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This is to certify that the

thesis entitled

MODELING CONDUCTED EMISSION
TRANSIENTS DUE TO DC MOTOR SWITCHING
IN AUTOMOTIVE APPLICATIONS

presented by

Matthew Raymond Feusse

has been accepted towards fulfillment
of the requirements for

M.S. Electrical

Engineering

W93 W ,

Major professor

degree in

 

 

Date 4-II— 0/

 

0-7639 MS U is an Affirmative Action/Equal Opportunity Institution

PLACE IN RETURN BOX to remove this checkout from your record.
TO AVOID FINES return on or before date due.
MAY BE RECALLED with earlier due date if requested.

 

DATE DUE

DATE DUE

DATE DUE

 

 

 

 

 

 

 

 

 

 

 

 

 

 

6/01 alClRC/DateDuepGS—p. 15

 

 

 

MODELING CONDUCTED EMISSION
TRANSIENTS DUE TO DC MOTOR SWITCHING
IN AUTOMOTIVE APPLICATIONS
By

Matthew Raymond Feusse

A THESIS
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of
MASTER OF SCIENCE

Department of Electrical Engineering

2001

 

 

 

ABSTRACT
MODELING CONDUCTED EMISSION
TRANSIENTS DUE TO DC MOTOR SWITCHING
IN AUTOMOTIVE APPLICATIONS
By

Matthew Raymond Feusse

Conducted emissions are currents that exit a device via its power harness. They
are undesirable as they can couple to other devices or cause unwanted radiation. DC
motors are common culprits for generating conducted emissions in an automobile, as they
generate a large transient current when they are switched on or off. Some of this
transient current is introduced onto the common power net of the vehicle.

Daimler Chrysler wishes to regulate the conducted emissions within their
vehicles. They have self—imposed limits to conducted emissions and methods with which
to test them. However, performing individual measurements on conducted emission
transients for every DC motor in every vehicle they produce is undesirable. The ability to
model unwanted emissions from a DC motor would reduce the need to individually test
each motor.

This thesis examines conducted emission transients from several DC motors
found in automobile applications. The conducted emission transients are measured and
examined. The natural frequencies of each motor are determined and with this
information the conducted emissions of the motor are modeled. Additionally, using the
measured currents and impedances of each motor, a model for worst-case radiated

emissions is also created.

For Grandpa

iii

ACKNOWLEDGMENTS

First of all, I’d like to thank Dr. Dennis Nyquist and Dr. Ed Rothwell for being
my advisors for this thesis and for helping me whenever I needed it. They were
instrumental in the completion of this thesis, not only because of the immense amount of
help and advice they provided me with, but also because they helped keep me focused on
my goal and they continuously pointed me in the right direction for my research.

My parents deserve special recognition as well. They may not have always
understood what I was doing, but they supported me nonetheless. Their continued
encouragement and prayers are greatly appreciated. They also bailed me out financially a
couple times when I found that graduate school had depleted my funds.

I would like to thank the people at the Daimler Chrysler who helped me.
Particularly Andrew Shune, who helped develop the concept Of this thesis, Dave
Schilling, who provided me with the help I needed to do my measurements whenever I
needed it, and Bob SchrOpshire, who helped me perform my conducted emission transient
measurements.

Finally, special thanks go out to my girlfriend Kristy Mietelka. She supported me
throughout my tenure as a graduate student, even though it lasted nearly a year longer
than expected. She provided me with transportation to and from the research complex
whenever I needed it. Most importantly she kept me focused on the goal of completing
this thesis and gave me support and encouragement throughout the process. I believe that

she is more excited about the completion of this thesis than I am.

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TABLE OF CONTENTS

LIST OF TABLES .................................................................................. vii
LIST OF FIGURES ................................................................................ viii
CHAPTER 1: INTRODUCTION .................................................................. 1
1.1 Overview ............................................................................. 1
1.2 NSF GOALI Project ............................................................... 3
1.3 Michigan State University / Daimler Chrysler Interaction .................... 4
CHAPTER 2: CONDUCTED EMISSIONS CONSIDERATIONS ........................... 5
2.1 Overview ............................................................................. 5
2.2 Conducted Emissions ............................................................... 5
2.3 Conducted Emissions Regulations ................................................ 6
2.4 Conducted Emissions Transients ................................................. 7
2.5 Broadband Artificial Network .................................................... 7
CHAPTER 3: MEASUREMENT OF MOTOR SWITCHING TRANSIENTS ........... 24
3.1 Overview ........................................................................... 24
3.2 Measuring Impedance ............................................................ 24
3.3 Measuring Conducted Emission Transients .................................... 25
CHAPTER 4: TRANSIENT ELECTRICAL MOTOR MODELS ........................... 54
4.1 Overview ........................................................................... 54
4.2 Derivation of E-Pulse Method ................................................... 54
4.3 Results and Discussion of Modeling for Each Motor ........................ 60
CHAPTER 5: ELECTROMAGNETIC COMPATIBLIT Y IMPLICATIONS OF

MOTOR SWITCHING TRAN SIENT S ..................................... 138

5.1 Overview .......................................................................... 138
5.2 Radiated Emissions .............................................................. 138
5.3 Radiated Emissions Modeling ................................................. 139
5.4 Radiated and Conducted Emission Model Results ........................... 146
CHAPTER 6: CONCLUSIONS ................................................................ 153
APPENDIX: FORTRAN PROGRAMS ....................................................... 157
Al Overview .......................................................................... 157
A2 Extinction Pulse Program ...................................................... 157
A3 Source Code for ep. for .......................................................... 158
A4 Radiated Emissions Program ................................................... 183
A5 Source Code for Vome. for ...................................................... 184
BIBLIOGRAPHY ................................................................................. 187

vi

LIST OF TABLES

Table 2-1: Impedance Specifications for Broadband Artificial Network ................... 10
Table 3-1: Measured Rise Time and Peak-to-Peak Voltage for Each Motor State ........ 27

Table 5-1: Modeled Conducted Emission Currents at the
Predicted Natural Frequencies ................................................. 147

vii

LIST OF FIGURES

Figure 2-1: Equivalent Circuit for Linear Model of Conducted Emission Transients. . ....8

Figure 2-2: System Connected With a Broadband Artificial Network ........................ 9
Figure 2-3: Equivalent BAN at DC Frequencies ................................................ 9
Figure 2-4: Equivalent BAN at Conducted Emissions Frequencies

(250 kHz — 500 MHz) ............................................................ 10
Figure 2—5: BAN Impedance Spectrum ......................................................... 11

Figure 2-6: Impedance Spectrum of the Actuator Motor Compared
to BAN Impedance ............................................................... 12

Figure 2-7: Impedance Spectrum of the Blower Motor Compared
to BAN Impedance ............................................................... 13

Figure 2-8: Impedance Spectrum of the Blue Line Motor Compared
to BAN Impedance ............................................................... 14

Figure 2-9: Impedance Spectrum of the Green Line Motor Compared
to BAN Impedance ................................................................ 15

Figure 2-10: Comparison of Measured and Adjusted Frequency Content
for Actuator Motor ................................................................ 16

Figure 2-11: Comparison of Measured and Adjusted Time Domain Content
for Actuator Motor ................................................................ 17

Figure 2-12: Comparison of Measured and Adjusted Frequency Content
for Blower Motor .................................................................. 18

Figure 2-13: Comparison of Measured and Adjusted Time Domain Content
for Blower Motor .................................................................. 19

Figure 2—14: Comparison of Measured and Adjusted Frequency Content
for Blue Line Motor ............................................................... 20

Figure 2-15: Comparison of Measured and Adjusted Time Domain Content
for Blue Line Motor ............................................................... 21

viii

Figure 2-16: Comparison of Measured and Adjusted Frequency Content
for Green Line Motor ............................................................. 22

Figure 2-17: Comparison of Measured and Adjusted Time Domain Content
for Green Line Motor ............................................................. 23

Figure 3-1: Conducted Emission Transient Test Setup ........................................ 24

Figure 3-2: Conducted Emission Transient for Forward Biased Actuator
Motor with Positive Triggering (Act 19) ....................................... 28

Figure 3-3: Conducted Emission Transient for Forward Biased Actuator
Motor with Negative Triggering (Act 18) ..................................... 29

Figure 3-4: Conducted Emission Transient for Reverse Biased Actuator
Motor with Positive Triggering (Act 21) ....................................... 30

Figure 3-5: Conducted Emission Transient for Reverse Biased Actuator
Motor with Negative Triggering (Act 20) ..................................... 31

Figure 3-6: Conducted Emission Transient for Forward Biased Blower
Motor with Positive Triggering (Blow 23) .................................... 32

Figure 3-7: Conducted Emission Transient for Forward Biased Blower
Motor with Negative Triggering (Blow 22) .................................... 33

Figure 3—8: Conducted Emission Transient for Forward Biased, Stalled,
Blue Line Motor with Positive Triggering (Blue 00) ........................ 34

Figure 3-9: Conducted Emission Transient for Forward Biased, Stalled,
Blue Line Motor with Negative Triggering (Blue 01) ........................ 35

Figure 3-10: Conducted Emission Transient for Reverse Biased, Stalled,
Blue Line Motor with Positive Triggering (Blue 05) ........................ 36

Figure 3-11: Conducted Emission Transient for Reverse Biased, Stalled,
Blue Line Motor with Negative Triggering (Blue 04) ........................ 37

Figure 3-12: Conducted Emission Transient for Forward Biased, Traveling,
Blue Line Motor with Positive Triggering (Blue 07) ........................ 38

Figure 3-13: Conducted Emission Transient for Forward Biased, Traveling,
Blue Line Motor with Negative Triggering (Blue 06) ........................ 39

Figure 3-14: Conducted Emission Transient for Reverse Biased, Traveling,
Blue Line Motor with Positive Triggering (Blue 03) ........................ 4O

Figure 3-15:

Figure 3-16:

Figure 3-17:

Figure 3-18:

Figure 3-19:

Figure 3-20:

Figure 3-21:

Figure 3—22:

Figure 3-23:

Figure 3-24
Figure 3-25
Figure 3-26
Figure 4-1:
Figure 4-2:
Figure 4—3:
Figure 4-4:

Figure 4-5:

Figure 4-6:

Conducted Emission Transient for Reverse Biased, Traveling,

Blue Line Motor with Negative Triggering (Blue 02) ........................ 41
Conducted Emission Transient for Forward Biased, Stalled,
Green Line Motor with Negative Triggering (Green 16) .................... 42
Conducted Emission Transient for Reverse Biased, Stalled,
Green Line Motor with Positive Triggering (Green 13) ..................... 43
Conducted Emission Transient for Reverse Biased, Stalled,
Green Line Motor with Negative Triggering (Green 12) .................... 44
Conducted Emission Transient for Forward Biased, Traveling,
Green Line Motor with Positive Triggering (Green 15) ..................... 45
Conducted Emission Transient for Forward Biased, Traveling,
Green Line Motor with Negative Triggering (Green 14) .................... 46
Conducted Emission Transient for Reverse Biased, Traveling,
Green Line Motor with Positive Triggering (Green 11) ..................... 47
Conducted Emission Transient for Reverse Biased, Traveling,
Green Line Motor with Negative Triggering (Green 10) .................... 48
Frequency Content of the Actuator Motor ....................................... 49
: Frequency Content of the Blower Motor ......................................... 50
: Frequency Content of the Blue Line Motor ...................................... 51
: Frequency Content of the Green Line Motor .................................... 52
Natural Modes for the Actuator Motor ............................................ 55
Modeled Actuator Motor Data Assuming 6 Natural Modes .................... 62-
Modeled Actuator Motor Data Assuming 5 Natural Modes .................... 63
Modeled Actuator Motor Data Assuming 4 Natural Modes ..................... 64

Frequency Content of Modeled Actuator Motor Data
Assuming 6 Natural Modes ...................................................... 65

Frequency Content of Modeled Actuator Motor Data
Assuming 5 Natural Modes ...................................................... 66

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Figure 4-7: Frequency Content of Modeled Actuator Motor Data

Figure 4-10:

Figure 4-11:

Figure 4-12:

Figure 4—13:

Figure 4-14:

Figure 4-15:

Figure 4-16:
Figure 4-17:
Figure 4-18:

Figure 4-19:

Assuming 4 Natural Modes ...................................................... 67
Figure 4-8: Modeled Actuator Motor Data with Frequency
Truncated at 100 MHZ Assuming 5 Natural Modes .......................... 69
Figure 4-9: Modeled Actuator Motor Data with Frequency

Truncated at 100 MHz Assuming 4 Natural Modes .......................... 7O
Modeled Actuator Motor Data with Frequency

Truncated at 100 Nfliz Assuming 3 Natural Modes .......................... 71
Modeled Actuator Motor Data with Frequency

Truncated at 100 MHz Assuming 2 Natural Modes .......................... 72
Frequency Content of Modeled Actuator Motor Data with

Frequency Truncated at 100 MHz Assuming 5 Natural Modes ............ 73
Frequency Content of Modeled Actuator Motor Data with

Frequency Truncated at 100 MHz Assuming 4 Natural Modes ............ 74
Frequency Content of Modeled Actuator Motor Data with

Frequency Truncated at 100 MHz Assuming 3 Natural Modes ............ 75
Frequency Content of Modeled Actuator Motor Data with

Frequency Truncated at 100 MHz Assuming 2 Natural Modes ............ 77
Modeled Blower Motor Data Assuming 6 Natural Modes .................... 78
Modeled Blower Motor Data Assuming 5 Natural Modes .................... 79
Modeled Blower Motor Data Assuming 4 Natural Modes .................... 80
Modeled Blower Motor Data Assuming 3 Natural Modes .................... 81
Modeled Blower Motor Data Assuming 2 Natural Modes .................... 82

Figure 4-20:

Figure 4-21:

Figure 4-22:

Figure 4-23:

Frequency Content of Modeled Blower Motor Data
Assuming 6 Natural Modes ...................................................... 83

Frequency Content of Modeled Blower Motor Data
Assuming 5 Natural Modes ...................................................... 84

Frequency Content of Modeled Blower Motor Data
Assuming 4 Natural Modes ...................................................... 85

xi

Figure 4-24:

Figure 4-25:

Figure 4-26:

Figure 4-27:

Figure 4-28:

Figure 4-29:

Figure 4-30:

Figure 4-31:

Figure 4-32:
Figure 4-33:
Figure 4-34:
Figure 4-35:
Figure 4-36:

Figure 4-37:

Figure 4-38:

Figure 4-39:

Figure 4-40:

Frequency Content of Modeled Blower Motor Data

Assuming 3 Natural Modes ...................................................... 86
Frequency Content of Modeled Blower Motor Data

Assuming 2 Natural Modes ...................................................... 87
Modeled Blower Motor Data with Frequency Truncated at 100 MHz

Assuming 3 Natural Modes ...................................................... 89
Modeled Blower Motor Data with Frequency Truncated at 100 MHz

Assuming 2 Natural Modes ...................................................... 9O
Modeled Blower Motor Data with Frequency Truncated at 100 MHz

Assuming 1 Natural Mode ....................................................... 91
Frequency Content of Modeled Blower Motor Data with

Frequency Truncated at 100 MHz Assuming 3 Natural Modes ............ 92
Frequency Content of Modeled Blower Motor Data with

Frequency Truncated at 100 MHZ Assuming 2 Natural Modes ............ 93
Frequency Content of Modeled Blower Motor Data with

Frequency Truncated at 100 MHz Assuming 1 Natural Mode ............. 94
Modeled Blue Line Motor Data Assuming 8 Natural Modes ................ 96
Modeled Blue Line Motor Data Assuming 7 Natural Modes ................ 97
Modeled Blue Line Motor Data Assuming 6 Natural Modes ................ 98
Modeled Blue Line Motor Data Assuming 5 Natural Modes ................ 99
Modeled Blue Line Motor Data Assuming 4 Natural Modes ............... 100

Frequency Content of Modeled Blue Line Motor Data
Assuming 8 Natural Modes .................................................... 101

Frequency Content of Modeled Blue Line Motor Data
Assuming 7 Natural Modes .................................................... 102

Frequency Content of Modeled Blue Line Motor Data
Assuming 6 Natural Modes .................................................... 103

Frequency Content of Modeled Blue Line Motor Data
Assuming 5 Natural Modes .................................................... 104

xii

Figure 4—41:

Figure 4-42:

Figure 4-43:

Figure 4-44:

Figure 4-45:

Figure 4-46:

Figure 4-47:

Figure 4-48:

Figure 4-49:

Figure 4-50:

Figure 4-51:

Figure 4-52:
Figure 4-53:
Figure 4-54:
Figure 4-55:
Figure 4-56:

Figure 4-57:

Frequency Content of Modeled Blue Line Motor Data

Assuming 4 Natural Modes .................................................... 105
Modeled Blue Line Motor Data with Frequency

Truncated at 200 MHz Assuming 8 Natural Modes ........................ 106
Modeled Blue Line Motor Data with Frequency

Truncated at 200 MHz Assuming 7 Natural Modes ........................ 107
Modeled Blue Line Motor Data with Frequency

Truncated at 200 MHz Assuming 6 Natural Modes ........................ 108
Modeled Blue Line Motor Data with Frequency

Truncated at 200 MHz Assuming 5 Natural Modes ........................ 109
Modeled Blue Line Motor Data with Frequency

Truncated at 200 MHz Assuming 4 Natural Modes ........................ 110
Frequency Content of Modeled Blue Line Motor Data with

Frequency Truncated at 200 MHz Assuming 8 Natural Modes ........... 111
Frequency Content of Modeled Blue Line Motor Data with

Frequency Truncated at 200 MHz Assuming 7 Natural Modes ........... 112
Frequency Content of Modeled Blue Line Motor Data with

Frequency Truncated at 200 MHz Assuming 6 Natural Modes ........... 113
Frequency Content of Modeled Blue Line Motor Data with

Frequency Truncated at 200 MHz Assuming 5 Natural Modes ........... 114
Frequency Content of Modeled Blue Line Motor Data with

Frequency Truncated at 200 MHz Assuming 4 Natural Modes ........... 115
Modeled Green Line Motor Data Assuming 8 Natural Modes ............. 117
Modeled Green Line Motor Data Assuming 7 Natural Modes ............. 118
Modeled Green Line Motor Data Assuming 6 Natural Modes ............. 119
Modeled Green Line Motor Data Assuming 5 Natural Modes ............. 120
Modeled Green Line Motor Data Assuming 4 Natural Modes ............. 122

Frequency Content of Modeled Green Line Motor Data
Assuming 8 Natural Modes .................................................... 123

xiii

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Figure 4-59:

Figure 4-60:

Figure 4-61:

Figure 4-62:

Figure 4-63:

Figure 4-64:

Figure 4-65:

Figure 4-66:

Figure 4-67:

Figure 4-68:

Figure 4-69:

Figure 4-70:

Figure 4-71:

Frequency Content of Modeled Green Line Motor Data
Assuming 7 Natural Modes .................................................... 124

Frequency Content of Modeled Green Line Motor Data
Assuming 6 Natural Modes .................................................... 125

Frequency Content of Modeled Green Line Motor Data
Assuming 5 Natural Modes .................................................... 126

Frequency Content of Modeled Green Line Motor Data
Assuming 4 Natural Modes .................................................... 127

Modeled Green Line Motor Data with Frequency
Truncated at 200 MHz Assuming 8 Natural Modes ........................ 128

Modeled Green Line Motor Data with Frequency
Truncated at 200 MHz Assuming 7 Natural Modes ........................ 129

Modeled Green Line Motor Data with Frequency
Truncated at 200 MHz Assuming 6 Natural Modes ........................ 130

Modeled Green Line Motor Data with Frequency
Truncated at 200 MHz Assuming 5 Natural Modes ........................ 131

Modeled Green Line Motor Data with Frequency
Truncated at 200 MHz Assuming 4 Natural Modes ........................ 132

Frequency Content of Modeled Green Line Motor Data with
Frequency Truncated at 200 MHz Assuming 8 Natural Modes ........... 133

Frequency Content of Modeled Green Line Motor Data with
Frequency Truncated at 200 MHz Assuming 7 Natural Modes ........... 134

Frequency Content of Modeled Green Line Motor Data with
Frequency Truncated at 200 MHz Assuming 6 Natural Modes ........... 135

Frequency Content of Modeled Green Line Motor Data with
Frequency Truncated at 200 MHz Assuming 5 Natural Modes ........... 136

Frequency Content of Modeled Green Line Motor Data with
Frequency Truncated at 200 MHz Assuming 4 Natural Modes ........... 137

Figure 5-1: Illustration of Common and Differential Mode Currents on the

Figure 5-2: Dipole Antenna Model of a Single Conductor in the Two-Wire Model. . ..

