'EMP 2.4K

R11 0 2 RTEMP12.34K

MODEL RTEMP RES(R=1 TC1=0.0021 TC2=0)
MODEL R'I'EMP] RES(R=1 TC1=0.002075 TC2=0)

RT (-40 to 130 C) P=0

2015 2063 2112 2160 2209 2257 2306 2355 2403
2452 2500 2549 2597 2646 2694 2743 2792 2840
2340

V(2,5) for (-40 to 130 C) P=0

0.0584235 0.0592480 0.0600348 0.0607853 0.0615034 0.0621896
0.0628471 0.0634775 0.0640821 0.0646625 0.0652204 0.0657568
0.0662732 0.0667706 0.0672498 0.0677118 0.0681577 0.0685887
0.0632912

******************************************************

SNS5bl, 2.5%tracking 8111018 fmm snsSb:-20% (Structur-2)

Rpl 2 3 RTEMP 1.6K

R11 0 2 RTEMP] 1.64K

Model RTEMP RES(R=1 TC1=0.0017 TC2=0)
Model RTEMP] RES(R=1 TC1=0.00]725 TC2=0)

RT (-40 to 130 C) P=0

1450 1479 1507 1535 1564 1592 1620 1648 1677
1705 1733 1762 1790 1818 1847 1875 1903 1931
1640

V(2,5) for (-40 to 130 C) P=0

0.0569987 0.0577812 0.0585341 0.0592599 0.0599594 0.0606341
0.0612855 0.0619149 0.0625229 0.0631113 0.0636802 0.0642314
0.0647650 0.0652819 0.0657830 0.0662694 0.0667415 0.0671997

155

0.0617284

*************4|*IIHIHOHI*Ik******************************************

SNSSb2, -2.5%tracking errors fnom snsSb:-20% (Stmctur-Z)

Rp1 2 3 RTEMP 1.6K

R11 0 2 RTEMP] 1.56K

Model RTEMP RES(R=] TC]=0.0017 TC2=0)
Model RTEMP] RES(R=1 TC1=0.001675 TC2=0)

RT (-40 to 130 C) P=0

1385 141] 1437 1463 1489 1516 1542 1568 1594
1602 1646 1672 1698 1725 1751 1777 1803 1829
1560

V(2,5) for (-40 to 130 C) P=0
0.0585704 0.0593500 0.0601010 0.0608249 0.0615234 0.0621972
0.0628486 0.0634775 0.0640860 0.0646749 0.0652447 0.0657964

0.0663314 0.0668497 0.0673528 0.0678406 0.0683146 0.0687742
0.0632912

156

B.3 The Compensated Outputs

**************************************************************

snsSl (2.5% tracking enors-stmctuneZ)

***** V(out) mVs for OFFSET(P=0psi)

0.0001 0.0001 0.0002 0.0000 0.0000 0.0001
0.0000 0.0001 0.0000 0.0001 0.0003 0.0003
0.0000 0.0001 0.0000 0.0003 0.0003 0.0006

***** V(out) for P=15psi

0.6126539 0.6005496 0.5884401 0.5763251 0.5642048 0.5520791
0.5399476 0.5278103 0.5156674 0.5035184 0.4913634 0.4792025
0.4670357 0.4548625 0.4426832 0.4304972 0.4183052 0.4061064

***** V(out) for P=30psi

1.2278417 1.2035103 1.1791737 1.1548307 1.1304816 1.1061257
1.0817630 1.0573921 1.0330130 1.0086259 0.9842307 0.9598266
0.9354126 0.9109903 0.886558308621161 0.8376643 0.8132021

mm V(out) for P=45psi _

1.8455777 1.8088963 1.7722148 1.7355297 1.6988426 1.6621517
1.6254550 1.5887531 1.5520461 1.5153309 1.4786078 1.4418766
1.4051375 1.3683882 1.331630012948605 1.2580817 1.2212902

***** V(out) for T=40 "C
0.0000001 0.2039375 0.4081552 0.6126539 0.8174341
1.0224967 1.2278417 1.4334698 1.6393818 1.8455777

***** V(out) for T=0 "C
0.0000000 0.1878387 0.3759068 0.5642048 0.7527330
0.9414916 1.1304816 1.3197036 1.5091566 1.6988426

***** V(out) for T=40 "C
0.0000000 0.1717032 0.3435922 0.5156674 0.6879291
0.8603776 1.0330130 1.2058361 1.3788470 1.5520461

***** V(out) for T=80 ”C
0.0000000 0.1555298 0.3112084 0.4670357 0.6230121
0.7791378 0.9354126 1.0918376 1.2484126 1.4051375

mm V(out) for T=120 "c
0.0000003 0.1393180 0.2787531 0.4183052 0.5579743
0.6977606 0.8376643 0.9776857 1.1178247 1.2580817

*************************************************************

157

sn852(-2.5% tracking enors-structureZ)

***** V(out) in mVs for OFFSET(P=0psi)

0.0000 0.0001 0.0103 0.0003 0.0000 0.0003
0.0003 0.0000 0.0001 0.0002 0.0001 0.0000
0.0001 0.0004 0.0002 0.0003 0.0004 0.0003

“*1"- V(out) for P=15psi

0.6120594 0.5999683 0.5878708 0.5757674 0.5636582 0.5515424
0.5394210 0.5272941 0.5151612 0.5030226 0.4908782 0.4787282
0.4665728 0.4544121 0.4422454 0.4300737 0.4178966 0.4057138

***** V(out) for P=30psi

1.2308054 1.2063789 1.1819432 1.1574984 1.1330434 1.1085804
1.0841097 1.0596299 1.0351429 1.0106481 0.9861461 0.9616370
0.9371213 0.9125991 0.8880700 0.8635349 0.8389937 0.8144463

***** V(out) for P=45psi

1.8563484 1.8193380 1.7823161 1.7452843 1.7082454 1.6711963
1.6341416 1.5970805 1.5600131 1.5229406 1.4858633 1.4487814
1.4116968 1.3746086 1.3375173 1.3004242 1.2633289 1.2262318

***** V(out) for T=-40 "C
0.0000000 0.2032835 0.4073020 0.6120594 0.8175597
1.0238072 1.2308054 1.4385594 1.6470724 1.8563484

***** V(out) for T=0 "C
0.0000000 0.1872550 0.3751400 0.5636582 0.7528127
0.9426069 1.1330434 1.3241274 1.5158594 1.7082454

***** V(out) for T=40 "C
0.0000001 0.1711890 0.3429086 0.5151612 0.6879495
0.8612759 1.0351429 1.2095530 1.3845091 1.5600131

***** V(out) for T=80 "C
0.0000001 0.1550857 0.3106093 0.4665728 0.6229782
0.7798269 0.9371213 1.0948628 1.2530538 1.4116968

**“‘** V(out) for T=120 "C
0.0000004 0.1389457 0.2782440 0.4178966 0.5579048
0.6982701 0.8389937 0.9800771 1.1215219 1.2633289

*tﬁtiltttttidllddltt********************************************

SNSSal, 2.5%tl'acking errors from snsSa:20% (Stmcmr-Z)

***** V(out) in 1nVs for OFFSET(P=0psi)
0.0000 0.0003 0.0003 0.0000 0.0003 0.0000

158

0.000] 0.0003 0.0001 0.0001 0.11302 0.0003
0.0001 0.0001 0.0001 0.0006 0.0007 0.0005

mm V(out) for P=15psi

0.6320340 0.6193998 0.6067602 0.5941151 0.5814651 0.5688091
0.5561476 0.5434808 0.5308074 0.5181286 0.5054433 0.4927522
0.4800550 0.4673514 0.4546414 0.4419246 0.4292017 0.4164726

***** V(out) for P=30psi

1.2670356 1.2416244 1.2162076 1.1907856 1.1653581 1.1399245
1.1144835 1.0890366 1.0635819 1.0381191 1.0126487 0.9871691
0.9616812 0.9361843 0.9106782 0.8851620 0.8596366 0.8341015

***** V(out) for P=45psi

1.9050256 1.8666923 1.8283596 1.7900267 1.7516941 1.7133595
1.6750214 1.6366806 1.598334015599821 1.5216236 1.4832592
1.4448862 1.4065063 1.3681165 1.3297174 1.291309012528913

V(out) for T=27 "C
0.0000950 0.1768928 0.3525745 0.5271509 0.7006319
0.8730289 1.0443499 1.2146080 1.3838100 1.5519681

***** V(out) for T=-40 "C
0.0000000 0.2103495 0.4210273 0.6320340 0.8433704
1.0550376 1.2670356 1.4793656 1.6920286 1.9050256

***** V(out) for T=0 "C
0.0000003 0.1935531 0.3873745 0.5814651 0.7758256
0.9704561 1.1653581 1.3605311 1.5559760 1.7516941

