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LIBRARY
Michigan Qtate
University

 

 

 

This is to certify that the
thesis entitled

A Self Tuning Electromagnetic Shutter

presented by

Raoul Ouatagom Ouedraogo Jr.

has been accepted towards fulfillment
of the requirements for the

 

 

 

 

MS. degree in Electrical Engineerm
Méjgfi’rofessor’s Signature
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5/08 KlProj/AodPreleIRC/Daleoue indd

A Self Tuning Electromagnetic Shutter
By

Raoul Ouatagom Ouedraogo Jr.

A THESIS

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

MASTER OF SCIENCE
Electrical Engineering

Department of Electrical and Computer Engineering

2008

ABSTRACT

A Self Tuning Electromagnetic Shutter
By

Raoul Ouatagom Ouedraogo Jr.

A self-tuning electromagnetic shutter (STEMS) is a slotted metallic surface with
computer-controlled switchable shorting wires placed across the slots. By opening
and closing the shorting wires, the transmissitivity of the surface may be adjusted.
In particular, the surface may be placed into open and closed states, creating an
electronically-controllable iris. Since the states of the switches needed to create a
selected transmissitivity depend on frequency, a binary search technique, such as a
genetic algorithm, is used to find an acceptable state. A feedback signal, such as
from a receiving probe, is used to judge whether a given state produces the desired
behavior.

To investigate the feasibility of STEMS, and to study its dependence on frequency,
polarization, and angle of incidence, the STEMS is used to seal the opening to a
cubical box containing a monopole antenna. The monopole is used as a receiving
probe to measure the coupling from an incident electric field into the box. A closed
STEMS is sought by minimizing the field entering the box, while an open STEMS is

sought by maximizing the received field.

To my parents and my wife: Justin, Charlotte & Clarice Ouedraogo

iii

ACKNOWLEDGMENTS

There are many people who deserve acknowledgment for both the work contained
in this thesis, and the countless other things that I was able to be involved in through-
out my first two years at Michigan State University. First and foremost, a special
thanks to Dr. E. Rothwell for being a very resourceful and exceptional adviser, and
also for always making time to help and provide guidance to your students. Thanks
to Dr. B. Shanker and Dr. L. Campbell for all your helpful inputs and for agreeing
to serve on my masters committee.

A thank you is also in order for Gary Dexter and my classmates Lynn (3., Michael
A., Nate K. and Rodolph S. for cheering me up and supporting me throughout the
two years. A big thank you to Brian G., Chien .H and Andrew T. for helping me with
the experimental set up and assisting me with the codes. Thank you to Dr. John
E. Ross, for allowing me to use GA-NEC for my simulations and also for providing
helpful input. Another thank you to the MSU ECE shop for fabricating the STEMS.

A special acknowledgment to my parents, Justin and Charlotte 0., for their
tremendous sacrifice to get me where I am, and for their unconditional love and
support. Also to my in-laws and Ms. Julie K. who have loved and supported me
as their own throughout my studies. My deepest gratitude is reserved for my wife,
Clarice 0., who has always been understanding and supportive of me throughout my
studies. Without your help and support, all this would not have been possible. You

are my angel and I love you with all my heart.

iv

TABLE OF CONTENTS

LIST OF TABLES ................................. vii

LIST OF FIGURES ................................ viii

KEY TO SYMBOLS AND ABBREVIATIONS ................. xv
CHAPTER 1

Introduction ..................................... 1
CHAPTER 2

Concept And Theory ................................ 3

2.1 Introduction ................................ 3

2.2 ST EMS design concept .......................... 4

2.3 Self Tuning Electromagnetic Shutter Template ............. 7

2.4 Box and Probe .............................. 9

2.5 Receiver .................................. 11

2.6 Microprocessor .............................. 11

2.7 Search Algorithm ............................. 12

2.8 Literature Review ............................. 12

2.9 Conclusion ................................. 18
CHAPTER 3

NEC4 Overview and Box Design ......................... 19

3.1 Introduction ................................ 19

3.2 NEC4 Modeling Guidelines ........................ 22

3.3 Box Design ................................ 28

3.4 Conclusion ................................. 49
CHAPTER 4

STEMS Template Design and Simulation Results ................ 50

4.1 Introduction ................................ 50

4.2 GA-NEC Overview and Switch Model ................. 50

4.2.1 GA-NEC Overview ........................ 50

4.2.2 Genetic Algorithm ........................ 51

4.2.2.1 Encoding Parameters .................. 54

4.2.2.2 Initial Population .................... 54

4.2.2.3 Evaluating the Fitness ................. 54

4.2.2.4 Mating Pool selection ................. 54

4.2.2.5 Crossover ........................ 55

4.2.2.6 Mutate and Fill Next Generation ........... 56

4.2.2.7 Stopping Criteria .................... 56

4.2.3 Switch model ........................... 56

4.3 Initial Design Approach and Observations ............... 57

4.4 Slot STEMS Design and Simulation Results .............. 63

4.4.1 Slot STEMS Template ...................... 63
4.4.2 Slot STEMS Simulation Results ................. 66
4.4.2.1 Results at 625MHz ................... 75
4.4.2.2 Results at 650MHz ................... 80
4.4.2.3 Results at 675MHz ................... 84
4.4.2.4 Results at 700MHz ................... 88
4.4.2.5 Results at 725MHz and 750MHz ........... 92
4.4.2.6 Study of shutter effectiveness with reference to loca-
tion within the box .................. 99
4.5 Conclusion ................................. 103
{CHAPTER 5
Measurement set-up and and results ....................... 104
5.1 Design and fabrication of STEMS prototype .............. 104
5.2 Open box and probe fabrication ..................... 115
5.3 Experiment Set Up ............................ 117
5.4 Evaluating the STEMS shutter effectiveness .............. 124
5.5 Measurement results ........................... 125
5.5.1 Random Search .......................... 128
5.5.2 Genetic Algorithm ........................ 162
5.5.3 STEMS optimized using a GA for an oblique incidence angle 199
5.6 Conclusion ................................. 205
CHAPTER 6
Conclusion and Future Work ........................... 206
6.1 Conclusion ................................. 206
6.2 Fixture Work ................................ 207
APPENDIX A
CODES ....................................... 210
A1 Visual Basic Source Code ........................ 210
A11 Random Search .......................... 210
A12 Genetic Algorithm: Closed STEMS ............... 214
A13 Genetic Algorithm: Open STEMS ................ 222
A2 Matlab Code ............................... 230
A21 Random Search Histogram, histogramm ............ 230
A22 GA Nec Switch State Histogram, gaNecHisto.m ........ 232
BIBLIOGRAPHY ................................. 237

vi

Table 3.1

Table 3.2

Table 3.3

Table 4.1

Table 4.2

Table 4.3

Table 4.4

Table 4.5

Table 4.6

Table 4.7

Table 4.8

Table 4.9

Table 4.10

Table 4.11

Table 5.1

Table 5.2

LIST OF TABLES

Description of the field used to excite the box ............

Best % ratios and their respective box effectiveness.

Description of the two waves used to excite the boxes.

Wire STEMS loop dimensions.

Description of the two waves used to excite the boxes.

Characteristics of the probe and box .................

Parameters used to set the genetic algorithm.

Genetic algorithm set-up for slot STEMS.

ooooooooooooo

Slot STEMS wire segments and radii characteristics.

Description of the normal and oblique incident waves ........

Closed STEMS best switch configurations: normal incidence angle.

Closed STEMS best switch configurations: oblique incidence angle.

Open STEMS best switch configurations: normal incidence angle.
Open STEMS best switch configurations: oblique incidence angle.

Patch Sizes ...............................

Properties of Coto technology SIP REED relay switch. ......

vii

30

37

37

59

62

62

62

68

68

68

70

71

72

73

107

107

Figure 2.1

Figure 2.2

Figure 2.3

Figure 2.4

Figure 2.5

Figure 3.1

Figure 3.2

Figure 3.3

Figure 3.4

Figure 3.5

Figure 3.6

Figure 3.7

Figure 3.8

Figure 3.9

Figure 3.10

Figure 3.11

LIST OF FIGURES

Images in this thesis are presented in color

Block Diagram of STEMS ......................
Self Tuning Electromagnetic Shutter ................
Box with probe covered by a STEMS ................
Frequency Selective Surface .....................
Self Structuring Antenna .......................
Box with top open ..........................
Box with top covered by a STEMS .................
Wire segmentation ..........................
Thin Wire Approximation error ..................
Equal Area Rule Representation ...................
Total E—field of box designed using the EAR ............
Box Effectiveness with different ratios of %— at 750M Hz.

Box Effectiveness with varying %— at 750MHz and 725MHz.

Box Effectiveness with varying % at 725MHz and 700MHz.

Box Effectiveness with varying % at 700MHz and 675MHz.

Box Effectiveness with varying %— at 675MHz and 650MHz.

viii

10

16

17

20

21

25

27

31

34

35

38

39

40

Figure 3.12

Figure 3.13

Figure 3.14

Figure 3.15

Figure 3.16

Figure 3.17

Figure 3.18

Figure 3.19

Figure 4.1

Figure 4.2

Figure 4.3

Figure 4.4

Figure 4.5

Figure 4.6

Figure 4.7

Figure 4.8

Figure 4.9

Figure 4.10

Figure 4.11

Box Effectiveness with varying % at 650MHz and 625MHz.

Box Effectiveness ...........................
Box effectiveness for %—=6.37 for both normal and oblique waves
Box effectiveness for %—=6.17 for both normal and oblique waves
Box effectiveness for %—=5.94 for both normal and oblique waves
Box effectiveness for %-=5.76 for both normal and oblique waves
Box effectiveness for %=5.6 for both normal and oblique waves .
Box effectiveness for %=5.47 for both normal and oblique waves
Block Diagram of a basic genetic algorithm ............
4NEC2 screen shot of a the first wire STEMS ...........
Figure showing the location of the probe and load inside the box
4NEC2 screen shot of the slot STEMS ...............
Drawing of a slot ST EMS on a box with a loaded probe .....
Switch location on STEMS template ................
Frequency sweep of STEMS optimized at 625MHz: normal incidence
Frequency sweep of STEMS optimized at 625MHz: oblique incidence
Histogram of the best switch states found for all 4 cases at 625MHz

Frequency sweep of STEMS optimized at 650MHz: normal incidence

Fiequency sweep of STEMS optimized at 650MHz: oblique incidence

ix

41

42

43

44

45

46

47

48

53

58

61

65

69

74

77

78

79

81

82

Figure 4.12

Figure 4.13

Figure 4.14

Figure 4.15

Figure 4.16

Figure 4.17

Figure 4.18

Figure 4.19

Figure 4.20

Figure 4.21

Figure 4.22

Figure 4.23

Figure 4.24

Figure 4.25

Figure 4.26

Figure 5.1

Figure 5.2

Figure 5.3

Figure 5.4

Histogram of the best switch states found for all 4 cases at 650MHz
Ftequency sweep of STEMS optimized at 675MHz: normal incidence
Hequency sweep of STEMS optimized at 675MHz: oblique incidence
Histogram of the best switch states found for all 4 cases at 675MHz
Frequency sweep of STEMS optimized at 700MHz: normal incidence
Ftequency sweep of STEMS optimized at 700MHz: oblique incidence
Histogram of the best switch states found for all 4 cases at 700MHz
Frequency sweep of STEMS optimized at 725MHz: normal incidence
Frequency sweep of STEMS optimized at 725MHz: oblique incidence
Frequency sweep of STEMS optimized at 750MHz: normal incidence
Frequency sweep of STEMS optimized at 750MHz: oblique incidence
Histogram of the best switch states found for all 4 cases at 725MHz
Histogram of the best switch states found for all 4 cases at 750MHz
Total field within the box based on location for closed STEMS . .
Total field within the box based on location for open STEMS
Design of the STEMS template ....................
Screenshot of the location of a switch marked by copperpads.

Coto technology SIP REED relay switch series 9011-05-10. . . . .

Photograph Showing the placement of each switch.

83

85

86

87

89

90

91

93

94

95

96

97

98

101

102

108

109

110

Figure 5.5

Figure 5.6

Figure 5.7

Figure 5.8

Figure 5.9

Figure 5.10

Figure 5.11

Figure 5.12

Figure 5.13

Figure 5.14

Figure 5.15

Figure 5.16

Figure 5.17

Figure 5.18

Figure 5.19

Figure 5.20

Figure 5.21

Figure 5.22

Figure 5.23

Bottom layer of the fabricated prototype with the switches. 112
Top layer of the fabricated prototype ................. 113
Photograph Showing the control board ................ 114
Fabricated box with a probe. .................... 116
Diagram of the set-up used to measure the STEMS ......... 118
Signal generator connected to the transmit antenna ......... 119
Box and transmit antenna inside the anechoic chamber. ..... 120
Photograph showing the receiver .................. 121
National Instrument Data Acquisition cards ............ 122
National Instrument split ribbon cable ............... 123
Box placement for normal and oblique measurements ....... 127

Distribution of Se for a random sample of 50000 states at 700MHz 133
Close view of the distribution of Se for the random sample at 700MH2134
Distribution of Se for a random sample of 50000 states at 725MHz 135
Close view of the distribution of Se for the random sample at 725MHzl36
Distribution of Se for a random sample of 50000 states at 750MHz 137
Close view of the distribution of Se for the random sample at 750MH2138
Distribution of Se for a random sample of 50000 states at 775MHz 139

Close view of the distribution of Se for the random sample at 775MH2140

xi

Figure 5.24
Figure 5.25
Figure 5.26
Figure 5.27
Figure 5.28
Figure 5.29
Figure 5.30
Figure 5.31
Figure 5.32
Figure 5.33
Figure 5.34
Figure 5.35
Figure 5.36
Figure 5.37
Figure 5.38
Figure 5.39
Figure 5.40
Figure 5.41

Figure 5.42

Distribution of Se for a random sample of 50000 states at 800MHz 141
Close view of the distribution of Se for the random sample at 800MHzl42
Distribution of Se for a random sample of 50000 states at 825MHz 143
Close view of the distribution of Se for the random sample at 825MHzl44
Distribution of Se for a random sample of 50000 states at 850MHz 145
Close view of the distribution of Se for the random sample at 850MHzl46
Distribution of Se for a random sample of 50000 states at 875MHz 147
Close View of the distribution of Se for the random sample at 875MHzl48
Distribution of Se for a random sample of 50000 states at 900MHz 149
Close view of the distribution of Se for the random sample at 900MHz 150
Distribution of Se for a random sample of 50000 states at 925MHz 151
Close view of the distribution of Se for the random sample at 925MH2152
Distribution of Se for a random sample of 50000 states at 950MHz 153
Close View of the distribution of Se for the random sample at 950MHzl54
Distribution of Se for a random sample of 50000 states at 975MHz 155
Close view of the distribution of Se for the random sample at 975MH2156
Distribution of Se for a random sample of 50000 states at 1000MHz 157
Close View of the distribution of Se for the random sample: 1000MHzl58

Percentage of states for a sample of 50000 states .......... 160

xii

Figure 5.43

Figure 5.44

Figure 5.45

Figure 5.46

Figure 5.47

Figure 5.48

Figure 5.49

Figure 5.50

Figure 5.51

Figure 5.52

Figure 5.53

Figure 5.54

Figure 5.55

Figure 5.56

Figure 5.57

Figure 5.58

Figure 5.59

Figure 5.60

Figure 5.61

Close view Percentage of states for a sample of 50000 states
Diagram of the genetic algorithm used in the experiment

Closed STEMS Se obtained through the GA at 700MHz .....
Open STEMS Se obtained through the CA at 700MHz .....
Closed STEMS 38 obtained through the CA at 725MHz .....
Open ST EMS Se obtained through the CA at 725MHz .....
Closed STEMS Se obtained through the GA at 750MHz .....
Open STEMS Se obtained through the CA at 750MHz .....
Closed STEMS Se obtained through the CA at 775MHz .....
Open STEMS Se obtained through the CA at 775MHz .....
Closed STEMS Se obtained through the CA at 800MHz .....
Open STEMS Se obtained through the CA at 800MHz ......
Closed STEMS Se obtained through the GA at 825MHz .....
Open STEMS Se obtained through the CA at 825MHz .....
Closed STEMS Se obtained through the GA at 850MHz .....
Open STEMS Se obtained through the CA at 850MHz .....
Closed STEMS Se obtained through the GA at 875MHz .....

Open STEMS Se obtained through the CA at 875MHz ......

Closed STEMS Se obtained through the GA at 900MHz .....

xiii

161

164

171

173

175

177

179

180

181

183

185

186

187

Figure 5.62

Figure 5.63

Figure 5.64

Figure 5.65

Figure 5.66

Figure 5.67

Figure 5.68

Figure 5.69

Figure 5.70

Figure 5.71

Figure 5.72

Figure 5. 73

Figure 5. 74

Figure 5.75

Figure 5.76

Open STEMS Se obtained through the GA at 900MHz ..... 188
Closed STEMS Se obtained through the CA at 925MHz ..... 189
Open ST EMS Se obtained through the CA at 925MHz ..... 190
Closed STEMS Se obtained through the CA at 950MHz ..... 191
Open STEMS Se obtained through the CA at 950MHz ..... 192
Closed STEMS Se obtained through the CA at 975MHz ..... 193
Open STEMS 58 obtained through the CA at 975MHz ...... 194
Closed STEMS Se obtained through the GA at 1000MHz 195
Open STEMS Se obtained through the CA at 1000MHz ..... 196
Best STEMS Se for both GA and random search: Closed STEMS 197
Best ST EMS Se for both GA and random search: Open STEMS 198
Closed and open STEMS best states frequency sweep at 700MHz 201
Closed and open STEMS best states frequency sweep at 775MHz 202
Closed and open STEMS best states frequency sweep at 872MHz 203
Closed and open STEMS best states frequency sweep at 1000MHz 204

xiv

KEY TO SYMBOLS AND ABBREVIATIONS

STEMS: Self Tuning Electromagnetic Shutter

GA: Genetic Algorithm

NEC: Numerical Electromagnetic Code

GA-NEC: Genetic Algorithm based Numerical Electromagnetic Code

N I-DAQ: National Instrument Data Acquisition

MEMS: Micro Electromechanical systems

EAR: Equal Area Rule

LAPACK: Linear Algebra PACKage

FACTR: Linear Algebra Factor

MOM: Method of Moment

EFIE: Electric Field Integral Equation

XV

CHAPTER 1

INTRODUCTION

Genetic algorithms (GAS) are a special class of evolutionary computational schemes
that have been utilized for a variety of applications in electromagnetics, such as
designing self-structuring antennas (SSA), and frequency selective surfaces (FSS).
Combining the ideology of SSA and FSS, a new class of electromagnetics devices
called self tuning electromagnetic shutter (STEMS) is introduce in this thesis.

STEMS is a slotted metallic surface capable of adjusting its transmissivity through
the use of computer-controlled switches. In particular, the surface may be placed into
open and closed states, creating an electronically-controllable iris. Though similar to
the idea of reconfigurable filters, the fundamental differences between STEMS and
those existing devices will be shown in the literature review contained in chapter 2.
The chapter also provides the theory behind the operation of STEMS along with their
conceptual design.

A cavity approach has been undertaken to analyze the performance of STEMS and
chapter 3 provides detailed coverage of this approach, as well with an insight into the
wire grid modeling of closed conducting surfaces using the Numerical Electromagnetic
Code 4 (NEC4).

Chapter 4 presents a detailed coverage of the steps followed to design the final
STEMS template, along with a detailed analysis of the results obtained from the

simulation of the STEMS.

Chapter 5 presents a prototype STEMS built at Michigan State University, in-
cluding experimental results attesting of the capability of STEMS to attain both
open and closed states over a broad frequency range through the use of the genetic
algorithm. Chapter 5 also provides an insight into the random distribution of states
within a random sample space of 50000 at various frequencies.

A conclusion to this thesis is given in chapter 6, in addition to possible future
work.

Finally, appendix A provides a description of the genetic algorithm and random

search codes that are used to analyze the STEMS.

CHAPTER 2

CONCEPT AND THEORY

2.1 Introduction

It is important to point out that at the start of this project there was no specific
literature on devices capable of electronically creating both transparent and opaque
surfaces. Microwave filters such as frequency selective surfaces (F SS), though funda-
mentally different from STEMS, were the only devices slightly similar. As a results,
they will be referenced frequently in this chapter.

Tiaditionally, electromagnetic filters such as FSS are planar structures made of
periodic metallic screens, usually backed by a dielectric slab. When exposed to elec-
tromagnetic waves, the metallic screen, made of unit cells, resonates at frequencies
depending on both the characteristics of the substrate and the geometry of the unit
cells [1]. These devices can be made to behave as IOWpass, highpass, bandstop, or
bandpass filters. In order to achieve the desired results, several variables have to be
taken into consideration in the design process. For instance, the shape, spacing and
orientation of the metallic elements, along with the dielectric properties and thickness
of the substrate, have to be simultaneously adjusted prior to being used as a filtering
device on a reflector antenna.

Even though coupling with the reflector antenna itself and other devices present
at the vicinity of the filter can be taken into consideration during the design process,

there is still the effect of environmental conditions and unforeseen elements. These

effects can adversely impact the performance of the filter, rendering it useless in the
current condition. To solve this problem, techniques such as the use of varactors,
micro—electromechanical systems (MEMS) and optimizers have been employed by
several authors [21H24] to design broadband and multiband filters.

This thesis introduces a different type of planar surface with a new concept that
combines the ideology of the filters explained above with the concept of self structuring
antennas (SSA). The introduced surface, referred to as self tuning electromagnetic
shutter (STEMS), is capable of creating both open and closed surfaces for various
angles of incidence over a broad range of frequencies. A STEMS is a non—periodic
slotted metallic surface with computer-controlled electro-mechanical switches placed
across the slots. By turning the switches on and off, the transmissitivity of the surface
can be adjusted to be transparent or opaque to incoming waves.