Two-Wire Model ................................................................ 139

141

xiv

Figure 5-3:

Figure 5-4:

Figure 5-5:

Figure 5-6:

Figure 5-7:

Figure 5-8:

Far Zone Approximations for the Dipole Antenna Model of a
Single Conductor in the Two-Wire Model ................................... 142

Geometry for Total Electric Field Using the Two—Wire Model .............. 144

Modeled Radiated Emissions vs. Harness Length
for the Actuator Motor .......................................................... 148

Modeled Radiated Emissions vs. Harness Length
for the Blower Motor ............................................................ 149

Modeled Radiated Emissions vs. Harness Length
for the Blue Line Motor ......................................................... 150

Modeled Radiated Emissions vs. Harness Length
for the Green Line Motor ....................................................... 151

XV

 

 

 

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CHAPTER 1

INTRODUCTION
1.1 Overview
Electromagnetic compatibility (EMC) has become an important part of electrical
engineering. Government regulations and safety issues have forced companies to take a I
greater interest in the electromagnetic properties of their products. One of these regulated
properties is the unintended current exiting a device via the power cable. This unwanted
current is known as a conducted emission. The Federal Communications Commision
(FCC) regulates conducted emissions for most products in the United States. However,
the FCC does not regulate automobiles manufactured in the United States. Automobile
manufacturers maintain their own standards for EMC, which are considerably more
stringent than the FCC standards. This is because it is in the automobile manufacturers’
best interest to produce a reliable, safe product in order to avoid lawsuits. Furthermore,
automobiles manufactured in the United States are subject to regulations from the Comité
International Special Des Perturbations Radioe’letriques (CISPR) if they are to be sold in
Europe.

In order to comply with the CISPR regulations, the Daimler Chrysler Corporation
has dedicated a semi-anechoic chamber for the testing of electromagnetic compatibility
issues outlined in the CISPR 25 electromagnetic compatibility regulations document [2].
Furthermore, they have developed a series of in-house EMC tests, such as conducted
emission transient tests, in addition to those in the CISPR 25 document [3]. This thesis
investigates the effects of conducted emission currents generated by the switching of DC

motors used in automobiles by developing a numerical model of the testing setup and

 

 

 

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comparing the model to results gathered using the conducted emission transients test
method described in Daimler Chrysler’s DCC EMC Test specifications and lab
procedures [3].

This thesis is organized as follows. First, a brief explanation of the NSF GOALI
project, which funded the research for this thesis, is given in Section 1.2 of this chapter.
A brief description of the Michigan State University (MSU) / Daimler Chrysler
interaction fostered through this project will follow.

The remainder of this thesis is divided into several chapters. Chapter 2 discusses
the significance of conducted emissions and examines the measurement procedures for
conducted emission transients employed by Daimler Chrysler. This includes an
introduction to conducted emissions in Section 2.2, a discussion of conducted emission
regulations in Section 2.3, and a more specific discussion of conducted emission
transients in Section 2.4. Section 2.5 investigates the conducted emission transient
measurement technique employed by Daimler Chrysler. More specifically, it investigates
the use of the Broadband Artificial Network and discusses the linear model that this
technique assumes.

Chapter 3 is dedicated to the measurement techniques used to acquire the
necessary data for this thesis. Section 3.2 discusses the technique for acquiring the
impedance characteristics of each motor and the Broadband Artificial Network. Section
3.3 discusses the conducted emission transient measurement procedures and presents the
actual measured data.

Chapter 4 is devoted to the numerical modeling of conducted emission transients.

Section 4.2 presents a derivation of the modeling procedure, using the extinction pulse

 

 

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technique. Section 4.3 presents and discusses the numerical models generated using this
technique and compares them to the measured data.

Chapter 5 discusses the implications of motor switching transients as they relate
to electromagnetic compatibility concerns. Section 5.2 introduces radiated emissions and
discusses their importance. A model for radiated emissions is developed in Section 5.3
that uses the previously modeled conducted emission transient data. Modeled conducted
emission transient currents and radiated emissions are presented and discussed in Section
5.4.

Following the conclusion of this thesis in chapter 6, the two Fortran programs

used in this thesis are included in Appendix A.

1.2 NSF GOALI Project

The research completed in this thesis was funded by the National Science Foundation
(NSF) through the Grant Opportunities for Academic Liaison with Industry (GOALI)
program. Additionally, this program helped fund the development of an EMC course to
be taught at Michigan State University. The program was set up to foster an interaction
between industry and academia. The funding provided by this program allowed graduate
research assistants from MSU to help design an EMC course backed by the advice and
expertise from industry provided by Daimler Chrysler. Furthermore, this project afforded
graduate students the means to perform research guided by both Daimler Chrysler’s

industry experience and MSU’s academic experience.

 

 

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As discussed in the previous section, funding through the NSF GOALI program opened
the door for interaction between Michigan State University and Daimler Chrysler.
Through this interaction, experts from the Electrical / Electronic Systems Compatibility
(EESC) group at Daimler Chrysler identified a research project in the field of
electromagnetic compatibility that would both be useful for their group and suitable for a
thesis. The professors at MSU then guided the research on this project so that it would be
within the scope of the academic requirements required for a Master of Science Thesis.
Thus, this thesis is influenced by both industry and academia, with the goal that the

research herein is both practical and scholarly.

 

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CHAPTER 2

CONDUCTED EMISSIONS CONSIDERATIONS
2.1 Overview
This chapter discusses the concepts of conducted emissions. First, an explanation is
given about what conducted emissions are and why they are important to the automobile
industry. A discussion of conducted emissions transients follows, discussing what
conducted emissions transients are and why they are important. A simple linear model
for conducted emissions transients is presented and a discussion of the Broadband
Artificial Network, which is used in this model, follows. The chapter concludes with an
investigation into the limitations of the simple linear model for conducted emissions

transients.

2.2 Conducted Emissions

Conducted emissions are the currents that are passed through a unit’s power harness and
placed on the common power net. Conducted emissions are undesirable for a couple of
reasons. First, the conducted emission currents exiting a device may affect other devices
on the common power network through direct coupling. That is, the current exits one
device, travels through the common power net and enters another device, potentially
causing interference with the second device. Conducted emissions can also cause
unwanted radiation. As the conducted emissions are placed onto the wiring external to a
particular unit they cause radiation to occur. This unwanted radiation can, in turn, induce

currents on other wires and ultimately cause interference with other devices.

2.3 Conducted Emissions Regulations

Most products sold in the United States must comply with conducted emissions standards
set forth by the Federal Communication Commision. Automobiles manufactured in the
United States are exempt from FCC regulations, while automobiles imported into the
United States must meet FCC standards. If an automobile manufactured in the United
States is to be sold in Europe, however, it is subject to the regulations from the Comité
International Special Des Perturbations Radioe’letriques. In general, automobile
manufacturers have their own self-imposed conducted emissions limits, which are more
stringent than those set forth by the FCC or CISPR. Automobile manufacturers self-
police themselves in this manner to avoid the necessity of government imposed
regulations as well as the importance to provide a safe and reliable product for the
consumer.

The emphasis of CISPR and FCC regulations falls upon devices that have ac
power cords. As such, devices that require ac power are required to be tested with a Line
Isolation Stabilization Network (LISN). A LISN is a circuit that filters the ac power
coming into the device under test, such that at 60 Hz the device receives unpolluted
power. However, at the conducted emissions test frequencies inductors in the LISN act
as open circuits, isolating the device under test from the ac power supply. The LISN also
provides affixed load impedance to the device under test at those radio frequencies. This
insures that during testing, conducted emissions are only being tested due to the device
under test and not the ac power net [1]. Automobiles do not use ac power, but are instead
powered by a dc battery supply. Thus, conducted emissions testing for automobiles

require something other than a LISN. Daimler Chrysler has developed a Broadband

 

 

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Artificial Network (BAN), which serves much the same purpose as the LISN, but is used

with a dc power supply.

2.4 Conducted Emissions Transients

DC motors are common components throughout an automobile and are subject for
concern when considering conducted emissions. Whenever a DC motor is switched off a
transient current is generated, which is induced onto the power cable exiting the motor.
This current is very large compared to any conducted emissions generated by the motor
during its normal operation. As such, these transient currents are typically worst-case
scenarios for conducted emissions generated by a DC motor. Automobile companies
wish to keep these conducted emissions transients below their self-imposed conducted
emissions limits.

Often automobile manufacturers fabricate a DC motor to perform a specific task,
without designing it to meet conducted emissions regulations. They then test the motor
for conducted emission compliance and modify its design if it fails to meet the self-
imposed conducted emission transient constraints. It is desirable to be able to predict if a
motor will pass these tests without testing them. Thus, Daimler Chrysler has asked the
author to investigate a method to model the conducted emissions transient behavior of

DC motors.

2.5 Broadband Artificial Network

It is assumed that a linear model for DC conducted emission transients can be created.

Figure 2.1 shows this linear model for DC motor conducted emission transients.

 

 

 

 

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Figure 2-1: Equivalent Circuit for Linear Model of Conducted Emission Transients

V8 is the modeled source voltage. ZS is the known source impedance. Vmeas is the
measured voltage. The modeled voltage VS approximates Vmeas as long as ZBAN>>Z,,
where ZBAN is the impedance of the Broadband Artificial Network (BAN). The inclusion

of the BAN allows for a known impedance and repeatable results.

Daimler Chrysler developed the Broadband Artificial Network for the purpose of
conducted emissions testing. Similar to the LISN, the BAN is designed to provide power
to the device under test, while isolating it from the power supply at conducted emissions
frequencies. This is achieved by placing several inductors in series between the source
and the device under test, as well as a capacitor to ground. The BAN has three
connection terminals. Terminal one is the output terminal. This terminal connects to the
motor under test. Terminal two is the input terminal, which is conducted to the power
supply. The BAN isolates the motor under test at terminal one from the power supply at
terminal two at radio frequencies. Terminal three is a low current BNC connection which

connects to an output device such as an oscilloscope.

 

 

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Figure 2-2: System Connected With a Broadband Artificial Network

The component values of the BAN are chosen such that the equivalent impedance
of the BAN remains relatively constant over the entire conducted emissions frequency
test range. This is a consequence of the variable frequency dependence of the constituent
inductors. In the case of this BAN the frequency test range is 250 kHz — 500 MHz.

At dc frequencies the capacitors act as open circuits and the inductors act as short
circuits. Thus, the BAN acts as a short circuit at DC frequencies and the test circuit

performs as if no BAN were present.

Terminal 2 Terminal 1
C O

 

Terminal 3

I
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Figure 2-3: Equivalent BAN at DC Frequencies

At conducted emissions frequencies, however, the capacitors act as short circuits
and the inductors act to provide the desired, relatively high, loading impedance, which is
independent of the harness impedance. This isolates the measuring equipment from the

dc power source and prevents low frequency noise from affecting measurements.

 

 

figu:

Terminal 2 50—30009 Terminal 1

0 WV 0

Terminal 3
O

 

 

 

 

 

Figure 2-4: Equivalent BAN at Conducted Emissions Frequencies (250 kHz — 500 MHz)

According to the Daimler Chrysler BAN specifications this broadband isolator

has impedance characteristics shown in Table 2-1.

 

 

 

 

 

 

Frequency Range Minimum Magnitude of
Impedance (52)
0.25 MHz — 0.50 MHz 50
0.50 MHz — 1.0 MHz 100
1.0 MHz — 2.0 MHz 200
2.0 MHz - 150 MHz 400
150 MHz — 500 MHz 100

 

 

 

 

Table 2-1: Impedance Specifications for Broadband Artificial Network

The measured impedance of the BAN coincides with the impedance specifications rather
well, as seen in Figure 2-5. The measured impedance dips to around 350 52 between 65-
95 MHz. However, the measured impedance of the BAN is what is of true importance
for this research. The impedance curve of the BAN remains the same for each motor

tested. This allows for repeatable test results and makes the data easier to interpret.

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_ —~ —— — BAN Impedance Specifications
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Frequency (MHZ)

Figure 2-5: BAN Impedance Spectrum

With a known impedance spectrum it is possible to predict how well a linear model
will work. It is desired to model the conducted emissions of each motor over the
conducted emissions spectrum of 250 kHz-500 MHz. However, the voltage that is
measured is the actual source voltage if and only if the impedance of the BAN is large
compared to the source impedance. The source impedance of each motor is known, so
the frequency range that this linear model is effective over can be determined by
comparing the BAN impedance to the source impedance of each motor. Results for

several typical motors are presented below in Figures 2-6 — 2-9.

11

 

E

 

 

 

 

 

 

 

— — — Measured BAN Impedance
303$ —— —— Measured Actuator Motor Impedance
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Frequency (MHZ)

Figure 2-6: Impedance Spectrum of the Actuator Motor Compared to BAN Impedance

Figure 2-6 shows that the measured actuator motor induce radio frequency voltage,
Vmws, can be modeled as equal to VS over the frequency range 250 kHz-100 MHz and
200 MHz—300 MHz. In practice the measurement is not corrected for voltage division

between ZBAN and 2,.

12

 

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I — —— — Measured BAN Impedance
I ————— Measured Blower Motor Impedance

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Frequency (MHZ)

 

Figure 2-7: Impedance Spectrum of the Blower Motor Compared to BAN Impedance

Figure 2-7 shows that the blower motor can be modeled similarly over the

frequency range 250 kHz-100 MHz and 200 MHz-300 MHz.

13

 

._ ~— — Measured BAN Impedance

 

Measured Blue Line Motor Impedance

 

 

Magnitude Of Impedance (0)

 

IIIIII] 7 IIIIIIII TNIIIIIIl I III

1 re 1%
Frequency (MHZ)

Figure 2-8: Impedance Spectrum of the Blue Line Motor Compared to BAN Impedance

Figure 2-8 shows that the induced radio frequency voltage of the blue line motor

can be modeled without con‘ection over the frequency range 4 MHz-200 MHz.

14

 

— L. — Measured BAN Impedance
_fi —— Measured Green Line Motor Impedance J

 

Il/lagnitudc Of Impedance ((2)

 

 

 

Frequency (I-IHZ)

Figure 2-9: Impedance Spectrum of the Green Line Motor Compared to BAN Impedance

Figure 2-9 shows that the green line motor transient induced voltage can be
modeled similarly over the frequency range 2 MHz-200 MHz.

Since the validity of the linear model falls in doubt for the four motor types over
certain frequency ranges it is useful to examine the data as measured as well as adjusted
to remove any frequency content that is in doubt. This is accomplished by taking the
Fourier transform of the measured data and then truncating the data at the appropriate

frequency. Taking the Fourier transform of this data returns the adjusted time domain

 

data. Figures 2-10 through 2-17 show the measured data compared to the adjusted data
with frequency content removed. In each case frequency is truncated at the upper limits,
but not the lower limits due to the negligible extent of the lower frequency range. The

data in these plots is obtained using the methods described in Chapter 3.

 

4e-007 —-—

Actuator Motor
Measured Data

—————————— Adjusted Data (Frequency Truncated at 100 MHZ)

 

 

 

3.5e-007 ~
39-007 —~

2.5e-007 1 I A

2e-007 ——~

Amplitude

1.5e-007 a

 

 

 

 

 

 

 

 

 

 

 

 

 

1e-007 ——

5e-oos _, M j
m I I I I I I

0.0 0.15 0.25 0.35 0.45
0 0.1 0.2 0.3 0.4 0.5

Frequency (GHZ)

 

 

0'!

Figure 2-10: Comparison of Measured and Adjusted Frequency Content for Actuator Motor

16

 

20 _ Actuator Motor
Measured Data

—————————— Adjusted Data (Frequency Truncated at 100 MHz)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

.15 _
-20 —n
.25 _«
'30 I I I I I I
50 150 250
O 100 200 300

Time (ns)

Figure 2-11: Comparison of Measured and Adjusted Time Domain Content for Actuator Motor

17

iAnlplfinide

5e-007 ~—

4.5e-OO7 -1

49-007 ._

3.5e-007 ~

3e-007 E

2.58-007 H

2e-007 —

1.5e-007 e

1e-007 —-*

58-008 m

 

 

---------- Adjusted Data (Frequency Truncated at 100 MHz)

Measured

Blower Motor
Data

 

 

 

 

 

 

 

0.05

 

 

 

 

 

Ii

0.15

l \
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l ' l ' l ' l ' l
0 25 0 35 0.45
0.1 0.4

0.5

Frequency (GHZ)

Figure 2-12: Comparison of Measured and Adjusted Frequency Content for Blower Motor

18

(

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Voltage (V)

 

 

Blower Motor
Measured Data

—————————— Adjusted Data (Frequency Truncated at 100 MHZ)

 

 

 

 

 

 

 

 

 

   

 

 

 

Time (ns)

.5 fi
-10 m
15 4
‘20 I I I I I I u I
50 150 250 350
0 100 200 300 400

Figure 2-13: Comparison of Measured and Adjusted Time Domain Content for Blower Motor

The actuator and blower motors both are truncated in the frequency domain at 100

M12. In both cases some significant frequency content is removed. This is reflected in

the variations of the measured and adjusted time-domain plots.