***** V(out) for T=40 "C
0.0000001 0.1767179 0.3536536 0.5308074 0.7081798
0.8857712 1.0635819 1.2416120 1.4198630 1.5983340

***** V(Out) for T=80 "C
0. 0000001 0.1598441 0.3198624 0. 4810550 0. 6404221
0.8009641 0.9616812 1.1225742 1.2836422 1.4448862

***** V(out) for T=120 "C
0.0000007 0.1429302 0.2859975 0.4292017 0.5725428
0.7160210 0.8596366 1.0033900 1.1472809 1.2913090

##1##!!!*#***********************************#***********#******

snsSaZ (-2.5% tracking error from snsSa {20%} )

***** V(out) in mVs for OFFSET(P=0psi)
0.0002 0.0003 0.0000 0.0003 0.0002 0.0002

159

0.0001 0.0001 0.0001 0.0000 0.0001 0.0001
0.0002 0.0004 0.0004 0.0003 0.0002 0.0006

"m V(out) for P=15psi

0.6315585 0.6189337 0.6063030 0.5936652 05810220 0.5683720
0.5557163 0.5430548 0.5303873 0.5177140 0.5050351 0.4923504
0.4796603 0.4669647 0.4542634 0.4415565 0.4288443 0.4161271

***** V(out) for P=30psi

1.2704846 1.2449629 1.2194318 1.1938913 1.1683414 1.1427835
1.1172172 1.0916425 1.0660611 1.0404727 1.0148774 0.9892753
0.9636671 0.9380529 0.9124325 0.8868064 0.8611747 0.8355381

***** V(out) for P=45psi

1.9169085 1.8782110 1.8395038 1.8007873 1.7620624 1.7233306
1.6845921 1.6458495 1.6071022 1.5683504 1.5295963 1.4908388
1.4520802 1.4133196 1.3745588 1.3357968 1.2970337 1.2582728

V(out) for T=27 "C
0.0000949 0.1769816 0.3533061 0.5288833 0.7037180
0.8778151 1.0511789 1.2238140 1.3957250 1.5669169

***** V(out) for T=-40 "C
0.0010002 0.2097086 0.4202266 0.6315585 0.8437089
1.0566827 1.2704846 1.4851195 1.7005925 1.9169085

***** V(out) for T=0 "C
0.0000002 0.1929806 0.3866533 0.5810220 0.7760905
0.9718625 1.1683414 1.3655324 1.5634384 1.7620624

***** V(out) for T=40 "C
0.0000001 0.1762133 0.3530080 0.5303873 0.7083541
0.8869111 1.0660611 1.2458081 1.4261541 1.6071022

***** V(out) for T=80 "C
0.0000002 0.1594076 0.3192935 0.4796603 0.6405100
0.8018449 0.9636671 1.1259792 1.2887822 1.4520802

***** V(out) for T=120 "C
0.0000002 0.1425635 0.2855110 0.4288443 0.5725650
0.7166746 0.8611747 1.0060669 1.1513526 1.2970337

****************#********#****************************¢******

snsSb] (2.5% tracking error from sns5b {-20%} )

**“* V(out) in rnVs for OFFSET(P=0psi)
0.0004 0.0001 0.0003 0.0001 0.0000 0.0002

160

0.0002 0.0000 0.0001 0.0002 0.0001 0.0004
0.0004 0.0002 0.0000 0.0001 0.0003 0.0003

***** V(out) for P=15psi

0.5897038 0.5782259 0.5667433 0.5552550 0.5437615 0.5322627
0.5207582 0.5092479 0.4977323 0.4862104 0.4746831 0.4631495
0.4516102 0.4400651 0.4285140 0.4169565 0.4053927 0.3938229

m" V(out) for P=30psi

1.1815133 1.1584548 1.1353918 1.1123211 1.0892426 1.0661578
1.0430655 1.0199641 0.9968561 0.9737377 0.9506118 0.9274763
0.9043319 0.8811783 0.8580150 0.8348417 0.8116584 0.7884651

***** V(out) for P=45psi

1.7754393 1.7406977 1.7059538 1.6712061 1.6364526 1.6016939
1.5669285 1.5321561 1.4973761 1.4625877 1.4277909 1.3929846
1.3581691 1.3233432 1.2885070 1.2536587 1.2187996 1.1839293

V(out) for T=27 "C
0.0000945 0.1732745 0.3482089 0.5249243 0.7034483
0.8838086 1.0660337 1.2501528 1.4361955 1.6241920

***** V(out) for T=-40 "C
0.0000004 0.1963349 0.3929026 0. 5897038 0. 7867390
0.9840083 1.1815133 1.3792523 1.5772272 1.7754393

***** V(out) for T=0 "C
0.0000000 0.1810633 0.3623170 0.5437615 0.7253972
0.9072242 1.0892426 1.2714536 1.4538566 1.6364526

***** V(out) for T=40 "C
0.0000001 0.1657566 0.3316672 0.4977323 0.6639519
0.8303263 0.9968561 1.1635401 1.3303812 1.497376]

"-1" V(out) for T=80 "c
0.0000004 0.1504132 0.3009501 0.4516102 0.6023937
0.7533009 0.9043319 1.055487012067660 1.3581691

***** V(out) for T=120 "C
0.0000003 0.1350339 0.2701649 0.4053927 0.5407175
0.6761394 0.8116584 0.9472746 1.0829885 1.2187996

*****##******43*****************************************

snsSb2 (-2.5% tracking error from snsSb {-20%} )

***** V(out) in mVs for OFFSET(P=0psi)
0.0004 0.0003 0.0002 0.0002 0.0001 0.0003

161

0.000100001001110 0.01113 00103 0.0002
0.0004 0.0003 0.01115 0.01134 0.(X)06 0.0001

***** V(out) for P=15psi

0.5893613 0.5778916 0.5664157 0.5549338 0.5434462 0.5319523
0.5204532 0.5089477 0.4974369 0.4859207 0.4743986 0.4628708
0.4513379 0.4397991 0.4282553 0.4167057 0.4051511 0.3935904

***** V(out) for P=30psi

1.1845974 1.1614480 1.1382880 1.1151189 1.0919404 1.0687522
1.0455558 1.0223507 0.9991377 0.9759168 0.9526879 0.9294512
0.9062074 0.8829560 0.8596979 0.8364323 0.8131604 0.7898811

***** V(out) for P=45psi

1.7857974 1.7507520 1.7156960 1.6806289 1.6455514 1.6104652
1.5753706 1.5402675 1.5051570 1.4700398 1.4349157 1.3997864
1.3646504 1.3295097 1.2943637 1.2592136 1.2240585 1.1889002

V(out) for T=27 "C
0.0000225 0.1718173 0.3456911 0.5216817 0.6998282
0.8801703 1.0627489 1.2476060 1.4347844 1.6243279

***** V(out) for T=-40 "C
0.0010004 0.1958061 0.3922590 0.5893613 0.7871164
0.9855275 1.1845974 1.3843304 1.5847294 1.7857974

***** V(out) for T=0 "C
0.0000001 0.1805922 0.3617401 0.5434462 0.7257131
0.9085435 1.0919404 1.2759055 1.4604415 1.6455514

***** V(out) for T=40 "c
0.0000000 0.1653419 0.3311536 0.4974369 0.6641941
0.8314270 0.9991377 1.167328013360009 1.5051570

***"'* V(out) for T=80 ”C
0.0000004 0.1500563 0.3005016 0.4513379 0.6025666
0.7541892 0.9062074 1.0586227 1.2114364 1.3646504

**"‘** V(out) for T=120 "C
0.0000006 0.1347350 0.2697848 0.4051511 0.5408351
0.6768378 0.8131604 0.9498041 1.0867696 1.2240585

162

13.4 The Half Bridge Outputs

************ half bridge outputs with subtractor *************

snsS (Temperatulc), V (7,0)

0.308213 0.260822 0.213430 0.166036 0.118642 0.0712477
0.0238526 0.0235429 0.07093710.118326 0.165711 0.213090
0.260465 0.307835 0.355203 0.402565 0.449926 0.497284
0.00932422

snsSa (Temperature), V (7,0)

0.125588 0.182340 0.239082 0.295815 0.352538 0.409251
0.465954 0.522648 0.579332 0.636006 0.692670 0.749325
0.805971 0.862608 0.919237 0.975857 1.03247 1.08908
0.50564]

sns5b ('1‘e1nperatu1e), V (7.0)

0.742622 0.704634 0.666642 0.628646 0.590647 0.552645
0.514640 0.476632 0.438621 0.400608 0.362591 0.324570
0.286545 0.248520 0.210488 0.172452 0.134411 0.0963648
0.488035