In section 2.2 of this chapter, the concept of STEMS is explained while the STEMS
template is discussed in section 2.3; sections 2.4-2.6 discuss the remaining elements
associated with the STEMS operations that are the receiver, microprocessor and the
search algorithm. This chapter also provides a review of the literatures that helped

provide insight into the current project.

2.2 STEMS design concept

In this section, the concept of STEMS design is presented. A grid of unidentical
metallic patches interconnected by electromechanical switches represents the stems
template. By changing the states of the switches, the electrical characteristics of

the surface can be adjusted into open and closed states at any given frequency. To

determine the performance of each STEMS template configuration, the STEMS is
used to seal the opening of a conducting box that contains a probe connected to a
receiver. The term configuration is used in this thesis to represent the combination
of ‘on’ or ‘off’ states of the switches.

The probe Within the box is used to measure the level of signal that passes through
the STEMS. The receiver in turn provides a feedback signal to a computer that
analyzes the received signal and uses an evolutionary computational scheme (a genetic
algorithm in this case) to generate a new switch configuration. The main goal of the
STEMS is very simple: to successfully model a transparent or opaque surface at
any desired frequency by changing the switch configurations. A block diagram of
the STEMS is shown in Figure 2.1 and a detailed explanation of each component is

provided in the following sections.

STEMS

 

 

 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

Template /
fn control
lines
‘\
Probe
Box» if i in
Feed line —.
MICRO-

 

 

 

 

RECEIVER —’— PROCESSOR

 

 

 

 

Figure 2.1. Block Diagram of STEMS

2.3 Self 'lhning Electromagnetic Shutter Template

The STEMS template as shown in Figure 2.2 is the main building block of the system.
It is a slotted metallic surface composed of unidentical patches interconnected by a
matrix of controllable switches. A switch can be set to a ‘on’ or ‘off’ state, and a
template using n switches can be arranged into a total of (2”) switch configurations.
Since the switches are used to connect the patches, by turning the switches on or off,
the current flow through neighboring patches changes, altering the electrical charac-
teristics of the surface. Another View is that the switches control the electrical length
of the slots, hence determining the field transmitted through the slots The switches
on the surface are purposely placed in an asymmetric manner to avoid instances of
different switch configurations yielding the same frequency response. This guarantees

a unique template configuration for every set of switch states.

Incident Wave

k

    

Switch- Metal- 1

Figure 2.2. Self Tuning Electromagnetic Shutter

2.4 Box and Probe

The Box and the probe are important components used to test the STEMS. The box is
made of six continuous metallic walls that provide complete shielding against incoming
plane waves. The probe is a monopole antenna located inside the box and used to
receive signals from the outside. When all six walls of the box are present, the probe
is completely shielded from all incoming electromagnetic waves and unable to receive
signals. The box and probe have been designed using the numerical electromagnetic
code (NEC4) and chapter 3 provides a detailed explanation of the design process.

To evaluate the performance of the STEMS, one of the sides of the box is removed
and the probe is used to measure the strength of the incoming plane wave. The open
box is then sealed with the STEMS template as shown in Figure 2.3 and the received
signal strength on the probe is measured for various switch configurations. The ratio
of the open box signal to the signal from the box sealed with the STEMS determines
the ability of the stems to create either an open or closed surface. Simulated and
experimental results shown in chapters 4 and 5 demonstrate that the STEMS is
capable of performing efficiently in an open, closed or intermediate states for various
frequencies and angles of incidence of incoming waves.

It should be noted that this is not the only way to test the STEMS. It could be
used in many different applications that do not include boxes. The box technique is

selected because it is easy to implement and sufficient to prove the concept of STEMS.

'9
' be
5.... g.... :0 ..
3 "

 

STE

 

Load

 

1
Probe
z” “—Box

 

 

 

Figure 2.3. Box with probe covered by a STEMS

10

2.5 Receiver

To configure the STEMS, a feedback signal is required to ascertain its performance.
For the test configuration shown in Figure 2.1. the feedback signal is the probe current
as measured using a receiver. A receiver such as a vector voltmeter or field intensity
meter can be used to measure the induced current on the probe for a given optimized
switch configuration at a single frequency. More sophisticated devices such as network
analyzers can then be used to obtained a sweep of the induced current over a broad
frequency range. Network analyzers can also be used to optimize the STEMS at
multiple frequencies, although this is not implemented in this thesis. The quantity
measured by the receiver is then sent to the microprocessor for processing. Every
subsequent switch configuration depends on the value of the quantity measured by

the receiver and extra care should be put toward proper calibration of the receiver.

2.6 Microprocessor

The microprocessor represents the control unit of the STEMS structure and all the
computations are made here. The information sent by the receiver is quantified
by the microprocessor and used to determine the subsequent switch configuration.
In order to optimize the switch setting to meet the requested design criteria, the
microprocessor is programmed with an evolutionary search algorithm. In the present
work, a laptop is used to perform all the duties of the micro processor and a genetic
algorithm is used as the search algorithm. The computer communicates with the
receiver and the STEMS template using the National Instruments data acquisition

driver software NI-DAQ.

11

2.7 Search Algorithm

A robust and efficient search algorithm is essential to the operations of STEMS.
It determines how fast the STEMS can find a template configuration capable of
yielding the desired characteristics at any given frequency and angle of incidence.
For a template with n switches, there are 2” possible configurations. As the number
of switches (n) is increased, the number of possible configurations increases quickly
to overwhelming values. As an example, a template with 16 switches has a total
of 65,536 possible switch configurations while doubling the switch number to 32
leads to 4,295,000,000 switch configurations. With such numbers, coupled with
the time it takes to measure the frequency response associated with each switch
configuration, doing an exhaustive search might take months. A random search could
be implemented to find acceptable states among all possible configuration but, as its
name implies, the search is random and might take a long time to find a configuration
with the required characteristics. As a result, a robust self evolving computational
scheme becomes indispensable for quickly finding the needed switch configuration.
Since it is fairly simple to represent the two states of each switch with a binary
string, a binary genetic algorithm has been investigated as the search algorithm for
the STEMS. An in depth description of the genetic algorithm is provided in chapters

4 and 5.

2.8 Literature Review

A Self Tuning Electromagnetic Shutter is a new class of electromagnetic devices ca-

pable of exhibiting characteristics of both a closed and open surface. It combines

12

the ideology of self-structuring antennas [26]-[32], with the concept of microwave fil-
ters such as frequency selective surfaces [1]. Frequency selective surfaces are devices
that were first introduced in the late 19505 at the Ohio State University [1]. The
concept was generated from an Air Force program focused on investigating tuned
surfaces capable of limiting the range of frequencies over which an antenna would be
a principal source of echo. Dr. B. A. Munk approached the issue by combining the
basic physics of interaction between elements with the Moment of Method principles,
leading to the idea of FSS. Classical FSS used as electromagnetic filters are planar
structures composed of an assembly of periodic metallic elements called unit cells,
usually backed by one or several dielectric layers Figure 2.4.

The frequency response of the FSS depends on the geometry of the unit cell and
its properties depend on the mutual interactions of the periodic elements. Therefore,
to observe a desired frequency response, a large number of unit cells must be present.
When the FSS is illuminated by an incoming wave, it behaves as a band pass or band
stop filter, depending on the type of elements used and their frequency of resonance.
Band pass characteristics are obtained by using slot elements while band stops are
obtained via the use of dipole type elements.

This marks a very profound difference from the concept of STEMS, where a single
surface, made of non identical elements can be tuned at any desired frequency to
exhibit both open and closed surfaces with narrow or broad band characteristics. It
is also important to note that the overall size of the STEMS may be small compared

to the electromagnetic filters mentioned above. The electrical length of the STEMS

13

presented in this thesis is approximately '2' at its lowest operational frequency. This
dimension represents the electrical length of a single FSS unit cell and a matrix of
several unit cells has to be employed to get the desired frequency response

Traditional FSSs suffer from the fact that they are narrow band and exhibit a
single stopband or passband characteristic. Intensive work has been put forth toward
designing multiband FSS. One technique used by several authors[2]-[8] has been to
take advantage of multiple resonant elements such as fractal antennas and multi rings
or loops. Using such elements as unit cells of the periodic surface enables for the design
of band pass or band stop filters with resonances equivalent to those of the elements.

Another technique used to obtain multi-resonance is to use a multi layered or
stacked FSS [1], [9], [10]. In this approach two or more FSS screens backed by
dielectric layers are used to obtain multiband characteristics or to improve other
design specifications. A combination of both techniques has also been presented as a
successful method of achieving multiband characteristics.

Even though desired frequency response can be obtained with these techniques,
it comes at a high cost of time consuming trial and error analysis in simultaneously
tuning the elements of the periodic surface (shape and spacing between elements) and
the characteristics of the dielectric.

To avoid the strenuous process of selecting the proper variables, such as unit
cell element shape, spacing between elements, orientation and dielectric properties,
genetic algorithms have been used as search algorithms to synthesize the design of

FSS [11]- [15]. This process still suffers from the fact that the designs are final and

14

they lack the ability to adapt to changing conditions such as interactions with other
devices or environmental effects.

Lumped elements and MEMS, in combination with search algorithms have been
used as a way to design reconfigurable frequency selective surfaces [16]-[25]. Though
frequency tunability is obtained through these techniques, the concept and design
is the same as that of classical FSS, therefore, they are still fundamentally different
from STEMS.

One of the most crucial elements to the understanding of STEMS is the con-
cept of self structuring antennas (SSA). They were were first introduced by Dr. E.
Rothwell and his team at Michigan State University [26]. SSAs are antennas made
of an arrangement of wires or patches interconnected via switches Figure 2.5 . By
changing the states of the switches, the electrical characteristics of the antenna are
changed as well [26]—[32]. The switches are controlled via a microprocessor that uses
an optimizer to determine the best switch state that will produce the desired antenna
properties. This new methodology has been proven to yield excellent results and the

same approached is used in this thesis.

15

 

 

++++I
++++tmm
++++.W

++++

 

Metal —

 

 

   

 

Figure 2.4. Fiequency Selective Surface

16

 

 

 

 

 

Wire —'

 

 

 

 

 

 

 

 

Feer Pt

Figure 2.5. Self Structuring Antenna

17

2.9 Conclusion

In this chapter, the concept and theory of self tuning electromagnetic shutters is
presented. A discussion of the concept of STEMS is presented in section 2.2 while
the fundamental components along with a block diagram of STEMS are provided in
sections 2.3-2.7. A literature review showing the different ideologies used to generate
the concept and design methodology of STEMS is also presented in section 2.8.

The next chapter presents in detail the approach used to analyze the performance

of STEMS.

18

CHAPTER 3

NEC4 OVERVIEW AND BOX DESIGN

3.1 Introduction

To analyze the effectiveness of the self tuning electromagnetic shutter, a closed con-
ducting box containing a probe is designed. One of the sides of the box is removed
and the probe is used to measure the signal strength of an incoming plane wave as
shown in Figure 3.1. The open box is then sealed with the STEMS template as shown
in Figure 3.2 and the received signal strength on the probe is measured for various
switch configurations. The ratio of the open box signal to the signal from the box
sealed with the STEMS determines the shutter effectiveness to either shut itself or to
be transparent to incoming waves.

To ensure accuracy in the results, it is crucial that the designed box effectively
shields the probe within its interior from external fields. To simulate the STEMS,
box, and probe, an electromagnetic simulation package developed at the Lawrence
Livermore National Laboratory [33] called NEC4 (Numerical Electromagnetic Code,
version 4) is selected. This chapter presents modeling guidelines for NEC4 along with

the designed box and simulated results of its effectiveness.

19

Top open

 

 

Figure 3.1. Box with top open

20

 

 

 

Load

 

1
Probe
z‘i *—Box

 

 

 

Figure 3.2. Box with top covered by a STEMS

21

3.2 NEC4 Modeling Guidelines

NEC4 is a method of moments computer program for analyzing the electromagnetic
response of antennas and scatterers. It utilizes the electric field integral equation
for modeling thin wires and the magnetic field integral equation for modeling closed
perfectly conducting surfaces. The code has been used throughout the years with
great success in the analysis of various complex geometries including ships, airplanes
and automobiles, [36] - [39]. Modeling objects in NEC4 can be done using wires
or surface patches depending on the characteristics of the structure being analyzed.
Surface patches are only used in N EC4 to model closed perfectly conducting surfaces
while a wire grid model is used for all open surface models [33]. STEMS are not
perfectly closed conducting surfaces because of their slotted aperture. Therefore,
only the wire grid model is used in this section.

Wire modeling in NEC4 involves both electrical and geometrical factors. Every
wire in the model is parsed into several segments and each wire segment is defined by
its radius, a, and its length, A, as shown in Figure 3.3. Electrically, the most crucial
aspects are the ratios of each segment length to its radius, and to the wavelength
A. Generally, the value of A is selected to be 0.1/\ or less at the center frequency,
but smaller values of A with A S 0.05/\ are required for modeling critical regions
such as corners. Selecting the appropriate segment radius is relative to the conditions
imposed by the thin wire approximation kernel used by NEC4. This approximation

27m

imposes the condition that the wire radius is selected such that A <<1. Under

these conditions, every wire is reduced to a current filament on the axis of the wire;

22

 

this assumes that the current is uniformly distributed around the circumference of
the wire and only the axial component of the current is considered.

For a single thin wire of axial path I‘ the axial current I (u) due to an incident field
E8 can be determined by solving the electric field integral equation (EFIE) given in

Eq-3.1 of [40] as

 

81008 A Ar I I /_ A “’1;
[Fl 8,, 6u+k2(u-u)l(u)lg<ulu)du ,7 -E<u).

(3.1)

where the term g(u|u’) represents the reduced Green’s function kernel of the integral

equation

e_ij(07 ulsl, u’)

g(ulu’)= fie) Mammy”), ds’ (3.2)

 

When the conditions imposed on the radius a and the segment length A are met,
Eq—3.2 can be simplified by using the approximated reduce Green’s function given by
' I I
e—ij(0, uls ,u)
47rR(0, uls’, u’)

 

9(UIU’) = (3.3)

It was found in [40] that the error introduced by using the thin wire approximation

in computing the current on the wire is related to the ratio %— and is given by

du — dlu _ (a/A)2

 

 

(3.4)

23

A plot of the error introduced for various values of A/ a is shown on Figure 3.4.
Analyzes of this plot shows that a minimum value of %=3.55 is needed to maintain
the error below 1%.

Several authors have successfully used previous versions of NEC4 to model con-
tinuous conducting surfaces by use of a wire grid model and it is found that optimum
results can be obtained for a value of %=27r, [41]-[43]. This observation is known as
the equal area rule (EAR), and it states that the surface area of the segments in the
grid should be made equal to the surface area of the solid surface being modeled as
demonstrated in Figure 3.5. Using the equal area rule as a reference, the next section

discusses the design of the Box using NEC4.

24

 

 

Figure 3.3. Wire segmentation

25

 

0.04

 

 

 

2 3.35 5 a s 10
A\ a

Figure 3.4. Thin Wire Approximation error

26

 

2.Tr.a

Figure 3.5. Equal Area Rule Representation

27

3.3 Box Design

As discussed in section 3.1, the shutter effectiveness of the STEMS can be determined
through the use of a box. By mounting the STEMS template on the opening of a box,
a probe is used to measure the intensity of the field that passes through the STEMS
template into the box. The box is defined by its width W', its length L and height
H. It is made of 6 continuous conducting surfaces and each surface is represented as
an array of identical wire grids as shown in Figure 3.5.

Modeling the continuous conducting surfaces of the box using wire grids introduces
a number of variables that could affect both the accuracy and simulation time. With
reference to section 3.2, the accuracy of the simulation depends on the values of the
segment radius, a, and length, A,. Every wire is parsed into multiple segments and
the total current is determined by computing the currents at the centers of all the
segments. As a result, increasing the number of segments per wire leads to better
accuracy but also an increase in the total computation time.

It is important to mention that the total number of segments used to model a
box of arbitrary dimensions does not need to change if the dimensions of the box are
changed. This can be proven by referring to the discussion on cavities provided in [40]
and [44]. By analogy to the cavity, the resonant frequencies of the box are dependent

on its dimensions (H, W', L) as given by

 

fr = - * (--)2 + ('—)2 + (-)2, (35)

where the integer values m, n and p determine the modes of the box being excited

28

and c is the speed of light in vacuum. By utilizing the relationship A = C fr, it
is observed that a change in the resonant frequency also leads to a change in the
wavelength A. Therefore, for any given box the ratio €— can be kept the same as the
dimensions of the box are changed just by altering the length of the segments A.

In order to determine an optimum %— ratio suitable for the analysis of the STEMS
template, various cubical boxes, W = L = H, with different wire radii but identical
segment length have been designed. Each cavity has a side length of L = 29.3cm and
segment length of A = 9.75cm. These dimensions give a total of 28 segments per
wire and 9408 segments for the whole box. The reasons for selecting L = 29.3mm are
explained in chapter 5.

Given these dimension and using Eq—3.5, the resonant frequency of the dominant
TElOl mode is determined to be 777.04M Hz with /\ = 38.6cm. This yields a 3%
ratio of 0.025, well below the value of 0.05 mentioned in [33]. It should be pointed
out that analysis at close proximity of the resonant frequency are not considered in
this thesis because of the properties of cavities at resonance. In [33] and [44], it is
shown that at resonance, the computed total E-field inside a cavity is inaccurate due
to the singularity of the EFIE. To verify this statement with the box, the total E-field
due an incoming normal incident field with magnitude 1V/ m is evaluated within a
cubical box designed using the equal area rule with%=6.283 and L = 29.3cm. The
characteristics of the normal incident wave are given in Table 3.1.

For a perfectly conducting box, the total field within its interior would be zero at

all frequencies. In the case of this study, the box designed is a model made of wire

grids and therefore, the total field within its interior would not be zero. Analysis of

29

the total Ex-ficld magnitude plotted in Figure 3.6 reveals a total field with magnitude
near zero at lower frequencies until 770MHz where the magnitude starts to increase
and suddenly peaks to 9.5V/m at 777.04M H 2 before it decreases back down to near
zero. The readings of the total field around 777.04M H z are inaccurate, given that the
incoming field intensity is only 1V/ m. As a result of these observations, frequencies
near to the resonance value of 777.04M Hz are not considered in this study. The term
‘box effectiveness’ is used throughout the thesis to represent the ability of the box to

prevent electromagnetic fields from leaking through its surface.

 

7 Wave description
Incidence [] Incidence Angle (degrees) Magnitude(V/m)
Normal ][ 9 = O, 43 = 0 1

 

 

 

 

 

 

 

 

Table 3.1. Description of the field used to excite the box.

30

 

 

 

 

 

8 p

E

Z, 5 _

2

0)

Li".

oh 4 -

3

r3
2* L
650 760 750 860

Frequency (MHz)

850

Figure 3.6. Total E-field of box designed using the EAR

31

To determine the value of the ratio %— that provides the most box effectiveness,
various boxes with identical segment length but varying radii are created and analyzed
at frequencies ranging from 625MHz to 750MHz with frequency steps of 25MHz. Each
box is loaded with a quarter wavelength monopole at the base and the entire structure
is illuminated by the incident plane wave as described in Table 3.1. The current on
each monopole is recorded for every box with and without the top surface for both
normal and oblique polarization of the incident field. The box effectiveness (S) is

evaluated in dB using,

I
s = 20 * loglo—Q, (3.6)
10

where IQ is the current on the first segment of the probe, recorded for the box with
no top surface and IC is the current recorded for the box completely closed.

Considering the radius calculated from the equal area rule with a=24fi=0155cm
for A = 0.975cm as a reference point, 19 different boxes with radii ranging from
0.144cm — 0.162cm are designed and simulated at 750M H z. The plot of the box
effectiveness for normal polarization of the incident field is displayed in Figure 3.7
Analysis of this plot reveals a maximum reduction of 64dB obtained for a % ratio
of 6.372 while the equal area rule ratio of %—=6.283 yields a maximum reduction of
62.18dB.

Further simulations of the boxes at 725M Hz reveal that a smaller ratio of %
is needed for optimum shielding. Figure 3.8 shows a shift of the maximum box

A

effectiveness provided by 3:6'372 to %=6.17. The shielding obtained at 725M H z

32

has a maximum value of 74dB. This shift implies that boxes with smaller ratios of

% are needed for analysis at lower frequencies.

33

 

A .54-
3 -S6r
5 -58~
..>.
g .60»
In]
g 62.2
an

.64»

 

 

 

6:1 6.2 6.3 6:4 6.5 6:6 6.7
A\a

Figure 3.7. Box Effectiveness with different ratios of %— at 750M H z.

34

 

 

 

 

a ‘55 5s“ ’1’
5-60
5 \ ,” \
E. x , 750MHz
g '70 ‘ \ ’1'
an 725MHz ,:
6 6.2 6.4 6.6
A\ a

Figure 3.8. Box Effectiveness with varying %— at 750MHz and 725MHz.

35

With regards to that observation, 42 boxes with varying %— are simulated and their
frequency response plotted in Figure 3.9 - Figure 3.12. As expected, as the frequency
is lowered, the ratio of 46% has to be lowered as well in order to obtain optimum
shielding. At every frequency considered, shielding of 60dB or more is obtained, with
an outstanding shielding of 93dB found at 700M H z for %—=5.94. Considering 60618
to be an acceptable shielding value, it can be concluded that the wire grid model can
adequately represent continuous conducting surfaces provided the right ratio of %
is selected. The equal area rule did not provide the best box effectiveness but was
essential as a reference point to determine better ratios as the frequency of interest
is varied.