19

 

59-007 -—
Blue Line Motor
Measured Data

 

459.007 4 —————————— Adjusted Data (Frequency Truncated at 200 MHZ)

 

46—007 —

3.5e-007 4

39-007 —

2.56-007 m

28-007 ——

Amplitude

 

 

 

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0.05 0.15 0.25 0.35 0.45
0.1 0.2 0 3 0.4

 

 

 

 

0.5

Frequency (GHZ)

Figure 2-14: Comparison of Measured and Adjusted Frequency Content for Blue Line Motor

20

 

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20 fl Blue Line Motor
—— Measured Data

—————————— Adjusted Data (Frequency Truncated at 200 MHZ)

 

 

 

 

 

 

 

 

 

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~20 -—
-25 __
‘30 I I I I I I
50 150 250
0 100 200 300

Time (ns)

Figure 2-15: Comparison of Measured and Adjusted Time Domain Content for Blue Line Motor

21

 

te-ZI

 

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4e-007 —1

 

Green Line Motor

Measured Data 1

---------- Adjusted Data (Frequency Truncated at 200 MHZ) i

3.5e-007 —

*n

 

 

 

 

3e-007 —j

 

 

 

Cl) 2.5e-007 —
"U
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:2 2e-007 —
Q
<3 1.5e-007 a \i
l I
1e-007 — l j l I

 

 

 

 

 

 

 

 

5 e - 0 0 8 —1 ‘ I
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0.05 0.15 0.25 0.35 0.45
0.1 0.2 0.3 0.4
Frequency (GHZ)

Figure 2-16: Comparison of Measured and Adjusted Frequency Content for Green Line Motor

22

 

Green Line Motor
Measured Data

20 _fi —————————— Adjusted Data (Frequency Truncated at 200 MHZ)

 

 

 

l

15~ l

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Voltage (V)

 

 

 

 

 

 

 

-15 —
-20 _Z
-25 ._.
-30 ' l 7 I ' l
50 150 250
o 100 200 300

Time (ns)

Figure 2-17: Comparison of Measured and Adjusted Time Domain Content for Green Line Motor

The blue line and green line motors, however, are both truncated at 200 MHZ and
no significant frequency content is removed. This also is reflected in the time domain

plots, as neither motor shows significant variation between measured and adjusted data.

23

 

 

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CHAPTER 3

MEASUREMENT OF MOTOR SWITCHING TRAN SIENTS
3.1 Overview
This chapter discusses the measurement techniques used in this thesis. All measurements
were performed at the Daimler Chrysler Technical Center Electromagnetic Compatibility
Lab. First, a discussion of the method used to measure the impedance spectrums
presented in Chapter 2 is presented. Next, the test method for measuring conducted
emission transients is presented, and measured data is presented. Finally, a discussion of

repeatable measurements is presented.

3.2 Measuring Impedance

Impedance measurements are performed using the HP 4195A Network Analyzer. The
power for the HP 4195A is turned on and it is allowed to warm up for a period of 30
minutes. Minimum frequency is set to 250 kHz. Maximum Frequency is set to 500
MHZ. All connections to the network analyzer are via a BNC connection on the
impedance measurement module. Calibrations are performed by individually connecting
a short-circuit termination, an open-circuit termination, and a 50 52 load to the BNC
connector and performing a calibration sweep for each termination. The HP 4195A
computes the calibration coefficients and calibration is confirmed by measuring the
impedance of the 50 £2 load across the entire frequency range. After the network
analyzer is calibrated the BAN is connected to the BNC termination and an impedance
sweep is performed across the entire frequency range. This data is saved to disk in LIF

format, which is readable only by a Hewlett Packard operating system. Measurements

24

are similarly performed on each motor with no power applied to the motor. Daimler
Chrysler’s Electromagnetic Compatibility department provided software that converted
the data from LIF format to a tab delimitated ASCH format, which can easily be entered
into a spreadsheet. Plots of the impedance spectrums of the BAN and the motors are

found in Chapter 2: Figures 2-5 to 2-9.

3.3 Measuring Conducted Emission Transients

Conducted emission transients occur when a DC motor is switched off from a running
state. Thus, it is desirable to create a test procedure that measures the currents exiting the
wire harness from a motor as it is switched off. However, it is also important that just the
conducted transient currents are measured, and that any other noise, such as that from the
DC power supply be excluded from such measurements. Furthermore, the emphasis on
conducted emission transients is placed on worst-case scenarios. That is, automobile
companies are only interested in the maximum transient currents generated by any given
motor, as these worst-case currents cause the greatest threat to produce interference in

other devices.

Switch
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Figure 3-1: Conducted Emission Transient Test Setup

 

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Figure 3.1 shows the test setup used to measure conducted emission transients. The
entire test setup is arranged over a ground plane, which also serves as circuit ground. All
wires in the circuit are as short as possible. The switch in the figure is a handheld
pushbutton momentary contact switch that controls the relay. The pushbutton switch is
provided power from the same battery that powers the rest of the circuit, which is fully
charged to 12.7 V at the start of the testing. When the switch is activated, it energizes the
relay, completing the circuit and providing power to the motor. When the pushbutton
switch is depressed the circuit becomes incomplete and the motor loses power. When the
motor loses power it generates a conducted emission transient current.

The oscilloscope is adjusted so that when this transient occurs the scope will
trigger and capture the waveform. The circuit must be completed and broken several
times to properly adjust the triggering. Triggering can be set for “positive” or “negative”
triggering. Positive triggering triggers the oscilloscope only when the waveform slope is
positive, and negative triggering, likewise, only triggers the scope when the waveform
slope is negative. Two measurements are used for each motor state measurement, one
using positive triggering and the other using negative triggering. Data for the green wire
motor stalled state with forward bias measured with negative triggering was stored on a
damaged disk sector and will not be presented in this paper. After the triggering is
properly adjusted the circuit is again completed and broken numerous times and the user
observes the waveforms displayed on the scope. After observing the waveforms, the user
repeats the test several times until a representative worst-case transient can be recorded.

A fast rise time and a large peak-to-peak voltage should characterize this worst-case

26

 

 

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transient. Table 3-1 shows the measured rise time and peak-to-peak voltage for each

motor state measurement.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

. . . . . ' Peak-to-Peak
Data Set Motor Bras Triggering Rise Time Volta e
Act 19 Actuator Forward Positive 200 ps 31.6 V pp
Act 18 Actuator Forward Negative 400 ps 37.2 V p-p
Act 21 Actuator Reverse Positive 200 ps 34.8 V P‘L
Act 20 Actuator Reverse Negative 6.6 ns 33.2 V p-p
Blow 23 Blower Forward Positive 800 ps 32.0 m-p
Blow 22 Blower Forward Negative 400 ps 31.6 V p-p
Blue Line, . .
Blue 00 Stalled Forward Posrtive 500 ps 44.0 V p-p
Blue Line, ,
Blue 01 Stalled Forward Negative 600 ps 42.8 V p-p
Blue Line, . .
Blue 05 Stalled Reverse Posrtive 300 ps 45.2 V p-p
Blue Line, .
Blue 04 Stalled Reverse Negative 400 ps 45.2 V p-p
Blue Line, . .
Blue 07 Traveling Forward Posrtrve 500 ps 42.8 V p-p
Blue Line, .
Blue 06 Traveling Forward Negative 400 ps 44.4 V p—p
Blue 03 Blue Line, Reverse Positive 500 ps 44.4 V p-p
Traveling
Blue Line, .
Blue 02 Traveling Reverse Negative 1.8 ns 46.0 V p—p
Green Line, . .
Green 17 Stalled Forward Posmve 4.2 ns 44.0 V p-p
Green Line, .
Green 16 Stalled Forward Negative 400 ps 45.6 V p-p
Green Line. . .
Green 13 Stalled Reverse Posrtrve 400 ps 46.8 V p-p
Green Line, .
Green 12 Stalled Reverse Negative 2.8 ns 48.4 V p-p
Green 15 Green Erne, Forward Positive 2.4 ns 54.0 V p—p
Traveling
Green 14 Green Lane, Forward Negative 1.7 ns 42.8 V p—p
Traveling
Green Line, . .
Green 11 Traveling Reverse Posrtive 400 ps 48.8 V p-p
Green Line, .
Green 10 Traveling Reverse Negative 400 ps 45.2 V p-p

 

 

 

 

 

 

Table 3-1: Measured Rise Time and Peak-to-Peak Voltage for Each Motor State

Each motor is tested in each of its available states. The actuator motor was tested

with both forward and reverse bias. The blue line and green line motors, both position

27

 

 

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adjustment motors for rearview mirrors, have two states. The first state, where the motor
is moving the mirror adjustment plate is called the traveling state. The stalled state is
when the motor is running but the adjustment plate can go no further. These motors are
tested with both forward and reverse bias in both the traveling and stalled states. The
blower motor does not function with reverse bias. Thus, it is only tested in the forward
bias state. Figures 3-2 through 3-22 show the measured conducted emission transients

for each motor state.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

20 —n
15 -‘
10 —
A
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V
CD
CD 0 —
(t5
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O
> '5 T
.10 —«
-15 -‘
'20 F I T I ‘ I
50 150 250
0 100 200 300

Time (ns)

Figure 3-2: Conducted Emission Transient for Forward Biased Actuator Motor with Positive
Triggering (Act 19)

28

Voltage (V)

-20

20—

157

10—

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

_I

I l I I I
50 150 250
100 200 300

Time (ns)

Figure 3-3: Conducted Emission Transient for Forward Biased Actuator Motor with Negative

Triggering (Act 18)

20—n

 

 

 

 

 

 

 

 

I
5 ~ I I
f; \ I Bl fl \ B I A II I“ II
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-20 ._.__
.25 _
-30 I 7 I I 7 I
0 50 100 150 200 250 300

Time (ns)

Figure 3-4: Conducted Emission Transient for Reverse Biased Actuator Motor with Positive

Triggering (Act 21)

3O

Voltage (V)

20-—

 

 

 

 

 

 

 

 

 

 

 

 

 

III

 

 

 

 

15 —I
10 —I
5 _.
0 _
.5 _
.10 _.
.15 _
-20
0

I I I I I I
50 150 250
100 200 300

Time (ns)

Figure 3-5: Conducted Emission Transient for Reverse Biased Actuator Motor with Negative

Triggering (Act 20)

31

20—

 

 

 

 

 

 

 

 

Voltage (V)
42
g
g

 

 

 

 

 

 

 

 

 

 

 

 

'20 I r r I I I I I
50 150 250 350
0 100 200 300 400
Time (ns)

Figure 3-6: Conducted Emission Transient for Forward Biased Blower Motor with Positive
Triggering (Blow 23)

32

Voltage (V)

-10 __a

-20

20—-

15m

10‘

 

 

 

 

 

 

 

 

 

 

 

 

 

I I I I I I
so 150 250
100 200 300

Time (ns)

Figure 3-7: Conducted Emission Transient for Forward Biased Blower Motor with Negative

Triggering (Blow 22)

33

 

Voltage (V)

20—

 

 

 

 

 

 

 

 

 

 

 

 

 

15 -
10 _.
5 _
0 a
-5 _ I
.10 fl
.,, _
-20 .—
-25 e
'30 I I I T I I
O 50 100 150 200 250 300

Time (ns)

Figure 3-8: Conducted Emission Transient for Forward Biased, Stalled, Blue Line Motor with

Positive Triggering (Blue 00)

34

 

 

Voltage (V)

20—-

 

 

 

 

 

 

 

 

 

 

 

°“ II III

. II
.10 __.

.15 z
.20 —'I
-25 -—
'30 T I I j T I
0 so 100 150 200 25° 300

Time (ns)

Figure 3-9: Conducted Emission Transient for Forward Biased, Stalled, Blue Line Motor with

Negative Triggering (Blue 01)

35

Voltage (V)

.10 __

.20 ._.

-30

20——

15“

10“

.25 _,

 

 

 

 

 

, IIIIIIIIIIIIIIIIIII

 

 

 

 

 

 

 

 

 

I I I T F I
5° 100 15° 200 25° 300

Time (ns)

Figure 3-10: Conducted Emission Transient for Reverse Biased, Stalled, Blue Line Motor with

Positive Triggering (Blue 05)

36

20——

 

 

 

 

 

 

 

 

Voltage (V)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

‘30 I I I I I I
50 150 250
0 100 200 300
Time (ns)

Figure 3-11: Conducted Emission Transient for Reverse Biased, Stalled, Blue Line Motor with
Negative Triggering (Blue 04)

37

Voltage (V)

20—

15 "

10m

 

 

 

 

 

 

 

 

 

 

 

 

-10 —
~15 —*
~20 —1
.25 _
'3" u I I I I I
50 150 250
O 100 200 300

Time (ns)

Figure 3-12: Conducted Emission Transient for Forward Biased, Traveling, Blue Line Motor with

Positive Triggering (Blue 07)

38

Voltage (V)

-10 —I

20m

15 —'

10—d

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

‘ I - I I I I
50 150 250
100 200 300

Time (ns)

Figure 3-13: Conducted Emission Transient for Forward Biased, Traveling, Blue Line Motor with

Negative Triggering (Blue 06)

39

 

 

( V

()l‘rl."_('

\ ,

 

Voltage (V)

-10 _.

-20 —'—1

ZO—fi

10fl

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

I WW

 

 

I f I I I I
50 150 250
100 200 300

Time (ns)

Figure 3-14: Conducted Emission Transient for Reverse Biased, Traveling, Blue Line Motor with

Positive Triggering (Blue 03)

4O

Voltage (V)

-30

20—.

15m

10—

 

 

 

 

 

 

 

 

 

 

 

 

 

I I I 1 I I
50 150 250
100 200 300

Time (ns)

Figure 3-15: Conducted Emission Transient for Reverse Biased, Traveling, Blue Line Motor with

Negative Triggering (Blue 02)

41

 

 

 

 

 

 

 

 

 

 

 

Voltage (V)
I T
A,
2;”)
;
K:
S

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

, - ‘ I I
I I
-10 ———+
-15 __I
.20 __~
.25 —1
'3" I I I T I I
50 150 250
O 100 200 300

Time (ns)

Figure 3-16: Conducted Emission Transient for Forward Biased, Stalled, Green Line Motor with
Negative Triggering (Green 16)

42

Voltage (V)

.10 _.

-20 .—

-30

20——

15—

10—~

.25 _.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

I I I I I I
50 150 250
100 200 300

Time (ns)

Figure 3-17: Conducted Emission Transient for Reverse Biased, Stalled, Green Line Motor with

Positive Triggering (Green 13)

43

Voltage (V)

.10 .—

-20 —<

-30

20——

15 —

10—

.25 —q

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

I I I I I I
50 150 250
100 200 300

Time (r13)

Figure 3-18: Conducted Emission Transient for Reverse Biased, Stalled, Green Line Motor with

Negative Triggering (Green 12)

44

 

 

40—I

30 —

20—“

 

I I WWW

 

Voltage (V)
I
$5.

 

 

 

 

 

 

 

-20 _

 

 

 

 

.30 .—

 

 

‘40 I I I I T I
50 150 250
0 100 200 300
Time (ns)

Figure 3-19: Conducted Emission Transient for Forward Biased, Traveling, Green Line Motor with
Positive Triggering (Green 15)

45

20—

Voltage (V)

-30

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

I I I I I I
250
so 100 I50 200 300

Time (ms)

Figure 3-20: Conducted Emission Transient for Forward Biased, Traveling, Green Line Motor with

Negative Triggering (Green 14)

46

20 ‘—1

10—

 

I Ix II

I I III/MIWIVM

 

 

 

 

 

 

 

 

“,4

 

 

 

 

 

 

(I,

 

Voltage (V)

 

 

.15 —

 

 

 

 

-20 —4

.25 ._.

 

 

 

 

 

 

 

'30 I I I I I 7
50 150 250
O 100 200 300
Tim e (ns)
Figure 3-21: Conducted Emission Transient for Reverse Biased, Traveling, Green Line Motor with
Positive Triggering (Green 11)

47

ZOfi

 

 

Voltage (V)

 

 

 

 

-20
-25 ,
-30 " *"'“* v I“* ‘r f* “i Iik‘rF—I
I 50 150 250
0 100 200 300

Time (ns)

Figure 3-22: Conducted Emission Transient for Reverse Biased, Traveling, Green Line Motor with
Negative Triggering (Green 10)

3.4 Interpretation

Chapter 4 discusses the modeling of the conducted emission waveforms that are
measured in the previous section. These models accurately reflect the natural modes of
each motor. However, before moving on to modeling the motor transients it is important
to examine the data. The frequency content of these measurements is of particular

interest. By taking the Fourier transform of each measured waveform, the frequency

48

 

\

\'(\"I\

1.1,»,
..rn l-

5L2.

. . -
. . . ~
. u. a n .v—H
VIA . .
.\i\~ i. .—v . .
.1. v! I‘

. .

.-. . .
0. I c
a .. ru-
A/s

.e_.___.__a_._~/..

L.
.. .

C.
.h..

 

 

content is observed. The following figures 3-23 to 3-26 show the frequency content of

each motor. For each motor, all of the measured states are plotted on the same figure.