163

11.5 The Final Temperature Compensated Outputs
*************** Final compensated data #:1111111!**#******************
snsS (No Tracking errors)

**** Pressure Sensitivity (mV/psi)
37.71 36.540 35.370 34.200 32.724

"11* goes (includes snsS] and 811852) Temp = 40 c
0.0000000 0.1651100 0.3307258 0.5353755 0.7405347
0.8691515 1.0753355 1.2820345 1.4892505 1.6969855

**** sns5 (includes snsSl and 811852) Temp = 0 C
0.0000000 0.1727435 0.3459151 0.5343463 0.7232085
0.8828426 1.0725709 1.2627350 1.4533360 1.6443750

**** snsS (includes snsS] and 811852) Temp = 30 C
0.0000000 0. 0.3572631 0.5335140 0.7101414
0.8930321 1.0704165 1.2481804 1.4263254 1.6048534

**** snsS (includes sn851 and sns52) Temp = 40 C
0.0000000 0.18034 0.3610369 0.5332246 0.7057714
0.8964126 1.0696815 1.2433115 1.4173065 1.5916656

**** snsS (includes MS] and 811852) Temp = 80 C
0.0000000 0.1878920 0.3760762 0.5319952 0.6882080
0.9098319 1.0666349 1.2237345 1.3811305 1.5388255

**** 81185 (includes sns5] and 811852) Temp = 120 C

0.0000000 0. 0.3910288 0.5306540 0.6705142

0.9230917 1.0634240 1.2039933 1.3448000 1.4858450

**** snsS (includes snsS] and 811852) Temp = 130 C

0.0000000 0.1972669 0.3947542 0.5303019 0.6660711

0.9263833 1.0625972 1.1990340 1.3356949 1.4725790
Pressure output at -40,0,40,80,130

** Pressure = 5psi
0.1651100 0.1727435 0.18034 0.1878920 0.1972669

** Pressure = 15psi
0.5353755 0.5343463 0.5332246 0.5319952 0.5303019

** Pressure = 30psi

164

1.0753355 1.0725709 1.0696815 1.0666349 1.0625972

** Pressure = 45psi
1.6969855 1.6443750 1.5916656 1.5388255 1.4725790

4!*************************************************************

mm“ snsSa (20% tracking errors)

**** Pressure Sensitivity (mV/psi)
43.860 42.962 42.060 41.150 40.001

**** snsSa (includes snsSa] and sns5a2 ) Temp = -40 C
0.0000000 0.2257546 0.4520757 0.6632671 0.8750296
1.1187620 1.3316740 1.5451640 1.7592340 1.9738870

**** snsSa (includes snsSa] and snsSaZ ) Temp = 0 C
0.0000000 0.2373615 0.4752017 0.6694551 0.8641906
1.1475446 1.3432500 1.5394430 1.7361250 1.9332991

**** snsSa (includes snsSa] and snsSaZ ) Temp = 30 C
0.0000000 0. 0.4924739 0.6740075 0.8559619
1.1690001 1.3518000 1.5350239 1.7186749 1.9027541

**** snsSa (includes snsSa] and sns5a2 ) Temp = 40 C
0.0000000 0.2489097 0.4982175 0.6755083 0.8532001
1.1761270 1.3546250 1.5335269 1.7128360 1.8925531

**** snsSa (includes snsSa] and sn85a2 ) Temp = 80 C
0.0000000 0.2603990 0.5211231 0.6814269 0.8420577
1.2045095 1.3657974 1.5274155 1.6893644 1.8516464

**** snsSa (includes snsSa] and snsSaZ ) Temp = 120 C
0.0000000 0. 0.5439219 0.6872139 0.8307667
1.2326987 1.3767753 1.5211149 1.6657180 1.8105860

**** sns5a (includes 8118581 and snsSaZ ) Temp = 130 C

0.0000000 0.2746813 0.5496067 0.6886419 0.8279225‘

1.2397192 1.3794928 1.5195135 1.6597819 1.8002999
Pressure output at -40,0,40,80,130

** Pressure = 5psi
0.2257546 0.2373615 0.2489097 0.2603990 0.2746813

** Pressure = 15psi ,
0.6632671 0.6694551 0.6755083 0.6814269 0.6886419

 

165

“- Pressure = 30psi
1.3316740 1.34325001.354625013657974 1.3794928

** Pressure = 45psi
1.9738870 1.9332991 1.8925531 1.8516464 1.8002999

**********************I!*****##1-*4!*#************************#******

****** snsSb (-20% tracking errors)

**** Pressure Sensitivity (mV/psi)
31.320 29.910 28.490 27.070 25.300

**** Pressure Sensitivity (mV/psi) for Pmax = 30psi
27.062 26.513 25.960 25.404 24.704

**** Pressure Sensitivity (mV/psi) for Pmax = 25psi
25.542 24.507 24.467 24.423 24.363

**** snsSb ( includes snsSb] and snsSb2 ) Temp = -40 C
0.0000000 0.1032680 0.2069739 0.4039467 0.6013602
0.6135603 0.8118600 1.0106039 1.2097950 1.4094341

**** snsSb ( includes snsSbl and snsSb2 ) Temp = 0 C
0.0000000 0.1070228 0.2144170 0.3960146 0.5779861
0.6126706 0.7953925 0.9784925 1.1619705 1.3458275

**** snsSb ( includes snsSbl and sns5b2 ) Temp = 30 C
0.0000000 0. 0.2199636 0.3900132 0.5603900
0.6119369 0.7829710 0.9543350 1.1260300 1.2980559

**** sns5b ( includes snsSbl and snsSb2 ) Temp = 40 C
0.0000000 0.1107475 0.2218055 0.3880026 0.5545120
0.6116794 0.7788161 0.9462675 1.1140355 1.2821195

**** sns5b ( includes snsSbl and snsSb2 ) Temp = 80 C
0.0000000 0.1144420 0.2291390 0.3799101 0.5309374
0.6105858 0.7621281 0.9139285 1.0659884 1.2183084

**** snsSb ( includes snsSb] and snsSbZ ) Temp = 120 C
0.0000000 0. 0.2364193 0.3717386 0.5072639
0.6093931 0.7453320 0.8814785 1.0178324 1.1543955

**** snsSb ( includes sns5b] and sns5b2 ) Temp = 130 C
0.0000000 0.1190192 0.2382320 0.3696842 0.5013309
0.6090811 0.7411179 0.8733503 1.0057787 1.1384037

Pressure output at 40.040.80.130

166

** Pressure = 5psi
0.1032680 0.1070228 0.1107475 0.1144420 0.1190192

** Pressure = 15psi
0.4039467 0.3960146 0.3880026 0.3799101 0.3696842

** Pressure = 30psi
0.8118600 0.7953925 0.7788161 0.7621281 0.7411179

** Pressure = 45psi
1.4094341 1.3458275 1.2821195 1.2183084 1.1384037

APPENDIX C

PSPICE SIMULATION CODE

APPENDIX C

PSPICE SIMULATION CODE

C.1 The Op-amp Circuit

CMOS Operational Ampliﬁer

VDD 3 0 5.0

V88 4 0 -5.0

*VP 1 0 ;non-inverting input
*VM 2 0 ;inverting input

MP1 6 2 13 3 PMOS L=30U W=60U

MPZ 7 1 13 3 PMOS L=30U W=60U

MN3 6 6 4 4NMOS L=15U W=210U

MN4 7 6 4 4NMOS L=15U W=210U

MN6 8 7 4 4 NMOS L=6U =240U

MP8 12 12 3 3 PMOS L=6U W=12U

MP5 13 12 3 3 PMOS IFOU W=12U

MP7 8 12 3 3 PMOS L=6U W=18U

MN9 5 7 4 4 NMOS L=6U W=360U

MP1011 711 3PMOS L=96U W=96U

MNll 8 311 4 NMOS L=6U W=6U

MP12 8 411 3PMOS b6U W=6U

MN131212 4 4NMOS L=6U W=12U

Q1 3 8 5 QMOD

CPAR 11 0 4P

.MODEL NMOS NMOS LEVEL=2 VTO=0.8 KP=36.72U LAMBDA=0.01
+ GAMMA=1.4 TOX=650E-10 LD=0.4U UO=680 CGSO=4.32E-16

+ CJ=5.4E-4 CGDO=4.32E-16 CGBO=6.48E-16 RSI-1:25 CJSW=5.4E-10
.MODEL PMOS PMOS LEVEL=2 VTO=0.8 KP=13.5U LAMBDA=0.01
+ GAMMA=0.4 UO=250 CJ=1.22E~4 TOX=650E-10 LD=0.5U