In order to determine the usable frequency range of each of the six boxes, a
frequency sweep of each box is performed for a vertical incident E—field. Figure 3.13
shows a plot of the box effectiveness of each box as the frequency is varied. Still
considering 60dB to be an acceptable box effectiveness value, close observation of
Figure 3.13 shows that each box has a usable bandwidth of 50M H 2. Even though
there are six boxes with 50M H z bandwidth, the overall bandwidth considering all
six boxes is only 160M H 2 due to the overlapping.

The performance of each box for an incident field with oblique incidence is also
evaluated and plotted as shown in Figure 3.14—Figure 3.19 but, as observed in [42],
the box effectivenesses of all boxes designed are tremendously decreased for oblique
incidence compared to normal incidence. Table 3.3 provides the characteristics of the

normal and oblique waves used.

36

A list of the selected %— ratios along with their respective box effectiveness for

each of the six frequencies considered is provided on Table 3.2.

 

 

 

 

 

 

 

 

selected boxes characteristics
Frequency (MHz) Radius (mm) A/a a/A Shielding (dB)
750 1.53 6.37 0.0037 64.693
725 1.58 6.17 0.00381 73.819
700 1.64 5.94 0.00382 92.291
675 1.69 5.76 0.00380 73.904
650 1.74 5.60 0.00377 67.750
625 1.78 5.47 0.00370 63.233

 

 

 

 

 

 

 

 

Table 3.2. Best %- ratios and their respective box effectiveness.

 

Wave description
Incidence Incidence Angles(degrees) Magnitude(V/m)
Normal 6 = 0, q) = 0 1
Oblique 0 = 30, (15 = 60 1

 

 

 

 

 

 

 

 

 

Table 3.3. Description of the two waves used to excite the boxes.

37

 

 

I
l
I
I
I
I
I
II
II
II
II
II

"""

 

 

 

7

as mass.

80-

5
8

saw an

6.5

6.4

6.3

6.2
A\ a

6.1

5.9

5.8

Figure 3.9. Box Effectiveness with varying %— at 725MHz and 700MHz.
38

 

‘\
‘
‘s
\

Box Effectiveness (dB)

I I I I I I
q a as

83 3 d c u. e

x'c
c

 

 

Figure 3.10. Box Effectiveness with varying % at 700MHz and 675MHz.

5.6 5.8 6 6.2
A\ a

39

 

 

Box Effectiveness (dB)
in L1 és éx éx a 5x 1'» c'n
N e on as a. N e on ex

 

 

 

 

5.3 5.4 5.5 5.6 5.7 5.8 5.9 6
A\a

Figure 3.11. Box Effectiveness with varying % at 675MHz and 650MHz.

40

 

2'1: ('1:
00 as

és
a

Box Effectiveness (dB)
éx 5x
43. N

éx
as

 

Figure 3.12. Box Effectiveness with varying % at 650MHz and 625MHz.

 

41

%\\‘s 1””
625MH‘z~~.- \
650MHz
5.3 5.4 5.5 5.6 5.7 5.8 5.9
A\ a

 

 

 

Box Effectiveness (dB)

 

 

 

 

i :' A\a
-so~ :'
-85- A\a=5.94—> i
.90. '1
600 650 700 750
Frequency (MHz)

Figure 3.13. Box Effectiveness

42

 

.I
I
O’-
45 I ~
I ’— .I
.I
.I
‘l

-50 ‘

.
\
".
‘-
‘0
‘0
‘0
‘I
‘-
‘-
‘0
~I
s,‘
's

n
‘
0‘.
~-
‘0
‘.~
-
........

n
........

-55

 

Box Effectiveness (dB)

     

Vertical ‘
Polarization

 

 

 

 

700 720 740 760 780
Frequency (MHz)

Figure 3.14. Box effectiveness for %—=6.37 for both normal and oblique waves

43

 

 

   
   
   

 

 

 

 

\_

.20- T
A Oblique Polarization
Q .30—
3‘:
8
40-
i?
It: _
F‘l '50 Vertical Polarization
ii /
an -60 _

-70 r

680 700 720 740 760

Frequency (MHz)

Figure 3.15. Box effectiveness for %=6.17 for both normal and oblique waves

44

 

.
c —-—

-|-- .-.—0
CM- -0-
u-I- .—0-‘
i-.- _.—-C
'9 cl
6... ._ _ _.—---
' .-I-b-n u—l I

:1.)
C
——>

Oblique Polarization

     

 

 

 

A -30 -
a
g! -40 :
8
.3 -50 ~ Vertical
g) Polarization
8: -60 -
II]
E -70—
-80 ~
-90 - -
650 700 750
Frequency (MHz)

Figure 3.16. Box effectiveness for %—=5.94 for both normal and oblique waves

45

 

,v'
If
,'
’.'
"
‘,"
' "
“~,‘ ,a".
I‘.~. —.‘.‘
‘. .’o
‘u- .a
u‘ .‘
u.. ‘1'-
—. .—
"~u... .-"’"
-I-I-D-l-D-l-I-I- o-u—u—"’

   
   

a: _55 _ Oblique Polarization

3

8

g -60 .

a:

8

8::

a -65~ ‘
a Vertical

    

Polarization

in
c

 

 

 

620 640 660 680 760
Frequency (MHz)

Figure 3.17. Box effectiveness for %=5.76 for both normal and oblique waves

46

 

_ --
'--_ _.—v '
'---._ ._.—n—---"‘

I—._, -.-.—o—
-I-I-I-o-g l—'-'

1'9
6

Oblique Polarization

2'»
c

Box Effectiveness (dB)
1'1: 4';
? c

    

Vertical Polarization

   

is
c

  

 

 

 

 

620 640 660 680 700
Frequency (MHz)

Figure 3.18. Box effectiveness for %—=5.6 for both normal and oblique waves

47

 

   
         

 

 

 

-50 :.~ ' T ............. ‘
- 5 2 _ ............................ T. ................... ..
A Oblique Polarization
E -54- .
5
5 -56
.3 Vertical Polarization
8 -58+ ‘ ~
8:
LI]
’3 -60 r —
a:
-62 - 4
'64 [— J 1 1 1 A
600 620 640 660
Frequency (MHz)

Figure 3.19. Box effectiveness for %—=5.47 for both normal and oblique waves

48

3.4 Conclusion

In this chapter, an overview of the numerical electromagnetic code, version 4, along
with the design of the boxes used in STEMS simulations are presented. A discussion
of the design constraints to be observed while using the electromagnetic simulation
source code NEC4 is presented in section 3.2, while details of the design and simulation
results of the boxes used to analyze the STEMS are presented in section 3.3. The next

chapter presents in detail the design and simulation results of the STEMS template.

49

CHAPTER 4

STEMS TEMPLATE DESIGN AND SIMULATION RESULTS

4.1 Introduction

As a proof of concept of STEMS, intensive designs and simulations were conducted at
Michigan State University. The selected ST EMS template layout is created using a
NEC geometry editor called 4NEC2 [46] and the input file is imported into GA-NEC
for encoding and optimization. An overview of GA-NEC along with the optimization
scheme and the switch model is given in section 4.2. A brief overview of the first
STEMS considered is provided in section 4.3 while section 4.4 presents the details of

the final design along with a discussion of the simulated results.

4.2 GA-N EC Overview and Switch Model

4.2.1 GA-NEC Overview

GA-NEC is a visual basic front end optimizer for NEC4. Dr. John Ross [34] created
the software package by developing a genetic algorithm optimization tool in Visual
Basic that uses the NEC4 executable file as a basic shell. To reduce the run time
of the executable file, Dr. Ross replaced the original linear algebra solver (FACTR)
with a much faster routine call LAPACK [35].

GA-NEC enables the optimization of NEC4 models by providing a framework
through which three different tasks are performed. First, the NEC4 input file is

created or imported through a netlist display and the parameters to be optimized

50

within the input file are encoded into binary chromosomes. Then, a fitness function
is defined and the NEC4 output file is used to determine the fitness of the parameters
to be optimized. Finally, a genetic algorithm is executed as a means to perform the
optimization. A detailed description of a genetic algorithm is presented in section

4.2.2.
4.2.2 Genetic Algorithm

As discussed in section 2.7, GAS are robust self-evolving computational schemes that
are used as optimization tools. They are search algorithms based on the principles of
genetics and natural selection that follow the concept of a Darwinian evolution where
only the fittest survive. The process of a genetic algorithm can be explained through
the concept of natural evolution of beings.

In nature, the physical characteristics of an individual can be determined through
analysis of its chromosomes. Within a given population, individuals with chromo-
somes that have the highest fitness have a higher probability to survive longer and
produce offspring. As a result, subsequent generations of that population will be
composed of individuals with genetic material inherited from the parents with the
highest fitness.

This process is mimicked in GAS where every parameter is encoded into chro-
mosomes and the fitness of each chromosome is evaluated through a defined fitness
function. The individuals with the highest fitnesses are then selected to produce off-
spring that will continue on to the next generation. Applied to STEMS, every switch

configuration is encoded into a chromosome as a binary string of ‘0’s and ‘1’s. A one

51

is used to represent a switch that is turned on, while a zero is used for a switch turned
off. This implies that for a STEMS, the binary string or chromosome contains all the
information needed to set the states of the switches.

A block diagram of the steps involved in a genetic algorithm is shown in Figure

4.1 and an explanation of each step is provided in section 4.2.2.1 to section 4.2.2.7.

52

 

Encode
Parameters

Generate Initial

      

 

 

 

 

 

Population i
1 . YES
Evaluate , , ; Termination
Fitness Criteria met?

 

 

[to
Perform
Selection

 

 

 

Perform

Crossover
Fill New Perform
Generation Mutation

 

 

Figure 4.1. Block Diagram of a basic genetic algorithm

53

4.2.2.1 Encoding Parameters

As discussed in section 4.2.1, the parameters to be optimized need to be encoded
into chromosomes. The lengths of the chromosomes determine the search space and
longer chromosomes are needed for more complex problems. In the case of STEMS,

the chromosome length is equal to the number of switches used on the template.

4.2.2.2 Initial Population

The initial population represents the first set of chromosomes to be considered for
evaluation. This first set is usually generated randomly but a pre—existing pool can

also be used as the starting set.
4.2.2.3 Evaluating the Fitness

In order to determine the fitness of the chromosomes within the population, a fitness
function is defined. Each chromosome is then decoded and the fitness function is

evaluated.
4.2.2.4 Mating Pool selection

The mating pool is composed of selected chromosomes also referred to as parents,
that pass on their genetic information to the next generation. Selection of the mating
pool can be done through various methods among which are elitist, thresholding,

roulette wheel and tournament selection:

0 Elitist: the chromosomes are ranked based on their fitness value and a prede—

termined number of chromosomes, counting from the fittest, are selected.

0 Thresholding: a preselected fitness value or a ratio between a chromosome fit-

ness and the average fitness is used as selection criteria.

54

o Roulette wheel: chromosomes with higher fitness values have higher probabil-
ities to be selected compared to chromosomes with lower fitness values. The

roulette wheel method allows for more diversity in the mating pool.

0 Tournament: two or more chromosomes are selected randomly from the popu-
lation and the chromosome with the highest fitness is selected for the mating

pool. This process is repeated until the mating pool is filled.

4.2.2.5 Crossover

After the selection process is completed, the selected chromosomes or parents are
paired and crossovers are performed with reference to a crossover probability Pcross.
Crossover can be done at one or multiple points between two or multiple chromosomes.
A simple one point crossover between two chromosomes can be described as follows.
Consider a pair Cl and 02- Crossover is performed by randomly selecting a crossover
point and each of the two chromosomes are split into two strings at that specific point.
The strings are then swapped, creating two new chromosomes, or offspring, 01 and
02 as shown below.

Assume the parents:

CI = X0X1X2X3X4X5 ........ Xn, (4.1)

02 = Y0Y1Y2Y3Y4Y5 ......... Yn, (4.2)

A crossover performed between points 4 and 5 will produce the following offspring:

55

01 = X0X1X2X3X4Y5 ........ Yn, (4.3)

02 = Y0Y1Y2Y3Y4X5 ........ Xn. (4.4)

4.2.2.6 Mutate and Fill Next Generation

Once crossover is completed, random mutations are performed with mutation prob-
ability Pmut- Mutation is carried on by toggling a random bit within the binary
string of the chromosome. For instance, a chromosome with binary string {11I111}
will become the binary string {110111} if mutation is performed on the third bit of
its string. After the mutation process, the generation of offspring then becomes the

new generation of parents and their fitness is evaluated once again.
4.2.2.7 Stopping Criteria

Often, the GA is stopped after a set number of generations has been evaluated. More
often, a stepping condition can be imposed when a chromosome with a fitness value

higher than a preselected value is found.
4.2.3 Switch model

Switches are not available in the current version of NEC4 but a switch model can
be created in GA-NEC through the use of resistors by applying the basic concepts
of circuits. Resistors are electrical components used to limit or regulate the flow
of electrical current. The current through a resistor is inversely proportional to its
resistance; therefore, the current flow through a wire segment can be controlled by

loading the wire with a resistor. A low resistance allows for a current flow while a

56

very high value of resistance stops the current through the wire. The same behavior is
observed for switches. When the switch is on, the current flows and when the switch is
turned off the flow steps. In other words, an ‘on’ switch state is modeled by applying
a low resistance while an ‘off ’ switch state is obtained using a high resistance. In
GA-NEC the high and low values of each resistor are encoded to O and 1. When a
switch state is generated by the GA, the string of Os and ls are decoded back to their
nominal values (0=low resistance; 1=high resistance) and each resistor is then set to
its corresponding value. Through this thesis, the two values used for the resistors are

0.019 for low and 100000000010 for high resistance.

4.3 Initial Design Approach and Observations

The STEMS template described in this thesis is the result of various studies performed
on a different design configuration. The initial STEMS that was considered is a planar
surface made of rectangular wire loop and switches, created with reference to the SSA
mentioned in section 2.8. Its template is a square surface of side length 40cm, made
of 28 wire loops and 34 switches as shown in Figure 4.2. The wires are designed
with the same radius a = 1.9mm and segment length A = 12.5mm following the
guidelines mentioned in section 3.2. The layout and dimensions (width, length) of

the loops were arbitrarily chosen and are shown in Table 4.1.

57

 

Figure 4.2. 4NEC2 screen shot of a the first wire STEMS

58

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Wire Characteristics
Wire loop Lengths (mm)

1 37.5, 125
2 62.5, 125
3 62.5, 100
4 62.5, 125
5 37.5, 137.5
6 75, 87.5
7 15, 62.5
8 37.5, 87.5
9 62.5, 87.5
10 75, 100
11 50, 100
12 62.5, 100
13 62.5, 100
14 62.5, 100
15 62.5, 112.5
16 62.5, 125
17 37.5, 150
18 50, 100
19 62.5, 150
20 37.5, 50
21 37.5, 137.5
22 50, 137.5
23 50, 87.5
24 50, 112.5
25 50, 125
26 50, 100
27 62.5, 87.5
28 87.5, 37.5

 

 

 

 

Table 4.1. Wire STEMS loop dimensions.

59

To analyze the wire STEMS, an open box and a probe are also designed. The
box is a cubical box with Side length of 40cm and the probe is a quarter wavelength
monopole (10.7cm) connected to the middle of one of the plates of the box as shown
in Figure 4.3. The probe is also loaded with a 5052 resistor on its first segment.
The whole structure is then excited at 700M H z with a normal incident plane wave
with its electric field polarized along the x-direction and of magnitude IV/ m, and
the current induced on the loaded segment of the probe is recorded as 10. The
characteristics of the incident plane wave are given in Table 4.2 while the open box
and probe characteristics are given in Table 4.3. The wire STEMS is then used to
seal the opening of the box containing the probe and the structure is excited once
again at 700M Hz with the same plane wave. To determine the shutter effectiveness
Se, which is the ability of the STEMS to create an open or closed surface, the value
of the current on the loaded segment of the probe is recorded. This current value,
termed as I S" is used with the open box current IO in Eq4.5 to find 53. To either
maximize Se (STEMS open) or minimize Se (STEMS closed) simulations are run
using GA-NEC with the parameters of the GA given in Table 4.4. Initial results of
the simulated wire STEMS showed good results when trying to create an open surface
but very poor results were observed for the closed surface case with with values of Se
no less than -30dB.

I
38 = 20 * loglOI—S, (4.5)
0

60

 

Top plate
removed

 

 

Load

 

Probe
‘* F—Box

 

 

 

Figure 4.3. Figure showing the location of the probe and load inside the box

61

 

Wave description
Incidence Incidence Angles(degrees) Magnitude(V/m)
Normal 9 = 0, d) = 0 1
Oblique 0 = 30, 45 = 60 1

 

 

 

 

 

 

 

 

 

 

Table 4.2. Description of the two waves used to excite the boxes.

 

 

 

 

 

 

 

 

Cubical Box
Length(mm) Wire Radius(mm) Segment Length (mm)
400 1.9 12.5
Probe
Length(mm) Wire Radius(mm) Segment Length (mm)
107 0.56 10.7

 

 

 

 

 

Table 4.3. Characteristics of the probe and box.

 

 

 

 

 

 

 

 

GA parameters
Population Size 100
Generations 50
Crossover Probability 0.7
Mutation Probability 0.1
Selection type Elitist
‘70 of population replaced 90

 

 

 

 

Table 4.4. Parameters used to set the genetic algorithm.

62

Different wire configurations were also analyzed, but all failed to create an efficient
closed surface. A possible explanation of the poor performance of the wire STEMS
is the large spacing between wires, ranging from 15mm to 150mm. In Figure 4.2, it
is observed that the smallest area or hole is 15mm x 62.5 mm for wire set 7 while
the biggest is observed for wire set 19 with an area of 62.5mm x 150mm is. These
spacings are too wide for waves at 700M H z and hence explain the inability of the
wire STEMS to find a switch configuration capable of creating a closed surface.

As a second attempt to create STEMS a slot version of the wire STEMS is created.
Initial Simulations of the slot STEMS revealed promising results with reference to the
effectiveness of the slot STEMS to open or close itself to incoming plane waves. Details
of the Slot STEMS template and a thorough discussion of the simulation results are

provided in section 4.4.

4.4 Slot STEMS Design and Simulation Results

4.4.1 Slot STEMS Template

With reference to the observations made in section 4.3, a slotted surface is designed
as a means to create a self tuning electromagnetic shutter. The new model is a square
surface of side length 27.3cm made of 12 conducting patches and 32 switches. The
4NEC2 model of the surface is as shown in Figure 4.4. The conducting patches are
created using a wire grid model with each grid having a segment length of A =
9.75mm which also corresponds to the width of the slots between the patches. The
radius of the wires are frequency dependent and the appropriate radius is used at

each frequency of interest with reference to the results of section 3.3. A discussion of

63

the simulated results of the slot STEMS is provided in section 4.4.2

64

IIIIIIIIIIIIIIIIIII: I:II
IIIIIIIIIIIIIIIIIII III-I

"nag-AH... nu

II IIIII IIIIII [III

"u IIIII III-I IIII

II . ,.

II

II

nu

II IIIIIIII IIIIII IIIII
II IIIIIIII—IIIIII IIIIII

III-II III-II,
IIIIII

h

 

Figure 4.4. 4NEC2 screen shot of the slot STEMS

65

4.4.2 Slot STEMS Simulation Results

The details of the GA—NEC simulations of the slot STEMS are provided in this
section. The procedure used to determine the shutter effectiveness Se of the wire
STEMS discussed in section 4.3 is also used in this section. Six different frequencies
are selected to analyze the behavior of the ST EMS and the parameters used to set
up the CA are given in Table 4.5.

Recall that in section 3.3, 42 boxes with different %— ratios are Simulated at six
different frequencies with the goal of determining the optimum % ratio that provides
the best shielding effectiveness at each frequency. The same six frequencies are used
in this section and for every frequency, the best % ratio found in section 3.3 is used
to determine the radius and segment length of the wires used to design the STEMS.
In other words, six frequencies are considered for analysis and for every frequency, a
new STEMS template and a new box are designed. A description of the wires selected
to design the Slot STEMS at each frequency is provided in Table 4.6.

For every frequency, the structure (STEMS + open box +probe) as shown in
Figure 4.5 is excited with a normal and an oblique linearly polarized plane wave that
are described in Table 4.7. To evaluate the shutter effectiveness Se of the STEMS for
each incident wave, the current on the first segment of the probe is determined for the
open box first. Then, the open box is sealed with the STEMS template and GA—NEC
is ran using the parameters of Table 4.5. To seek a STEMS template configuration

capable of creating a closed surface, the GA fitness function is set to minimize the

current on the first segment of the probe while and an open surface is sought by

66

setting the GA fitness function to maximize the current. For each case, the STEMS
shutter effectiveness is determined by using Eq4.5.

For every case, the STEMS is optimized at each of the six frequencies to create
an open or closed surface using GA-NEC with the GA parameters given in Table
4.5. The best switch configuration found at each frequency for each case is then
used to obtain the STEMS shutter effectiveness Se over a frequency range of 100MHz
centered at the frequency it has been optimized. The goal of the optimization is to
find the state with the lowest value of Se for the closed case and the highest value of
$8 for the open case.

Discussions of the results obtained at each frequency for both incident plane waves
are given in sections 4.4.2.1-4.4.2.6 while section 4.4.2.7 presents an analysis of the
shutter effectiveness evaluated at 200 different locations within the box using the
best switch configuration found at 700MHz. Table 4.8 through Table 4.11 show the
best switch configuration found at each frequency for every case studied. Figure

4.6 references the corresponding location and number of all 32 switches used on the

STEMS template. Note that:

0 ‘normal incidence angle’ is used to reference the wave incident with 6 = 0°,

¢=m
o ‘oblique incidence angle’ is used to reference the wave incident with 6 = 30°,

65:600

0 ‘closed STEMS’ is used to reference the STEMS optimized to create a closed

surface

67

0 ‘open STEMS’ is used to reference the STEMS optimized to create an Open

surface

 

GA parameters
Population Size 70
Generations 50
Crossover Probability 0.7
Mutation Probability 0.1
Selection Type Elitist
Generation Gap 0.9

 

 

 

 

 

 

 

 

 

 

 

 

Table 4.5. Genetic algorithm set-up for slot STEMS.