 

 

 

 

 

 

 

 

 

 

 

4.5e-007 —
I I Actuator Motor
4e 007 —— I Act 18
II —————— Act 19
II - ————————— Act 20
3.5e-007 ~ , III : ---------------- Act 21
36-007 -—
(D
”U
:5 2.5e-007 -
4.)
-r—l
r—-l
{l
E 29-007 ——-
1.5e-007 —l . '3
19-007 a
I.
5e-ooa 4).
.l .
I:
0

 

 

0.1 I 0.2 0 3 0.4 I 0.5

Frequency (G—Hz)

Figure 3-23: Frequency Content of the Actuator Motor

49

Amplitude

59-007 —1

 

 

 

 

 

 

 

 

 

 

 

 

 

0.5

I
I I Blower Motor
4.5e-007 T I I Blow 22
—- -— — —- Blow 23
4e-007 —
3.5e-007 —
3e-007 —a I
II
Ii-
2.5e-007 ~ I
I
2e-007 -— n
l
1.56-007 a I! I
II I
1e-007 e 'I
l
5e-008 ‘ I
I I I A
0 II I I W
I T T I I l ' I
0.05 0.15 0.25 0.35 0.45
0 0.1 0.2 0.3 0.4

Frequency (GHZ)

Figure 3-24: Frequency Content of the Blower Motor

50

Amplitude

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

. 7 ——
58 00 Blue Line Motor
Blue 00
4.5e-007 e _ ________ BI“ 01
l I - ---------- Blue 02
I I II II ---------------- Blue 03
49-007 — I ‘ II III ———————— Blue 04
I IIIIIIII ————————— Blue 05
III-III ------------------------ Blue 06
3.5e-oo7 - IIgIII .. ~— — —~ Blue 07
I .
l I I:I
I IIII
IffIII
III
2.5e-007 ~ IIIIIIIII
'IIIIIII:
[III-(III
'II'III
2e-007 — ,;,I.II
.‘EI I
III III
1.5e-007 a II II
.6 .
: II I I
1e-007 — :‘III III
:‘I I, II I 'II
IIII'” I II;
5e-ooe —| i ' I'II
i I III 'bIH- IV"... I fj’IN I;
o r I v «.v \z . M...
I I I
0.15 0.25 0.35 0.45
0 0.2 0.3 0.4

Frequency (GHz)

Figure 3-25: Frequency Content of the Blue Line Motor

51

0.5

 

L. . v .u. . ~
... . ... _

 

. r.»

Amplitude

46-007 _—I

3.5e-007 ~
39-007 ——
2.5e-007 e
29-007 ——~
1.56-007 -—
1e-007 -—

5e-ooa — '

 

“—
-—-—

 

 

W"
o,_

 

 

 

 

 

 

 

 

 

 

---------- Green 11
........... Green 12
................ Green 13
.HH ................... Green 14
————————— Green 15
_”_I__-__-~—- Grcmnl 16

 

Green.ldne Motor —T
Green 10

 

J

 

 

005 015
0.1

0.35 0.45
0.4

Frequency (GHZ)

Figure 3-26: Frequency Content of the Green Line Motor

52

 

. W 5‘ .
".1 A‘ \J.
L~_,.I.s

.

Y
m t ‘
, J
In.» mu
. o
I.

, I . ‘, 0
Or .‘tu-nbv. IL

I- vv-‘l “m
I~.A.‘:U. i.‘

 

Figure 3-23 shows that the triggering method used for measurements does not affect the
frequency content of the motor. However, the actuator motor has different frequency

behavior for forward and reverse biasing. Figures 3-24 through 3-26, on the other hand
display similar frequency content for all motor states. Whether the motors are traveling
or stalled, forward or reverse biased, the frequency content remains the same. With this
in mind, modeling in Chapter 4 is done for only one representative motor state for each

motor type.

53

CHAPTER 4
TRANSIENT ELECTRICAL MOTOR MODELS
4.1 Overview
This chapter discusses the modeling of transient electrical motors. It begins with a
theoretical discussion of motor modeling [4,5]. A discussion of accomplishing this
model using a computer program follows. Data is presented for transient motor models
generated using the previous theory and computer program. Finally, the modeled data is

discussed and compared to the measured data.

4.2 Derivation of the E-Pulse Method
It is assumed that the motor switching voltage transient can be represented as a finite sum

of damped sinusoids.

N
m (t) = 2 anew cos (cunt + (1)” ), TL <t < TW (4.1)
n=l

where s" = 0'" + jwn is the natural frequency of the nth mode, an and (2),, are the

amplitude and phase of the nth mode, respectively, TL is the beginning of the late time
period, and TW is the end of the measurement window. N is the number of natural modes

and is chosen by inspecting the measured frequency content of each motor. Examining
the frequency spectrum of the actuator motor voltage, as seen in Figure 4-1, it can be
observed that this motor has five natural frequencies, which are represented by the five

major peaks with arrows pointing to them.

54

l\\
(h
-

I\lll[)|llll(i(‘

 

 

 

 

49-007 —1

3.5e-007 — \I/

6

39-007 -—

fl-

2.59-007 4

2e-007 — \l,

Amplitude

1.5e-oo7 4
1e-007 ”HI I I I

5e-008 -‘

 

 

 

 

 

 

 

 

 

0 I I f f m I l I I I
0 0.1 0.2 0.3 0.4 0.5

Frequency (GHZ)

Figure 4-1: Natural Modes for the Actuator Motor

There exists a waveform function that yields a zero result when convolved with

the motor switching transient, m (t). This waveform function is known as an extinction

pulse, or E-pulse. Thus, an E-pulse, e(I) is defined as a waveform of finite duration, Te,

that satisfies

55

 

“I133

 

 

ill)

3230 Will

Nuns

c(t)=e(t)*m(t)

T,
= Je(t')m (t —t')dt' (4-2)
0
N I
= 20.60" [An cos (wnt) + B" sin (wnt)], t > TL + T.
n=l
where
A" T“ , -0”, cos wnt’ ,
{Biz-([60 )e {sinwnt'Idt' (4.3)

It is desirable that the E-pulse convolved with the motor switching transient yield

a zero result. Thus

c(t)=e(t)*m(t)=0, t>TL+T€ (4.4)

requires

A,=B,,=0, ISnSN (4.5)

This convolution waveform can also be written in the form

c(t)=n2:an

e°"I cos (cunt + w” ), t > TL + Te (4.6)

 

 

E(SI)

where

E(sn)= L{e(t)}=J:e(I)e_‘I"Idt, n 1, 2,...,N (4.7)

is the Laplace transform of the E-pulse waveform, and

 

m

1]!" = q)" + tan’1 [ — j" I (4.8)

56

where

Em = Im {E (s, )} E = Re{E(sn )} (4.9)

Since c(t)=0 for t>TL +Te,

Em =Em =0 ISnSN (4.10)
which also requires
E(s,,)=E(s;)=o ISIISN (4.11)

Now, e(t) is broken into two components,

e(t)=ef (t)+e‘(t), (4.12)

where ef (I) is a forcing component that excites a waveform, and e" (t) is an extinction
component that extinguishes the response due to ef (t). The forcing component is user

defined, while the extinction component is determined by expanding e" (I) into a set of

basis functions

M
e‘ (I) = 20:me (t) (4.13)
Thus, equation (4.12) becomes
M
6(I) = 6’ (t)+ ZamfI. (t) (4.14)

m=l

where M = 2N and {fm (1)} are defined as unit pulse basis functions with unknown

durations, and {am} are the unknown amplitudes of the basis functions.

57

The solution of the basis function pulse widths and amplitudes is solved using the

program EP.FOR, written by Dr. Ed Rothwell, Dr. Ponniah Ilavarasan, and Dr. John E.

Ross III. This program defines the total width of the e-pulse as T, , and the number of

basis functions as 2N + l (the forcing function plus 2N extinction components). The
program iteratively steps through a series of E-pulse widths and the basis function
amplitudes are computed at each iteration. Substituting equation (4.14) into equation

(4.4) yields

c(t)=[ef (0+i0‘mfm (1)]*m(t)=0, t>TL+Y;. (4.15)

This equation is solved in the program, forcing c(t) = Oat chosen time points. It must be
noted that c(t) is forced to equal zero only at these matching points and it is very

possible that c (I) i O at points in between the matching points. Thus the program

generates unique values for am for each iteration of T, .

Now that the extinction pulse is known, it must be used to reconstruct the
measured waveform. The first step for this reconstruction is determining the natural
frequencies. Taking the Laplace Transform of equation (4.13) yields

M
E! (s. ) = 24.410. (2)}

5“ (4.16)
=20: F (s,,) n =1,2,...,N

The extinction pulse must be zero at the natural frequencies, thus

M
E(sn)= ZaMFm (sn)=0, n =1,2,...,N (4.17)
m=l

58

Equation (4. 17) can be solved for each s" using the definition of the Laplace transform.

 

 

 

 

 

 

EAg)=JfiAQe“UL n=leJV MJ$
The pulse fm (t) has a duration of A = 213/1 1 . Thus equation (4.18) can be rewritten as
+
mA .
Fm (Sn) = I le_‘I"Idt
(m—1)A
1 —s 1 mA
=——Ie ,. l
S (m-I)A
_snmA —sn(m-1)A (4.19)
_ -— e
s"
—snA
WI 1’6 , n=l,2,...,N
Sn
Now, substituting the result from equation (4.19) into equation (4.17) yields
M 1_ e-snA ‘
E(sn)=2am[ ]e_I"mA =0, 11 =1,2,...,N (4.20)
m=l Sn
_ —snA
Now, moving [ I outside the summation and letting z" =2 e“~“‘ the problem
Sn
reduces to a polynomial equation
M
Zamz: = 0 n =1,2,...,N (4.21)

with known am already determined by the program. The polynomial in equation (4.21)

is solved for each z" , which can now be used to determine the natural frequencies.

2,, — e "
ln 2:" = —sn A (4.22)
%=—im;,
A

59

With the natural frequencies now known, it is possible to recreate the waveform.

Let r (I) be the recreated waveform

N

r (t) = 2 Aneo"t cos (wnt + W) (4.23)

n=1
where an and a)" are the real and imaginary parts of the natural frequencies respectively
3,, = on + jwn (4.24)
and A" and q)" are the unknown amplitude and phase of the reconstructed waveform.

Equation (4.18) can be rewritten as

N
r (t) = 2 e0": [An cos (out + B" sin cont] (4.25)

n=1

A" and B" can be determined by using least squares curve fitting to the measured data.
This gives a reconstructed waveform for each value of Tk . The iteration with the least

squared error is chosen as optimal and given as output from the program.

4.3 Results and Discussion of Modeling for Each Motor

Modeling for each motor is accomplished by first choosing a representative data set for
each motor type. Data set Act 18 is chosen for the actuator motor while data sets Blow
23, Blue 00, and Green 10 are chosen for the blower motor, blue line motor, and green
line motor respectively. Next, the frequency content of each motor is examined and a
number of expected modes is determined. Often the actual number of expected modes is

not readily apparent, so a range of possible natural modes is modeled for each motor.

60

By examining the frequency content of the actuator motor in Figure 2-10 it is seen
that the actuator has four to six significant natural modes. Thus, Figures 4-2 through 4-7
show the modeled actuator motor for six, five and four natural modes. Examining the
frequency content of the modeled data for six and five expected natural modes in Figures
4-5 and 4-6, it can be seen that five natural modes are modeled in both cases. This is
reflected in the nearly identical modeled time-domain data they produce, which is seen in
Figures 4-2 and 4-3. Additionally, it is noted that the frequency data beyond 100 MHz
does not match up nearly as well as the data below 100 MHz. The modeled time-domain
data seen in Figure 4-4, assuming four expected modes, however, does not match up with
the measured data nearly as well. This is reflected in the frequency data as the three
natural modes below 100 MHZ match up very well, while there is very little agreement

between measured and modeled data beyond 100 MHz.

61

Voltage (V)

-10 ——~

 

 

 

 

 

 

 

 

 

 

 

Actuator
Measured Data

—————————— Modeled Data — 6 modes

 

 

 

 

 

 

 

 

 

 

 

1 l l l l
50 150 250
100 200

Time (ns)

Figure 4-2: Modeled Actuator Motor Data Assuming 6 Natural Modes

62

300

 

20
j Actuator
Measured Data
—————————— Modeled Data — 5 modes

 

 

 

 

Voltage (V)

 

 

 

.10 .—
-15 ,4.
'
.20 a
l
-25 4
.30 4* ‘__ 7— ,,__ s¥ ,
l ‘ T F 7 fi—‘fl
so 150 250
0 100 200 300

Time (ns)

Figure 4-3: Modeled Actuator Motor Data Assuming 5 Natural Modes

63

Voltage (V)

20 -—7

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

  
 

 

 

 

 

 

 

Actuator
Measured Data
15 _ Modeled Data — 4 modes
10 —-
5 _‘ ,\ [.1
.\./\ “A / I“!
0 __. » Hi“ , fl
ill/7 I /)
X" \ 0’ l 1 VJ
., .. l ~
-10 ___
-15 -
~20 —
-25 —
-30 r T ”T l l l
50 150 250
0 100 200 300

Time (ns)

Figure 4-4: Modeled Actuator Motor Data Assuming 4 Natural Modes

4e-007 —

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Actuator
Measured Data
3.5e-007 ~ ---------- Modeled Data — 6 Modes
3e-007 —
Q) 2.59-007 —
"C
4..)
L: 26-007 —4
0..
<3 1.5e-007 4
19-007 —
5e-008 ~
‘ T ' T l l ' l
0.15 0.25 0.35 0.45
0 0.2 0.3 0.4 0.5

 

Frequency (GHZ)

Figure 4-5: Frequency Content of Modeled Actuator Motor Data Assuming 6 Natural Modes

65

Amplitude

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

49-007 T
l Actuator
_— Measured Data
359.007 q —————————— Modeled Data - 5 Modes j
3e-007 —-
2.5e-007 ~ i
26-007 m I“ I
. l
: . I
I
. l
1.5e-007 —- '
l ,‘
l , ‘
19-007 -~
59-008 - ‘\
N w
W‘s-wp,“ ,-, i- W935
° | ' l T l . l ' l
0.15 0.25 0.35 0.45
0 0.1 0.2 03 0.4 0.5

Frequency (GHZ)

Figure 4-6: Frequency Content of Modeled Actuator Motor Data Assuming 5 Natural Modes

66

.
o
. u
. .
. -

'AI
(9

f N.)

(Y.

(1‘

lgux

 

 

 

Amplitude

49-007 __

 

 

 

 

 

 

 

 

F m
I Actuator
—-——————- Measured Data
3.5e-007 ~ ---------- Modeled Data — 4 Modes
36-007 fl
: l
l l
, I
256-007 ~ 1 :l
l
; .‘l
. H
l I
‘ i
26-007 A p’ n
: :
: I '
l l
1.5e-007 — . ; 1
| l
u : 1':
l l\ <
19-007 —4 l, I 1 A," l
‘ .1 : l
l I I
l K

 

5e-008 a m 1%
I l," ‘
v ‘ I \‘ ‘ ~

. N
.- .V, , \
, ’ ‘I l ’ \ ”W
l | ‘U/ \/‘ W Wrwvm
I \’ I q I \ ‘ / \ . a A
O I \., \\/ \I- \z \I \I ‘/\’/\,\\V/\/ \WRAW‘C“
l l l

l I l
0.05 0.15 0.25 0.35 0.45
0.1 0 2 0 3 0.4

 

. . 0.5
Frequency (GHZ)

Figure 4-7: Frequency Content of Modeled Actuator Motor Data Assuming 4 Natural Modes

67

 

‘__..
Li‘- )h,

f X‘u
n" b‘r-fl ||
‘-

‘.u: ~-5

;,‘~ -‘ :l"
‘94)‘9225h -
‘xla-"3a0 If

uku-snik kl .

‘n‘n . 4.3 .
Mdlt'5u\l\b

5);?ch ‘ '
iii-.1835 17.
“misfit.

“err ml t

 

 

It was noted in Chapter 2 that the linear model for each motor tends to break
down beyond a certain frequency. For the actuator motor this occurs beyond 100 MHz.
This breakdown in the linear model appears to have affected the actuator motor as
discussed above. Modeling has also been done on the motors with their frequency
content truncated in order to observe the effect on the models.

By examining the frequency content of the actuator motor with frequency
truncated at 100 MHZ in Figure 2-10, it can be seen that the actuator motor now has three
expected natural modes. Models were computed for two through five expected natural
modes in Figures 4-8 through 4-15. As expected, in the cases of three through five
expected natural modes, shown in Figures 4-12 through 4-14, only three natural modes
were modeled. The accuracy of the model was not improved through the additional
modeled modes. This is also reflected in the nearly identical time domain models in
Figures 4-5 through 4-10, all of which match the measured data fairly well. In the case
where only two expected natural modes were modeled, the first two modes were modeled
nicely, as seen in Figure 4-15, yet the third natural mode at 100 MHz was not. The effect
of this third natural mode being omitted can be observed in the deviation of the time

domain modeled data from the measured data in Figure 4-11.