+ CGSO=4.32E-16 CGDO=4.32E-16 CGBO=6.48E-16 RSH=15 CJSW=1.22E-10
.MODEL QMOD NPN IS=1E-15 BF=100 NF=1 VAF=200 IKF=.01 ISE=lE—l3
+ NE=2 BR=0.1 NR=1 VAR=200 IKR=.01 ISC=1E~13 NC=1.5 RB=100

+ IRB=.1 RBM=10 RE=1 RC=10 CJE=2P VJE=.6 MJE=.33 TF=.1N

+ CJC=2P VJC=.5 MJC=.5 TR=10

*RL 5 0 ;output

.END

167

168

C.2 The Analog Circuit for the ADC

ADC Analog Circuit

*

.Options nopage ITLS=5000
.LIB oamp.1ib

*************************************************

Voltages
*************************************************
VDD 3 0 DC 5.0
V88 4 0 DC 00
VIN 8 0 DC -3.5
VREFP 13 0 DC 2.5
VREFN 14 0 DC ~2.5
VG 7 0 PULSE(0.0 5.0 0.0 ION 10N 0.04M 30.9M) ; Discharge C
VCON] 11 0 PULSE(0.0 5.0 0.06M 10N 10N 10.24M 30.9M) ; integrate Vin
VCON2 12 0 PULSE(0.0 5.0 10.3M 10N ION 20.48M 30.9M) ; De-integrate

*************************************************

Circuit Resistances
t******************************************f$****
RINTEG 6 1 1.3MEG ;integrator resistor
CINTEG 1 5 8.3N ;integrator capacitor
RLS 16 0 25K ;Load for sign comparator
RPS 16 3 5.1K ; Pull up for sign comparator
RLO 21 0 25K ; Load for output comparator
RPO 21 3 5.1K ; Pull up for output comparator

*************************************************

The subcircuits
*************************************************
Xoamp 0 1 3 4 5 oamp ;opamp for integration
Xst 1 5 7 0 idswp ;control discharge of C
XszN 8 6 11 0 idswp ;control Vin
XszEF 9 6 12 0 idswp ;control Vref
XpREF13 9 16 0 idswp ;control positive Vref
XnRBF 14 9 16 0 idswn ; control negative Vref
Xsign 42 41 3 0 16 LM139 ; comparator for sign
Xout 32 31 3 0 21 LM139 ; comparator for output

*************************************************

169

Zero Crossing Detector Components
*************************************************
R1 5 30 5.1K
R2 30 3] 5.1K
R3 31 3 100K
R4 32 3 100K
R5 32 0 10K
R6 32 21 20MEG
Dout 0 30 DMOD
.model DMOD D

*************************************************

Sign Detector Components
*************************************************

R11 8 40 5.1K

R12 40 41 5.1K

R13 41 3 100K

R14 42 3 100K

R15 42 0 10K

R16 42 16 20MEG

DsgnO 40 DMOD

*************************************************
Analysis

*************************************************

.TRAN 10.0U 30.9M 0.0

.PRINT TRAN V(5) V(7) V(6)

**** V(11)V(12) V(6) V(7) V(16) V(9) V(21) V(23)

.END

 

APPENDIX D

VHDL SIMULATION CODE

APPENDIX D

VHDL SIMULATION CODE

__****************************************************

«Description of an AND gate

ENTITY andgate 1S
PORT ( in]. in2 : BIT; out] : OUT BIT );
END andgate;

ARCHITECTURE behav OF andgate IS

BEGIN
out] <= in] AND in2 AFTER 4 ns;
END behav;

."**********t*#***************************************

--Description of an OR gate

ENTITY orgate 18
PORT ( in]. in2 : BIT; outl : OUT BIT);
END orgate;

ARCHITECTURE behav OF orgate IS

BEGIN
out] <= in] OR in2 AFTER 4 ns;
END behav;

.u****************************************************

-- Description of a 50Khz Clock Circuit.

ENTITY clock IS

PORT (go : 1N BIT; clok : OUT BIT );
END clock;

ARCHITECTURE behav OF clock IS

BEGIN
PROCESS
BEGIN
IF go = ’0’ THEN
WATT UNTIL go = ’1’:
END IF;

170

171

clok <= ’1’.’0’ after 10 us;
wait FOR 20 us;
END PROCESS;
END behav;

_- *************************************************It

-- Description of a 2x4 Decoder with reset

ENTITY dec IS
PORT ( c1. c0. clr : IN BIT; zer. one. two. thr : OUT BIT );
END dec; '

ARCHITECTURE behav OF dec IS

BEGIN
PROCESS (c1. c0. clr)

CONSTANT delay: time := 8 ns ;

BEGIN

-- check for clear

IF (clr = ’1’) THEN
zer <= ’0’ AFTER delay ;
one <= ’0’ AFTER delay ;
two <= ’0’ AFTER delay ;
thr <= ’0’ AFTER delay ;

ELSIF (c1 = ’0’) AND (CO = ’0’) THEN
zer <= ’1’ AFTER delay ;
one <= ’0’ AFTER delay ;
two <= ’0’ AFTER delay ;
thr <= ’0’ AFTER delay ;

ELSIF (c1 = ’0’) AND (CO = ’1’) THEN
zer <= ’0’ AFTER delay ;
one <= ’1’ AFTER delay ;
two <= ’0’ AFTER delay ;
thr <= ’0’ AFTER delay ;

ELSIF (c1 = ’1’) AND (CO = ’0’) THEN
zer <= ’0’ AFTER delay ;
one <= ’0’ AFTER delay ;
two <= ’1’ AFTER delay ;
thr <= ’0’ AFTER delay ;

ELSIF (c1 = ’1’) AND (CO = ’1’) THEN
zer <= ’0’ AFTER delay ;
one <= ’0’ AFTER delay ;
two <= ’0’ AFTER delay ;

172

thr<= ’1’ AFTER delay;
END IF;
END PROCESS;
END behav;

__**********#************t****************************

-- Description of a level triggered D type ﬂip ﬂop
-- with preset.

ENTITY dff IS
PORT(set:INBTT;q:OUTBTT);
END dff;

ARCHITECTURE behav OF dff IS

BEGIN
-- ﬂip ﬂop operation
PROCESS (set)
CONSTANT delay: time := 10 n8 ;
BEGIN
-- check for clear
IF set = ’1’ THEN
q <= ’1’ AFTER delay ;
ELSE
q <= ’0’ AFTER delay ;
END IF;
END PROCESS;
END behav;

--****************************************************

-- Description of a edge triggered ONE SHOT
- (40 microsecond pulse)

ENTTTY shot IS
PORT ( in] : IN BIT; outl : OUT BTI‘ );
END shot;

ARCHTTECTURE behav OF shot IS
BEGIN
PROCESS (inI)
BEGIN
IF (inI’EVENT) AND (inl = ’0’) THEN
out1<= ’1’ AFTER 20 ns.
’0’ AFTER 60 ns;

END IF;

END PROCESS;
END behav;

4173

.“****************************************************

-- Description of a 10 bit Counter

ENTTTY tenbit 18
PORT (clok. clr : IN BTT; q9 : OUT BTT );
END tenbit;

ARCHTIECTURE behav OF tenbit IS

BEGIN
PROCESS (c1r.clok)
CONSTANT delay: time := 20 ns ;
VARIABLE counter: integer := 0;
BEGIN
IF (clr = ’1’) THEN
q9 <= ’0’ AFTER delay ;
counter := 0;
ELSIF (clok’EVENT) and (clok = ’0’) THEN
counter 2: counter + 1;
IF (counter = 8) THEN
q9 <= ’1’ AFTER delay ;
ELSIF (counter = 16) THEN
q9 <= ’0’ AFTER delay;
counter := 0;
END IF;
END IF;
END PROCESS;
END behav;

.“****************************************************

-- Description of a 2 bit Counter

ENTITY twbit IS '

PORT (clok. clr : IN BTT; out]. out2 : OUT BIT );
END twbit; '

use std.simulator_standard;
ARCHTIECTURE behav OF twbit IS

BEGIN
PROCESS (clr.clok)
CONSTANT delay: time := 20 ns ;
VARIABLE counter: integer := 0;
VARIABLE mem: bit := ’0’;
BEGIN
1F clr = ’1’ THEN

174

out] <= ’0’ AFTER delay;
out2 <= ’0’ AFTER delay;
ELSIF clok’EVENT and clok = ’0’ THEN
counter := counter + 1;
IF counter = 1 THEN
out] <= ’1’ AFTER delay;
out2 <= ’0’ AFTER delay;
ELSIF counter = 2 THEN
out] <= ’0’ AFTER delay;
out2 <= ’1’ AFTER delay;
ELSIF counter = 3 THEN
outl <= ’1’ AFTER delay;
out2 <= ’1’ AFTER delay;
counter := 0;
END IF;
END IF;
END PROCESS:
END behav;

-_******#**************ItIll=1!************************Illin]!!!