 

 

 

 

 

 

 

 

Wire description
Frequency(MHz) Wire radius(mm) Wire segment(mm)
750 1.53 9.75
725 1.58 9.75
700 1.64 9.75
675 1.69 9.75
650 1.74 9.75
625 1.78 9.75

 

 

 

 

 

Table 4.6. Slot STEMS wire segments and radii characteristics.

 

Wave description

 

Incidence Tilt Angle (degrees) Incidence Angle (degrees) Magnitude (V/m)

 

Normal 0 6=0,¢=0 1

 

 

 

 

 

 

 

Oblique 0 6 = 30, ¢ = 60 1

 

 

Table 4.7. Description of the normal and oblique incident waves.

68

 

 

 

 

 

 

STEMS
Load
Probe
“ ‘—Box
Z
Y
X >

Figure 4.5. Drawing of a slot STEMS on a box with a loaded probe

69

 

 

Normal: closed STEMS

625MHz 650MHz 675MHz

750MHz

 

725MHz

 

700MHz

 

 

 

 

 

 

 

switch number

 

 

 

 

 

 

 

 

 

 

10
11
12
13
14
15
16
17
18
19
20
21

 

 

 

 

 

 

 

 

 

 

 

 

22
23
24
25
26
27
28
29
30
31

 

 

 

 

 

 

 

 

 

 

32

 

 

Table 4.8. Closed STEMS best switch configurations: normal incidence angle.

70

 

oblique: closed STEMS
625MHz 650MHz 675MHz 700MHz

 

 

725MHz 750MHz

 

 

 

 

 

 

 

switch number

 

 

 

 

 

 

 

 

 

 

 

10
11

 

 

12
13
14
15
16
17
18
19
20
21

 

 

 

 

 

 

 

 

 

 

22
23
24
25
26
27
28
29
30
31

 

 

 

 

 

 

 

 

 

 

32

 

 

Table 4.9. Closed STEMS best switch configurations: oblique incidence angle.

71

 

 

Normal: open STEMS
625MHz 650MHz 675MHz 700MHz

 

725MHz 750MHz

 

 

 

 

 

 

 

 

switch number

 

 

 

 

 

 

 

 

 

 

10
11

 

 

12
13
14
15
16
17
18
19
20
21

 

 

 

 

 

 

 

 

 

 

22

 

23
24
25

 

 

 

26
27
28
29
30

 

 

 

 

 

31

 

32

 

 

Table 4.10. Open STEMS best switch configurations: normal incidence angle.

72

 

Oblique: open STEMS

625MHz 650MHz 675MHz 700MHz

 

 

725MHz 750MHz

 

 

 

 

 

 

switch number

 

 

 

 

 

 

 

 

 

 

 

10
11

 

 

12
13
14
15
16
17
18
19
20
21

 

 

 

 

 

 

 

 

 

 

22

 

23
24
25

 

 

 

26
27
28
29
30
31

 

 

 

 

 

 

 

Table 4.11. Open STEMS best switch configurations: oblique incidence angle.

73

 

Figure 4.6. Switch location on STEMS template

74

4.4.2.1 Results at 625MHz

The first frequency analyzed is 625MHz. For a vertical incidence angle, the open box
current is recorded to be Iboxopen = 2.314E - 03 (A) while the optimized STEMS
produced a current I ST E M 3 = 1.2798E -— 06 (A) for the closed closed STEMS. Using
Eq4.5, this yields a shutter effectiveness of Se=-65.144dB. The frequency sweep of
the optimized template as shown in Figure 4.7 reveals an even lower Se at 625.5MHz
with Se=-73.69dB. When optimized to create an open surface, GA—NEC found a state
with a shutter effectiveness of Se=1.23dB, obtained with 13 of the 32 switches turned
on. The frequency sweep of the open STEMS, also displayed in Figure 4.7, Shows a
frequency range of 595MHz to 640MHz with a shutter effectiveness of O or higher.
At 625MHz, the difference between closed and open STEMS shutter effectiveness is
found to be 66.27dB.

For the oblique incidence angle, the best switch configuration found over the 50
generations run for the closed STEMS has 15 switches on and 17 switches off with a
shutter effectiveness Se=-43.dB. The frequency sweep as shown in Figure 4.8 shows
that the same switch configuration produces a shutter effectiveness Se = —58.597B
at 624MHz. This represents a difference of 15dB for just a lMHz shift in frequency.
An interesting result is also obtained for the the open STEMS where the frequency
sweep of the best switch configuration produces a shielding effectiveness greater than
OdB from 585MHz to 670Mhz, shown in Figure 4.8 as well.

The histogram of the best switch states found for all 4 cases as shown in Figure

4.9 reveals that switches 1, 27 and 29 are off each time and none of the 32 switches

75

is used for all 4 cases. These results do not necessarily mean that switches 1, 27 and
29 can be deleted from the template because a different environment might require a
different switch configuration that involves 1, 27 and 29. Also, the results found by
the CA are not necessarily the best of the bunch. With a population of 70 and a total
of 50 generations, the GA only evaluates 3500 states out of the possible 4.2950 billion
states. There are still over 4.294 billion unexplored states and a definitive answer

cannot be given unless all states are evaluated.

76

 

’ I
.................._....._........._..._.+.....\

O

~.._.-.s--*O-O.-I-. .1

r...-.+.--¢----o»-—-+'
‘

>—

as;
COO

 

 

STEMS Effectiveness (dB)
4':
o

 

 

 

 

 

 

-50 -
-6O
7O _ —Closed STEMS
' "rs-Open STEMS
_80 1 1 L l 1
580 600 620 640 660
Frequency (MHz)

Figure 4.7. Frequency sweep of STEMS optimized at 625MHz: normal incidence

77

 

‘o
t
t

.L.
o

r'o
o

 

 

STEMS Effectiveness (dB)
t'»
o

 

 

 

 

 

 

 

 

-40 » i
-- Closed STEMS
'50 '- --+-- Open ST EMS
-60 . . 1 . .
5 80 600 620 640 660

Frequency (MHz)

Figure 4.8. Frequency sweep of STEMS optimized at 625MHz: oblique incidence

78

 

A

Num. of Occurrences
N on
I
l

 

 

 

 

 

 

 

 

 

 

 

01]-

10 15 20 25 30
Swtich

Figure 4.9. Histogram of the best switch states found for all 4 cases at 625MHz

79

4.4.2.2 Results at 650MHz

At 650MHz, for a normal incidence angle, the best state found for the closed STEMS
yields a shutter effectiveness of Se =-60.6937dB. Similar to the results at 625MHz, the
frequency sweep of best state as shown in Figure 4.10 reveals a shutter effectiveness
Se=-77dB obtained at 649MHz. This is an even bigger difference in the value of Se
for only a 1MHz shift, compared to the result at 625MHz. A frequency sweep of
the best state found for the open STEMS case is also shown in Figure 4.10. This
state produces a shutter effectiveness of 1.179dB and a frequency range of 645MHz
to 665MHz with value of Se greater than 0.

For the oblique incidence angle as shown in Figure 4.11, the open STEMS fre—
quency sweep shows a positive Se from 600MHz to 675MHz with its highest value of
4.58dB found at 655MHz. A value of 36:4.44dB is found at the frequency of interest
which is 650MHz. The best Se values for the closed STEMS is obtained at exactly
650MHz with Se=-44.7266dB

The histogram of the best switch states found for all 4 cases as shown in Figure
4.12 also reveals that none of the 32 switches is used for all 4 cases but this time,
only switch 19 is turned off for all 4 cases. Only 7 switches are turned on only once

compared to 11 switches for 625MHz.

80

 

('03..

o ogo
i.
I
*

 

1'»
:3

dz.
o

 

 

STEMS Effectiveness (dB)
is
o

c'n
o

-—Closed STEMS i
--+-- Open STEMS

 

 

L)
o

 

 

 

 

66
oxO
8r

620 640 660 680
Frequency (MHz)

Figure 4.10. Frequency sweep of STEMS optimized at 650MHz: normal incidence

81

 

 

 

 

 

 

 

 

 

10
A O .-..’_ -,._,_.. - -.. -.+.-..-.--¢----—1I
S
s -10 ~
8
0.)
.2
s -20
8‘3
DJ
E -30
E

-40 —Closed STEMS

-.+-- Open STEMS
-5 I 1 l I
800 620 640 660 680

Figure 4.11. Frequency sweep of STEMS optimized at 650MHz: oblique incidence

82

 

h

Num of Occurrences
N 0)

 

 

 

 

 

 

 

 

O
L.
p—

5 1o 15 2’0 2’5 3’0
Swtich

Figure 4.12. Histogram of the best switch states found for all 4 cases at 650MHz

83

4.4.2.3 Results at 675MHz

Figure 4.13 show the frequency sweep of the closed and open STEMS at 675MHz for
a normal incidence angle. Unlike 625MHz and 650MHz, the GA was unable to find
a switch state that yields a value of Se greater than 0 when set to create an open
surface. The best state found has a shutter effectiveness of Se: -1.652dB for the
open STEMS and Se=-54.6269dB for the closed STEMS.

The oblique incidence angle produced the worst results for the closed STEMS
case with 532—14376 found with a switch configuration that had only 13 of the 32
switches turned on. As Shown in Figure 4.14, the frequency sweep revealed a better
shutter effectiveness with Se=-21.23dB at 690MHz. More simulations are still being
performed to find a better state. The optimization for the open STEMS on the other
hand produced a state with 38:5.67dB as also shown in Figure 4.14.

Unlike the precedent frequencies, the histogram of the best switch states found
for all 4 cases as shown in Figure 4.15 shows that all switches are used at least once

and switches 1, 7, 11 and 26 are always turned on.

84

 

STEMS Effectiveness (dB)

 

 

 

 

 

 

 

 

—Closed STEMS
-:+-- Open STEMS
'60 640 660 680 760
Frequency (MHz)

Figure 4.13. Frequency sweep of STEMS optimized at 675MHz: normal incidence

85

STEMS Effectiveness (dB)

Figure 4.14. Frequency sweep of STEMS Optimized at 675MHz: Oblique incidence

 

10

 

 

-— Closed STEMS

 

 

 

  
   

 

 

--+-- Open STEMS
640 660 680 700
Frequency (MHz)

86

720

 

 

 

 

Num of Occurrences
—: N 0:1 -§
I"'—’l I
l I

 

 

 

 

 

 

 

 

O
L

5 1o 15 20 2’5 30
Swtich

Figure 4.15. Histogram of the best switch states found for all 4 cases at 675MHz

87

4.4.2.4 Results at 700MHz

Analysis at 700MHz for a normal incidence angle produced states capable of creating
an open and closed STEMS as shown in Figure 4.16. For the closed STEMS case, the
best shutter effectiveness is found to be Se=-67.4928dB while for the open STEMS
case, the best switch configuration produces a shutter effectiveness of 35:0.709dB.

Figure 4.17 shows an interesting plot of Se for a frequency sweep of the Oblique
incidence angle case. It is Observed that the sweep of the open STEMS best con-
figuration shows a positive value of Se for all frequency points evaluated between
650MHz and 745MHz with a value of 38:8.285dB found at 700MHz. The plot of
$6 for the frequency sweep of the closed STEMS Shows the best value of Se=-43dB
found exactly at the optimized frequency.

The Histogram of the best states for all 4 cases is shown in Figure 4.18. This
figure shows that 18 switches are tuned on only once and no switch is on for all 4

C8883.

88

 

 

 

 

 

 

 

 

 

,\_10.
S
g -20~
s:
3
3:: -30-
U
E
m -40~
U)
2
[fl -50~
C0
60~ —Closed STEMS
' --+-- Open STEMS
-7O ‘ ‘ ‘ ‘ *
660 680 700 720 740
Frequency (MHz)

Figure 4.16. Frequency sweep of STEMS optimized at 700MHz: normal incidence

89

 

10 . . __.__;_.
".*.—-""'..- -'.~.‘_..

‘-

MC

 

 

 

 

 

 

 

 

55.
6
t:
d)
>
2:
U
E
m
m
a
m
40_ —Closed STEMS .
- --+-- Open STEMS
660 680 700 720 740
Frequency (MHz)

Figure 4.17. Frequency sweep of STEMS Optimized at 700MHz: Oblique incidence

90

 

 

 

 

 

 

 

 

 

 

 

 

5L -
m
8 4- -
5
t
5
o 3 ‘ " ' ‘
"5

1_ .

0 _ 1 1 _ 1 1 1

5 1O 15 20 25 30
Swtich

Figure 4.18. Histogram of the best switch states found for all 4 cases at 700MHz

91

4.4.2.5 Results at 725MHz and 750MHz

For a normal incidence angle, the best state found for the closed STEMS has a shutter
effectiveness of Se =-46.6479dB at 725MHz and -32dB at 750MHz. The open STEMS
optimization, returned Se=1.048dB at 725MHz and 56:1.665dB at 750MHz. Figure
4.19 and Figure 4.21 show respectively the plot of the frequency sweep of the best
states found 725MHz and 750MHz.

For an Oblique incidence angle, the GA produced Se =-54dB at 725MHz and Se:-
36dB at 750MHz for the closed STEMS and 53:6.39dB at 725MHz and Se=8.2294dB
at 750MHz. The plot of Se for the frequency sweep of the best states found at 725MHz
and 750MHz are respectively shown in Figure 4.20 and Figure 4.22

The histogram of the best switch states for all 4 cases at 725MHz as shown in
Figure 4.23 shows that switches 1, 22 and 27 are turned off while switches 2 and 19
are turned on in all cases. Figure 4.24 shows the histogram of the best switches at
750MHz where switches 14 and 32 are turned Off in all cases while 14 and 23 are

turned on for all 4 analysis.

92

 

T l I

_‘—.--o-."-".—'-'.'-'-.0-.+.-..

 

 

 

 

 

 

 

 

0 h ._.-cr--"""'. "’° ----- ""~-¢~ I
it -...--— *"d I" “-1-.-.“
.3 -10 ~
5
5 -20 ~
.2
5
CH
“til -30
Q
[a -40
V)
_50 _ —Closed STEMS
--+--Open STEMS
680 700 720 740 760
Frequency (MHz)

Figure 4.19. Frequency sweep of STEMS Optimized at 725MHz: normal incidence

93

 

,.-.—r- -.‘___

 

 

STEMS Effectiveness (dB)

-— Closed STEMS

 

 

-50 ~ --+-- Open STEMS

 

 

 

 

680 700 720 740 760
Frequency (MHz)

Figure 4.20. Frequency sweep of STEMS optimized at 725MHz: oblique incidence

94

 

.-..-.-o—--'*""'"'+"°+""’""°"+'--O---cam»

_ ”fig--
0 W.

>---+---o---o----'"'

A

p.

I
(It

STEMS Effectiveness (dB)

 

 

—Closed STEMS d

 

 

 

 

 

 

 

-35 -
--+--Open STEMS
_4 1 1 L 4
900 720 740 760 780
Frequency (MHz)

Figure 4.21. Frequency sweep of STEMS optimized at 750MHz: normal incidence

95

 

 

STEMS Effectiveness (dB)

 

 

 

 

 

 

 

—Closed STEMS
--+-- Open STEMS
-40 - 1 1 1 1 -
700 720 740 760 780
Frequency (MHz)

Figure 4.22. Frequency sweep of STEMS optimized at 750MHz: oblique incidence

96

 

 

 

 

 

 

 

 

6 V I v 1 1
5- q
(I)
34- - ~
8
l:
§
03" — -
"5
§2~ fl — —-|.;
1_

 

 

 

 

 

 

5 1o 15 2o ' 25 ‘ 30
Swtich

Figure 4.23. Histogram of the best switch states found for all 4 cases at 725MHz

97

 

A
l
I

Num. of Occurrences
N (a)
l
]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

5 1o 15 20 25 30 '
Swtich

Figure 4.24. Histogram of the best switch states found for all 4 cases at 750MHz

98

4.4.2.6 Study of shutter effectiveness with reference to location within

the box

The shutter effectiveness of the STEMS is optimized based on the ratio of the current
on the loaded segment of the probe. This represents a single observation point inside
the box. In order to determine the effect on the shutter effectiveness of a given
template configuration due to changes of location within the box, a new study is
performed. In this study, the best switch configurations found for a normal incidence
wave at 700MHz for the open and closed STEMS are used.

Given the open box of Figure 4.3 without the probe and the lead, 200 points are
selected and the open box is excited with the normal incident wave described in Table
4.7. Using NEC4, the total electric field at each point is evaluated. The box is then
sealed with the ST EMS and the switches are set to the states found to be the best
at creating a closed surface for the normal incidence wave. The total electric field at
the location of the same 200 points is evaluated once more. The process is repeated
by changing the configuration of the switches to the states found to be the best at
creating an open surface.

Let S f be defined to be the ratio of the total field for the box sealed with the
STEMS to the total field of the open box. Using that definition, the value of S f for
the open and closed STEMS is evaluated at each of the 200 point and plotted. Figure
4.25 shows a plot of S f for a closed STEMS. In that figure, it can be seen that there
is very little change (2.3dB) of the value of S f as the line is moved from (Y=0, 2:0)

to (Y=-0.05, Z=-0.05). The biggest variation (17dB) is recorded when moving along

99

the X axis from one end of the box to the other. The same observation applies to the
open STEMS S fas shown in Figure 4.26 where the maximum variation of S f from
(Y=O, Z=0) to (Y=-—0.05, Z=-0.05) is only 1.5dB. There is less variation in this case
as the location is moved along the X axis from one end of the box to the other, with

a maximum difference of 1.7dB, compare to the 17dB obtained for the closed STEMS

100

 

-10’

-20 “

Shutter effectiveness (dB)

 

 

 

I I L

——Y:O, 2:0 I
-~-o--- Y:0.05, Z:-0.05 H

 

 

 

 

 

 

'\
9
|

 

{F‘-
1

4

 

-0.l

-0.0S O 0.05 0.1
Position along the X axis inside the box

Figure 4.25. Total field within the box based on location for closed STEMS

101

 

 

Shutter effectiveness (dB)

 

 

 

 

 

 

-5
-6 -
— Y=O, 2:0
-7 ~ "*- Y=0.05, Z=-0.05 -
-O.l -0.05 O 0.05 0.1

Position along the X axis inside the box

Figure 4.26. Total field within the box based on location for open STEMS

102

4.5 Conclusion

In this chapter, an overview of GA-NEC along with the optimization scheme and the
switch model is given in section 4.2. A brief overview of the first STEMS considered is
provided in section 4.3 while section 4.4 presents the details of the final design along
with a discussion of the simulated results. The next chapter discusses measurement

results of a prototype STEMS fabricated at Michigan State University

103

CHAPTER 5

MEASUREMENT SET-UP AND AND RESULTS

In this chapter, the fabrication, measurement set-up and measured results of a pro-
totype STEMS are presented. The template of the prototype is made of 12 patches
with 32 switches. In section 5.2, the design and fabrication of the STEMS prototype
are presented. Details of the fabricated conducting box and monopole antenna are
given in section 5.3. The experimental set-up for measuring the STEMS shutter ef-
fectiveness is detailed in section 5.4. The results of the measured shutter effectiveness

using a random search code and a genetic algorithm are discussed in section 5.5.

5.1 Design and fabrication of STEMS prototype

To fabricate the STEMS prototype, a layout of the template geometry is first realized
using ORCAD10.0. The template is laid out as a single layer, square surface of side
27.3cm with 12 surface patches. This layout is selected to be identical to the simulated
STEMS of section 4.4. The initial slot width of 9.75mm used in section 4.4 is changed
to 7.62mm so that the spacing between surface patches is equivalent to the spacing
between the two end pins of the switches that are placed on the template.

To enable the placement of the switches on the template, small areas of copper
with diameter 1.5mm are placed on the surface. The diameter of 1.5mm is selected
to provide sufficient area to solder the switch pins to the copper. Figure 5.1 shows
a. sketch of the STEMS template and a screen shot of a copper pad as drawn in

orcad is shown in Figure 5.2. Table 5.1 provides the dimensions of the patches used

104

to create the STEMS surface. The layout of the finished surface was then sent to
the Michigan State University ECE Shop where the STEMS template is realized by
milling out copper at the location of the slots on an F R4 epoxy circuit board of
thickness 1.25mm. This board was selected based on availability.

The type of switch selected for the purpose of this project is a Coto technology
SIP REED relay switch series 9011-05-10. This type of switch is selected because it
is the same type used on a prototype of the SSA antenna mentioned in section 3.7. A
photograph of the switch is shown in Figure 5.3 and its characteristics are presented
in Table 5.2.

The switches are soldered on the milled FR4 eproxy board by first drilling through
holes of 0.52mm in diameter at the location of the copper pads. The switches are
then placed on the bottom layer of the FR4 Eproxy board in such way that the pins
go through the holes to the top layer that has the patches and copper pads. The
two outer pins of the switches are soldered to the patches while the two inner pins
get soldered to the copper pads as shown in Figure 5.4 . Wires are then soldered to
the inner pins and connected to the header of a six-inch 64-line ribbon cable. The
ribbon cable header is epoxied to the edge of the top layer of the FR4 Eproxy to
avoid movements from the wires. A photograph of the switches on the bottom layer
is shown in Figure 5.5 while Figure 5.6 shows a photograph of the top layer with the
soldered pins, wires, surface patches and ribbon cable.

Prior to soldering the switches, their functionality is tested by conducting a con-
tinuity test. The continuity test is performed by measuring the resistance between

the two end pins of the switches using an ohmmeter. When the two inner pins are

105

connected to a 5V supply, the reading of the resistance should be near 052 and when
the inner pins are left unconnected, a value of -1 should be displayed on the screen
of the ohmmeter, indicating an open circuit. A closed switch is characterized by the
near 00 reading while an open switch is characterized by the value of -1.