68

 

Actuator with Frequency Content Removed
' —————— Measured Data

12 —* ,
' Modeled Data — 5 Modes

 

 

 

 

 

 

Volatage (V)
J

 

 

 

300

.2 --1
-4 —— [I i! ,
-6 —< l!
8 ___J
-10 -
"2 I I I T I I
50 150 250
0 100 200

Time (ns)

Figure 4-8: Modeled Actuator Motor Data with Frequency Truncated at 100 MHz
Assuming 5 Natural Modes

69

Volatage (V)

 

Actuator with Frequency Content Removed
Measured Data

—————————— Modeled Data — 4 Modes

 

 

 

 

 

 

 

 

'

 

 

‘ l I | l l
50 150 250
100 200 300

Time (ns)

Figure 4-9: Modeled Actuator Motor Data with Frequency Truncated at 100 MHz

Assuming 4 Natural Modes

70

Volatage (V)

10*“

K

 

Actuator with Frequency Content Removed
Measured Data

---» ——————— Modeled Data — 3 Modes

 

 

 

 

 

 

I T I l I I
so
50 100 150 200 2 300

Time (ns)

Figure 4-10: Modeled Actuator Motor Data with Frequency Truncated at 100 MHz

Assuming 3 Natural Modes

71

Volatage (V)

 

12 ? Actuator with Frequency Content Removed
Measured Data

—————————— Modeled Data — 2 Modes

 

 

 

 

 

 

 

 

 

 

“2 I I I I I I

50 250
o 100 15° 200 300

Time (ns)

Figure 4-11: Modeled Actuator Motor Data with Frequency Truncated at 100 MHz
Assuming 2 Natural Modes

72

Anrphtude

 

46-007 .2

 

 

 

 

 

 

 

 

 

 

 

   

 

 

Actuator with Frequency Content Removed
Measured Data
---------- Modeled Data — 5 Modes
3.5e-007 ~
36-007 —
I
I
I
I l
2.5e-007 ~ {l i
I' I
I I
II 'I
1
I1 I
29-007 4 i
I
l
I
1.5e~007 ~ ' '
‘1
l
|
l
16-007 —- i
F l
' I
5e-ooe — ‘
I a \ (\H , \ / ‘ I
,‘/\/ \«\l /\ \ jv\/\/\/\"’\F"\/\/\\/\/\/~\/l“/\
0 T r l I l I 1
0.05 0.15 0.25 0.35 0.45
0 0.1 0.2 0 3 0.4 0.5

Frequency (GHZ)

Figure 4-12: Frequency Content of Modeled Actuator Motor Data
with Frequency Truncated at 100 MHz Assuming 5 Natural Modes

73

iAnilenide

 

46-007 —

Actuator with Frequency Content Removed
Measured Data

—————————— Modeled Data — 4 Modes

 

 

 

3.56-007 m

3e-007 —

2.56-007 m

29-007 m

——_u-‘_‘-_-_—_—-
-'——‘I-’-——:—_31’q

1.5e-007 2

 

19'007 —__J I

 

 

 

 

 

 

 

_w—w—v ‘—

5e-008 #

/\ , \ h ‘ \ f

I IAI‘V‘fil’t ”‘I’ ’xx‘..l\.—~.,~ Il~\\/——~l I
0.15 0.25 0.35 0,45
0-2 0 3 0.4

 

\
\‘ 'F\l -"\,/\

_

 

 

. 0.5
Frequency (GHZ)

Figure 4-13: Frequency Content of Modeled Actuator Motor Data
with Frequency Truncated at 100 MHz Assuming 4 Natural Modes

74

Amplitude

 

46-007 -—

 

 

 

 

 

 

 

 

 

 

Actuator with Frequency Content Removed
Measured Data
---------- Modeled Data — 3 Modes
3.56-007 ‘1
3e-007 —
2.56-007 —
2e-007 fl
156-007 2
1e-007 .4
5e-008 4
/\‘\"\\\/P\l’\‘ \/\ ,\’/\ ’\,\r\ ‘ :“\/_’\/\/\ /-/\ ,\\/\’- ’\,/\/\r\,\
0 I T n l l I I l

 

 

0.15 0.25 0.35 0.45
0.2 0.3 0.4

Frequency (GHZ)

Figure 4-14: Frequency Content of Modeled Actuator Motor Data
with Frequency Truncated at 100 MHz Assuming 3 Natural Mode:

75

0.5

Amplitude

46-007 ——

3.56-007 ~

36-007 A

2.5e-007 —-

2e-007 —~

1.5e-007 e

1e-007 #

 

56-008 “s

 

 

 

 

 

 

 

 

 

 

Actuator with Frequency Content Removed
-————————— Measured Data

—————————— Modeled Data —- 2 Modes

 

 

 

 

 

 

 

0.15 0.25 0.35 0.45
0.2 0 3 0.4

Frequency (GHZ)

Figure 4-15: Frequency Content of Modeled Actuator Motor Data
with Frequency Truncated at 100 MHz Assuming 2 Natural Modes

76

Examining the frequency content of the blower motor in Figure 2-12, it is seen
that this motor is dominated by two natural modes below 100 MHz, with some smaller
natural modes occurring after 100 MHz. Modeling is done for two through six expected
natural modes. Similar to the findings with the actuator motor, only the frequency
content before 100 MHz is accurately modeled, as seen in Figures 4-21 through 4-25.
This seems to agree with the theory made in Chapter 2 that the linear model for the

blower motor breaks down beyond 100 MHz.

77

 

20 —-
Blower Motor
Measured Data

Modeled Data — 6 Modes

 

 

 

 

 

 

.‘w

 

 

 

 

 

 

 

 

 

 

 

 

.. I 5
l I

-10—

45.4

'2" I I I I I a I I

50 150 250 350
0 100 200 300 400
Time (ns)

Figure 4-16: Modeled Blower Motor Data Assuming 6 Natural Modes

78

 

20—

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Blower Motor
Measured Data
—————————— Modeled Data — 5 Modes
15 m
10 —
5 —<
0 4M
.5 —I
10 *4
.15 -I
~20
I I I I . T ' l
50 150 250 350
0 100 200 300 400

Time (ns)

Figure 4-17: Modeled Blower Motor Data Assuming 5 Natural Modes

79

20 ——

 

 

Blower Motor
Measured Data

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

—————————— Modeled Data — 4 Modes
15 m
10 —4
Ill
/'\ ’
> 5 _, I“ l
, , 1" . l ,
Q) ‘ I' ll : "I I) "I
I I I | l ' . A I I ’ I 1"
QC 0 %M II] I g ‘1" I) I“ II it I‘ ‘\ l“ 1' \ ‘ l ‘1 ’l I, “
(U I HI I II ' | I l " I U ‘I
‘l \ l, U
:J-l Il 1| i '1 l ’ ‘ l I \I
l I i l \ J
o -5 - W I:
> . I
-10 ——
45 m
50 150 250 350
0 100 200 300 400

Time (ns)

Figure 4-18: Modeled Blower Motor Data Assuming 4 Natural Modes

80

 

20%

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Blower Motor
Measured Data
—————————— Modeled Data — 3 Modes
15 ‘1
10 — '
/'\
> 5 7
V l l\l
' Il 1|
)1 l I
<1) ,I .
CD 0 “N ‘1’ ‘ 1
CU " i l
-+-) ’ I I
r—l | I)
O "
> -5 m It:
-10 fl
~15 -‘
~20 I T l l j l I I
50 150 250 350
o 100 200 300 400

Time (ns)

Figure 4-19: Modeled Blower Motor Data Assuming 3 Natural Modes

81

Voltage (V)

20—*

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Blower Motor
Measured Data
—————————— Modeled Data - 2 Modes
15 r
10 -—
5 fl
0 fill/[Mm
-5 1
~10 A
-15 —
50 150 250 350
o 100 200 300 400

Time (ms)

Figure 4-20: Modeled Blower Motor Data Assuming 2 Natural Modes

82

59-007 —

 

Blower Motor
Measured Data

4.59.007 — ---------- Modeled Data — 6 Modes

 

 

 

4e-007 —

“‘_

3.5e-007 fl

3e-007 ——

2.5e-007 —

26-007 —

Amplitude

 

 

 

1.56-007 fl

 

 

 

1e-007 —a

 

5e-ooa — {.1

 

 

 

 

 

Frequency (Gliz)

Figure 4-21: Frequency Content of Modeled Blower Motor Data Assuming 6 Natural Modes

83

56-007 '—l

 

Blower Motor
Measured Data

4.59.007 .4 —————————— Modeled Data — 5 Modes

 

 

 

 

 

 

 

 

 

 

 

 

4e-007 —
3.5e-007 — .
ll
l‘
l
0) I
“U 38-007 ~ I
:5 .'
.4.)
:1 2.5e-007 ~ I
Q E ,
E 2e-007 — i
‘< :
1.5e-007 4 '.
19'007 —J I i
'I i
l 5'
58-003 m “l
I
I‘. ,
0 1'
0.05 0.15 0.25 0.35 0.45 I
0 0.1 0.2 0.3 0.4 0.5

Frequency (GHZ)

Figure 4-22: Frequency Content of Modeled Blower Motor Data Assuming 5 Natural Modes

84

56-007 _l

 

Blower Motor
I —————— Measured Data

453.007 4 i ---------- Modeled Data - 4 Modes

 

 

4e-007 —

3.5eo007 A

3e-007 —-

———-.__._I

.H
2.5e-007 A l.

2e-007 ~

Amplitude

 

 

 

19-007 -—-

 

I

l

l
1.59-007 — I“

I

|

l

 

 

58-008 ‘ I f
l l‘
Wit l,

 

    

I M

0.15 0.25 0.35 0.45
0.2 0.3 0.4 0.5

Frequency (GHZ)

Figure 4-23: Frequency Content of Modeled Blower Motor Data Assuming 4 Natural Modes

85

Amplitude

 

59-007 —

Blower Motor
Measured Data

459.007 ~ ---------- Modeled Data — 3 Modes

 

 

 

49-007 ~

3.58-007 H

3e-007 — i

2.56-007 —

_‘_

2e-007 —

 

1.5e-007 H

 

 

1e-007 -—~

 

 

—-_— ,_.

 

 

0.15 0.25 0.35 0.45
0 0.1 0.2 0.3 0.4 0.5

Frequency (GHZ)

Figure 4-24: Frequency Content of Modeled Blower Motor Data Assuming 3 Natural Modes

86

58-007 "7

 

Blower Motor
Measured Data
4.58-007 —i ---------- Modeled Data — 2 Modes

 

 

49-007 -—I

3.5e-007 —-

36-007 ——l

E“"-:-;-__

2.56-007 -

Amplitude

26-007 —*

 

1.59-007 *

 

 

1e-007 fl

 

 

-_-_._____—_’-

 

 

 

5e-ooe FM ‘. .
o 1"" U ‘ W “EMA-1;me
w i I F '

0.05 0.15 0.25 0.35 0.45
0.1 0.2 0.3
Frequency (GHZ)

Figure 4-25: Frequency Content of Modeled Blower Motor Data Assuming 2 Natural Modes

87

The blower motor with frequency data truncated at 100 MHZ appears to have two
natural modes, as seen in Figure 2-12. Models were computed with one through three
expected natural modes. As expected, both the models with two and three expected
modes contained two natural modes, as seen in Figures 4-29 and 4-30. However, the
match between measured and modeled time domain data seen in Figures 4-26 and 4-27
appears to be no better than for the non-truncated models in Figures 4-16 through 4-20.
Looking back at the comparison of the time domain data with and without the frequency
content beyond 100 MHz in Figure 2-13, however, it is observed that the missing
frequency content beyond 100 MHz actually has very little impact on the shape of the
time domain curve. The modeled data for one expected mode is shown in Figures 4-28
and 4-31, and is interesting as it shows a waveform consisting of a single damped
sinusoid, as well as another waveform consisting of the same damped sinusoid combined

with a second damped sinusoid, which is due to the other natural frequency.

88

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

d l
e
V
m
e
R
tL S r
n m u
e
.L O IIIIII
n M i i
0 II
C 3 \III\
w _ ,

a T
nt a ll
e a t IIIIII
wiD a \II III
ma D I -
F m .w

u l.
h S e
n a w
wM M
P.
O _
l. _
O _
M _ l

_
r _
e _
w _
w _
B _
_
5

15

 

E mafia“;

 

Figure 4-26: Modeled Blower Motor Data with Frequency Truncated at 100 MHz
Assuming 3 Natural Modes
89

 

 

Blower Motor with Frequency Content Removed

Measured Data
---—-~—-—- Modeled Data — 2 Modes

 

 

 

 

llt‘ll
‘|l

’III
III",
llllll'

 

 

 

 

 

 

 

 

 

 

T

200

Time (ns)

1

150

 

 

15

10—4

E $315

-10

-15

400

350

250

300

Modeled Blower Motor Data with Frequency Truncated at 100 MHz
Assuming 2 Natural Modes

Figure 4-27

90

 

15 — Eflower Motor‘wnh Frequency Contentihnnoved
————————-—— Measured Data
—————————— Modeled Data - 1 Mode

 

 

 

10*

 

 

 

 

 

 

-10 —-l

"5 I T I I I r I I
250 350 400

50 150
100 200 300

Time (ns)

Figure 4-28: Modeled Blower Motor Data with Frequency Truncated at 100 MHz
Assuming 1 Natural Mode

 

 

91

Amplitude

59-007 ——7

 

Blower Motor with Frequency Content Removed
4.5e-007 — —— Measured Data

—————————— Modeled Data — 3 Modes

 

 

49-007 —I

 

 

3.5e-007 —

3e-007 —-

2.59-007 ‘ '

29-007 ——-

 

 

 

I

I
1.59-007 * :A

I

 

 

19-007 --1 '

 

59-008 -

   

 

 

0.05 0.15 0.25 0.35 0.45
0.1 0.2 0.3 0.4
Frequency (GHZ)

Figure 4-29: Frequency Content of Modeled Blower Motor Data
with Frequency Truncated at 100 MHz Assuming 3 Natural Modes

92

Amplitude

59-007 ——

 

459-007 —- ————-— Measured Data
——————— --—~ Modeled Data — 2 Modes

 

49-007 —

3.59-007 -

39-007 —4

2.59-007 *

29-007 #

 

1.59-007 —-

 

 

 

19-007 'm

 

 

 

59-008 #

«.-
'\'/“\vi\h—vv.\vg

Blower Motor with Frequency Content Removed

l‘I-v'-~~AJ\’\Auv—~\Avfilvn~~——-a-v\

 

 

-I T I i I
0.15 0.25 0.35
0.2 0.3 0.4

Frequency (GHZ)

 

Figure 4-30: Frequency Content of Modeled Blower Motor Data
with Frequency Truncated at 100 MHz Assuming 2 Natural Modes

93

0.45
0.5

Amplitude

59-007 —

 

Blower Motor with Frequency Content Removed
459-007 B ———-— Measured Data
—————————— Modeled Data — 1 Mode

 

 

 

 

49-007 ——

3.59-007 ~

39-007 —-

2.59-007 m I

29-007 fl

 

1.59-007 —

 

 

 

 

 

19-007 -—

5e-ooe 4

 

 

 

l I l l l I l
0.15 0.25 0.35 0.45
0.2 0.3 0.4

Frequency (GHZ)

 

C

Figure 4-31: Frequency Content of Modeled Blower Motor Data
with Frequency Truncated at 100 MHz Assuming 1 Natural Mode

94

~—_

0.5

The frequency content for the blue line motor can be observed in Figure 2-14.
Truncating the frequency data at 200 MHz does not appear to remove any significant
frequency content. This waveform appears to consist of between four and seven
significant natural modes. The last major natural mode, at about 150 MHz, has a
remarkably wide frequency content. Modeling was done for both the measured and
truncated data models with four through eight expected natural modes.

The best time domain fit occurred using eight assumed natural modes as seen in
Figures 4-32 and 4-42. The frequency content, seen in Figures 4-37 and 4-47, modeled
the first 5 natural modes, but nothing was successfully modeled beyond 100 MHZ. Seven
expected natural modes, shown in Figures 4-33, 4-38, 4-43, and 4-48, yielded nearly as
accurate models, with only the first four natural modes modeled. Perhaps the most
interesting blue line model was the one with six expected natural modes. As seen in
Figures 4-39 and 4-49, the first two modes were successfully modeled, while the next two
modes were partially modeled. Yet this is the only blue line motor model to successfully
replicate any natural modes beyond 100 MHz. The frequency data for the model using
five expected modes in Figures 4-40 and 4-50 is nearly identical to the six mode model
except it lacks the natural mode beyond 100 MHz. Comparing the two models in the
time domain, in Figures 4-34, 4-35, 4-44, and 4-45, it is seen that the modeled natural
mode beyond 100 MHz contributes to the shape of the earliest part of the modeled time
domain. Finally, the model assuming 4 natural modes, seen in Figures 4-36, 4-41, 4-46
and 4-51 successfully models only the first two natural modes, which leads to a very poor

match between measured and modeled time-domain data.

95

Voltage (V)

20—

-25 '

-30 7‘

 

 

Blue Line Motor
Measured Data
— Modeled Data - 8 Modes

 

 

 

 

 

50 150
0 100

 

 

l—fi—fi‘ I I

250
200

Time (ns)

Figure 4-32: Modeled Blue Line Motor Data Assuming 8 Natural Modes

96

Voltage (V)

ZOfi

10—

.20 ——I

-25 ‘

 

 

Blue Line Motor
Measured Data

 

—————————— Modeled Data — 7 Modes

 

 

 

 

 

 

 

 

 

 

 

 

 

 

~30

 

I I I I I
50 150 250
100 200

Time (ns)

Figure 4-33: Modeled Blue Line Motor Data Assuming 7 Natural Modes

97

300

Voltage (V)

~30

20—

.10 .—

.15 —I

-20 __I

-25 _

 

 

 

 

 

 

 

 

 

 

Blue Line Motor
Measured Data

—————————— Modeled Data — 6 Modes

 

 

 

 

50
100

T I l

150 250
200

Time (ns)

Figure 4-34: Modeled Blue Line Motor Data Assuming 6 Natural Modes

98

 

20——

15 m

10—

 

 

Blue Line Motor
Measured Data

—————— Modeled Data — 5 Modes

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

l l

50
100

I I I
150 250
200

Time (ns)

Figure 4-35: Modeled Blue Line Motor Data Assuming 5 Natural Modes

99

300

 

! Blue Line Motor
20 _ I Measured Data

 

Modeled Data — 4 Modes

 

 

 

 

 

 

 

 

 

 

 

 

-20 -*q

-25 _.