-- Description of the control circuit for the ADC

ENTTTY conckt IS
PORT ( conv. pulse : IN BTT; charg. discharg. Ok : OUT BIT);
END conckt;

ARCHTTECTURE conckt_struc OF conckt IS

SIGNAL start. reset. again. msb. clk : BIT;
SIGNAL 8e10, sell. dischargl. discharg2 : BTT;
SIGNAL nc. run, done. conv]. conv2 : BTT;

-- Circuit components:

COMPONENT andgate -
PORT ( in]. in2 : BTT; out] : OUT BTT );
END COMPONENT;
FOR AND]. AND2. AND3. AND4 : andgate USE ENTTTY
work.andgate(behav);

COMPONENT orgate
PORT ( in]. i112 : BTT;out1 : OUT BTT );
END COMPONENT;
FOR OR]. 0R2. 0R3 : orgate USE ENTITY work.orgate(behav);

COMPONENT dff
PORT(set:INBTT;q:OUTBIT);

175

END COMPONENT;
FOR ff : dff USE ENTTTY work.dff(behav);

COMPONENT twbit

PORT ( clok. clr : 1N BIT; outl. out2 : OUT BTT );
END COMPONENT;
FOR conctr : twbit USE ENTTTY work.twbit(behav);

COMPONENT tenbit

PORT ( clok. clr : 1N BTT; q9 : OUT BIT );
END COMPONENT;
FOR adcctr : tenbit USE ENTTTY work.twbit(behav);

COMPONENT dec

PORT ( c1. c0. clr : IN BTT; zer, one. two. thr : OUT BIT );
END COMPONENT;
FOR decoder : dec USE ENTTTY work.dec(behav);

COMPONENT shot
PORT ( in] : IN BTT; out] : OUT BIT );
END COMPONENT;
FOR oneshot : shot USE ENTTTY work.shot(behav);

COMPONENT clock
PORT ( go : 1N BTT; clok : OUT BTT );
END COMPONENT ;
FOR cktclk : clock USE ENTTTY work.clock(behav);

-- Structural details

BEGIN

OR] : orgate

PORT MAP (start. again. reset):
0R2 : orgate

PORT MAP (dischargl. discharg2. conv2);
0R3 : orgate

PORT MAP (done. convl. run);
AND] : andgate

PORT MAP (pulse. conv2. done);
AND2 : andgate

PORT MAP (convl. convl. charg):
AND3 : andgate

PORT MAP (conv2. conv2. discharg):
AND4 : andgate

PORT MAP (done. done. 0k);

176

ff : dff
PORT MAP (conv. start);

conctr : twbit
PORT MAP (msb. start. 8e10, sell);

decoder : dec
PORT MAP (sell. 8e10, start. convl. dischargl.
discharg2. nc);

adcctr : tenbit
PORT MAP (clk. reset. msb);

oneshot : shot
PORT MAP (convl. again);

cktclk : clock
PORT MAP (run. clk);

END conckt_struc;
--*******#31:************************=1!*Ilnll******************

-- A test bench to test the above circuit

ENTTTY conckt_test IS
END conckt_test;

ARCHTTECTURE behav OF conckt_test IS
COMPONENT conckt
PORT (conv. pulse : IN BTT; charg. discharg. ok : OUT BTT);
END COMPONENT;
FOR ALL : conckt USE ENTITY work.conckt(conckt_struc);

SIGNAL do, analog. integ. deinteg, opulse : BTT := ’0’;

BEGIN
tester : conckt PORT MAP (do. analog, integ. deinteg, opulse);

do <= ’1’ AFTERO us.
’0’ AFTER 40 us.
’1’ AFTER 1150 ns;

analog <= ’1’ AFTER 0 us.
’0’ AFTER 1100 us;
END behav;

BIBLIOGRAPHY

 

10

11

12

BIBLIOGRAPHY

K. Najaﬂ. ” Sensor-System Interface: the Inﬂuence of on-Chip Electronics" IEEE Int’l.
Symposium on Circuits and Systems. Phila.. PA. May 4-7. 1987. Vol. I. pp. 233-36.

P.E.M. Frere. SJ. Prosser. "Temperature Compensation of Silicon Pressure Sensors for
Automotive Applications." Sixth Int’l Conf. on Automotive Electronics. London. U.K..
Oct. 12-15. 1987. pp. 270-74.

J.R. MaIIon Jr. and RH. Grace. "Automotive Applications of Solid State Sensors and Si]-
icon Microstructures," Proc. of Sensors Expo, Detroit. MI, Sept. 15-17. 1987. pp. 395-
399.

S. Middelhoek and AC Hoogerwerf, "Smart Sensors: When and Where." Sensors and
Acmators. (Switzerland). Vol. 8. NO. 1. Sept. 1985. PP. 39-48.

J. Bryzek. "Temperature Compensation for Silicon Sensors." Mach. Des.. Vol. 56. No.
14. June 21. 1984. pp. 95-96.

B. Grant. "Pressure Sensor Applications." Proc. of Sensors Expo. Detroit. MI. Sept. 15-
17. 1987. pp. 297-303.

T. Ishihara. K. Suzuki. and M. Hirata. "CMOS Integrated Silicon Pressure Sensor." Proc.
IEEE Custom Integrated Circuits Conf.. May 1986. pp. 34-37.

E. Obermeier. "Polysilicon Layers Lead to a New Generation of' Pressure Sensors." Proc.
Int’l. Conf. on Solid State Sensors and Actuators. Phila. . 1985. pp. 430-433.

J.E. Gragg. W.B. McCulley. W.B. Newton. and CE. Derrington, "Compensation and
Calibration of a Monolithic Four Terminal Silicon Pressure Transducer." IEEE Solid-state
Sensors Conf.. Hilton Head Island. SC. June 1984. pp. 21-27.

H. Tanigawa. T. Ishihara. M. Hirata. and K. Suzuki. "MOS Integrated Silicon Pressure
Sensor." IEEE Trans. Electron Devices. Vol. ED-32. No. 7. July 1985. pp. 1191-1195.

G. Kowalski. "Miniature Pressure Sensors and their Temperature Compensation." Sensors
and Actuators (Switzerland). Vol. 11. No. 4. May-June 1987. pp. 367-76.

S. Weatherwax. "Automotive Tire Pressure Sensing." Proc. of Sensors Expo. Detroit. MI.
Sept. 15-17. 1987. pp. 379-384.

177

 

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

178

"I989 Solid-State Sensor Handbook." Sensym. Inc.. Sunnyvale. CA.

R.E. Brown. and D.M. Koglin. "Bipolar Integrated Pressure Transducer." IEEE Solid
State Sensor and Actuator Workshop. Hilton Head Island. SC. June 6-9. 1988. pp. 106.

C. Gross. and T. Worst. "Intelligent Interface for Electronic Pressure Sensors." WES-
CON/87 Conf. Record. San Francisco. CA, Nov. 18-20 1987. pp. 24/3 1-6.

P. Kopsytynski and E. Obermeier. "An Interchangeable Silicon Pressure Sensor with On-
chip Compensation Circuitry." Sensors & Actuators (Switzerland). Vol 18. No. 3-4, 1989.
pp. 239—45.

K.W. Lee. "Modeling and Simulation of Solid-State Pressure Sensors." Ph.D. Disserta-
tion. University of Michigan. Ann Arbor. MI. 1982.

J.H. Huijsing. "Signal Conditioning on the Sensor Chip." Sensors & Actuators (Switzer-
land), 10 (1986). pp. 219-237.

S. Kim and K.D. Wise. "Temperature Sensitivity in Silicon-piezoresistive Pressure Trans-
ducers." IEEE Trans. Electron Devices, Vol. ED-38. No. 7. July 1983. pp. 802-810.

R.E. Bicking. "A Piezoresistive Integrated Pressure Transducer." 3rd lnt’l. Conf. on
Automotive Electronics. 1981. pp. 21-26.

"Speciﬁer’s Guide for Pressure Sensors." Honeywell. Inc.. Micro Switch Division.
Freeport. IL. Catalog 15. Issue 4.

J. Bryzek. R. Mayer. and P. Barth. "New Generation of Disposable Blood Pressure Sen-
sors with Digital On-chip Laser Trimming." IEEE Solid State Sensor and Actuator
Workshop. Hilton Head Island. SC. June 6-9. 1988. pp. 121-122.

W.H. KO. J. Hynecek. and SF. Boettcher. "Development of a Miniature Pressure Trans-
ducer for Biomedical Applications." IEEE Trans. Electron Devices. Vol. ED-26. No. 12.
Dec. 1979. pp. 1896-1905.