To control the states of the switches, the ribbon cable is connected to a control
board that serves as interface between the STEMS and the computer. The control
board is used to provide the necessary current needed to power the switches. To
drive the relays, Toshiba TD62783AP integrated circuits are used. The TOSHIBA
TD62783AP are high-voltage source drivers that output 5V on each of the output pins.
Each IC has 8 input pins, 8 output pins, 1 ground and 1 VCC pin. To power the 32
switches, 4 Toshiba TD62783AP are needed. The input of the Toshiba TD62783AP
are connected to the computer via a 50 pin National Instrument cable connector and
a 10 pin ribbon cable connector while the output pins are connected to the switches
using a 64 pin ribbon cable connector. A protoboard PB104 is used to implement the
control board; a photograph of the finished board is shown in Figure 5.7.

It should be noted at this point that the NEC4 model of the STEMS as discussed
in section4.4 was not backed by any substrate. This is due to the fact that NEC4
does not support substrates. A prototype closer to the NEC4 model could have
been fabricated using a mesh of wires backed by a foam material because of the near
free space characteristics of the foam, but soldering the switches would have been
a problem. Besides, the simulation study of chapter4 is performed only to get an

insight into the concept of STEMS.

106

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Patch characteristics
Patch number Width and Length (mm)
1 49.815, 40.065
2a 49.815, 49.815
2b 20.565, 10.815
3 59.565, 40.065
4a 69.315, 40.065
4b 20.565, 20.565
5 79.065, 69.315
6a 79.065, 40.065
6b 49.815, 20.565
7a 79.065, 40.065
7b 49.815, 20.565
8 79.065, 30.315
9 49.815, 40.065
10a 79.065, 30.315
10b 40.065, 30.315
11 79.065, 40.065
12 49.815, 40.065

 

 

 

Table 5.1. Patch Sizes.

 

Switch Characteristics
Nominal Voltage = 5V
Nominal Current = 10mA
Vmax = 6.5V
Vmin = 3.75V
Coil Resistance = 5009
Switching Cycle = 2222/3
Lifetime = 250 million cycles

 

 

 

 

 

 

 

 

 

 

 

Table 5.2. Properties of Cote technology SIP REED relay switch.

107

 

I i ' Copper
Lo t'

Figure 5.2. Screenshot of the location of a switch marked by copperpads.

 

109

 

Figure 5.3. Cote technology SIP REED relay switch series 9011-05-10.

110

Control

 

Figure 5.4. Photograph Showing the placement of each switch.

111

 

Figure 5.5. Bottom layer of the fabricated prototype with the switches.

112

Ribbon cable to
control board

 

Figure 5.6. Top layer of the fabricated prototype.

113

To (‘umpult-r

”phi”.
anuflin
D

it

 

Figure 5.7. Photograph Showing the control board.

114

5.2 Open box and probe fabrication

As a means to measure the shutter effectiveness of STEMS, a conducting open box
and various probes were also fabricated. Fabrication of the conducting open box was
done at the Michigan State University Machine Shop using 5 aluminum sheets of
equal dimensions (27.3 by 27.3cm). The open box was fabricated by first creating a
frame out of aluminum rods. The aluminum sheets were then screwed to the frame
to create an open box. To avoid gaps at the edges of the box, copper tape is applied
over the contour of the edges of the box.

Three probes of different lengths were also fabricated. The probes are quar-
ter wavelength monopoles fabricated by simply cutting wires of length equal to 5}
then soldering each wire to an SMA connector. The wires have the same radius
(a=0.645mm) and their lengths are 10cm, 8.82cm and 7.894cm. Their respective res-
onant frequencies are 750MHz, 850MHz and 950MHz to enable measurements from
700MHz to lGHz. It is important to note that for the purpose of STEMS measure-
ments, a new monopole antenna does not need to be fabricated each time that a
new frequency is selected for measurement. The reason is that the STEMS shutter
efficiency is calculated as a ratio of the current on the probe for the box open with
the box sealed by the STEMS. A photograph of the fabricated box with a probe is

shown in Figure 5.8

115

 

Figure 5.8. Fabricated box with a probe.

116

5.3 Experiment Set Up

The set-up for the experiment is done following the diagram shown in Figure 5.9. A
Hewlett-Packard 8657A Signal Generator is used as a source to the transmit antenna
which in this case is a broadband horn antenna (500MHz to 6GHz). The connection
between the signal generator and the transmit antenna is done using a coaxial Type-N
cable as shown in Figure 5.10. A photograph showing how the horn antenna is placed
inside the anechoic chamber with reference to the box is shown in Figure 5.11.

The receiver as shown in Figure 5.12 is a Singer Stoddart N M-37/ 57 EMI/ Field
Intensity Meter that connects to the computer and the probe. The probe is connected
to the front input port of the receiver through a coaxial Type—N cable. The computer
used is a Fujitsu B-Series Lifebook laptop with a 700MHz Pentium 3 processor and
512MB of RAM that connects to the control board and the video log output port of
the receiver. These connections are achieved using two national Instrument PCMCIA
DAQ cards that are inserted into the computer. These cards are: DAQCard-DIO-24
and DAQCard—6024E as shown in Figure 5.13. The DAQCard-DIO-24 is a 24 bit
input/ output card that connects to the 50 pin header of the control board through a
ribbon cable. The DAQCard—6024E is a 12 bit input/ output card with a 16 channel
in, 2 channel out analog to digital converter (ADC) that has a sampling rate of
200,000/3. Only 1 of the ADC channels along with 16 channel in of the DAQCard-
6024B are used in this set up. The DAQCard-6024E connects to the 10 pin header
of the control board and the video log output port of the receiver via a split ribbon

cable that is shown is Figure 5.14

117

 

 

 

 

 

I
I
Probe STEMS Transmit I
°°°°° Antenna :
I
I
I
I
I
., I
...... I

Anechoic Source

Computer Chamber

 

 

 

 

 

Receiver

 

 

 

Figure 5.9. Diagram of the set-up used to measure the STEMS.

118

fi 7 a W o
lransnnt
Antenna

BNC

Cable III.

Signal
Generate

 

Figure 5.10. Signal generator connected to the transmit antenna.

119

Transmit
Antenna

Box with
probe

 

Figure 5.11. Box and transmit antenna inside the anechoic chamber.

120

 

Figure 5.12. Photograph showing the receiver

121

 

Figure 5.13. National Instrument Data Acquisition cards

122

 

Figure 5.14. National Instrument split ribbon cable

123

5.4 Evaluating the STEMS shutter effectiveness

In order to evaluate the STEMS shutter effectiveness, the transmit antenna is first
excited at the desired frequency X by the source with an amplitude of Y volts. Then
the open box voltage is measured by the receiver through the probe within the box. A
code written in Visual Basic (included in the appendix) is used to capture the reading
of the receiver through the use of the analog to digital converter card, DAQCard-
6024133. The open box voltage is saved in the code as reference voltage V0 and used to
evaluate the STEMS shutter efficiency at the same specific frequency X. The open box
is then sealed with the STEMS and the STEMS voltage, V5, measured by the receiver

is sent to the computer for evaluation. The shutter effectiveness Se is evaluated using:

V
S6 = 20 * 10910—0. (5.1)
V5

Notice that Eq-5.1 is the same as,

Se = 20 * logloflz, (5.2)
IS

as defined in chapter 4. The reason is due to the relationship V = 12* I which requires

V0 = 12* IO and VS = Ra: I S- Here R is the 500 impedance of the receiver; therefore,

Io __ V0
15 _. V5' (5.3)

It is important to point out that the system must be calibrated each time before

any measurement is made at a given frequency. It was observed in a previous project

124

[47] that the voltage reported by the computer is not the same as the input voltage
to the receiver. Therefore, the voltage at the receiver output V109 must be converted
to give the input voltage V0 . Through experimentation, it was found that the
conversion equation is:

V
log — AB
V0 = 10 ' (5.4)

where A and B are variables that need to be determined for each frequency. A and B
are found by connecting the input port of the receiver directly to the source. In this
manner, the value of V0 ia be the same as the amplitude at which the source is set.
Knowing V0, Eq—5.4 can be solved by setting V0 to two different values and using

the values obtain for V109 to solve for A and B.

5.5 Measurement results

To gain a better understanding of STEMS, several tests were performed on the built
prototype. The first analysis performed on the prototype was a statistical study to
determine the distribution of the STEMS shutter effectiveness for a random sample
space of 50000 switch configurations. The next study performed was an optimization
of the STEMS template using a genetic algorithm. The results obtained from the
random search and genetic algorithm are compared to determine the most efficient
approach for finding appropriate STEMS configurations.

To perform the random search and genetic algorithm analysis, the box and probe

are set up in the far field region of the transmit antenna in such a way that the

125

fields from the transmit antenna are normally incident on the the STEMS as shown
in Figure 5.15 with 6 = 90° and qi = 0°.

A third study of the STEMS behavior was performed where the ST EMS was
displaced 4Ft sideways from its original location, also shown in Figure 5.15. Even
though the STEMS is still located within the anechoic chamber, the displacement by
4Ft creates a different environment where the waves from the transmit antenna are
no longer normally incident on the STEMS. Hence, this technique enables the study

of the STEMS for an oblique incidence angle given by (9 = 900 and (15 = 41.6°).

126

-l
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
l
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I

.I

 

 

 

 

 

/41.6°

an lo

5 \ a

' \

I \

I \

I

I6 \ .

I \939

 

3315'?
R1
/
59
¢

 

 

 

 

 

Figure 5.15. Box placement for normal and oblique measurements

127

5.5.1 Random Search

The first experimental test performed on the prototype STEMS is a statistical study
of the STEMS shutter effectiveness for a random sample of 50000 switch configura-
tions. With 32 switches used on the STEMS template, 50000 switch configurations
represents only 0.001164% of the total 4.295 billion states. In order to carry out
the evaluation of the 50000 random states, a simple Visual Basic code was written.
Before all the states can be evaluated, the open box voltage is read and saved in the
Visual Basic code. Then, the box is sealed with the STEMS template and all of the
50000 random switch configurations are evaluated one at a time.

The code reads from a file of random 8 bit binary strings. Each bit is assigned to
a switch and the state of the switch is set with reference to the value of the binary
bit. For each switch, if the assigned bit is a 1, the switch is turned on and if the bit is
a 0, then the switch is left open. Since there are 32 switches on the STEMS template,
the code reads four 8 bit strings at a time.

Once the states of all 32 bits are set, the voltage on the probe is read and the
shutter effectiveness of the present state is evaluated with reference to the open box
voltage by using Eq—5.1. The shutter effectiveness is evaluated for all 50000 ran-
dom switch configurations and saved to a text file. The process starting with the
measurement of the Open box voltage was repeated for 13 evenly spaced frequencies
selected between 700MHz and 1000MHz with a step size of 25MHz using the same
50000 swtich configurations. Once all 50000 states are evaluated, the histogram of the

sample is plotted using a code written in Matlab. The random search and histogram

128

codes are included in the appendix.

The first frequency selected is 700MHz. As shown in Figure 5.16, the shutter
effectiveness of all 50000 states measured varies between -44dB and -5dB. It is also
observed that over 98% of all the states considered have a shutter effectiveness between
-32.3dB and —8.9dB. A closer view of Figure 5.16 as shown in Figure 5.17 reveals that
only 2 switch configurations have a sutter effectiveness of -40dB or lower, while only
one state is found with Se=-5dB. If -40dB is selected to be an acceptable shutter
effectiveness to create a closed surface, only 2 switch configurations or 0.004% of the
50000 random sample would be able to provide the desired result. Likewise, if -6dB
is selected as an acceptable value to create an open surface, only 5 out of the 50000
random sample would be able to perform as required. However, this implies that
approximately (5/ 50000) =I= 4295000000 = 429500 of the STEMS configurations have
at least this value. 429500 represents a big number of states. Thus, there is hope that
a good search algorithm may be able to quickly find one of these states, or perhaps
even a better state.

The second frequency considered is 725MHz. At this frequency, As shown in
Figure 5.18, the distribution of the shutter effectiveness is between -26dB and -6dB
with over 99% of the 50000 random states considered ranging between -24dB and
-7dB. Figure 5.19 shows that the -6dB required to create an open surface is achieved
by 3 states while none of the 50000 random sample was able to provide the requiered
-40dB to create a closed surface.

The third frequency selected for measurement is 750MHz. The histogram at this

frequency as shown in Figure 5.20 shows a pattern very different from those obtained

129

at 700MHz and 725MHz. The distribution of the shutter effectiveness is skewed
toward lower values with 37571 states having a shutter effectiveness of -43dB or less.
While there is an abundance of states capable of creating a closed surface, no state was
found with a shutter effectiveness of -6dB or higher. A closer view of the distribution
of the shutter effectiveness as shown in Figure 5.21 reveals that the highest Se value
obtained is —7dB, showing that none of the sample of 50000 states considered can be
used to create an open surface.

The distribution of the shutter effectiveness at 775MHz is shown in Figure 5.22 and
Figure 5.23. Analysis of these plots shows a distribution of the shutter effectiveness
skewed toward higher values with 804 random states having a shutter effectiveness of
-6dB or higher. This means that 1.61% of the 50000 states are able to create an open
surface. On the other hand, Only 23 states have a shutter effectiveness lower than
-40dB with the lowest value recorded to be -50.94dB.

At 800MHz, the distribution of the shutter effectiveness as shown in Figure 5.24
reveals 148 states with a positive value of Se. These positive values signify that the
voltage measured by the probe for all 148 different switch configurations have a value
greater than the open box probe voltage. 14817 states out of the 50000 random states
have a value of Se greater than -6dB. This implies that 29.63% of the sample space
considered can be used to create an open surface. Though over 25% of the sample
space states are capable of creating an open surface, Figure 5.25 shows that only 1
switch configuration with Set-40dB is capable of creating a closed surface.

At 825MHz, a distribution of the shutter effectiveness similar to that of Figure 5.24

is observed. As seen in Figure 5.26, over 97% of the 50000 random states considered

130

have a value of Se ranging between -14.6dB and 4dB. 1075 switch configurations have
a positive Se value and 16142 have a value of Se greater than -6dB. Unlike 800MHz,
the lowest shutter effectiveness was recorded to be -26.1925dB. A closer view of the
distribution of the shutter is shown in Figure 5.27.

The following frequency selected for measurement was 850MHz. This frequency
produced the worst results with regards to creating a closed surface. As shown in
Figure 5.28 and Figure 5.29. No state out of the 50000 random sample was able to
produce a shutter effectiveness lower than -13.06dB. On the other hand, up to 43466
states with a shutter effectiveness greater than -6dB were found.

The next frequency of interest was 875MHz. Though none of the 50000 random
states produced a shutter effectiveness capable of creating a closed surface, the his-
tograms as shown in Figure 5.30 and Figure 5.31 show a better distribution compared
with the distribution obtained at 850MHz. The lowest Se found was -38.523dB, which
is just -1.477dB short from the desired value of -40dB. 6128 states produced a shutter
effectiveness greater than -6dB.

At 900Mhz, the histogram of the shutter effectiveness as shown in Figure 5.32
reveals the lowest value of Se=-58.3022dB recorded among all frequencies measured
so far. A closer view of the distribution of the shutter effectiveness as shown in Figure
5.33 shows 28 different states with a shutter effectiveness less than -40dB. 1579 states
were also recorded to have a shutter effectiveness greater than -6dB. Unlike 875MHz
and 850MHz, no state was recorded to have a positive value of 33.

A 925 MHz, results similar to those recorded at 900MHz are observed. Figure

5.34 shows a distribution of the shutter effectiveness skewed toward higher values

131

of Se with its highest recorded to be —3dB. The lowest value of Se is found to be
-54.0146dB. Of all 50000 states measured, 104 were found to have a value of Se lower
than -40dB while 890 states produced a value Se greater than -6dB. A close view of
the distribution of the shutter effectiveness is shown in Figure 5.33.

At 950MHz, a pattern similar to that of 925MHz is observed as shown in Figure
5.34. The lowest Se recorded was found to be -56.37dB. One state produced a positive
value of 35:0.138dB and 9378 states have a value of Se higher than -6dB. Only 122
states were receded with Se lower than -40dB. A close view of the distribution of the
shutter effectiveness is shown in Figure 5.37.

The final 2 frequencies considered are 975MHz and 1000MHz. The distributions
obtained for these two frequencies were very similar to 950MHz, 925MHz and 900MHz.
As shown in Figure 5.38 and Figure 5.39 the distribution of the shutter effectiveness
at 975MHz reveals that over 49232 states are between -30dB and 2dB with 1278
states having a value of Se greater than -6dB. Only 56 states were receded to have a
shutter effectiveness of -40dB or lower. The distribution of the shutter effectiveness
at 1000MHz is shown in Figure 5.40 and Figure 5.41. Though the lowest value of Se
in the 900Mhz to 1000MHz range was recorded at 1000MHz with Se =-48.8005dB the
highest value of Se among all frequencies analyzed was recorded at 1000MHz with
53:8.585dB. A close view of the distribution of the shutter effectiveness at 975MHz
and 1000MHz are shown shown in Figure 5.37. At 1000MHz, 36 states have a value

of Se lower than -40dB while 13722 have a shutter effectiveness greater than -6dB.

132

 

1400 r w r

1200

1000

800 -

600 F

Number of States

400 -

200 -

 

 

 

-44 -36.2! -2é.4 -26.6 -12.8
Shutter Effectiveness (dB)

Figure 5.16. Distribution of Se for a random sample of 50000 states at 700MHz

133

 

“##UI
OU’IOU’IO

Number of States
N N on
C? 01

.II
01

10

 

 

 

 

-44 -36.2 -28.4 -20.6 -12.8
Close \erw of the Shutter Effectiveness (dB)

Figure 5.17. Close view of the distribution of Se for the random sample at 700MHz

134

 

800 . . .

700 ~

600 ~

500 -

Number of States
A
O
‘5’

 

 

 

36 -22 -18 -114 -10
Shutter Effectiveness (dB)

Figure 5.18. Distribution of Se for a random sample of 50000 states at 725MHz

135

 

(D‘s-#01
U'IOUIO

 

C

 

Number of States
N 8 0.)

 

 

 

 

 

36 -22 -18 -114
Close \erw of the Shutter Effectiveness (dB)

Figure 5.19. Close view of the distribution of Se for the random sample at 725MHz

136

 

3000 . . .

I

2500

N
O
O
O
I

1500 -

 

 

Number of States

—b
O
O
O

 

500 r |

Mt. .

- 2 -43

 

 

 

 

 

 

-34
Shutter Effectiveness (dB)

Figure 5.20. Distribution of Se for a random sample of 50000 states at 750MHz

137

 

##(fl
0010

 

OJ
(’1
I
J
1

0

Number of States
N (“If m

 

 

 

 

 

 

 

 

07 4
15L
10~ .
51
£52 -43 -34 -25 -16

Close \fiew of the Shutter Effectiveness (dB)

Figure 5.21. Close view of the distribution of Se for the random sample at 750MHz

138

 

1 400 1 .

1200-

1000*

800 - a

600 ~ 4

Number of States

400 ~ A

200 ~ ~

 

 

 

551 -41.2 __ - -3i.4 -21.6 -11.8
Shutter Effectiveness (dB)

Figure 5.22. Distribution of Se for a random sample of 50000 states at 775MHz

139

 

(Jab-50!
OU’IOU’IO

 

 

Number of States
N N 0)
C? 01

_a
GI

10*

 

 

 

  

 

   

 

351 -41.2 -31.4 -21.6 -11.8
Close View of the Shutter Effectiveness (dB)

Figure 5.23. Close view of the distribution of Se for the random sample at 775MHz

140

 

1400 r 1 .

1200* -

1000- ~

800 - -

600 7 .4

Number of States

4oo~ «

200 -

 

 

 

34 -34.6~ ' 252 -15.8 -6.4

Shutter Effectiveness (dB)

Figure 5.24. Distribution of Se for a random sample of 50000 states at 800MHz

141

 

b 01
01 O
I7

l

.5
O

 

(.0
01
-

O

 

Number of States
N N 0)
C? OI

 

.I.
(TI

10-

 

 

 

 

—44 -34.6 -25.2 -15.8 -6.4
Close View of the Shutter Effectiveness (dB)

Figure 5.25. Close view of the distribution of Se for the random sample at 800MHz

142

 

1400 .