 

 

 

'30 I I I I I I
50 150 250
0 100 200 300

Time (ns)

Figure 4-36: Modeled Blue Line Motor Data Assuming 4 Natural Modes

100

 

59-007 — ‘

Blue Line Motor
I —— Measured Data

 

Modeled Data — 8 Modes

 

4.59-007 —

 

49-007 —-

359-007 -I

39-007 —

2.59-007 -

29-007 —-

Amplitude

i—t_-——ufi

 

 

 

1.59-007 —-

 

 

19-007 —

 

 

 

 

 

59-008 —

 

/\ \ ’ .
\ l \, _ \/ ’ \’\/\.’ "\""J‘v.—" "’ ' ’

I I I I I —I I I
0.15 0.25 0.35 0.45
0.2 O 3 0.4

 

 

0.5

Frequency (GHZ)

Figure 4-37: Frequency Content of Modeled Blue Line Motor Data Assuming 8 Natural Modes

lOl

 

59-007 __ I

Blue Line Motor
Measured Data

—————————— Modeled Data — 7 Modes

 

4.59-007 —-

 

49-007 fl

3.59-007 —

39-007 —-

  
   

2.59-007 —

29-007 —

Amplitude

 

1.59-007 —I

 

 

 

19-007 —n

 

 

 

 

 

 

 

 

 

 

0.15 0.25 0.35 0.45
0.2 0.3 0.4
Frequency (GHZ)

Figure 4-38: Frequency Content of Modeled Blue Line Motor Data Assuming 7 Natural Modes

102

Amplitude

59-007 a

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Blue Line Motor
Measured Data
4.5e-oo7 ~ --------- Modeled Data — 6 Modes
49-007 —
3.59-007 —
39-007 —
I
259-007 — I
I
I
I
l
29-007 — . I
I
l
l
ii I
1.59-007 ~ 'I ‘.
I I
I
l
I i I : I
l |
19'007 “‘I II I I A : I I
II I i I II' I '
I I I I “’I‘ "
5e-ooa — I ' I.‘ 'I I.
i i' l ‘ ‘
\ I I, l‘
0 I I j "I“~ "j’""‘I“" "' I -----
0.05 0.15 0.25 0.35 0.45
0 0.1 0.2 0 3 0.4 0.5

Frequency (GHZ)

Figure 4-39: Frequency Content of Modeled Blue Line Motor Data Assuming 6 Natural Modes

103

 

I Blue Line Motor

I I— Measured Data

59-007 —5 I

I
4.59-007 a! Modeled Data — 5 Modes

 

 

49-007 —-

3.59-007 -

39-007 --

2.59-007 #

29-007 —-

Amplitude

‘i—h--__

 

 

1.59-007 —

 

 

 

19-007 .3

 

 

 

 

 

5e-ooa a

 

 

 

  

0.15 0.25 0.35 0.45
0.2 0.3 0.4

Frequency (GHZ)

Figure 4-40: Frequency Content of Modeled Blue Line Motor Data Assuming 5 Natural Modes

104

59-007 —fi

4.59-007 '-

49-007 —

3.59-007 '-

39-007 —-

259-007 H

29-007 fl

Amplitude

159-007 —I

19-007 _

 

 

59-008 -

 

 

 

 

 

 

 

 

 

 

Blue Line Motor
Measured Data

---------- Modeled Data — 4 Modes

 

 

 

 

 

 

Figure 4-41: Frequency Content of Modeled Blue Line Motor Data Assuming 4 Natural Modes

0.1

0.15

0.2 ' 0 3

Frequency (GHZ)

105

 

Voltage (V)

20—

-10 —~

-15 —4

 

 

 

 

 

 

 

 

 

Blue Line Motor with Frequency Content Removed
Measured Data
---------- Modeled Data — 8 Modes

 

 

 

 

 

 

 

   

 

 

I F I I I
so 150 250
100 200

Time (ns)

Figure 4-42: Modeled Blue Line Motor Data with Frequency Truncated at 200 MHz

Assuming 8 Natural Modes

106

300

Voltage (V)

20—

15m

10—

5 d

-10 __

-15 —

.20 ___I

-25 ‘

 

 

Blue Line Motor with Frequency Content Removed
Measured Data

---------- Modeled Data — '7 Modes

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

-30

 

I I F I l I
so 100 150 200 25° 300

Time (ns)

Figure 4-43: Modeled Blue Line Motor Data with Frequency Truncated at 200 MHz

Assuming 7 Natural Modes

107

Voltage (V)

 

20 —
Blue Line Motor with Frequency Content Removed
~——————-———— Measured Data

15 r I —————————— Modeled Data — 6 Modes I

 

 

 

10—5

 

 

 

 

 

   

 

 

 

-20 _

 

 

 

 

 

 

'30 l I l I l l
50 150 250
0 100 200 300
Time (ns)

Figure 4-44: Modeled Blue Line Motor Data with Frequency Truncated at 200 MHz
Assuming 6 Natural Modes '

108

20—-

 

 

 

 

 

Blue Line Motor with Frequency Content Removed
Measured Data

—————————— Modeled Data — 5 Modes

 

 

 

 

 

 

 

 

 

 

 

     

 

 

I I I I I 1
50 100 150 200 250 300

Time (ns)

Figure 4-45: Modeled Blue Line Motor Data with Frequency Truncated at 200 MHz

Assuming 5 Natural Modes

109

20—

 

Blue Line Motor with Frequency Content Removed
Measured Data
15 —I

---------- Modeled Data — 4 Modes

 

10—r

 

 

 

 

 

   

 

 

 

 

 

 

-30

 

I l—

150
100

Time (ns)

F I 7

250
200 300

Figure 4-46: Modeled Blue Line Motor Data with Frequency Truncated at 200 MHz
Assuming 4 Natural Modes

110

Amplitude

_3e-007 ~

59-007 ——

 

Blue Line Motor with Frquency Content Removed
Measure Data

459-007 -I —————————— Modeled Data — 8 Modes

 

 

49-007 —-

3.59-007 m

259-007 a

29-007 —

 

‘1-.—

1.59-007 *-

 

 

 

 

 

 

 

 

 

 

 

h’\’\A”-’\’\l“-4_'k’\l\¢-_‘_ *‘f\r\4‘

0.05 0.15 0.25 0.35 0.45
0.1 0.2 0 3 0.4 0.5

 

 

Frequency (GHZ)

Figure 4-47: Frequency Content of Modeled Blue Line Motor Data
with Frequency Truncated at 200 MHz Assuming 8 Natural Modes

lll

Amplitude

59-007 —-

459-007 4

49-007 a

359-007 -*

39-007 —-

2.59-007 r

29-007 #

1.59-007 r

19-007 4

59-008 *

 

 

Blue Line Motor with Frquency Content Removed
Measure Data

---------- Modeled Data - 7 Modes

 

 

 

 

 

 

 

 

 

-"——‘_

 

 

 

 

 

 

 

 

 

 

 

FI'I
0.15 0.25 0.35 0.45
0.2 03 0.4

 

0.5

Frequency (GHZ)

Figure 4-48: Frequency Content of Modeled Blue Line Motor Data
with Frequency Truncated at 200 MHz Assuming 7 Natural Modes

112

Amplitude

59-007 —

 

Measure Data
---------- Modeled Data — 6 Modes

4.59-007 —

 

Blue Line Motor with Frquency Content Removed

 

 

49-007 —~

3.59-007 —

39-007 —I

259-007 —

 

 

 

29-007 —

‘I-‘-

 

1.59-007 -

 

 

19-007 — .’

 

 

 

 

 

 

59-008 -

 

 

’Al-‘_-\ _ -1

 

 

0.25 0.35
0.2

Frequency (GHZ)

Figure 4-49: Frequency Content of Modeled Blue Line Motor Data
with Frequency Truncated at 200 MHz Assuming 6 Natural Modes

113

I I I""I‘

0.3 0.4

0.45
0.5

Amplitude

 

59-007 a
Blue Line Motor with Frquency Content Removed
Measure Data

 

 

459-007 —I ——-- ——————— Modeled Data — 5 Modes

 

 

49-007 a

359-007 —

39-007 —

     

2.59-007 —-

29-007 —*

 

 

 

 

 

 

 

1.59-007 —

 

19-007 —

 

 

 

 

 

59-008 — .

 

 

 

0.05 0.15 0.25 0.35 0.45
O 0.1 0.2 0.3 0.4 0.5

Frequency (GHZ)

Figure 4-50: Frequency Content of Modeled Blue Line Motor Data
with Frequency Truncated at 200 MHz Assuming 5 Natural Modes

114

Amplitude

 

 

 

 

 

 

5e-007 j
Blue Line Motor with Frquency Content Removed
Measure Data

4-59'007 ‘ ---------- Modeled Data — 4 Modes

4e-007 —

3.56-007 e

3e-007 _l

2.5e-OO7 fi A

l t

. 1;!
2e-007 —l ’ :I‘ *

l

I
1.59-007 A '1 w

: n

l

l

 

1e-007 ~

5e-ooe 4M 1 fl
flLV \Vk/ ' x x
f ‘3' "Kl‘t,"\J’\\,\,\ \ ,V‘ ,V‘ , /‘ g ’\ ‘ _ ’\ ‘ fl ’\ ‘ _
° ' l ' “ ‘ WI ‘1“!
0.05 0.15 0.25 0.35 0.45
0 0.1 0.2 0.3 0.4 0.5

Frequency (Gllz)

 

 

 

 

 

 

 

Figure 4-51: Frequency Content of Modeled Blue Line Motor Data
with Frequency Truncated at 200 MHz Assuming 4 Natural Modes

115

Similar to the blue line motor, the green line motor has no significant frequency
contributions beyond 200 MHz, as seen in Figure 2-16. Additionally, the green line
motor also has a very wide natural mode at around 150 MHz; however, it has much
greater amplitude than the one for the blue line motor. Both the blue line and green line
motors are positional motors used in a rear view mirror unit, so it is expected that they
will have very similar characteristics.

The models for seven and eight expected modes, in Figures 4-52, 4-53, 4-57, and
4-58, are virtually identical. They match the time domain measured data fairly well, and
in the frequency domain the first four modes are matched to some extent. Additionally
both the modes beyond 100 MHz are also matched, although the amplitude of the
modeled mode at around 150 MHz is much less than the measured data. The modeled
data with frequency truncated at 200 MHz, in Figures 4-58 and 4-68, is the same as the
non-truncated model, except the wide pulse at 150 MHz is actually modeled as two
pulses, one at 150 MHz and one at 175 MHz. There is very little difference between the
modeled time domain data of the truncated (Figures 4-62 and 4-63) and non-truncated
(Figures 4-52 and 4-53) data Models, although the truncated data models appear to be
marginally less accurate. For the six expected natural mode models, seen in Figures 5-59
and 5-69, both the truncated and non-truncated models lack the first mode beyond 100
MHz, but also both break the larger pulse at 150 MHz into two smaller pulses. The five
expected natural mode models, in Figures 4-60 and 4-70, are very similar to the six
expected natural mode models, except the wide pulse at 150 MHz is modeled as a single
pulse. The time domain data for five and six expected natural modes, seen in Figures 4-

54, 4-55, 4-64, and 4-65, are all very similar and all agree with the measured data about

116

the same. The model for four expected natural modes does not model an frequency
content beyond 100 MHz and only models three of the earlier modes, as seen in Figures
4-61 and 4-71. The time domain data in Figures 4—56 and 4-66, retains the shape of the

measured data, but does not match as closely as the models with more expected modes.

117

Voltage (V)

20—

 

 

 

 

 

 

 

 

 

 

 

 

Green Line Motor
Measured Data
15 —————————— Modeled Data ~ 8 MOdeS
10 —‘
l
l. I
5 — ‘. :
1 I 1‘
I ,‘ ‘I 1‘ I
I: [I I, ‘\ \Il’l “ I" :I‘Illll‘
0 —l 1‘. ‘I I, 11.1 r “ lI ‘\ "’ ‘
II. I V ‘ l l '
\ l‘. \ I ll 1
| ‘ | I I
-5 —- \ It, ‘l:
’ \I
-10 —
l
-20 ,
-25 *
~30 —‘—r— r l
u T l l
50 150 250
o 100 200 300

Time (ns)

Figure 4-52: Modeled Green Line Motor Data Assuming 8 Natural Modes

118

Voltage (V)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

20 j
Green Line Motor
15 _. Measured Data
—————————— Modeled Data - '7 Modes
10 —* A
5 i l
0 _.
.5 e ’
~10 —n W
'15 — ~
-20 —
-25 *7
-3o ‘1 l l l l r l
0 100 200 300

Time (ms)

Figure 4-53: Modeled Green Line Motor Data Assuming 7 Natural Modes

119

20m

15“

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Green Line Motor
Measured Data

---------- Modeled Data - 6 Modes

 

 

 

 

 

 

.15 --t
-20 __.
.25 ——<
'3" ‘ a I . u
50 250
0 100 200 300

Time (ns)

Figure 4-54: Modeled Green Line Motor Data Assuming 6 Natural Modes

120

20—

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Green Line Motor
Measured Data
15 — __________ Modeled Data - 5 Modes
.‘
It
I
10 *m A I
5 _ l
A
> 0 _. ”
Cl) I
no 5 a l
CU I
_‘__J
I—--l
O -10 —
>
-15 m
-20 —1
-25 m
-30 l j I l T l
50 150 250
0 100 200 300

Time (us)

Figure 4-55: Modeled Green Line Motor Data Assuming 5 Natural Modes

121

20‘—l

 

 

 

 

 

 

 

 

 

 

 

 

 

 

_—
.—-'

 

 

 

1 Green Line Motor

 

 

 

 

 

l
l

I
Measured Data I
Modeled Data — 4 Modesj

 

-30

 

T l

150
100

l I l
250
200 300

Time (ms)

Figure 4-56: Modeled Green Line Motor Data Assuming 4 Natural Modes

122

 

4e-007 —

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Green Line Motor
Measured Data
—————————— Modeled Data — 8 Modes
3.5e-007 '4
36-007 __
(1) 2.5e-007 —
”O l
3 I
4.) t
: 2e-007 — l E
Q l 1
E I i 1
I" I
<5 1.5e-oo7 —« [I I':
ll I‘
I llw
;;: I
I ' ‘
Ie-oo7 — .' ‘I
l ‘1
l \‘
1 I 1"
-\‘_"\ \

 

—h'\)‘

 

 

0.15 0.25 0.35 0.45
0.2 0.3 0.4
Frequency (GHZ)

Figure 4-57: Frequency Content of Modeled Green Line Motor Data Assuming 8 Natural Modes

123

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

4e-007
j Green Line Motor
Measured Data
---------- Modeled Data — '7 Modes

3.5e-007 -
3e-007 -—

Q) 2.5e-007 - ‘

U :

53 5

:1. now — i

l

Q—t l

E I

l

I

<3 1.5e-007 e I

I
1e-007 —
5e-008 m

° I I T I I I
0.05 0.15 0.25 0.35 0.45
0 0.2 0.3 0.4 0.5

Frequency (GHZ)

Figure 4-58: Frequency Content of Modeled Green Line Motor Data Assuming 7 Natural Modes

124

 

4e-007 —

Green Line Motor
Measured Data

---------- Modeled Data — 6 Modes

 

 

 

3.5e-007 —
3e-007 fl

2.58-007 — I

 

29-007 —

 

Amplitude

1.5e-007 m

 

 

1e-007 —

 

 

 

 

l
I
l
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
l
l

 

 

 

 

5e-008 -‘

 

 

 

 

   

0.25 0.35 0.45
0 3 0.4

Frequency (GHZ)

Figure 4-59: Frequency Content of Modeled Green Line Motor Data Assuming 6 Natural Modes

125

4e-007 —

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Green Line Motor
Measured Data
—————————— Modeled Data — 5 Modes
3.5e-007 _.
3e-007 —
C1) 2.5e-007 4
U
.4.)
;: 29-007 —
Q.
<1 1.5e-007 —«
1e-007 #
5e-008 r
o ‘_, \lx,‘~’\/\,‘_ AVA/\VM
I l I l l I

 

0.05 0.15 0.25 0.35 0.45
0.1 0.2 0.3 0.4
Frequency (GHZ)

Figure 4-60: Frequency Content of Modeled Green Line Motor Data Assuming 5 Natural Modes

126

4e-OO7 fl

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Green Line Motor
Measured Data
3.5e-007 .. ---------- Modeled Data — 4 Modes
3e-007 —~
0) 2.5e-007 ~
”U
:1 29-007 # ,
Q l
E ,
<3 1.5e-oo7 a x
16-007 —‘< /
519-008 H
-\ \ ‘ ,4 MM]

 

0.15 0.25 0.35 0. 45
0.2 0.3 0.4

Frequency (GHZ)

Figure 4-61: Frequency Content of Modeled Green Line Motor Data Assuming 4 Natural Modes

127

Voltage (V)

20

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

—7
Green Line Motor with Frequency content Removed
Measured Data
15 e l ---------- Modeled Data — 8 Modes
1O — l
A
‘ l
5 A I ,
l :‘l
II I ’ ' I II I
“| \ 1 l \ l l ‘ I\
0 _J \ ‘ I" ‘ "I, ‘1 ”‘1"
l l] I 1‘ l ‘ ‘ \
\ \I ’ I '
I 1 " l I
I ‘ ’ '
.5 —I U' ‘ I“: \II ‘1,’
-10 m
.15 —I
.20 ——<
~25 n
'3" I I I I I I
50 150 250
O 100 200 300

Time (ns)

Figure 4-62: Modeled Green Line Motor Data with Frequency Truncated at 200 MHz

Assuming 8 Natural Modes

' 128

Voltage (V)

20fi

 

Green Line Motor with Frequency content Removed
Measured Data

15 ~ ---------- Modeled Data — '7 Modes

 

 

 

10—

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

'” I I I I I n
50 150 250
0 100 200 300
Time (ns)
Figure 4-63: Modeled Green Line Motor Data with Frequency Truncated at 200 MHz
Assuming 7 Natural Modes

129

 

20—

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Green Line Motor with Frequency content Removed
Measured Data
15 ~ P , ---------- Modeled Data — 6 Modes
10 a
5 —4 ’I IA\
1 I 1‘ I\
\ II I, ‘ |
P I‘ l | i l‘ I, 1‘ 1 1 \
0 — " ‘\/\ I, ||I \ I! ‘w “ ‘\ I" “ \ I, ‘1
' I I ‘ I
I, I H \ \‘ I
I I I 1| I H ‘1]
5 —I ' ' I
-10 _
.15 —I
-20 _
.25 —4
'30 I I I I I I
50 150 250
O 100 200 300

Time (ns)

Figure 4-64: Modeled Green Line Motor Data with Frequency Truncated at 200 MHz

Assuming 6 Natural Modes

130

 

Voltage (V)

20m

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Green Line Motor with Frequency content Removed
Measured Data
15 .- l —————————— Modeled Data — 5 Modes
10 — '
l
I ll
5 —_‘ I H H 1‘l
I1 I. ‘1
l l | ‘
‘ I ‘l “ l
I ‘ ‘ I
0 '—1 I \‘I l’\ I/ I ‘\,\ I“
' l I 'I ‘ I l I
II I \ l
(I! “I I II
.5 — ‘ ’
-10 A
.15 4
-20 _
-25 m
‘30 I I I I I
50 150 250
0 100 200

Time (ns)

Figure 4-65: Modeled Green Line Motor Data with Frequency Truncated at 200 MHz

Assuming 5 Natural Modes

131

300

Voltage (V)

20—

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Green Line Motor with Frequency content Removed
1 Measured Data
15 ~ ‘ ---------- Modeled Data — 4 Modes
10 —*
5 a
0 __I
.5 .-
10 —I
-15 _-
l
.20 _
-25 _
'3" I I I I I I
O 50 100 150 200 250 300

Time (ns)

Figure 4-66: Modeled Green Line Motor Data with Frequency Truncated at 200 MHz
Assuming 4 Natural Modes

132

 

Amplitude

4e-007 —

3.56-007 ‘

39-007 —

2.5e-007 _

29-007 #

1.5e-007 ~

1e-007 —~

58-008 _

w—V———‘u_—_l_-_-

 

 

 

 

 

 

 

 

___._.__—__._

 

 

 

Green Line Motor with Frequency Data Excluded
Measured Data

—————————— Modeled Data — 8 Modes

 

 

 

_-—___
§~—————___-_—___--.-_——_

 

 

 

0.15 0.25 0.35

Frequency (GHZ)

Figure 4-67: Frequency Content of Modeled Green Line Motor Data
with Frequency Truncated at 200 MHz Assuming 8 Natural Modes

133

Amplitude

 

 

46-007 —l
3.5e-oo7 ~
39-007 —
2.5e-007 a
:
2e-007 a i
:
1.5e-oo7 —
1e-007 —
5e-008 a
0