J.M. Borky and K.D. Wise. "Integrated Signal Conditioning for Silicon Pressure Sen-
sors." IEEE Trans. Electron Devices. Vol. ED-26. No. 12. Dec. 1979. pp. 1906-1910.

0. Tabata. H. Inagaki. and 1. lgarashi. " Monolithic Pressure-Flow Sensor." IEEE Trans.
Electron Devices. Vol. ED-34. No. 12. Dec. 1987. pp. 2456-62.

K.D. Wise. "Intelligent Sensors for Semiconductor Process Automation." Proc. Int’l.
Conf. on Industrial Electronics. Control. and Instrumentation (IECON). Milwaukee. WI.
Sept. 1986. pp. 213-217.

R. Allen. "Solid-state Sensors" Electron Des.. V01. 34. No. 26. Nov. 13. 1986. pp. 71-
80.

28

29

30

31

32

33

35

36

37

38

39

40

41

179

"Advances in VLSI Stimulate Solid-state Sensors Market." New Electron.. (GB). Vol. 19.
No. 16. Aug. 1986. pp. 45-50.

C.D. Fung and W.H. KO, "Integrated Solid-State Sensor Research at Case Western
Reserve University." CECON 1983 Record. Cleveland Electrical/Electronics Conf. and
Exposition. Cleveland. Oct 1983.

TS]. Lammerink and W. Wlodarski. "Integrated Thermally Excited Resonant Diaphragm
Pressure Sensor." Proc. Int’L Conf. on Solid State Sensors and Actuators. Phila.. 1985.
pp. 97-100.

A. Hanneborg, T.E. Hansen. P.A. Ohlckers. E. Carlson. B. Dahl, and O. Holwech. "A
New Integrated Capacitive Pressure Sensor with Frequency Modulation Output," Proc.
Int’l. Conf. on Solid State Sensors and Actuators. Phila.. 1985. pp. 186-188.

J. Neumeister. G. Schuster. and W. Von Munch. "A Silicon Pressure Sensor using MOS
Ring Oscillators." Sensors and Actuators. (FRG). Vol. 7. 1985. pp. 167-176.

R]. Schubert and J.H. Nevin. "A Polyimide Based Capacitive Humidity Sensor." IEEE
Trans. Electron Devices. Vol. ED-32. No. 7. July 1985. pp. 1220-23.

S. Sugiyarna. T. Suzuki. K. Kawahata. and K. Shimaoka. "Micro-diaphragrn Pressure
Sensor." IEEE Int’l. Electron Devices Meeting. 1986. pp. 184-187.

K. Suzuki. T. Ishihara. M. Hirata. and H. Tanigawa. " Nonlinear Analysis of a CMOS
Integrated Silicon Pressure Sensor." IEEE Trans. Electron Devices. Vol. ED-34. No. 6.
June 1987. pp. 1360-67.

P.J. French. A.P. Dorey. "Frequency Output Piezoresistive Pressure Sensors." Sensors &
Actuators (Switzerland). Vol. 4. 1983. pp. 77-83.

R. Frank. "Designing with Semiconductor Pressure Sensors." Machine Design. Vol. 57.
No. 21. Nov. 21. 1985. pp. 103-07.

H. Reimann. "Sensing Pressure with Silicon Crystals." Control and Instrumentation. Vol.
18. No. 6. June 1986, pp. 107-111.

G. Morton. "Integrated Pressure Sensors in Acoustics." Electron and Wireless World
(GB). Vol. 92. No. 1607. Oct. 1986. pp. 40—41.

T. Onnond. "Pressure Sensors and Transducers." EDN. Aug. 4. 1988. pp. 106-118.

B. Minhang and Y. Wang. "Analysis and Design of a Four Terminal Silicon Pressure
Sensor at the Center of'Diaphragm." Sensors and Actuators (Switzerland). VOL 12, No.
1. July 1987. pp. 45-56.

42

43

45

46

47

48

49

50

51

52

53

54

55

180

J. Binder. K. Becker, and G. Ehrler, "Silicon Pressure Sensors for the Range 2KPa to
40MPa 1." Siemens Components (England Ed.). Germany. Vol. 20. No. 2, April 1985.
pp. 6407.

SA. Loth. "Picking the Perfect Pressure Transducer." Intech. Vol. 35. No. 7. July 1988.
pp. 37-40.

K.D. Wise. "The Role of Thin Films in Integrated Solid-state Sensors." Jour. Vac. Sci.
and Tech., Vol. 4, No. 3. May-June 1986. pp. 617-622.

MR. Huskard. "General Purpose Intelligent Sensors." Microelectron. Jour. (GB). Vol.
17. No. 5. Sept-Oct. 1986. pp. 9-14.

K.E. Petersen. "Silicon Sensor Technologies." IEEE Int’l. Electron Devices Meeting.
Washington. DC. 1985.

RB. Brown. R.J. Huber. D. Petelenz. and J. Janata. "An Integrated Multiple-sensor
Chemical Transducer." Proc. Int’l. Conf. on Solid State Sensors and Actuators. Phila..
1985. pp. 125-127.

C. Wen. TC Chen. and LN. Zemel. "Gate-controlled Diodes for Ionic Concentration
Measurement." IEEE Trans. Electron Devices. Vol. ED-26. No. 12. Dec. 1979. pp.
1945-1951.

T. Ifo. H. Inagaki and I. Igarashi, "ISFET’s with 1011 Sensitive Membranes Fabricated by
Ion Implantation." IEEE Trans. Electron Devices, Vol. ED-35. NO. 1. Jan. 1988. pp. 56-
64.

PJ. Burt. "A Pyramid ’Smart Sensor’ for Machine Vision." Topical Meeting on Machine
Vision. Technical Digest Series. Opt. Soc. America. Vol. 12, March 1987.

J.M. Giachino. "Smart Sensors for Automotive Applications." Proc. of the 16th Int’l.
Symposium on Automotive Technology and Automation. Thermotech. Assoc., Tuscany
Univ.

A.R. Cooper and J.E. Brignell. "An Integrated Circuit Silicon Sensor for Magnetic
Fields." Jour. Inst. Electron. and Radio Eng.. (GB). Vol. 55, No. 7-8. July-Aug. 1985. pp.
263-267.

J.E. Brignell. "Interfacing Solid State Sensors with Digital Systems." Jour. of Physics
(GB). Vol. 18. No. 7. 1985. pp. 559-65.

T. Usuki. S. Sugiyarna. M. Takeuchi, T. Takeuchi, and I. Igarashi, "Integrated Magnetic
Sensor." Proc. 2nd Japanese Sensor Symposium. 1982. pp. 215-217.

V. Zieren and B.P.M. Duyndam. "Magnetic-ﬁeld-sensitive Multicollector n-p-n Transis-
tors." IEEE Trans. Electron Devices. Vol. ED-29. Jan. 1982. pp 83-90.

 

56

57

58

59

60

61

62

63

65

66

67

68

69

181

S. Kordic and RI. Munter. "Three-Dimensional Magnetic-Field Sensors." IEEE Trans.
Electron Devices. V01. 35. No. 6. June 1985. pp. 771-779.

J.M. Giachino. "Smart Sensors." Sensors and Actuators. (Switzerland). Vol. 10. No. 3-4.
Nov.-Dec. 1986, pp. 239-248.

W. Benecke. L. Csepregi. A. Heuberger. K. Kuhl. and H. Seidel. "A Frequency-selective.
Piezoresistive Silicon Vibration Sensor," in Proc. Int’l. Conf. on Solid State Sensors and
Actuators. Phila.. 1985. pp. 105-108.

A.P. Andrews. P.L. Chen and RS. Muller. "Integrated Silicon PI-FET Accelerometer
with Proof Mass." Sensors and Actuators. Vol. 5. 1984. pp. 119-126.

W.D. Frobenius. S.A. Zeitman. M.H. White. D.D. O’Sullivan. and RC. Hamel.
"Microminiature Ganged Threshold Accelerometers: Compatible with Integrated Circuit
Technology." IEEE Trans. Electron Devices. Vol. ED-19. I972.

L.M. Roylance and J .B. Angel]. "A Batch Fabricated Silicon Accelerometer," IEEE
Trans. Electron Devices. Vol. ED-26. No. 12. Dec. 1979. pp. 1911-1917.

B. Puers. L. Reynaert. W. Snoeys. and W.M. Sansen. "A New Uniaxial Accelerometer in
Silicon Based on the Piezojunction Effect." IEEE Trans. Electron Devices. Vol. 35. No.
6. June 1985. pp. 764-770.

J.L. Davidson. "Silicon Accelerometer Technology," Proc. Int’l. Conf. on Industrial
Electronics, Control and Instrumentation (IECON). Milwaukee. WI. Sept. 1986. pp. 218-
22.