1200

1000-

800 ~

600 ~

Number of States

400 -

200 r

 

 

527 ~20} -14.6 -8.4 -2.2
Shutter Effectiveness (dB)

 

Figure 5.26. Distribution of Se for a random sample of 50000 states at 825MHz

143

 

do It J8 01
O 01 O 01 O
I I I T
q

 

Number of States
N N co
0 UI

.I.
01

10-

 

 

 

 

 

527 -20.8 -1AI.5 -8:4
Close View of the Shutter Effectiveness (dB)

Figure 5.27. Close view of the distribution of Se for the random sample at 825MHz

144

 

2000 . T .
1 800 - ~
1 600 - .
1 400 r

 

 

 

 

 

 

 

 

Number of States
0 s ‘s‘ ‘s‘
8 o o o

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

I l M _
-6 -2 2
Shutter Effectiveness (dB)

Figure 5.28. Distribution of Se for a random sample of 50000 states at 850MHz

145

 

 

 

 

O

 

Number of States
N N 00
9 01

 

.3
01

 

 

10-

 

 

 

 

 

-14 -1O -6 -2 2
Close \erw of the Shutter Effectiveness (dB)

Figure 5.29. Close view of the distribution of Se for the random sample at 850MHz

146

 

1 600 l I

1400-

1200—

1000

 

800 -

Number of States

600 r

400 -

200 ~

 

 

 

 

39 55.2 -2i.4 -12.6 -3.8
Shutter Effectiveness (dB)

Figure 5.30. Distribution of Se for a random sample of 50000 states at 875MHz

147

 

##U’I
OU‘IO

 

(a)

0 0|
I I
1

Number of States
N N (A)
3 0'

 

_L A

(11 O 0|
I I I
i l

 

I I i i n
- 9 -30.2 -21.4 -12.6 -3.8
Close View of the Shutter Effectiveness (dB)

 

 

Figure 5.31. Close view of the distribution of 86 for the random sample at 875MHz

148

 

1 800 l T I
1600 . J

1400 ~ -

_II
N
O
O

 

1000*

800 ~

Number of States

600 ~
400 ~

200 — J

 

 

 

559 -47.8 -36.6 -25.4 -14.2
Shutter Effectiveness (dB)

Figure 5.32. Distribution of Se for a random sample of 50000 states at 900MHz

149

 

(ADA-#01
0010010

 

Number of States
N N 0)
e a"

.5
UI

 

 

10

I

 

 

 

 

 

3'19 -47.8 -36.6 -25.4 -14.2
Close \erw of the Shutter Effectiveness (dB)

Figure 5.33. Close view of the distribution of Se for the random sample at 900MHz

150

 

1 200 . w I

1000—

 

800 -

600 r

Number of States

400 -

200 ~

 

 

 

555 -44.6 i -34.2 -23.8 -13.4
Shutter Effectiveness (dB)

Figure 5.34. Distribution of Se for a random sample of 50000 states at 925MHz

151

 

0

 

Number of States
N N (a)
0 0|

.5
01
T

10*

 

 

 

 

 

355 444.5 -34.2 -23.3 -13.4
Close View of the Shutter Effectiveness (dB)

Figure 5.35. Close View of the distribution of Se for the random sample at 925MHz

152

 

900 . I .
800 ~ 4

700 r 1

 

Number of States
I: o: a)
8 8 8

O)
0
0

200 ~ ~

100—

 

 

 

357 J 145.6 v -34.2 -22.8 -11.4
Shutter Effectiveness (dB)

Figure 5.36. Distribution of Se for a random sample of 50000 states at 950MHz

153

 

45-501
0010

 

(a)
001

 

Number of States
N 8 (a)

 

 

 

 

 

 

o ..
15~ -
10-

5 ’- j
557 -45.5 -34.2 -22.8 -11.4

Close View of the Shutter Effectiveness (dB)

Figure 5.37. Close view of the distribution of Se for the random sample at 950MHz

154

 

2500

2000 ~ ~

1500- 1

T

1 000 ‘

Number of States

500 ~ -

 

 

 

-3o.4 45.5 -8.8
Shutter Effectiveness (d B)

352 -4I.2

Figure 5.38. Distribution of Se for a random sample of 50000 states at 975MHz

155

 

0000-5-50!
0010010

Number of States
N N
0 01

 

.3
01

10

 

 

 

 

 

352 -41.2 -3o.4 -19.6 -8.8
Close View of the Shutter Effectiveness (dB)

Figure 5.39. Close view of the distribution of Se for the random sample at 975MHz

156

 

1200 - .
1000- .
800— ‘ ~

600 ~ 4

Number of States

4oo~ -

200 . *

 

 

 

-49 -37.4 -25.8 44.2 -2.6
Shutter Effectiveness (dB)

Figure 5.40. Distribution of Se for a random sample of 50000 states at 1000MHz

157

 

#01
010
g

 

.5
0

 

Q)
01
_

0

 

 

 

Number of States
N a 0)

-3
010
'E:

 

10*

 

  

 

 

 

-49 -37.4 -25.8 44.2
Close View of the Shutter Effectiveness (dB)

Figure 5.41. Close view of the distribution of Se for the random sample: 1000MHz

158

Recall that a state is capable of creating a closed surface if it has a shutter effec-
tiveness of -40dB or lower. Similarly, a state is capable of creating an open surface
if it has a shutter effectiveness of -6dB or higher. A summary of the percentage of
states capable of creating an open or closed surface for all the frequencies analyzed is
shown in Figure 5.42 and Figure 5.43. From these plots, it can be observed that the
random search failed to find a state capable of creating a closed surface at 725MHz,
825MHz, 850MHz and 875MHz. It found only 1 state at 800MHz and 2 states at
700MHz. These are results obtained for a sample space of 50000 states and the total
measurement time per frequency for all 50000 states is 3hrs and 35mm. These results
are not satisfactory because of the low probability of finding acceptable states.

Better results are obtained as far as finding states capable of creating an open
surface. The random search only failed at 750MHz and barely made it at 700MHz
and 725MHz. At the frequencies where no acceptable values where obtained, a bigger
sample space of 100000 states was evaluated but still with no success. This does not
imply that there are no states at those frequencies capable of creating a closed or open
surface. With 32 switches, there are over 4.2 billion states and 100000 only represents
a mere fraction of the total possible states. To avoid evaluating all 4.2 billion states,

a more sophisticated search algorithm becomes needed to complete the task.

159

100

 

 

 

 

 

 

 

 

 

ClosedJSTEMS
3 “O“ Open STEMS
5 60~ "-.
5 i I|
.2 .-' i.
o g ‘.
5 40~ .-' '-._
_,..I' ‘-.
;" ‘-, .0
20 P .1" “ .‘\ if-
‘b‘ i" K" II
1 1 K? ..... ‘I. 4 K31.
900 800 850 900 950 1000
Frequency (MHz)

Figure 5.42. Percentage of states for a sample of 50000 states

160

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0.5 I I l I I 1
3 Closed STEMS
3 --~- Open STEMS
0.4
,3 0.3 '
5
H—I
o
5° 0.2- .
0.1
“$2.! ----- i \ 1 1 1
'900 750 800 850 900 950 1000

Frequency (MHz)

Figure 5.43. Close view Percentage of states for a sample of 50000 states

161

5.5.2 Genetic Algorithm

Upon completion of the random search, a genetic algorithm was run at the same
13 frequencies with the same experimental set up as that of the random search.
The CA used is written in visual basic following the diagram of Figure 5.44. For
each frequency, an initial population of 100 different switch configurations selected
randomly is generated. Each of the 100 configurations is used to set the states of
the switches on the template and the shutter effectiveness of each state is calculated
using (5.1) and the value of the shutter effectiveness is used to determine the fitness
of the configuration. The fitness is evaluated using a fitness function that was found
through trial and error. The fitness function used is F = m — V109, where V109
is the voltage at the video log output of the receiver.

Once the evaluation of the fitness of all switch configurations in the population
is completed and the population is not the last generation, a selection of the switch
configurations with the best fitness values are selected. The selection type used in the
code is tournament among three switch configurations. Three switch configurations
are selected randomly and their fitness values are compared. The switch configuration
with the highest fitness is selected.

This process is repeated till the mating pool is filled. Once the mating pool is
filled, mates are pared randomly and a 2 point crossover is performed with crossover
probability PC. After the crossover process, a single bit mutation is performed with
probability Pm. After the mutation, a new generation is filled and the process is

repeated until all the generations have been evaluated. The fitness function is set to

162

minimize or maximize \/ 0.584 — Vlog depending on the goal of the GA. If the goal
is to create a closed STEMS then the fitness function is set to minimize, and if the
goal is to create an open ST EMS then the fitness function is set to maximize.

All GA measurements are taken with the following parameters:

Population: 100

Generations=80

Crossover probability=0.7

Mutation probability: Evolving

Generation gap = 50%

The term evolving is used to represent a quantity that varies with time. The mutation
probability starts with a value of 0.5 and changes after each generation to 0.5/(gener-
ation number). The generation gap represents the number of individuals within the
population that are selected for crossover.

For every frequency evaluated the system is first calibrated and the open box

voltage is recorded and saved in the Visual Basic code for reference.

163

 

 

 

 

Generate Initial

 

 

   
 
   

 

 

 

Population
1 yes
Evaluate , Termination
Fitness Criteria met?

 

 

  

1....
Perform
Selection

 

 

  
   

Perform

Crossover
Fill New Perform
Generation Mutation

 

 

Figure 5.44. Diagram of the genetic algorithm used in the experiment

164

The first frequency selected for analysis is 700MHz. At that frequency, a value of
-40.038dB was recorded for the closed STEMS while 0.9966dB was found for the open
box. When the random search was ran, the best switch configuration for the closed
STEMS produced -43.108dB and -4.5dB for the best switch configuration found for
the open STEMS. Though the random search produced a lower value of the shutter
effectiveness compared to the GA, it should be pointed out that the GA reached the
value of -40.038 after 69 generations as shown in Figure 5.45. This implies that the
GA was able to find an acceptable state within 6900 evaluations.

Figure 5.46 shows a plot of the best shutter effectiveness found for each generation
that the GA is set to optimize for an open surface. The GA found an acceptable
state right from its first generation and continued to produce better results till all the
generation were exhausted. The best state is found at generation 77 with Se=.995dB.
generation 77 is 4 generations from the stopping point. With only 4 more generations
to run, it could be implied that the GA had not yet converge and better value of
the Shutter effectiveness could have been obtained is the number of generations was
increased.

The second frequency selected for optimization is 725MHz. As shown in Figure
5.47, the GA set up to optimize for a closed surface was able to find an acceptable state
after 70 generations. The random search was unable to find a state with a shutter
effectiveness less than -40dB at 725MHz. The best value of the shutter effectiveness
the random search found was -25.7702dB. The GA found a switch configuration with
a shutter effectiveness less than -25.7702dB after only 20 generation and the best

shutter effectiveness after all 80 generations was receded to be -40.09dB.

165

The best state found when optimized to create an open surface had a shutter
effectiveness of -1.86011dB while the best state produced by the random search had
a shutter effectiveness of -6.0007dB. As shown in Figure 5.48, the GA was run only
for 52 generations because it found the best switch configuration with the shutter
effectiveness of -1.86011dB after only 12 generations or 1200 evaluation. The GA ran
from generation 12 to generation 52 without finding any better states. At that point,
it was concluded that the GA had converged and the run was stopped.

The next frequency at which the GA was run is 750MHz. As shown in Figure
5.49, the GA set up to optimize for a closed surface was able to find an acceptable
state after only 12 generations. The best shutter effectiveness recorded after all 80
generations were evaluated was found to be -51.1512dB.

When optimized to create an open surface, the best state found had a shutter
effectiveness of -1.7926dB after only 23 generations. The random search failed to find
a state with a shutter effectiveness of -6dB or higher after all 50000 sample states
were evaluated. The CA was stopped after 33 generations and a plot of the best
shutter effectiveness found for each generation is displayed in Figure 5.50.

At 775MHz, the GA was able to find states capable of achieving the desired results.
As shown in Figure 5.51, when set up to optimize for a closed surface, the best state
found after all 80 generations were evaluated had a shutter effectiveness of ~56.7673dB.
The GA was able to find a switch configuration with a shutter effectiveness less than
-40dB on its second generation. A plot of the best shutter effectiveness obtained for
each generation when the GA is set up to create an open surface is shown in Figure

5.52. A shutter effectiveness higher than the desired value of -6dB was obtained after

166

only 7 generations and the best state found after all 80 generations was found to be
-2.9389dB.

After 775MHz, 800MHz was selected for measurement. The CA set up to optimize
for a closed surface was able to find an acceptable state after 40 generations. The best
shutter effectiveness recorded after all 80 generations were evaluated was found to be
-44.262dB and Figure 5.53 shows a plot of the best value obtained for the shutter
effectiveness with reference to the number of generations.

When optimized to create an open surface, the best state found had a shutter
effectiveness of 2.1972dB after only 17 generations. No better states were found for
the remainder of the generation. The Random search found a slightly higher value
for the shutter effectiveness, 2.88dB. A plot of the best shutter effectiveness found for
each generation is displayed in Figure 5.54.

The next frequency selected for optimization is 825MHz. As shown in Figure 5.55,
the GA set up to optimize for a closed surface failed to find an acceptable state after
all 80 generations. The random search was also unable to find an acceptable state.

Figure 5.56 shows a plot of the best shutter effectiveness found for each generation
when the GA is set to optimize for an open surface. The GA found an acceptable
state right from its first generation. The best state of all 80 generations is found at
generation 33, and no improvement was made afterward

At 850MHz, the GA was unable to find a state capable of achieving the desired
results. As shown in Figure 5.57, when set up to Optimize for a closed surface, the
best state found after all 80 generations had a shutter effectiveness of —27.179dB. The

best result produced by the random search was only -13.06dB

167

A plot of the best shutter effectiveness Obtained for each generation when the GA
is set up to create an open surface is shown in Figure 5.58. A shutter effectiveness
higher than the desired value of -6dB was Obtained from the first generation and the
best Of all the generation was found after 4 generations. The best value of 7.016dB
remained unchanged from the 4th generation until generation 80.

The next frequency at which the GA was run is 875Hz. As shown in Figure 5.59,
the GA set up to optimize for a closed surface was unable to find an acceptable
state. The best value returned after all 50 generations were evaluated is -33.55dB.
The random search was also unable to find an acceptable state at 875MHz.

When optimized to create an Open surface, the best state found had a shutter
effectiveness of 4.45dB. A positive effectiveness was recorded from the first start as
shown in Figure 5.60. The best shutter effectiveness was found after 15 generation
and no better results were obtained for the remaining generations.

At 900MHz, the GA was able to find states capable of achieving the desired
results. As shown in Figure 5.61, the best state found when the GA is set to optimize
for a closed surface has a shutter effectiveness of -53.713dB. The GA was able to
find a switch configuration with a shutter effectiveness less than -40dB on its third
generation.

A plot Of the best shutter effectiveness obtained for each generation when the GA
is set up to create an open surface is shown in Figure 5.62. A shutter effectiveness
higher than the desired value Of -6dB was Obtained from the first generation and the
best state found after all 80 generations were run was found to -2.375dB.

After 900MHz, 925MHz was selected for measurement. The best closed surface

168

Optimized switch configuration provided a shutter effectiveness of -54.7485dB, ob-
tained after 26 generations. The GA was able to produce an acceptable state on the
3rd generation as shown in Figure 5.63.

The best open surface Optimized switch configuration provided a shutter effective-
ness of -3.6004dB as seen in Figure 5.64 An acceptable state was found after only 2
generations.

The next frequency at which the GA was ran is 950MHz. As shown in Figure
5.65, the best closed surface switch configuration found has a shutter efiectiveness of
-55.78dB. By the 4th generation, the GA had already found a state with a shutter
effectiveness of —47.76dB.

When optimized to create an open surface, the best state found had a shutter
effectiveness of -0.8682dB. The first initial population contained already some states
with a shutter effectiveness above the required value of -6dB. A plot of the best shutter
effectiveness found for each generation is displayed in Figure 5.66.

Interesting results are obtained at 975MHz. The initial population generated
already contained a state with a shutter effectiveness Of -42.013dB. After all 50 gen-
erations were run, the best closed surface switch configuration found has a shutter
effectiveness of -55.263dB as shown in Figure 5.67

Likewise, the initial population generated when the GA is set to create an open
surface already contained states with positive values of shutter effectiveness. The opti-
mization was able to produce a state with an even higher value of shutter effectiveness.
the highest value Obtained was 1.24dB. A plot of the best shutter effectiveness found

for each generation is displayed in Figure 5.68.

169

The final frequency measured was 1000MHz. As shown in Figure 5.69, the GA
set up to optimize for a closed surface was able to find an acceptable state after only
11 generations. The best shutter effectiveness recorded after all 80 generations were
evaluated was found to be —56.2342dB.

When optimized to create an open surface, the first population created contained
states that already met the requirement of —6dB or higher. The best state found after
the GA was ran had a positive value of shutter effectiveness with 38:1.57dB. The
plot of the best shutter effectiveness found for each generation is displayed in Figure
5.70.

For all 13 frequencies considered, the genetic algorithm was able to find states
capable of creating an open surface. In most cases, the GA found an acceptable state
within the first 5 generations. The GA failed to find states capable Of creating a
closed surface at 825MHz, 850MHz and 875MHz. This pattern is also Observed with
the random search. Figure 5.72 and Figure 5.71 show a comparison of the best values

obtained for the GA and the random search.

170

 

 

—Closed STEMS (700MHz)

 

 

 

-37 ~

-38 _
-39 r \—
-40 *

O 20 4O 6O 80
Generation

 

Shutter Effectiveness (dB)

 

 

 

Figure 5.45. Closed STEMS Se Obtained through the GA at 700MHz

171

 

 

 

 

 

 

 

 

 

 

a
'8 -1 -
5
“3:!
8
s -3-
s
‘3 4-
.G
VJ
-5 —Open STEMS (700MHz)
-6 . . ,
o 20 4o 60 80

Generation

Figure 5.46. Open STEMS Se Obtained through the GA at 700MHz

172

 

L.
U:

 

 

—-Closed STEMS (725MHz)

 

 

[in
o

-25 ~

-30- 1

-40— L—ffi—x

'450 20 4o 60 80
Generation

 

Shutter Effectiveness (dB)

 

 

 

Figure 5.47. Closed STEMS Se obtained through the CA at 725MHz

173

Shutter Effectiveness (dB)

 

I
p—n
UI

1

—4

 

 

 

 

 

 

 

 

 

-2 -
-2.5

-3 —
-3.5 «

— Open STEMS (7 25MHz)
-4 . . . 1 1
0 10 20 3O 4O 50 60
Generation

Figure 5.48. Open STEMS Se Obtained through the CA at 725MHz

174

 

 

—Closed STEMS (750MHz)

 

 

 

 

Shutter Effectiveness (dB)
is
o

 

 

 

 

 

-45 ~
so
"550 20 40 6O 80

Generation

Figure 5.49. Closed STEMS Se obtained through the CA at 750MHz

175

Shutter Effectiveness (dB)

 

-1.5

 

—Open STEMS (750MHz)

-2- ,,_F

f

 

 

 

 

 

 

 

l

O 5 10 15 20 25 30 35
Generation

 

I
A
,_

Figure 5.50. Open STEMS Se Obtained through the CA at 750MHz

176

 

 

—Closed STEMS (775MHz)

 

 

 

 

Shutter Effectiveness (dB)
is
UI

-55r

 

 

 

 

O 20 40 6O 80
Generation

Figure 5.51. Closed STEMS Se obtained through the GA at 775MHz

177

 

 

 

Shutter Effectiveness (dB)
6:.

 

 

 

 

 

 

 

-6 -
-7 1
—Open STEMS (775MHz)
-8 i 1 r
0 20 40 60 80
Generation

Figure 5.52. Open STEMS Se Obtained through the CA at 775MHz

178

 

 

-—Closed STEMS (800MHz)

 

 

 

 

 

Shutter Effectiveness (dB)

I

—40

 

 

 

 

 

O 20 4O 6O 80
Generation

Figure 5.53. Closed STEMS Se Obtained through the GA at 800MHz

179

Shutter Effectiveness (dB)

 

I"
u:

 

N

I—I
M
I

H
I

 

.o
u:

0

 

.33
LII

 

—Open STEMS (800MHz)

 

 

 

 

 

4L 1

4O 60 80
Generation

 

OIL
N
C

Figure 5.54. Open STEMS Se obtained through the CA at 800MHz

180

 

 

 

-—Closed STEMS (825MHz)

 

 

'5:
f

I
p—I
00

I

:13
o

 

1'9
N

 

Shutter Effectiveness (dB)

I'O
4:.

 

 

 

'260 20 4o 60 80
Generation

Figure 5.55. Closed STEMS Se Obtained through the CA at 825MHz

181

Shutter Effectiveness (dB)

 

 

3.5-

2.5 -

 

1.5-

 

 

—Open STEMS (825MHz)

 

 

 

 

 

0 20 4O 60 80
Generation

Figure 5.56. Open STEMS Se Obtained through the GA at 825MHz

182

 

-23

 

-—Closed STEMS (850MHz)

 

 

 

 

['9
Ln

 

Shutter Effectiveness (dB)

 

IL)
\1

 

 

 

0 20 4O 6O 80
Generation

Figure 5.57. Closed STEMS Se obtained through the GA at 850MHz

183

 

 

0 \1

Shutter Effectiveness (dB)
til

 

 

 

 

 

 

 

 

4 _
3 _ 4
J —Open STEMS (850MHz)
2 l l I
0 20 4O 60 80
Generation

Figure 5.58. Open STEMS Se obtained through the GA at 850MHz

184

-18

 

 

 

4 —Closed STEMS (875MHz)]
-20 .