 

Green Line Motor with Frequency Data Excluded
Measured Data

—————————— Modeled Data — '7 Modes

 

 

 

 

 

 

 

 

 

 

 

." /
\ \/\ — ,-
I ‘ \’\l‘v‘—"\""—a—"\"/

 

 

 

l T l l l I

0.05 0.15 0.25 0.35 0.45
0.1 0.2 0 3 0.4 0.5

Frequency (GHZ)

Figure 4-68: Frequency Content of Modeled Green Line Motor Data
with Frequency Truncated at 200 MHz Assuming 7 Natural Modes

134

 

Amplitude

 

4e-007 —

Green Line Motor with Frequency Data Excluded
Measured Data

—————————— Modeled Data — 6 Modes

 

 

 

3.59-007 #

3e-007 —

2.59-007 —

a

2e-007 —-

 

1.5e-007 4

 

_——T-———.—_—__—

_,..____._...
J‘

1e-OO7 —

 

 

 

 

 

‘fl—r—wwur
_’-

 

 

56-008 —

 

 

V
I
\

~" I
\ \,\ _
d "\’\’\,—--_——\’\,\’— —

0 I I I I ‘ I I I I I ' I
0.05 0.15 0.25 0.35 0.45
0.1 0.2 0 3 0.4 0.5

Frequency (GHZ)

Figure 4-69: Frequency Content of Modeled Green Line Motor Data
with Frequency Truncated at 200 MHz Assuming 6 Natural Modes

135

Amplitude

 

4e-007 —

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Green Line Motor with Frequency Data Excluded
Measured Data
---------- Modeled Data — 5 Modes

3.5e-007 -4
3e-007 —«
2.5e-007 —

l

I

.1

ll

2e-007 —~ ;

i

l

I

1.5e-007 a l

I

I
1e-007 —
58-008 -—

0 I l I» T- ‘ I I ‘ l
0.05 0.15 0.25 0.35 0.45
O 0.1 0.2 0.3 0.4 0.5

Frequency (GHZ)

Figure 4-70: Frequency Content of Modeled Green Line Motor Data
with Frequency Truncated at 200 MHz Assuming 5 Natural Modes

136

lAnlpanidez

4e-OO7 ——w

3.56-007 ‘1

39-007 —

2.59-007 ~

2e-007 fl

1.5e-007 ~

1e-007 —~

59008 A

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Green Line Motor with Frequency Data Excluded
Measured Data

---------- Modeled Data — 4 Modes

 

 

 

I x ’ q
\, __ \,\’ 'a\’\"’~-.—\’\’\"_—"\"

 

 

 

l I l I l I
0.15 0.25 0.35 0.45
0.2 0 3 0.4 0.5

Frequency (GHZ)

Figure 4-71: Frequency Content of Modeled Green Line Motor Data
with Frequency Truncated at 200 MHz Assuming 4 Natural Modes

137

CHAPTER 5

ELECTROMAGNETIC COMPATIBLITY IMPLICATIONS OF
MOTOR SWITCHING TRANSIENTS

5.1 Overview

Up until this chapter this thesis has dealt with the topic of conducted emissions.
However, in the field of electromagnetic compatibility radiated emissions are also very
important. This chapter discusses radiated emissions and why they are undesirable. A
model for radiated emissions is developed and applied to the four motors studied in this
thesis. Results from these models are compared to the CISPR 25 radiated emission
limits. Conducted emission currents are also computed for each motor model and

discussed.

5.2 Radiated Emissions

Radiated emissions are the electric and magnetic fields radiated by one device that may
be received by other devices and cause interference in those devices. Although radiated
emissions include both electric and magnetic fields, CISPR and other regulatory agencies
only require that electric fields be measured for certification. The magnitudes of these
fields are measured in dBuV/m and the frequency range for radiated emissions extends
from 30 MHz to 40 GHz. CISPR has different sets of regulations for different types of
devices. Devices that are marketed for use in commercial, industrial, or business
environments are classified as Class A devices. Devices that are marketed for use in

residential environments, notwithstanding their use in commercial, industrial, or business

138

environments are classified as Class B devices. In general the regulations for class B
devices are more stringent than those for Class A devices.

Although automobile companies police themselves and often set their standards
for radiated emission limits to much more stringent levels than those dictated by CISPR,
it is not known exactly what radiated emission limits each automobile manufacturer sets
for itself. Thus, for comparison purposes in this thesis, the Class B CISPR limits will be

used as a baseline.

5.3 Radiated Emissions Modeling
A wire harness connected to the DC motor can be modeled as a pair of parallel wires of
identical length l and separation s. The currents on both wires are directed to the right

and are denoted as I1 and 12. As seen in Figure 5—1, these currents can be decomposed

into common and differential-mode currents

 

 

I = 1 +1
‘ C D (5.1)
12 =IC—ID.
ID 11 1c
T f F r
S
i ID 12 IC
4 > t

 

 

A L
‘ 7

Figure 5-1: Illustration of Common and Differential Mode Currents on the Two-Wire Model

139

 

At any given cross section along the harness the differential-mode currents are
equal in magnitude but opposite in direction. These differential-mode currents are the
ideal currents expected to flow in the harness. However, currents in the harness are not
always perfectly balanced in practice. Common-mode currents are the non-ideal,
unbalanced currents found in the harness. The common-mode currents are undesirable
because they are a source for radiated emissions [1]. For the purposes of this model, a
worst-case scenario is assumed where all of the conducted emission currents exiting the
motor are common-mode currents. Thus,

Il : I2 = 1C (5.2)
The total electric field of the harness is determined by superimposing the radiated fields

of both conductors in the harness model. Thus, the total radiated field, 15,, , is the sum of

the fields generated from the currents I1 and 12,
E9 = E0,l + E9; (5.3)

In order to determine these electric fields both wires are approximated as dipole antennas.

Current in the dipoles are maxrmrzed at the source (assuming I S a), which 18 Situated at

the center of the dipole, and zero at the ends of the dipole. Thus, the current I (z) is

proportional to sin([)’0z) such that

(1 sin ,8 -l-—z O>z>L
C 0 2 ’ 2

I(z)=< (5.4)

l l
[Sm —+z , ——>z>0
.6 lIIlz ll 2

 

 

 

140

The field of the total dipole is computed as the superposition of many small Hertzian

dipoles of length dz , having a constant current equal to I (z) at that point along the

dipole. This is illustrated in Figure 5-2

 

 

 

 

Figure 5-2: Dipole Antenna Model of a Single Conductor in the Two-Wire Model

where P is the observation point where EB.l or E9.2 is computed.

The field at point P due to each tiny dipole segment is

I(z)sin 0’
47rr.I

l

dEOJ. -_- jnofio e-jB”r"dz (5.5)

However, if P is in the far field, the system can be approximated as seen in Figure 5-3.

141

 

 

 

 

 

Figure 5-3: Far Zone Approximations for the Dipole Antenna Model of a Single Conductor
in the Two-Wire Model

Thus, for a far-field system, 6 E 6’ and r; E If. This approximation for If,

however, cannot be used in the phase term because it relies on the electrical distance

% rather than the physical distance r,’. A more reliable approximation for I}, in the
hase term iS r’ E r - z 0059 . Makin these substitutions into E uation (5.5) yields
P g q

I z Sing —' r.—zCOS
dE6,r : 177030 —(li—)7r—r_e m0(‘ ”dz (5.6)

The total radiated electric field due to a single wire is the sum of these tiny dipole

contributions

Z) Sin 6 e-jfior ejBOzcosfl

in nofio— ( dz (5.7)
471'

||

1'

rel--

Substituting Equation (5.4) into Equation (5.7) yields

142

 

0 sin Bo L+z
. . 2 ’IBOF' 1B :cosO
E9 :IJnOfiOICSInB . e ‘6 " dz

4n’r.

l

I Csin[fio[é—z]]
e‘J/Ioriejfiozcosadz (58)

47W.

I
. . o "
Inofio $1119 ‘15 r- - I If :cosO jsinfi l3 :c050
=——I e 0' srn —+z e’ 0 dz+ ——z 6’ ° dz
47“} C _J; [fl0(2 [I o

Allowing 6 = 90° to give fields in the broadside of the line and q) = 90° to give fields in

’1

1770130 Sin 9

the planes of the wire will maximize the modeled radiated electric field (assuming

I S g). Equation (5.8) is reduced to

L
177 B -J/30r,- o 2
EOi— _4_70n031Ce [sin[[3 0%“ z)]dz+Isin[B 0[——z)]dz (5.9)

2

This equation may be simplified to

171030 -J'l30r, 2 _ _l_
E“: 47” ——Ie {ED—[l cos[fi02)]} (5.10)

Thus,

 

(5.11)

 

where r1 and r2 are shown in Figure 5-4.

143

W 50.2

 

 

 

 

Figure 5-4: Geometry for Total Electric Field Using the Two-Wire Model

The distances rl and r2 can be written in terms of r as follows

q=r+A
(5.12)
er—A

where A = EssinG sin 4) . However, since 6 = 90° and (p = 90° this reduces to

A = %s sin (90° )sin (90° ) =

 

 

3. Thus
2
E9 = Ear + E92
. ‘130'1 ‘Ifiorz
1770 e e l
=—I + l—cos -— 5.13
2” [ r1 6 I (502)] < >
. ‘1/30(’+A) *1/30("A)
=J—no—Icsin9 e +6 l—cos 30L
2” r+£— r—3 2
2 2

144

 

 

Again, smce the observation pomt is in the far field, the physrcal distance, 5 IS

negligible, allowing it to be removed from the denominators. The phase terms cannot be
approximated in this way, however, as they depend on electrical distances as explained

earlier. Thus,

 

. -' r _.3 i 13 1
E0 = 1170 [Ce 1B0 [e 1,02 +6] 02 )[1_C08(fi0 1]] (5.14)
27Zr 2
- f; i '5 1
Furthermore, 770 512071', and [e j 02 +ej 03 J: 2cos[%fios], which leads to
_ 1201C —jfior 1 1
E9 — j r e cos[2 B0511 cos[flo 2)] (515)

But the wire spacing s is electrically small, so 003(3) 2 1. Also, BO = 211:, where c is
c

the speed of light. Thus, the magnitude of the maximum radiated electric field due to

common mode currents is

r

|E,,|m =120l—I—C—l[l—cos[fioé)] (5.16)

The current 1C should be the worst-case current on the wire harness. Since

current is voltage divided by impedance, these worst-case currents correspond to the

maximum modeled transient voltages. Since

v(t)= r(t)=§N;A,e°n' cos(a)nt+¢") (5.17)

and the maximum value of the cosine term is 1, the maximum transient voltage of each

term in the series is

145

= A,e"~’. (5.18)

max.n

 

lv (I)
The exponential term decays since 0'" is negative. Thus, the maximum value of equation
(5.18) occurs at the beginning of the late time period, t: TL.
vm. = Anew (5.19)
The maximum voltages occur at the natural frequencies,
vm = v(w,, ) = 21,th . (5.20)

Thus,

anTL

1C —1 =1(w,)=v(w")=4'e (5.21)

The frequency-domain impedance, z (0)), was measured earlier and is presented in
Chapter 2. The values of z (wn) are obtained through linear interpolation of the value of

z ((1)) at the imaginary part of the natural frequencies.

5.4 Radiated and Conducted Emission Model Results

The author wrote a program called VOME. FOR that reads in the modeled time-varying
voltage data and approximates the maximum voltages due to each natural mode. The
program also reads the measured impedance as a function of frequency and computes
maximum conducted emission currents due to each natural frequency. The input data for
this program corresponds to Figures 4-2, 4-16, 4-32, and 4-52. Predicted natural
frequencies that produce conducted emission currents less than 1 mA are considered

negligible and are not included. This data is presented in Table 5-1.

146

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Motor

M Natural Voltage at Impedance at Modeled

otor Type Natural Conducted
Frequency F Natural . .
requency Fre Ermssron Current
quency

23.72 MHz 3.75 V 35.05 $2 110.13 mA

Actuator 63.25 MHz 2.54 V 97.58 S2 26.01 mA
Motor 94.50 MHz 7.06 V 220.34 S2 32.03 mA
123.92 MHz 4.58 V 194.43 9 23.54 mA

149.41 MHz 10.55 V 1029.79 £2 10.24 mA
Blower 29.56 MHz 6.16 V 40.08 $2 153.79 mA

Motor 41.11 MHz 0.19 V 53.89 £2 3.54 mA
73.80 MHz 3.87 V 118.85 82 32.54 mA

10.72 MHz 1.01 V 419.47 52 2.42 mA

23.16 MHz 3.98 V 94.80 52 42.02 mA

Blue Line 54.51 MHz 0.54 V 59.23 92 9.21 mA
Motor 62.27 MHz 3.89 V 42.03 £2 92.55 mA
75.26 MHz 3.21 V 72.55 £2 44.22 mA

86.42 MHz 2.77 V 112.93 82 24.55 mA

93.83 MHz 2.59 V 126.79 S2 20.44 mA

23.22 MHz 2.83 V 117.24 52 24.16 mA

62.21 MHz 0.50 V 77.22 S2 6.50 mA

Green Line 89.59 MHZ 2.08 V 275.01 52 7.57 mA
Motor 122.79 MHz 1.72 V 200.06 £2 8.62 mA
148.80 MHz 9.41 V 94.72 S2 99.37 mA

174.01 MHz 2.98 v 43.54 52 68.54 mA

 

 

 

 

 

 

 

 

 

 

Table 5-1: Modeled Conducted Emission Currents at the Predicted Natural Frequencies

 

The voltages and currents on this table reflect the maximum values due to each natural I

frequency. This worst-case current is used to approximate [C in equation (5.16) and a

worst-case radiated electric field is computed. This computation is carried out by the

 

program vome. for for harness lengths ranging from 5 cm to 1m. These harness lengths
were chosen since they would be representative harness lengths found in an automobile.
The fields are computed at a distance of ten meters from the wire harness in each case in

accordance with CISPR Class B regulations. The results are plotted in Figure 5-5.

147

Radiated Electric Field (dbuV/m)

 

 

 

 

 

 

 

Actuator Motor
110 _ Natural Frequencies
' 23.72 MHZ
—————————— 63.25 MHZ
---------------- 94.50 Mllz 7’ ,
100 -m .. 123,92 MHz 11.4””
——— -- 149.41 MHz ,4’ ,-
90 e
80 —n
70 ~
i
‘1
60 —— '
50 —
40 A
3° I I I I I I I I I I
10 30 50 7O 90
0 20 40 60 80 100

Harness Length (cm)

Figure 5-5: Modeled Radiated Emissions vs. Harness Length for the Actuator Motor

 

 

148

 

110 —

 

 

 

 

 

 

Blower Motor
Natural Frequencies
E 29.56 MHz __
\ 100 _7 —————————— 41.11MHZ ”
> ---------------- 73.80 MHz
4
K
,5) 90 ~
"0
V
"O 30 —‘
r—i
Cl)
.,——4 ,
LL. 7o — , ’
C)
”—4
L4 50 _q
_',_J
C)
C)
r—-4
50 m
11131
G) 40 —r ,’
—+__) 1’
CU ,’
v r-——1 /
t S 30 —I //
CU ,
(v ,’
t-‘—4 I
2° ’I I n I I I I I I I
10 30 50 70 90
0 20 40 60 80

Harness Length (cm)

Figure 5-6: Modeled Radiated Emissions vs. Harness Length for the Blower Motor

149

100

IRadiated_IflexfiJic FHeld (dtnflfl/na)

 

 

Blue Line Motor
Natural Frequencies

10.72 MHZ

 

 

 

 

 

---------- 23.16 MHz
---------------- 54.51 MHZ
- 62.27 MHz ......
------------ 75.26 MHZ ' g
100 —« ————————— 86.42 MHz . - — ‘ ;:,.«rr"‘"”
——————————— — 93.83 Mllz , , "';-«—»4"”‘
.- ’ Ike"
“I'd/:"r --_ - -'
.“'"-",/’ ------- :‘J'—'3*"”’
80 — y',/ _, --
1.4"",/‘,/’ . —,L5:“"
I/// _ ":,”
/// " ”I,
// :”’
."'./// 1”
60 _‘ //
/ /
4O ——
20 -«
0 _.
I I 1 l ' I l l T l
10 30 50 7o 90
0 20 40 60 80 100

llarness Length (cni)

Figure 5-7: Modeled Radiated Emissions vs. Harness Length for the Blue Line Motor

150

 

 

Radiated Electric Field (dbuV/m)

 

 

 

 

   

 

 

Blue Line Motor
Natural Frequencies
23.22 MHZ
---------- 62.21 MHZ
---------------- 89.59 MHZ if
120 — w 122.79 MHz ’ ,.:.,—_v;;:—>-"’
— --—.— —u-. 148.80 MHZ ’ 3,2?”
110 fi ————————— 174.01 MHZ , ”22.;4/’
100 —~ ,1”
/‘7’
4//
l//
90 4
80 —
70 ~
60 —
50 —1
40 —~
30 -I
2° I r I I I I I I I I
10 30 50 7O 90
0 20 40 60 80 100

 

Harness Length (cm)

Figure 5-8: Modeled Radiated Emissions vs. Harness Length for the Green Line Motor

151

 

In each case the worst-case modeled fields are above the CISPR radiated emission
limits of 30 dBuV/m for frequencies between 30-230 MHZ. However, these modeled

field strengths are worst-case scenarios, computed with currents that are likely much

greater than the actual currents present on the wire harness.

 

 

152

CHAPTER 6

CONCLUSIONS

This thesis has presented a comparison between a numerical model and measured data for
conducted emission transients. The goal of this thesis was to create a numerical model
for conducted emission transients generated due to the switching of DC motors used in
automobiles. As discussed in Chapter 4, the numerical model developed does adequately
model the measured conducted emission transients. Furthermore, this model made it
possible to predict the conducted emission currents and radiated emission electric fields
due to the switching transients.

A discussion of conducted emissions as well as the theory behind the procedure
for measuring conducted emission transients was presented in Chapter 2. This theory
was put to use in Chapter 3 as the measurement procedures and data were presented. The
numerical model for the measured conducted emission transients was derived in Chapter
4, utilizing the extinction pulse technique. The modeled data generated through this
method was presented and compared to the measured conducted emission transients in
Chapter 4 as well.

Finally, Chapter 5 used the numerical model to predict the practical
electromagnetic compatibility issues of conducted emission currents and radiated
emission electric fields. Conducted emission currents due to each modeled natural
frequency were calculated. Also, a dipole model was applied to approximate a wire
harness connected to each DC motor. Using this model, the expected radiated electric

field was predicted for some representative harness lengths found in automobiles.