F. Rudolf. "A Micromechanical Capacitive Accelerometer with a Two Point Inertial Mass
Suspension." Sensors and Actuators. (Switzerland), Vol. 4. 1983, pp. 191-198.

P. Chen. et al.. "Integrated Silicon Microbeam PI-FET Accelerometer," IEEE Trans. Elec-
tron Devices. Vol. ED-29. 1982. pp. 27-33. 1

SC. Tzafestas. "Integrated Sensor Based Robot System." Proc. of 25th IEEE Conf. on
Decision and Control. Athens. Greece. Dec. 1986.

K. Petersen. C. Kowalski. J. Brown, H. Allen, and J. Knutti. "A Force Sensing Chip
Designed for Robotic and Manufacturing Automation Applications." Proc. Int’l. Conf. on
Solid State Sensors and Actuators. Phila.. 1985, pp. 3032.

K. Chun and K.D. Wise. "A High-performance Silicon Tactile Irnager Based on a Capa-
citive Cell," IEEE Trans. Electron Devices. Vol. ED-32. No. 7. July 1985. pp. 1196-
1201.

D.L. Polla. W.T. Chang. R.S. Muller. and RM. White. " Integrated Zinc-on-Silicon
Tactile-Sensor Array." IEEE Int’l. Electron Devices Meeting. Washington. D. C.. Dec 1-

 

70

71

72

73

74

75

76

77

78

79

80

81

82

182

4. 1985. pp. 133-36.

B. Tise. "A Compact High Resolution Piezoresistive Digital Tactile Sensor." IEEE Int’l.
Conf. on Robotics and Control. April 24-29. 1988. Phila.. PA. pp. 760-64.

C.S. Vaidyanathan and H.C. Wood. "A New Tactile Sensing System." IEEE Int’l. Conf.
on Robotics and Control. April 24-29. 1988, Phila.. PA, pp. 1311-12.

H. Wohltjen and A. Snow. "The Selective Detection of Vapors Using Surface Acoustic
Wave Devices." Proc. Int’l. Conf. on Solid State Sensors and Actuators. Phila.. 1985. pp.
66-70.

A.J. Polak. A.J. Beuhler. and S. Petty-Weeks. "Hydrogen Sensors Based on Protonic
Conducting Polymers." Proc. Int’l. Conf. on Solid State Sensors and Actuators. Phila.
1985. pp. 85-88.

S.C. Chang and DB. Hicks. "Tin Oxide Microsensor." Proc. Int’l. Conf. on Solid State
Sensors and Actuators. Phila.. 1985. pp. 381-384.

W. Mokwa. D. Kohl. and G. Heiland. "An Arsine Monitoring Device Using an SnOx
Thin Film." Proc. Int’l. Conf. on Solid State Sensors and Actuators. Phila. 1985. pp.
389-392.

T.L. Poteat and B. Lalevic. "Transition Metal-gate MOS Gaseous Detectors," IEEE
Trans. Electron Devices. Vol. ED-29. Jan. 82. pp. 123-129.

S.C. Terry. J.H. Jerman. and J.B. Angel]. "A Gas Chromatograph Air Analyzer Fabri-
cated on a Silicon Wafer." IEEE Trans. Electron Devices. Vol. ED-26, No. 12. Dec.
1979. PP. 1880-1886.

G.J. Maclay. "MOS Hydrogen Sensors with Ultrathin Layers of Palladium." IEEE Trans.
Electron Devices, Vol. ED-32, No. 7. July 1985. pp. 1158-1164.

K. Dobos and G. Zimmer. "Performance of Carbon Monoxide-sensitive MOSFET’s with
Metal-oxide Semiconductor Gates." IEEE Trans. Electron Devices. Vol. ED-32. No. 7.
July 1985. pp. 1165-1169..

S. Tsuchitani. T. Sugawara. N. Kinjo, and S. Ohara. "Humidity Sensor Using Ionic
Copolymer." Proc. Int’l. Conf. on Solid State Sensors and Actuators. Phila.. 1985. pp.
210-212.

M. Hijikigawa, T. Sugihara. J. Tanaka. and M. Watanabe. "Micro-chip F'E‘T Humidity
Sensor with a Long-term Stability." Proc. Int’l. Conf. on Solid State Sensors and Actua-
tors. Phila.. 1985. pp. 221-224.

K. E. Peterson, "Silicon as a Mechanical Material." Proc. of the IEEE. Vol. 70. No. 5.
May 1982. pp. 420-457.

 

83

84

85

86

87

88

89

90

91

92

93

95

96

183

P. Bergveld. "The Impact of MOSFET Based Sensors." Proc. Int’l. Conf. on Solid State
Sensors and Actuators. Phila.. 1985. pp. 142-143.

H. Preier. "Solid-state Sensors for Gas Analysis." Process Automation (Gen). No. 1.
1983. pp. 29-33.

R. Muller, E. Lange. and A. Hinterstocker. "Multidimensional Sensors for Gas Analysis."
Proc Int’l. Conf. on Solid State Sensors and Actuators. Phila.. 1985. pp. 81-84.

N. Yamazoe and T. Seiyarna. "Sensing Mechanism of Oxide Semiconductor Gas Sen-
sors." Proc. Int’l. Conf. on Solid State Sensors and Actuators, Phila.. 1985. pp. 376-379.

A.A. Sarnan and P. Bergreld. "A Classiﬁcation of Chemically Sensitive Semiconductor
Devices." Sensors and Actuators, Netherlands. No. 7. 1985. pp. 75-87.

S.D. Senturia. "Role of MOS Structure in Integrated Sensors." Sensors and Actuators.
(Switzerland), Vol. 4. No. 4. Dec. 1983. pp. 507-526.

2. Li and SJ. Fonash. "A High Sensitivity Solid State Sensor for H2 Detection in
Oxygen-rich Ambients at Room Temperature." IEEE Int’l. Electron Devices Meeting.
Washington. DC. Dec. 1-4 . 1985.

R.T. Howe. R.S. Muller. K.J.Gabriel. and W.S.N. Trimmer. "Silicon Micnnechanics:
Sensors and Actuators on a Chip." IEEE Spectrum. Vol. 27, No. 7. July 1990. pp. 29-35.

S. Middelhoek. and S. A. Audet. "Silicon sensors: full of promises and pitfalls." Jour. of
Physics B. Vol. 20. no. 9. Sept. 1987. pp. 1080-86.

K. Dobos and G. Zimmer. "A New Split Gate MOS Transistor Structure for Detection
Gases." Proc. lnt’l. Conf. on Solid State Sensors and Actuators. Phila.. 1985. pp. 242-
244.

P.W. Barth and J .B. Angel]. "Thin Linear Thermometer Arrays for Use in Localized
Cancer Hypertherrnia," IEEE Trans. ElectronDevices. Vol. ED-29. Jan. 1982. pp. 144-
150.

G. Chen and J.N. Zemd. "Temperature Dependence of Gate-controlled Portion of Ion-
controlled Diodes." IEEE Trans. Electron Devices. Vol. ED-29. Jan. 1982. pp. 115-123.

S.L. Garverick and SD. Senturia. "An MOS Device for AC Measurement of Surface
Impedance with Application to Moisture Monitoring.” IEEE Trans. Electron Devices.
Vol. ED-29. Jan. 1982. pp. 90-94.

U.J. Kroll and M. Thompson. . "The Lipid Membrane as a Selective Chemical Trans-
ducer." IEEE Trans. Electron Devices. Vol. ED-32. No. 7. July 1985. pp. 1180-1184.

 

97

98

99

100

101

102

103

104

105

106

107

108

109

184

H. Wohltjen. W.R. Barger. A.W. Snow. and N.L. Juruis. "A Vapor-sensitive Chemistor
Fabricated with Planar Microelectrodes and a Langmuir-Blodgett Organic Semiconductor
Film." IEEE Trans. Electron Devices, Vol. ED-32. No. 7. July 1985. pp. 1170-1174.

S.K. Clark and K.D. Wise. "Pressure Sensitivity in Anisotropically Etched Thin-
diaphragrn Pressure Sensors." IEEE Trans. Electron Devices. Vol. ED-26, No. 12. Dec.
1979. pp. 1887-1896.

K.E. Petersen. P. Barth. J. Poydock. J. Brown. J. Mallon Jr.. J. Bryzek. "Silicon Fusion
Bonding For Pressure Sensors." Int’l. Electron Devices Meeting. 1988.

D.L. Polla. R.M. White. and RS. Muller. "Integrated Chemical-reaction Sensor." Proc.
lnt’l. Conf. on Solid State Sensors and Actuators. Phila.. 1985. pp. 33-36.