-22 -

 

Shutter Effectiveness (dB)
:15
ON

do
N

 

 

 

 

 

O 20 4O 60 80
Generation

Figure 5.59. Closed STEMS Se Obtained through the CA at 875MHz

185

 

P
i

 

so i»
IJI U.) LII L
I I T

Shutter Effectiveness (dB)
N

 

 

p—I
UI
L

 

 

—Open STEMS (875MHz)

 

 

 

1 i I M

0 20 40 6O 80
Generation

 

Figure 5.60. Open STEMS Se Obtained through the CA at 875MHz

186

 

 

6»
o

 

 

 

 

 

 

 

 

—Closed STEMS (900MHz)

A -35 'l

m

E

8

g -40 -

>

'5

8

E -45-

923

‘5

.c:

(A _50_ _

-55 ' ' ‘
0 20 4O 60 80
Generation

Figure 5.61. Closed STEMS Se obtained through the GA at 900MHz

187

 

 

 

 

 

 

 

 

 

 

 

 

-2
E? 25 , I
'3
-s-
>
‘5
8
t...
“ii -3.5 ~ .
5‘3
*5
.C:
U) _4_I _
-—Open STEMS (900MHz)
'4'50 20 4e 60 80
Generation

Figure 5.62. Open STEMS Se Obtained through the GA at 900MHz

188

 

-25

-30 \

 

-—Closed STEMS (925MHz)

 

 

 

 

Shutter Effectiveness (dB)
1.
o
I

 

 

-55— \—\—\ 4

 

 

 

0 20 40 6O 80
Generation

Figure 5.63. Closed STEMS Se Obtained through the CA at 925MHz

189

Shutter Effectiveness (dB)

 

 

 

 

 

 

--Open STEMS (925MHz)

 

 

 

 

 

 

0 20 40 6O 80
Generation

Figure 5.64. Open STEMS Se Obtained through the CA at 925MHz

190

 

 

 

 

 

 

 

 

 

 

--Closed STEMS (950MHz)
-35 \
8
B
a 401
Q)
s:
d)
.2
g -45 i
t
m
is -50—
‘5
.I:
m
-55 L.“
_6 I I I
0O 20 40 60 80

Generation

Figure 5.65. Closed STEMS Se Obtained through the CA at 950MHz

191

 

 

Shutter Effectiveness (dB)
:1)

 

 

 

I] —Open STEMS (950MHz)

 

 

 

 

 

' O 20 40 60 80
Generation

Figure 5.66. Open STEMS Se Obtained through the GA at 950MHz

192

 

 

-—Closed STEMS (975MHz)

 

 

 

 

Shutter Effectiveness (dB)

I
UI
A

I
I

 

 

 

 

0 20 4O 6O 80
Generation

Figure 5.67. Closed STEMS Se obtained through the GA at 975MHz

193

 

 

p—u
N

 

p—a
h—I
I

 

Shutter Effectiveness (dB)

 

 

 

 

 

 

 

 

0.9 ~ 1
0.8
0.7 —Open STEMS (975MHz)
0 20 4O 60 80
Generation

Figure 5.68. Open STEMS Se obtained through the CA at 975MHz

194

 

 

 

 

 

 

 

 

 

—-Closed STEMS (1000MHz)
-35
E
'8
33 -40~
d)
s:
d.)
.2
8 -45
3::
in
§ -50
‘5
.2
V)
-55 - 4
'600 20 40 60 80
Generation

Figure 5.69. Closed STEMS Se obtained through the GA at 1000MHz

195

 

 

1.5— F 4

 

 

0.5 r )

 

Shutter Effectiveness (dB)
5':
E" C.”

 

 

 

 

 

 

 

 

- 1 -
-1.5 ./ —Open STEMS (1000MHz)
-2 . 1 1
O 20 4O 60 80
Generation

Figure 5.70. Open STEMS Se obtained through the GA at 1000MHz

196

 

“10 I I I I

I

-15

Shutter Effectiveness (dB)

 

 

l l

 

- + - Random Search
— GA Search

 

 

 

 

 

.6900 725 750 775 800

825 850 87
Frequency (MHz)

900 925 950 975 1000

Figure 5.71. Best STEMS Se for both GA and random search: Closed STEMS

197

 

10 I

Shutter Effectiveness (dB)

 

 

 

 

 

 

 

 

 

_6 ._ “ ~ 1 .a
‘ «I - + - Random Search
1 l l l 1 l L 1 GA SeaI'CI'I
foo 725 750 775 800 825 850 875 900 925 950 975 1000

Frequency (MHz)

Figure 5.72. Best STEMS Se for both GA and random search: Open STEMS

198

5.5.3 STEMS optimized using a GA for an oblique incidence angle

After the GA was completed, the box was moved to a different location still within
the anechoic chamber as shown in Figure 5.15. This set up is used to analyzed the
performance of STEMS based on location and angle of incidence of incoming waves.
Four different frequencies were selected and the genetic algorithm of section 5.5.2
was used to optimize the STEMS to create an Open and closed surface. Once an
acceptable state was found, a network analyzer was used to obtain a frequency sweep
of the state. For every frequency evaluated the system is first calibrated and the
open voltage is recorded and saved in the visual basic code for reference. The first
frequency selected for analysis was 700MHz. At that frequency, the genetic algorithm
was able to optimize the STEMS to create an open and closed surface. Figure 5.73
shows a frequency sweep of the best open and closed STEMS states Optimized at
700MHz. This plot shows a positive value of the shutter effectiveness extending over
a 50MHz range from 695MHz to 745MHz. the closed STEMS plot show a shutter
effectiveness of -48dB at exactly 700MHz. The bandwidth of the closed STEMS is
not as wide as that of the open STEMS but more plots provided in the appendix
show that the STEMS can be Optimized to to be narrow band or broad band.

The next frequency considered for analysis was 775MHz. Using the GA, a closed
STEMS state with a shutter effectiveness of -42.7dB and an open STEMS state with
a shutter effectiveness of -4.8dB are obtained. Figure 5.74 shows the frequency sweep
of the shutter effectiveness obtained using the best switch state obtained for each

case.

199

The third frequency was 872MHz. At that frequency, The shutter effectiveness of
the best state found for the closed STEMS is -48dB while the stutter effectiveness of
the best state found for the open STEMS is OdB. Figure 5.75 shows the frequency
sweep of the shutter effectiveness Obtained using the best switch state obtained for
each case.

The last frequency analyzed was 1000MHz. The GA was once more able to find

states capable of creating a closed and open surface as shown in Figure 5.76.

200

 

I

O ” .o"'.'.'.""'.'O-O-o-o-o-o-IO'0"'"PW-01..| 4

 

 

 

 

 

 

 

 

 

a -10

5

E

.2. -20

‘3

E

g -3e

2

m -40. Closed STEMS

--°-- Open STEMS
-5 .
850 700 750

Frequency (MHz)

Figure 5.73. Closed and open STEMS best states frequency sweep at 700MHz

201

 

OUI

‘.
It"

i
‘0
I
,r
\.
:

 

 

Shutter Effectiveness (dB)

 

 

 

 

 

 

 

35 _ Closed STEMS
' --°-- Open STEMS
-40 -
700 750 800 850
Frequency (MHz)

Figure 5.74. Closed and open STEMS best states frequency sweep at 775MHz

202

 

 

 

 

 

 

 

 

 

 

a -10~
5
8
.2. -20 "
‘5
Q
E -30—
2
V1 _40 _ Closed STEMS
--0-- Open STEMS
-5 . .
800 850 900 950
Frequency (MHz)

Figure 5.75. Closed and open STEMS best states frequency sweep at 872MHz

203

 

 

 

 

 

 

 

 

 

0 I" ~

8
'3 -10~
8
5
f6 -30-
i:
‘5 -40~
"m: -—Closed STEMS

_50~ --+-- Open STEMS

-6g . . 1

50 900 950 1000 1050
Frequency (MHz)

Figure 5.76. Closed and open STEMS best states frequency sweep at 1000MHz

204

5.6 Conclusion

In this chapter, the fabrication, measurement set-up and measured results of a pro-
totype STEMS are presented. The design and fabrication of the STEMS prototype
are presented in section 5.2. Details of the fabricated conducting box and monopole
antenna are given in section 5.3. The experimental set-up for measuring the STEMS
shutter effectiveness is detailed in section 5.4. The results of the measured shutter
effectiveness using a random search code and a genetic algorithm are discussed in

section 5.5.

205

CHAPTER 6

CONCLUSION AND FUTURE WORK

6.1 Conclusion

A new class of electromagnetic devices called self tuning electromagnetic shutters
(STEMS) is introduced in this thesis. The STEMS is a slotted metallic surface with
computer-controlled switches capable of creating an electronically—controllable iris.
An overview of the concept and theory of STEMS is presented in chapter 2. Chapter
3 details the design guidelines of the numerical electromagnetic code NEC4 along with
the modeling of closed conducting surfaces using wire grids. The design and simu-
lation of STEMS using GA-NEC is discussed in chapter 4, while chapter 5 presents
the details of the fabrication and measurement of a prototype STEMS. Several con-
cluding remarks based on the results of the simulation and the investigations of the

prototype STEMS can be drawn as follows:

0 STEMS Shutter Effectiveness

Both simulation and measurement results attest to the effectiveness of STEMS
to creating an electronically-controllable iris. The STEMS can behave as a
closed or Open surface with reference to incident electromagnetic waves by

changing the states of the switches on its template.

0 Frequency Tunability

Both simulation and measurement results also prove that the STEMS ability

206

to exhibit characteristics of an open or closed surface is not limited to a fixed
frequency. Through the use of evolutionary search algorithms such as GAS, the
frequency of operation of STEMS can be shifted to any desired frequency point
within a range of 300MHz. The value 300MHz represents the range in which
the prototype was tested and it does not represent the limit of the range of the

STEMS frequency tunability.

0 STEMS Shutter Effectiveness as a function of Angle of Incidence

The STEMS ability to create a closed and open surface with respect to differ-
ent angles of incidences Of electromagnetic waves has also been proven through
both simulation and measurement. Regardless of the incidence angle of incom-
ing electromagnetic wave, the STEMS can be optimized to produce a shutter
effectiveness lower than -40dB or higher than OdB depending on the task being

performed.

6.2 Future Work
Most of the work presented in this thesis has been focused toward the feasibility of

STEMS and several of their characteristics are yet to be investigated.

0 STEMS Shutter Effectiveness as a function of Location

The study performed in the measurement section shows that certain switch
configurations can produce similar effects at two different locations while others

produce very different results. A potential future experiment could be to place

207

various probes within the box and run an Optimization scheme to determine the

STEMS shutter effectiveness of all the probes combined.

STEMS Bandwidth:

An important property of STEMS that is worth analyzing is their bandwidth.
Bandwidth Optimization is not possible through the Singer Stoddart NM-37/ 57
EMI / Field Intensity Meter but this could be realized on the Network Analyzer

with LabView. This task could be done through simulation.

STEMS Multiple Frequencies of Operation:

Another important property of STEMS that could be investigated is their ability
to create a closed or open surface at multiple frequencies. The Field Intensity
Meter mentioned above allows for single frequency evaluations and therefore,
the Network Analyzer would have to be used for that purpose as well. This
could be done through simulation as well to get an insight into the multiple

frequency of operation of STEMS

208

APPENDICES

209

IAFU?EEQLHD{IA

CODES
A.1 Visual Basic Source Code
A.1.1 Random Search
XXZXXZXXXXXXXZXXXXXX2%XXZXZZXZZZZXZZXXXZZZXXXXZXXXXZXZXZXZXZXXZ
Z Raoul ouedraogo, cuedraog (at) man. edu %
X This Visual Basic code reads from a file of random states X
X to set the switches on the STEMS template %

XXZZXZZZZZZZXZ%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%ZZZZXXZXZ

Dim StopProcess As Boolean
Dim FilePath, VmFilePath As String
Dim OUFilePath As String
Dim DBRFilePath As String
Dim Best_StateFilePath, worst_StateFilePath As String
Dim Data As String

Dim n As String

Dim Iter As String

Dim Volt_0ut() As Double
Dim Vm As String

Dim Ratio, DBR As String
Dim Vsc As String

Dim LowRatio As String
Dim BeginTime As Date

Dim EndTime As Date

Dim ElapsedTime As Double
Dim InO, InpO As String
Dim In1, Inp1 As String
Dim In2, Inp2 As String
Dim In3, Inp3 As String
Dim BinaryCodes As Variant
Dim Voltages As Variant

Private Sub cmdDIOSet_Click()

Set8PinI0 txtDIDSet.Text
End Sub

210

Private Sub GetData(VoltAvg)
CWAI1.AcquireData Voltages, BinaryCOdes, 5
VoltAvg = CWStat1.Mean(Voltages)

DoEvents
CWGraph1.PlotY Voltages
End Sub

Private Sub Set24PinIO(ByteO, Bytel, ByteZ)
CWDIO2.Ports.Item(0).SingleWrite ByteO
CWD102.Ports.Item(1).SingleWrite Bytel
CWDIO2.Ports.Item(2).SingleWrite Byte2
StopProcess = True
End Sub

Private Sub Set8PinIOfoteO)
CWDI01.Ports.Item(0).SingleWrite ByteO
End Sub

Private Sub ConfigureCWAI1()
CUAI1.Configure
End Sub

Private Sub cmdSetState_C1ick()
StopProcess = True
’OPEN INPUT FILE
FilePath = InputBox("Enter file path here")
Open FilePath For Input As #1
’OPEN OUTPUT FILE AND FILE FOR BEST STATE
OUFilePath = InputBox("Enter file path here")
Open OUFilePath For Output As #2
DBRFilePath = InputBox("Enter file path here")
Open DBRFilePath For Output As #3
Best_StateFilePath = InputBox("Enter file path here")
Open Best_StateFilePath For Output As #4
worst_StateFilePath = InputBox("Enter file path here")

Open worst_StateFilePath For Output As #5
’COUNTER & Timer Start

Iter = 1

LodeR = -2

HigthR = -200

BeginTime = New

txtBeginTime.Text = (BeginTime)

211

MaxIter = InputBox("Enter number of random iteration", MaxIter)
’START LOOP

Do Until Iter = MaxIter

Line Input #1, Data ’(vbTab)

txtByteO.Text = VbCrTab & Data

InO = Data

Line Input #1, Data

txtByt61.Text - VbCrTab & Data

In1 = Data

Line Input #1, Data

txtByte2.Text = VbCrTab & Data

In2 = Data

Line Input #1, Data

txtByte3.Text = VbCrTab & Data

In3 = Data

Set8PinIO txtByteO.Text

Set24PinIO txtByte1.Text, txtByte2.Text, txtByte3.Text

’WAIT FOR SWITCHES TO SETTLE
For ii = 1 To txtVait.Text
Next ii

’DISPLAY NUMBER OF ITERATIONS
txtCounter.Text = Iter

’READ VOLTAGE AND RETAIN LOWEST SWR
Dim VoltAvg As Variant

Dim i As Integer

ConfigureCWAIl

GetData VoltAvg

Vm = 10 ‘ ((VoltAvg - 0.1040006) / (0.16415))
Vsc = txtVsc.Text

Ratio = Vm / Vsc

DBR = 20 * (Log(Ratio)) / Log(10)
If Abs(DBR) > Abs(LodeR) Then
LodeR = DBR

SI = InO

S2 = Inl

S3 = In2

S4 = In3

Print #4, SI, S2, S3, S4

End If

If Abs(DBR) < Abs(HigthR) Then
HigthR = DBR

HS1 = InO

212

HS2 = In1
H83 = In2
HS4 = In3
Print #5, H81, HS2, HS3, HS4
End If

’DISPLAY THE PARAMETERS
txtShoonlt.Text = Str$(Vm)
txtShowRatio.Text = Str$(VOltAvg)
txtShowDBR.Text = Str$(DBR)
txtShowLodeR.Text = Str$(LodeR)
txtShowHigthR.Text = Str$(HigthR)
txtShowInO.Text = Str$(81)
txtShowIn1.Text = Str$(S2)
txtShowIn2.Text a Str$(83)
txtShowIn3.Text = Str$(S4)

’WRITE VOLTAGE TO FILE "C:\07-O8 team\Vou1tage_Output.txt"
Print #2, Vm

Print #3, DBR

Iter = Iter + 1

Loop

’CDMPUTE AND DISPLAY ELAPSED TIME

EndTime = New

ElapsedTime = DateDiff("s", BeginTime, EndTime)
txtEndTime.Text = (EndTime)
txtElapsedTime.Text = (ElapsedTime)

’CLOSE FILES

Close #1

Close #2

Close #3

Close #4

Close #5

End Sub

Private Sub cdendProgram_Click()
Set8PinIO O
Set24PinIO O, O, 0

End

End Sub

213

A.1.2 Genetic Algorithm: Closed STEMS

ZZZZZXZZZX%%XXZ%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%Z

%
Z
%

Raoul ouedraogo, ouedraog (at) msu.edu %
This Visual Basic code is a genetic algorithm %
that optimizes for a closed STEMS %

ZZZZXXZZZZZZZX%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%Z

Dim
Dim
Dim
Dim
Dim
Dim
Dim
Dim
Dim
Dim
Dim
Dim
Dim
Dim
Dim
Dim
Dim
Dim
Dim
Dim
Dim
Dim

NewPop(1000, 64) As Boolean

01dPop<1000, 64) As Boolean

StateToSet<64) As Boolean

BestinPop(64) As Boolean

WorstinPop(64) As Boolean

Plotit(400) As

FitnessClOOO), DBR(1000) As Single

BigFit(500) As Single

GenBest(500) As Siuiyngle

Angitness, MaxFitness, MinFitness, PopSize, As Single
BestFitness, WorstFitness, TotalFitness, As Single
igenno As Integer

BitLength, NGen, INaxFitness As Integer

ifirst As Integer

ProbCross, ProbMut, Xmin, Xmax, X, Bi, kk, As Singe
ShowDBR, ShowDBRworst, Rate As Single

N0, N1, N2, N3 As String

B0, Bl, B2, B3, BinDigit, BestChrome As String
BinaryCodes As Variant

Voltages As Variant

VoltAvg As Variant

i As Integer

Private Sub cmdDIOSet_Click()
Set8PinIO txtDIOSet.Text

End

Sub

Private Sub cdeunAcquisition_Click()
ConfigureCWAIl
GetData VoltAvg

End

Sub

Private Sub GetData(VoltAvg)
CWAI1.AcquireData Voltages, BinaryCodes, 5
VoltAvg = CWStat1.Mean(Voltages)

214

DoEvents
End Sub

Private Sub Set8PinIO(Byte0)
CWDIOI.Ports.Item(O).SingleWrite ByteO
End Sub

Private Sub ConfigureCWAIl()
CWAIl.Configure
End Sub

Private Sub cmdSetIO24_Click()
Set24PinIO txtODIO24.Text, txt1DIO24.Text, txt2DIO24.Text
End Sub

Private Sub Set24PinIO(ByteO, Bytel, Byte2)
CWDIO2.Ports.Item(0).SingleWrite ByteO
CWDIO2.Ports.Item(1).SingleWrite Bytei
CWDIO2.Ports.Item(2).SingleWrite Byte2
StopProcess = True

End Sub

Private Sub cdeunGa_Click()
Call RunGA
End Sub

Private Sub RunGAC)

Best_StateFilePath = InputBox(" Enter file path here")

Open Best_StateFilePath For Output As #1
BestReduction_FilePath = InputBox(" Enter file path here")
Open BestReduction_FilePath For Output As #2
Worst_StateFilePath = InputBox(" Enter file path here")
Open Worst_StateFilePath For Output As #3
WorstReduction_FilePath = InputBox(" Enter file path here")
Open WorstReduction_FilePath For Output As #4

Dim p As String
BitLength = 32
p = InputBox("Enter population size (<=1000)")
PopSize = CInt(Val(p))
p = InputBox("Enter number of generations")
NGen = CInt(Val(p))
Randomize
Call InitPop

215

ifirst = 1
For igenno = 1 To NGen
txtGenNo.Text = igenno
txtGenNo.SetFoCus
Call EvaluateFitness
Call FitStats
Call ScaleFitness
Call SelectPop
Call CrossPop
Call MutatePop
Print #1, BestChrome
Next igenno

For j = 1 To 32
StateToSet(j) = BestinPop(j)
Next 3
Call SetState
Close #1
Close #2
Close #3
Close #4
End Sub

Sub InitPop()
’Initializes the population to random values
For i = 1 To PopSize
For j = 1 To BitLength
If Rnd() > 0.5 Then
OldPop(i, j) = True
Else
OldPop(i, j) = False
End If
Next j
Next i
End Sub
Sub EvaluateFitness()
Dim VoltAvg As Variant
For i = 1 To PopSize
For j = 1 To 32
StateToSet(j) = OldPop(i, j)
Next j
Call SetState

’wait while state settles
For ii = 1 To txtWait.Text

216

Next ii
Vsc = txtVsc.Text

’read voltage
ConfigureCWAIl
GetData VoltAvg
Fitness(1) = Sqr(0.5841) - (VoltAvg)
Vm = 10 ‘ ((VoltAvg - 0.1040006) / (0.16415))
Ratio 8 Vm / Vsc
DBR(i) = 20 * (Log(Ratio)) / Log(10)
Next i
End Sub
Sub ScaleFitness()
Dim cmult, a, b As Single
Dim i As Integer

’Scales the fitness of the population
cmult = 1.2
If MaxFitness > cmult * Angitness Then

a = (cmult - 1) * (Angitness / (MaxFitness - Angitness))
b = (1 - a) * Angitness
If a * MinFitness + b < 0 Then

a = Angitness / (Angitness - MinFitness)

b = -a * MinFitness

End If
For i = 1 To PopSize
Fitness(1) = a * Fitness(i) + b

Next 1

End If
End Sub
Sub FitStats()
Dim sum As Single
Dim i As Integer

’Calculates the statistics of the population fitness

If ifirst = 1 Then

For k = 1 To BitLength
BestinPop(k) = OldPop(1, k)

Next k
BestFitness = Fitness(1)
WorstFitness = Fitness(1)
Fmax = Fitness(1)
Fmin = Fitness(1)
ifirst = 0

End If

217

sum = O
IMaxFitness = O
Fmax = BestFitness
Fmin = WorstFitness
For i = 1 To PopSize
sum = sum + Fitness(i)
If Fitness(i) > BestFitness Then
BestChrome = ""
IMaxFitness = i
Fmax = Fitness(i)
ShowDBR = DBR(i)
BestFitness = Fitness(i)
For j = 1 To BitLength
BestinPop(j) = OldPop(i, j)
If BestinPop(j) Then
BestChrome = 1 & BestChrome
Else: BestChrome = 0 & BestChrome

End If
Next j
End If

If Fitness(i) < WorstFitness Then
Fmin = Fitness(i)
ShowDBRworst = DBR(i)
WorstFitness = Fitness(i)
For k = 1 To BitLength
WorstinPop(k) = OldPop(i, k)
If WorstinPop(k) Then
WorstChrome 8 1 A WorstChrome
Else: WorstChrome = O & WorstChrome
End If
Next k
End If
Next i
Angitness = sum / PopSize
MaxFitness = Fmax
MinFitness Fmin
TotalFitness a sum
GenBest(igenno) = MaxFitness
txtBest.Text = MaxFitness
txtBest.SetFocus
txtWorst.Text = MinFitness
txtWorst.SetFocus
txtGenAvg.Text = Angitness
txtGenAvg.SetFocus
txtBestIndividual.Text = BestChrome

218

txtWorstIndividual.Text = WorstChrome
txtXValue.Text ShowDBR
txtYValue.Text - ShowDBRworst
CWGraph1.PlotY GenBest
Print #2, ShowDBR
Print #3, WorstChrome
Print #4, ShowDBRworst
End Sub
Sub SelectPop()
Dim NNew, NSelect, Nallocate, i, j, k As Integer

’Selects the population for the next generation
’First select by expectd allocation
NNew = O
For i = 1 To PopSize
Rate = txtRatio.Text
Nallocate a Int(Fitness(i) / Angitness)
If Nallocate > Rate Then
For j = 1 To Nallocate
NNew = NNew + 1
For k = 1 To BitLength
NewPop(NNew, k) = OldPop(i, k)
Next k
Next j
End If
Next i
End Sub
Sub CrossPop()
ProbCross = txtXOver.Text
Dim breed1(64), breed2(64) As Boolean

’performs cross over of breeding population’
ncross = NNew
For i = 1 To NNew Step 2

’select pairs
i1 = Int(1 + Rnd() * ncross)
For k = 1 To BitLength
breed1(k) - NewPop(i1, k)
Next k
If 11 < ncross Then
For j = ii To ncross
For k = 1 To BitLength
NewPop(j, k) = NewPop(j + 1, k)
Next k

219

Next j
End If
ncross = ncross - 1
11 = Int(1 + Rnd() * ncross)
For k = 1 To BitLength
breed2(k) = NewPop(il, k)
Next k
If i1 < ncross Then
For j = 11 To ncross
For k = 1 To BitLength
NewPop(j, k) = NewPop(j + 1, k)
Next k
Next j
End If
ncross = ncross - 1
test = Rnd()
If ProbCross > test Then
i1 = Int(1 + (BitLength) * Rnd())
For k = 1 To 11
OldPop(i, k) = breed1(k)
OldPop(i + 1, k) = breed2(k)
Next R
For k = i1 + 1 To BitLength
OldPop(i, k) = breed2(k)
OldPop(i + 1, k) = breed1(k)
Next k
Else
For k = 1 To BitLength
OldPop(i, k) = breed1(k)
OldPop(i + 1, k) = breed2(k)
Next k
End If
Next i
End Sub
Sub MutatePop()
Mutate = txtMute.Text
ProbMut = Mutate / (igenno)
ii = Int(1 + (BitLength) * Rnd())
For i = 1 To NNew
test = Rnd()
If ProbMut > test Then
OldPop(i, i1) = Not (OldPop(i, 11))
End If
Next 1

220

’Now fill the rest randomly
Do While NNew < PopSize
NNew = NNew + 1
For j = 1 To BitLength
If Rnd() > 0.5 Then
OldPop(NNew, j) = True
Else
OldPop(NNew, j) = False
End If
Next j
Loop

’replace last with best result so far

For k = 1 To BitLength
OldPop(PopSize, k) = BestinPop(k)

Next k

End Sub

Sub SetState()

’ create bytes to set switch states
BO = O
For j = 1 To 8
If StateToSet(j) Then
BO=BO+2“(j-1)
End If
Next j
B1 = 0
N1 = 1
For j = 9 To 16
If StateToSet(j) Then
Bl = Bl + 2 “ (N1 - 1)
End If
N1 = N1 + 1
Next j
B2 = 0
N2 = 1
For j = 17 To 24
If StateToSet(j) Then
B2 = B2 + 2 ‘ (N2 - 1)
End If
N2 = N2 + 1
Next j
B3 = 0
N3 = 1
For j = 25 To 32

221

If StateToSet(j) Then
33 = BS + 2 “ (N3 - 1)

End If
N3 = N3 + 1
Next j

’set switch states
txtByte0.Text = BO

txtByte1.Text = B1
txtByte2.Text = B2
txtByte3.Text = B3

Set8PinIO BO
Set24PinIO B1, B2, BS

End

Sub

Private Sub cdendProgram_Click()

End
End

Set8PinIO 0
Set24PinIO O, O, 0

Sub

A.1.3 Genetic Algorithm: Open STEMS

ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ

Z
Z
Z

Raoul ouedraogo, ouedraog (at) msu.edu Z
This Visual Basic code is a genetic algorithm Z
that optimizes for an Open STEMS Z

ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ

Dim
Dim
Dim
Dim
Dim
Dim
Dim
Dim
Dim
Dim
Dim
Dim
Dim
Dim
Dim

NewPop(1000, 64) As Boolean

OldPop(lOOO, 64) As Boolean

StateToSet(64) As Boolean

BestinPop(64) As Boolean

WorstinPop(64) As Boolean

Plotit(400) As Boolean

Fitness(IOOO), DBR(1000) As Single

BigFit(500) As Single

GenBest(500) As Single

Angitness, MaxFitness, MinFitness, TotalFitness As Single
BestFitness, WorstFitness As Single

igenno As Integer

BitLength, NGen, IMaxFitness As Integer

ifirst As Integer

ProbCross, ProbMut, PopSize, Xmin, Xmax, X, Bi, kk As Single

222

Dim ShowDBR, ShowDBRworst, Rate As Single

Dim N0, N1, N2, N3 As String

Dim B0, B1, B2, BB, BinDigit, BestChrome As String
Dim VoltAvg As Variant

Dim i As Integer

Dim BinaryCodes As Variant

Dim Voltages As Variant

Private Sub cmdDIOSet_Click()
Set8PinIO txtDIOSet.Text
End Sub

Private Sub cdeunAcquisition_Click()
ConfigureCWAIl
GetData VoltAvg

End Sub

Private Sub GetData(VoltAvg)
CWAIl.AcquireData Voltages, BinaryCodes, 5
VoltAvg = CWStat1.Mean(Voltages)

DoEvents

End Sub

Private Sub Set8PinIO(ByteO)
CWDI01.Ports.Item(O).SingleWrite ByteO
End Sub

Private Sub ConfigureCWAI1()
CWA11.Configure
End Sub

Private Sub cmdSetIO24_C1ick()
Set24PinIO txtODIO24.Text, txt1DIO24.Text, txt2DIO24.Text
End Sub

Private Sub Set24PinIO(ByteO, Bytel, Byte2)
CWDIO2.Ports.Item(O).SingleWrite ByteO
CWDIO2.Ports.Item(1).SingleWrite Bytel
CWDIO2.Ports.Item(2).SingleWrite Byte2
StopProcess = True

End Sub

Private Sub cdeunGa_Click()

Call RunGA
End Sub

223

Private Sub RunGA()

Best_StateFilePath = InputBox(" Enter file path here")

Open Best_StateFilePath For Output As #1
Worst_StateFilePath = InputBox("Enter file path here")

Open Worst_StateFilePath For Output As #3
BestReduction_FilePath = InputBox(" Enter file path here")
Open BestReduction_FilePath For Output As #2
WorstReduction_FilePath = InputBox(" Enter file path here")
Open WorstReduction_Fi1ePath For Output As #4

Dim p As String
BitLength = 32
p = InputBox("Enter population size (<=1000)")
PopSize = CInt(Val(p))
’ProbMut = 1 / PopSize
’p = InputBox("Enter probability of crossover (<=1)")
’ProbCross = CSng(Va1(p))
’ProbCross = 0.5
p = InputBox("Enter number of generations")
NGen = CInt(Val(p))
Randomize

’Vsc = txtVsc.Text
Call InitPop
ifirst = 1
For igenno = 1 To NGen
txtGenNo.Text = igenno
txtGenNo.SetFocus
Call EvaluateFitness
Call FitStats
Call SelectPop
Call CrossPop
Call MutatePop
Print #1, BestChrome
Next igenno
For j = 1 To 32
StateToSet(j) = BestinPop(j)
Next j
Call SetState
Close #1
Close #2
Close #3

224

Close #4
End Sub
Sub InitPop()

’Initializes the population to random values
For i = 1 To PopSize
For j = 1 To BitLength
If Rnd() > 0.5 Then
OldPop(i, j) = True
Else
OldPop(i, j) = False
End If
Next j
Next i
End Sub
Sub EvaluateFitness()
Dim VoltAvg As Variant
For i = 1 To PopSize
For j = 1 To 32
StateToSet(j) = OldPop(i, j)
Next j
Call SetState

’wait while state settles
For ii = 1 To txtWait.Text
Next ii
Vsc = txtVsc.Text

’read voltage
ConfigureCWAII
GetData VoltAvg
Fitness(i) = Sqr(0.5841) - (VoltAvg)
Vm = 10 “ ((VoltAvg - 0.1040006) / (0.16415))
Ratio = Vm / Vsc
DBR(i) = 20 * (Log(Ratio)) / Log(10)
Next i
End Sub

Sub FitStats()
Dim sum As Single
Dim i As Integer
’Calculates the statistics of the population fitness
If ifirst = 1 Then
For k 8 1 To BitLength
BestinPop(k) = OldPop(l, k)

225

Next k
BestFitness = Fitness(1)
WorstFitness = Fitness(1)
Fmax = Fitness(1)
Fmin = Fitness(1)
ifirst = 0
End If
sum = 0
IMaxFitness = 0
Fmax = BestFitness
Fmin WorstFitness
For i 1 To PopSize
sum = sum + Fitness(i)
If Fitness(i) < BestFitness Then
BestChrome = ""
IMaxFitness = i
Fmax = Fitness(i)
ShowDBR = DBR(i)
BestFitness = Fitness(i)
For j = 1 To BitLength
BestinPop(j) = OldPop(i, j)
If BestinPop(j) Then
BestChrome = 1 & BestChrome
Else: BestChrome = O & BestChrome

End If
Next j
End If

If Fitness(i) > WorstFitness Then
Fmin = Fitness(i)
ShowDBRworst = DBR(i)
WorstFitness = Fitness(i)
For k = 1 To BitLength
WorstinPop(k) = OldPop(i, k)
If WorstinPop(k) Then
WorstChrome = 1 & WorstChrome
Else: WorstChrome = O & WorstChrome
End If
Next k
End If
Next 1
Angitness = sum / PopSize
MaxFitness = Fmax
MinFitness Fmin
TotalFitness = sum
GenBest(igenno) = MaxFitness

226

txtBest.Text = MaxFitness
txtBest.SetFocus
txtWorst.Text = MinFitness
txtWorst.SetFocus
txtGenAvg.Text = Angitness
txtGenAvg.SetFocus
txtBestIndividual.Text = BestChrome
txtWorstIndividual.Text = WorstChrome
txtXValue.Text = ShowDBR
txtYValue.Text = ShowDBRworst
CWGraph1.PlotY GenBest

Print #2, ShowDBR

Print #4, ShowDBRworst

Print #3, WorstChrome

End Sub

Sub SelectPop()
Dim NNew, NSelect, Nallocate, i, j, k As Integer
’Selects the population for the next generation
’First select by expectd allocation
NNew = O
For i = 1 To PopSize
Rate = txtRatio.Text
Nallocate = Int(Fitness(i) / Angitness)
If Nallocate < Rate Then
For j = 1 To Nallocate
NNew = NNew + 1
For k = 1 To BitLength
NewPop(NNew, k) = OldPop(i, k)
Next k
Next j
End If
Next i
End Sub
Sub CrossPop()
ProbCross = txtXOver.Text
Dim breed1(64), breed2(64) As Boolean

’performs cross over of breeding population’
ncross = NNew
For i = 1 To NNew Step 2

’select pairs

ii = Int(1 + Rnd() * ncross)
For k = 1 To BitLength

227

breed1(k) = NewPop(i1, k)
Next k
If ii < ncross Then
For j = 11 To ncross
For k = 1 To BitLength
NewPop(j, k) = NewPop(j + 1, k)
Next k
Next j
End If I
ncross = ncross - 1
i1 = Int(1 + Rnd() * ncross)
For k = 1 To BitLength
breed2(k) = NewPop(i1, k)
Next k
If 11 < ncross Then
For j = ii To ncross
For k = 1 To BitLength
NewPop(j, k) = NewPop(j + 1, k)
Next k
Next j
End If
ncross = ncross - 1
test = Rnd()
If ProbCross > test Then
11 = Int(1 + (BitLength) * Rnd())
For k = 1 To 11
OldPop(i, k) = breed1(k)
OldPop(i + 1, k) = breed2(k)
Next k
For k = i1 + 1 To BitLength
OldPop(i, k) = breed2(k)
OldPop(i + 1, k) = breed1(k)
Next k
Else
For k = 1 To BitLength
OldPop(i, k) = breed1(k)
OldPop(i + 1, k) = breed2(k)
Next k
End If
Next 1
End Sub
Sub MutatePop()
Mutate = txtMute.Text
ProbMut = Mutate / (igenno)
11 = Int(1 + (BitLength) * Rnd())

 

228

 

For i = 1 To NNew
test = Rnd()
If ProbMut > test Then
OldPop(i, 11) = Not (OldPop(i, 11))
End If
Next 1

’Now fill the rest randomly
Do While NNew < PopSize
NNew = NNew + 1
For j = 1 To BitLength
If Rnd() > 0.5 Then
OldPop(NNew, j) = True
Else
OldPop(NNew, j) = False
End If
Next j
Loop

’replace last with best result so far

For k = 1 To BitLength
OldPop(PopSize, k) = BestinPop(k)

Next k

End Sub

Sub SetState()
’ create bytes to set switch states
B0 = 0
For j = 1 To 8
If StateToSet(j) Then
Bo=BO+2“(j—1)
End If
Next j
Bl = 0
N1 = 1
For j = 9 To 16
If StateToSet(j) Then
Bl = Bl + 2 ‘ (N1 - 1)
End If
N1 = N1 + 1
Next j
B2 = 0
N2 = 1
For j = 17 To 24
If StateToSet(j) Then

229

B2 = B2 + 2 ‘ (N2 - 1)
End If
N2 = N2 + 1
Next j
BB = 0
N3 = 1
For j = 25 To 32
If StateToSet(j) Then
B3 = B3 + 2 “ (N3 - 1)
End If
N3 = N3 + 1
Next j

’set switch states

txtByteO.Text = BO
txtByte1.Text = B1
txtByte2.Text = B2
txtByte3.Text = B3

Set8PinIO BO
Set24PinIO Bl, B2, BB

End Sub
Private Sub cdendProgram_Click()

Set8PinIO O
Set24PinIO O, O, 0

End
End Sub

A.2 Matlab Code

A.2.1 Random Search Histogram, histogram.m

ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ

Z
Z
Z
Z
Z
Z

histogram. m

Random search result histograms

Andrew Temme, temmeand (at) msu.edu

This m file uses random search results for various
frequencies to produce histograms of the shutter
effectiveness found for each frequency.

Z
Z
Z
Z
Z
Z

ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ

Zfrequencies

230

freq = [600 620 650 675 700 725 750 775 801 8254
850 875 900 925 950 975 1000];

Znumber of divisions for the histogram
num_bins = 200;

Zprocess each file

for j=1:max(size(freq))

path = [int2str(freq(j)) ’-Random-DB_R.txt’];
dB,data = load(path);

Zhist(dB_data,200);

max_dB = max(dB_data); Zfind the max and min
min_dB min(dB_data);

dB_range = cei1(max_dB - min_dB);

dB_step = dB_range / num_bins;

dB_data = dB_data + -1*min_dB;

histo = zeros(num_bins,1);
data_size = max(size(dB_data));

for i=1:data-size Zprocess each result
bin = cei1( dB_data(i)/dB_range * num_bins);
if ( bin == 0 )
bin = 1;
end
histo(bin) = histo(bin) + 1;
end

Zplot

figure(j)

subplot(2,1,1) qull histogram

stairs(histo)

title([’dB Reduction for ’ int2str(freq(j)) ’ MHz’l);
x1abel(’Current Reduction (dB)’)

tick = floor(min_dB):dB-range/10:ceil(max_dB);
set(gca,’XTickLabel’,tick);

ylabel(’Number of States’);

subplot(2,1,2)

stairs(histo) Zzoomed in histogram (smaller y range)
title([’dB Reduction for ’ int2str(freq(j)) ’ MHz’J);
x1abel(’Current Reduction (dB)’)

tick = floor(min_dB):dB_range/10:ceil(max_dB);
set(gca,’XTickLabel’,tick);

ylabel(’Number of States’);

ylim([0 50])

231

 

 

save_file_as = [int2str(freq(j)) ’MHz-rand-histo.pdf’];
saveas(j,save_fi1e_as)
end

A.2.2 GA Nec Switch State Histogram, gaNecHisto.m

ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ

Z gaNecHisto. m Z
Z GA Nec Switch State Histogram Z
Z 21 Jul 2008 Z
Z Andrew Temme, temmeand (at) msu.edu Z
Z This m file generates a histogram showing how many Z
Z times a switch is turned on in a set GA NEC results Z
Z files, both vertical orientation and oblique Z
Z orientation, maximum and minimum searches. Z

ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ

Z frequencies of result files
freq = [525 650 675 700 725 750];

num_freq = size(freq); Znumber of frequencies
hist = zeros(32,7); Zhistogram variable
Zmaximum

for i = 1:num_freq(2)
vert_name = [’max’ int2str(freq(i)) ’-O-O.ni4’];
obli_name = [’max’ int2str(freq(i)) ’-30-60.ni4’];

vert = load(vert_name); Zload files
obli = load(obli_name);
for j = 1:32

if vert(j,5) == 0.100000001490116
hist(j,1) = hist(j,1) + 1;
end
if obli(j,5 == 0.100000001490116
hist(j,2) = hist(j,2) + 1;
end
end
end
hist(:,3) = hist(:,l) + hist(:,2); Zsum vert. and oblique
Z minimum
for i = 1:num-freq(2)
vert_name = [’min’ int2str(freq(i)) ’-O-O.ni4’];
obli_name = [’min’ int2str(freq(i)) ’-30-60.ni4’];
vert = load(vert_name); Zload files
obli = load(obli_name);

232

for j = 1:32
if vert(j,5) == 0.100000001490116
hist(j,4) = hist(j,1) + 1;
end
if ob1i(j,5 == 0.100000001490116
hist(j,5) = hist(j,2) + 1;
end
end

end
hist(:,6) = hist(:,4) + hist(:,5);
hist(:,7) = hist(:,3) + hist(:,6);
Zplot all on one figure
figure(1)
subplot(4, 2, 1)
stairs(hist(:,1))
title(’Vertica1 Orientation Maximum Best Switch States’)
x1abe1(’Swtich’)
ylabe1(’Num. of Occurrences’)
xlim([1,32])
ylim([0,10])
subplot(4, 2, 3)
stairs(hist(:,2))
title(’Obligue Orientation Maximum Best Switch States ’)
xlabel(’Swtich’)
ylabe1(’Num. of Occurrences’)
xlim([1,32])
ylim([0,10])
subplot(4, 2, 5)
stairs(hist(:,3))
title(’A11 Maximum Best Switch States Histogram’)
xlabel(’Swtich’)
ylabel(’Num. of Occurrences’)
xlim([1,32])
ylim([0,15])
subplot(4, 2, 2)
stairs(hist(:,4))
title(’Vertical Orientation Minimum Best Switch States’)
x1abel(’Swtich’)
ylabel(’Num. of Occurrences’)
xlim([1,32])
ylim([0,10])
subplot(4, 2, 4)
stairs(hist(:,5))
title(’Obligue Orientation Minimum Best Switch States’)
xlabel(’Swtich’)

233

 

 

ylabe1(’Num. of Occurrences’)
xlim([1,32])

ylim([0,10])

subplot(4, 2, 6)
stairs(hist(:,6))

title(’A11 Minimum Best Switch States Histogram’)
x1abel(’Swtich’)

ylabel(’Num. of Occurrences’)
xlim([1,32])

ylim([0,15]

subplot(4, 2, 7)
stairs(hist(:,7))

title(’All Best Switch States Histogram’)
xlabel(’Swtich’)

ylabel(’Num. of Occurrences’)
x1im([1,32])

ylim([0,30])
saveas(1,’NEC_switch_histogram.pdf’)
Zplot each on an individual figure
figure(2)

stairs(hist(:,1))
xlabe1(’Swtich’)

ylabel(’Num. of Occurrences’)
x1im([1,32])

ylim([O,10])
saveas(2,’max-vert-hist.pdf’)
figure(3)

stairs(hist(:,2))
x1abe1(’Swtich’)

ylabe1(’Num. of Occurrences’)
xlim([1,32])

y11m<[o,1o])
saveas(3,’max-obli-hist.pdf’)
figure(4)

stairs(hist(:,3))
x1abel(’Swtich’)

ylabe1(’Num. of Occurrences’)
xlim([1,32])

ylim([0,15])
saveas(4,’max-all-hist.pdf’)
figure(S)

stairs(hist(:,4))
xlabel(’Swtich’)

ylabel(’Num. of Occurrences’)
xlim([1,32l)

234

 

 

 

ylim([0,10])
saveas(S,’min-vert-hist.pdf’)
figure(6)

stairs(hist(:,5))
xlabe1(’Swtich’)

ylabe1(’Num. of Occurrences’)
xlim([1,32])

ylim([0,10])
saveas(6,’min-obli-hist.pdf’)
figure(7)

stairs(hist(:,6))
x1abe1(’Swtich’)

ylabel(’Num. of Occurrences’)
x1im([1,32])

ylim([0,15])
saveas(7,’min-all-hist.pdf’)
figure(8)

stairs(hist(:,7))
xlabel(’Swtich’)

ylabel(’Num. of Occurrences’)
xlim([1,32])

ylim([0,30])
saveas(B,’all-hist.pdf’)

235

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