M. Hirata. S. Suwazono. and H. Tanigawa. "A Silicon Diaphragm Formation for Pressure
Sensor by Anodic Oxidation Etch-810p," Proc. Int’l. Conf. on Solid State Sensors and
Actuators. Phila.. 1985. pp. 287-290.

H. Guckel and D.W. Bums. "Fabrication Techniques for Integrated Sensor Microstruc-
tures." Int’l. Electron Devices Meeting. Los Angeles. Dec. 1986.

K. Suzuki. T. Ishihara. M. Hirata. and H. Tanigawa. "Nonlinear Analyses on CMOS
Integrated Silicon Pressure Sensor." Int’l. Electron Devices Meeting. 1985. pp. 137-140.

E.R.Peake. A.R.Zias. and J.V.Egan. "Solid-state digital pressure transducer." IEEE Trans.
Electron Devices. ED-I6. no. 10. Oct. 1969. pp. 870-76.

M. Poppinger. "Silicon Diaphragm Pressure Sensors." 15th European Solid State Device
Research Conf.. Aachen. Germany. Sept. 9-12. 1985. (Amsterdam. Netherland: Elsevier
1986) pp. 53-70.

J. Binder. G. Ehrler, K. Heimer. B.Krisch. and M. Poppinger. "Silicon Pressure Sensors
for the 2KPa to 40MPa Range." Siemens Forschungs- und Entwicklungsberichte (Ger-
many). Vol. 13. No. 6. 1984. pp. 294-302.

A.Yasukawa. S.Shimada. Y.Matsuoka. and Y.Kanda. "Design Considerations for Silicon
Circular Diaphragm Pressure Sensors." Japanese Jour. of Applied Physics. Vol. 21. No.
7. July 1982. pp. 1049-1052.

S. Sugiyarna. H. Funabashi. S. Yarnashita. M. Takigawa. and I. Igarashi, "Nonlinear
Temperature Characteristics in Silicon Piezoresistive Pressure Sensors," Proc. 5th Sensor
Symposium. Tsukuba. Ibaragi. Japan, 1985. pp. 103-107.

S. Sugiyarna. M. Takigawa. and I. Igarashi, "Integrated Piezoresistive Pressure Sensor
With Both Voltage and Frequency Output." Sensors & Actuators (Switzerland). Vol. 4.
no. . 1983. pp. 113-120.

 

110

111

112

113

114

115

116

117

118

119

120

121

122

123

185

W.J. Orvis. C.F. Mc Conaghy. D.R. Ciarlo. J.H. Yee. and E.W. Hee. "Modeling and
Fabricating Micro-cavity Integrated Vacuum Tubes," IEEE Trans. Electron Devices. V01.
36. No. 11. Nov. 1989. DP. 2651-2658.

R.S. Lee. C. Patel. H.A. Williams. and NA. Cade. "Semiconductor Fabrication Technol-
ogy Applied to Micrometer Valves." IEEE Trans. Electron Devices. Vol. 36, No. 11.
Nov. 1989. pp. 2703-2708.

M. Mehregany. K.G. Gabriel. and W.S.N. Trimmer. "Integrated Fabrication of Polysili-
con Mechanisms." IEEB Trans. Electron Devices. Vol. 35. No. 6. June 1988. pp. 719-
723.

L. Fan. Y. Tai. and RS. Muller. "Integrated Moveable Structures for Sensors and Actua-
tors." IEEE Trans. Electron Devices. Vol. 35, No. 6. June 1988. pp. 724-730.

K.D. Wise. "Circuit Techniques for Integrated Solid-state Sensors." IEEE 1983 Custom
Integrated Circuits Conf.. Rochester, NY. May 1983.

J. Bryzek. "Temperature Compensation for Silicon Sensors," Mach. Des.. Vol. 56, No.
14. June 21. 1984. pp. 95-96.

W.J. Lian and S. Middelhoek. "Flip-ﬂop Sensor - A New Class of Silicon Sensors." Int’l.
Conf. on Solid State Sensors and Actuators. Phila.. June 1985. pp. 45-48.

SAE Int’l. Congress and Exposition (1984: Detroit, Mich). "Sensors & Actuators".

W.G. Wolber. "Smart Sensors." Proc. 9th IMEKO Congress of the Int’l. Measurement
Confederation. Berlin. Germany. May 1982. pp. 24-28.

J. Bryzek. "Modeling Performance of Piezoresistive Pressure Sensors." Proc. Int’l. Conf.
on Solid State Sensors and Actuators. Phila.. 1985. PP. 168-173.

M.W. Hauser and R.W. Brodersen. "Circuit and Technology Considerations for MOS
Delta-Sigma AID Converters." IEEE 1986 Int’l Symposium on Circuits and Systems.
Vol. 3. San Jose, California. May 5-7, 1986. pp. 1310-15.

M. McMaster and M. Driels. "Intelligent Sensor System Communication for Robot
Workcell Integration." Int’l. Jour. of Adv. Manuf. Tech., (GB). Vol. 1. No. 3. May 1986.
pp. 19-33.

R.B. Brown. F.L. Terry and KC. Wu. "High Temperature Microelectronics-expanding
the Applications for Smart Sensors". Int’l Electron Devices Meeting 87. pp. 274-77.

R.B. Brown. K.C. Wu. M. Ghezzo. and D.M. Brown, "A CMOS Process For High Tem-
perature Sensors and Circuits. " IEEE Solid State Sensor and Actuator Workshop. Hilton
Head Island. SC. June 6-9. 1988. pp. 117-118.

 

124

125

126

127

128

129

130

131

I32

133

I34

I35

136

137

138

186

K. Lee and K.D. Wise. "SENSIM: A Simulation Program for Solid-State Pressure Sen-
sors.” IEEE Trans. Electron Devices. Vol. ED-29. No. 1. Jan. 1982. pp. 34-41.

O.N. Tufte. P.W. Chapman. and D. Long. "Silicon Diffused-Element Piezoresistive
Diaphragms." Jour. of Applied Physics, Vol. 33. Nov. 1962. pp. 3322-3327.

N. Najaﬁ. K.W. Clayton. W. Baer. K. Najaﬂ. and K.D. Wise. " An Architecture and
Interface for VLSI Sensors. " IEEE Solid State Sensor and Actuator Workshop. Hilton
Head Island. SC. June 6-9. 1988. pp. 76-79.

P.C. Tack and D. Mei. "Finite Element Modeling of Pressure Sensor Structures." Proc. of
Sensors Expo. Detroit. MI. Sept. 15-17. 1987. pp. 285-290.

P.H. Peykov and RD. Lazarov. "Modeling and Investigation by Simulation of Semicon-
ductor Pressure Sensors," Bulgarian Jour. of Physics (Bulgaria). VOL 14. No. 6. 1987. pp.
530—41.

P.C. Tack. "Finite Element Modeling of Silicon Pressure Sensor Structures." WES-
CON/87 Conf. Record. San Francisco. CA. Nov. 18-20 1987. pp. 24/2 1-5.

O.N. Tune and EL. Steltzer. "Piezoresistive Properties of Silicon Diffused Layers." Jour.
of Applied Physics. Vol. 34. No. 2, Feb. 1963. pp. 313-18.

Y. Kanda. "A Graphical Representation of Piezoresistance Coefﬁcients in Silicon." IEEE
Trans. Electron Devices. Vol. ED-29. NO. 1. Jan. 1982. pp. 64-70.

C.S Smith, "Piezoresistive Effects in Germanium and Silicon." Phys. Rev., Vol. 94.
April 1954. pp. 42-49.

H.R. Camenzind. "Electronic Integrated System Design." Van Nostrand Reinhold Com-
pany, New York. 1976.

DJ. Hamilton and W.G. Howard. "Basic Integrated Circuit Engineering." McGraw-Hill.
Inc.. USA.

Motorola. Inc. (RM Warner. Jr.. and J.N. Fordemwalt. eds): "Integrated Circuits:
Design Principles and Fabrication." McGraw-Hill Book Company. New York. 1965.

J. Millman. and C. Halkias, "Integrated Electronics: Analog and Digital Circuits and Sys-
tems." McGraw-Hill Book Company. New York. 1979.

RE. Allen. and DR. Holberg. "CMOS Analog Circuit Design." Holt. Rinehart and Wins-
ton. Inc.. New York. NY. 1987.

GM. Glassford. "Analog Electronic Circuits." Prentice-Hall. Englewood Cliffs. N.J..
I986.

 

187

139 RC. Gregorian. and CC. Tames. "Analog MOS Integrated Circuits for Signal Process-
ing." John Wiley & Sons Inc.. New York. 1986.

140 W.J. Tompkins. and JG. Webster. "Interfacing Sensors to IBM PC." Prentice-Hall.
Englewood Cliffs. N.J.. I987.

141 "PSpice Library of Linear ICs." Microsim Corporation. Dec. 1989.