153

 

 

Although the goal of this research was achieved, further research could produce
better results and possibly improve the utility of the conducted emission transient model.
Investigation into a wider variety of motors could lead to the identification of expected
natural frequency content for similar motor types. This identification of expected natural
frequency spectrums for different motors could lead to a simple method of identifying
expected conducted and radiated emissions due to the switching of those motors. Rather
than needing to test each motor over a wide frequency range for both conducted and
radiated emissions, this natural frequency information would allow the conducted and
radiated emission characteristics to be modeled, necessitating only the measurement of
the impedance spectrum of the motor.

The radiated emission model developed in Chapter 5 used worst-case currents to
model the radiated electric field. These worst-case currents led to modeled radiated
emissions that exceed the CISPR 25 limits. However, in practice, the worst-case currents
are likely not present on the harness. The current contributions due to each natural
frequency will be attenuated somewhat, although this attenuation was difficult to
accurately approximate. Future research could attempt to develop a more accurate
current model to be used for radiated emission modeling.

The Broadband Artificial Network is a useful tool for measuring conducted
emission transients. However, in this thesis, the BAN was found to have a few
shortcomings. For the motors tested in this thesis, the BAN did not have sufficiently
large impedance at higher test frequencies to support the linear model assumed in the
measurement process. Future research could take two approaches to improving the

performance of the BAN. The first approach would be to alter the components of the

154

 

 

BAN such that the inductor and capacitor component values would force the BAN to
have greater impedance at higher frequencies. This would ensure the impedance of the
BAN will be large with respect to the impedance of the motors at higher frequencies and
the assumed linear model will remain valid at those frequencies. The second approach to
improving the performance of the BAN would require that the assumed linear model be
discarded and treat the measurement circuit as a voltage divider. With a known
impedance of the motor under test and the BAN over the entire test frequency range a
voltage divider would be able to accurately measure the transient voltage.

The area of electromagnetic compatibility is an interesting and fast-growing field
of electrical engineering. EMC is becoming prominent in both industry and academia as
technology continues to push the limits of high frequency devices, necessitating new
testing standards and regulations. This thesis illustrates the need for more research into
numerical simulations and measurement techniques in the field of electromagnetic

compatibility.

155

 

 

APPENDIX

156

 

 

APPENDIX
FORTRAN PROGRAMS
A.l Overview
The modeling done in this thesis could not have been accomplished without the aid of
computers. The computational speed and efficiency provide by computers is invaluable.
This appendix briefly discusses the functions of the two Fortran programs used in this

thesis. The source code for these two programs is also included.

A.2 Extinction Pulse Program

The program ep. for generates an extinction pulse based on user input. This program was
originally used for target identification, but the extinction pulse method can be adopted to
model conducted emission transients. The program requires an input file with a
measured conducted emission transient data set. The user identifies the time period over
which an extinction pulse should be generated as well as an expected number of natural
modes. The program then generates an extinction pulse based on the input file and user
information. From this extinction pulse, the amplitude and phase of the measured data is
approximated, as well as the complex natural frequencies of that data. A modeled

waveform is reconstructed using this information.

157

 

A.3 Source Code for ep.for

The following is the source code for ep.f0r.

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

Double precision version of 27 March 1992
Modified by Ed Rothwell

***********************************~k*******

EP - This program creates a forced E-pulse. The complex natural
frequencies contained in the data are obtained as a by
product of making the E—pulse.

EP requires the following files during execution.

1. EP.INP — contains information on which data files to use,

how many modes to look for, etc. The format for this file
is described below.

2. Response Files — contain the measured or synthetic transient
data in NDF format.

The EP.INP file has the following format.
Line # Datatype Explaination

1 L,L,L,L Logical switches for program control
dpsw, szsw, dcsw, irsw

dpsw = .true. >>>> discard positive sigma terms
szsw = .true. >>>> set positive sigma mode amplitudes to
zero
dcsw = .true. >>>> generate E—pulse to kill DC
irsw = .true. >>>> print intermediate results
2 A30 filename for results summary
3 A30 filename for E—pulse output
4 A30 filename for best fit data
5 A30 filename for complex natural frequencies
6 I # data sets used k
7 A30 filename of data set #1
8 R,R start and end of late-time of data set #1
9 A30 filename of data set #2
To R,R start and end of late—time of data set #2
6+2k—1 A30 filename of data set #k
6+2k R,R start and end of late—time of data set #k
7+2k I # of modes to extract, # of match points
in late—time
8+2k I # points to skip
9+k R,R,R lower limit, upper limit, increment
in search for optimum E-pulse duration
lO+k I # significant digits squared error per
point

000GOO000000000000000000000000000000OOOOOOOOOOOOOOOOOOOOOOO

158

 

 

00000000000000OOOOOOOOOOOOOOOOOOOOOOOO000OOOOOOOOOOOOOOOOOOOOOOO

Sample EP.INP

The natural mode frequencies of Boieng 747 (B747) are extracted
using three different aspect angle measurements.

.false., .false., .true., .false. Program control switches

B747.res Filename for results summary

B747.epu Filename for E—pulse output

B747.dat Filename for best fit data

B747.frq Filename for natural frq

3 # of data sets

B747l.ndf B747 data at aspect #1

7.0,20.0 start, end of late-time #1

B7472.ndf B747 data at aspect #2

6.5,20.0 start, end of late-time #2

B7473.ndf B747 data at aspect #3 .
6.0, 20.0 start, end of late time #3 "
5, 40 # modes, # match points

1 skipping every other point

2.0, 7.0, 0.1 lower, upper, increment

3 # significant digits

Overview of program operation:
1. EP reads the EP.INP file

Note #1 : The late-time period of each data set does not have
to start or end at the same time. Each data set
must have the same sampling interval.

Note #2 : To provide good estimates of the complex natural
frequencies it is best to use responses that have
large late-time energy. Often, it is not necessary
to use all measured responses in order to obtain good
estimation of natural frequencies. Unused responses
can de used as an independent check of the quality of
the resulting E-pulses with the program DISCRIMS.FOR.

 

2. EP searches for the optimum E—pulse duration. The optimum duration
is the one that yields the minimum squared error per point between
the original data and a waveform constructed using the extracted
modal frequencies, amplitues, and phases.

3. The program computes the amplitudes for an E—pulse of each value
of duration in the search. Based on the pulse amplitudes of the E—
pulse the complex natural frequencies are obtained. The amplitudes
and phases that result in a best fit to the data are then
computed. The squarred error per point for that value is then
reported via SQRTOT.

4. After the optimum value of duration within the specified search
range is obtained the pulse amplitudes of the E—pulse is computed
and written to the specified disk file.

5. The natural frequencies are written to a specified disk file.

6. The amplitudes and phases that result in the best fit to each-

data set is computed. The summary of mode frequencies, amplitudes
and phases is written to a specified disk file.

159

 

OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO00000000000000

00

O

7. The squarred error per point for each value on duration is written
to the file TKDATA.DAT. This data is useful in estimating the
limits of the duration search and the number of evaluation points
in the search.

Note #4 : Natural mode frequencies with a positive damping
coefficient (sigma) may be encountered with measured data.
These values are obviously non—physical. All modes of
passive targets must have a negative sigma. The cause of
the non—physical values is usually due to excessive noise
present in the measurement or by imperfect modeling of the
transmitted pulse. It is also conceivable that choosing the
time window for mode extraction too small can also result
in poor estimates natural frequencies. Incorrect estimates
of the number of modes in the data could also cause the
same effect.

P. Ilavarasan has attempted make a version of EP.FOR that
would constrain the sigma to be negative. This problem
seems to be very difficult and has not yet been
successfully implemented.

Note #5 z The duration of the natural E—pulse width is given as

number of modes
Natural E-pulse duration : _________________________________
highest natural frequency excited

From this relationship, the duration of the forced E-pulse
can be estimated as follows.

0.25 natural duration < forced duration < 4 natural duration

EP searches for the optimum forced E-pulse duration within the
specified range.

References:

1. E. J. Rothwell and K. M. Chen, "A Hybrid E—pulse/
Least Squares Technique for Natural resonance Extraction,"
Proceedings of the IEEE, pp. 296—298, March 1988.

2. C. E. Baum, E. J. Rothwell, K. M. Chen and D. P. Nyquist,
"The Singualrity Expansion Method and its Application to
Target Identification," to appear in Special Proceedings of
IEEE on Electromagnetics, October 1991.

program ep

implicit real*8 (a—h,o—z)

parameter (luna=10, luntk=11, mxpts=2048, mxdts=10,
& mxnms=20, mxnps=42, mxtkpts=1024)
character*30 respnm(mxdts), filers, fileep, filefr

logical dpsw, szsw, dcsw, irsw

common /switch/ dpsw, szsw, dcsw, irsw

common /files/ respnm, filers, fileep, filefr

common /system/ nresp, tstart(mxdts), tend(mxdts), nskip
& , modes, nptslt

160

O

0 O

()0f30

O O

()0

O()O()O

O 0

common /sample/ npulse, dtl, dt2(mxdts), te(mxdts), nmodes

write(*, *) l***********************************************l
write(*,*) '** Program : EP.FOR **'
write(*,*) '** Version 1.1 **'
write(*,*) I** **I
write(*,*) '** Purpose : Natural Mode Extraction via **'
write(*,*) '** Hybrid E—Pulse/Least Squares **'
write(*,*) '** Technique. **'
write(*,*) I** **I
write(*,*) '** Update : November 12, 1991 **'
write(*,*) '** **n
write(*,*) '** Authors : Ponniah Ilavarasan **'
write(*,*) '** John E. Ross III **'
write(*,*) '** Edward J. Rothwell **'
write(*,*) '** **'
write(*,*) '** Department of Electrical Engineering **'
write(*,*) '** Michigan State University **'
write(*,*) ‘** East Lansing, MI 48824 **'
write(*,*) c** **I
write(*,*) '** Copyright (c) 1991 **'
write(*, *) |******'*****************************************'

write(*,*)
read ep.inp file to get start up information

call rdepinp
write (*,*) 'passed rdepinp'

read in specified response data sets and put in array h(,)

call rdresp
write (*,*) 'passed rdresp'

process response data sets, round off start & stop times, generate
arrays with slopes and time values

call procres
write (*,*) 'passed procres'

skip data points for best fit and put in array hbf(,)

call skip
write (*,*) 'passed skip'

calculate energy in late time of responses

call energy
write (*,*) 'passed energy'

open file for output of search for optimum E—pulse duration (tk)
open(luntk,file='tkdata.dat')

Number of pulses used here is twice the # of modes plus one

because forcd E—pulse. In the case dc forced E-pulse, it is

plus one to the above number

npulse = 2*modes+1
if (dcsw) npulse = npulse + 1

Minimize the function sqrtot(tk) to find optimum tk and best E-pulse

call minfunc

161

c Write summary, best fit, and E—pulses to disk files

call wrres

c
Close(luntk)
c
end
c
C _______________________________________________________________________
c
C RDEPINP — Reads EP.INP file information.
c
subroutine rdepinp
c
parameter (luna=10, mxdts=10)
c
implicit real*8 (a-h,o—z)
c
character*30 respnm(mxdts), filers, fileep, filefr
logical dpsw, szsw, dcsw, irsw
c
common /switch/ dpsw, szsw, dcsw, irsw
common /files/ respnm, filers, fileep, filefr
common /system/ nresp, tstart(mxdts), tend(mxdts), nskip
& , modes, nptslt
common /search/ tkstrt, tkend, tkstep, nsigtk
c
l format(a)
c
c open file for input
c
open(luna,file='ep.inp')
c
c read in program control
c dpsw = .true. >>>> discard positive sigma terms
c szsw = .true. >>>> set positive sigma mode amplitudes to zero
c dcsw = .true. >>>> generate E—pulse to kill DC
c irsw = .true. >>>> print intermediate results
c
read(luna,*) dpsw, szsw, dcsw, irsw
c
c read filename for results summary output
c
read (luna,1) filers
c
c read filename for E-pulse output
c
read (luna,1) fileep
c
c read filename for complex natural frequency output
c
read(luna,1) filefr
c
c read in # of data sets
c
read (luna,*) nresp
write (*,*) 'number of data sets is ',nresp
c
c read the response filenames and it's corresponing
c start and end of late—time
c

do 10 i = 1, nresp
read(luna,1) respnm(i)

162

00

0000 O 0000 0000

0

0000

write (*,*) ‘i=',i

write (*,*) 'respnmz',respnm(i)

read(luna,*) tstart(i),tend(i)

write (*,*) 'tstart,tend=',tstart(i),tend(i)
continue

read # modes, # of match points in late time
read(luna,*) modes, nptslt
write (*,*) 'modes=',modes
write (*,*) 'nptslt=',nptslt

read in number of points to skip

read(luna,*) nskip
write (*,*) 'nskipz',nskip

read in lower, upper limit, increment in duration search
of optimum E-pulse

read(luna,*) tkstrt, tkend, tkstep
write (*,*) 'tkstrt,tkend,tkstep=',tkstrt,tkend,tkstep

read in accuracy in squared error per point in duration search
of optimum E-pulse

read(luna,*) nsigtk
write (*,*) 'nsigtk=',nsigtk

write (*,*) 'All info read OK'
Close(luna)

write out a message, when upper limit used in search of optimum
exceeds the minimum late—time period

temp = 1.0d10

do 20 i = 1, nresp
if(temp .ge. (tend(i)—tstart(i))) temp = tend(i)-tstart(i)

if (tkend .ge. temp) then
write(*,*)' Upper limit used in search of optimum E—pulse'
write(*,*)' has exceeded the minimum late-time period'
stop

end if

return

end

RDRESP — Reads response files and loads data into two dimensional
array H( , ).

subroutine rdresp
implicit real*8 (a-h,o—z)
parameter (mxpts=2048, mxdtsle)

character*30 respnm(mxdts), filers, fileep, filefr
character*30 fname, ftype

163

real*8 xr(mxpts), xi(mxpts)

c
common /files/ respnm, filers, fileep, filefr
common /system/ nresp, tstart(mxdts), tend(mxdts), nskip

& , modes, nptslt

common /rtime/ dt, nstart(mxdts), nend(mxdts), npts
common /btime/ dtbf, nptsbf(mxdts), nbftot

common /harray/ h(mxdts,mxpts), hbf(mxdts,mxpts)
common /tarray/ t(mxpts), tbf(mxpts)

c

c read in all responses one at a time

c
do 20 i = 1, nresp

c

fname = respnm(i)
call rddata(fname,ftype,sO,ds,npts,sigma,omega,xr,xi)

c

c put response data in H(,) array

c

do 10 j = 1, npts
10 h(i.j) = xr(j)
c
20 continue

c

c construct an array containing time values

c
do 30 j = 1, npts

30 t(j) = (j-l)*dS

c

c save sampling interval in common block variable

c
dt = ds

c
return

c
end

c

C _______________________________________________________________________

c

C PROCRES — Round off start and end times. Calculate slopes of

c response data.

c
subroutine procres

c
implicit real*8 (a—h,o—z)

c
parameter (mxpts=2048, mxdts=10)

c
common /system/ nresp, tstart(mxdts), tend(mxdts), nskip

& , modes, nptslt

common /rtime/ dt, nstart(mxdts), nend(mxdts), npts
common /btime/ dtbf, nptsbf(mxdts), nbftot

common /harray/ h(mxdts,mxpts), hbf(mxdts,mxpts)
common /sarray/ slope(mxdts,mxpts)

c

c Round off start and end time of each data set

c
do 10 i = 1, nresp

nstart(i) = 1 + int(tstart(i) / dt)
nend(i) = int(tend(i) / dt)

10 continue

c

do 15 i = l, nresp
tstart(i) = dt * nstart(i)

164

tend(i) = dt * nend(i)

15 continue

c

c Calculate slopes of responses
c

iend = npts - 1
do 30 i = 1, nresp
do 20 j = 1, iend

slope(i.j) = (h(i,j+1) — h(i.j)) / dt
20 continue
30 continue
c
return
c
end
c
C _______________________________________________________________________
c
c SKIP - Skips the specified number of points in the late time data.
c Skipping allows use data of sets with dense sampling without
c excessive run time.
c
subroutine skip
c
implicit real*8 (a-h,o-z)
c
parameter (mxpts=2048, mxdts=10)
c
logical dpsw, szsw, dcsw, irsw
c
common /switch/ dpsw, szsw, dcsw, irsw
common /system/ nresp, tstart(mxdts), tend(mxdts), nskip
& , modes, nptslt
common /rtime/ dt, nstart(mxdts), nend(mxdts), npts
common /btime/ dtbf, nptsbf(mxdts), nbftot
common /harray/ h(mxdts,mxpts), hbf(mxdts,mxpts)
common /tarray/ t(mxpts), tbf(mxpts)
c
c Calculating sampling interval in best fit
c
dtbf = dt * (nskip+1)
c
c Take every nskip th point and put it into hbf(,) array and tbf()
c array
c
i = 0
n = —nskip
c
10 i = i + 1
n = n + nskip + 1
if (n .gt. npts) goto 30
tbf(i) = t(n)
c
do 20 k = l, nresp
hbf(k,i) = h(k,n)
20 continue

goto 10
30 nbftot = i—1
c recalculate nstart and nend to match the skipped data

do 40 i = 1, nresp
nstart(i) = 1 + int(tstart(i) / dtbf)

165

nend(i) = int(tend(i) / dtbf)

nptsbf(i) = nend(i) — nstart(i)
40 continue
c
if (irsw) then
do 50 i = 1, nresp
50 write (*,*) '# points in best fit in data #1: ',nptsbf(i)
endif
c
return
c
end
c
C _______________________________________________________________________
c
c ENERGY — Calculates energy.
c
subroutine energy
c
implicit real*8 (a-h,o-z)
c
parameter (mxpts=2048, mxdts=10)
c
common /system/ nresp, tstart(mxdts), tend(mxdts), nskip
& , modes, nptslt
common /rtime/ dt, nstart(mxdts), nend(mxdts), npts
common /btime/ dtbf, nptsbf(mxdts), nbftot
common /harray/ h(mxdts,mxpts), hbf(mxdts,mxpts)
common /enerlt/ enerl(mxdts)
c
do 10 i = 1, nresp
10 enerl(i) = 0.d0
c
c Calculate the late-time energy of each response
c
do 25 k = 1, nresp
do 20 i = nstart(k), nend(k)
enerl(k) : enerl(k) + hbf(k,i)*hbf(k,i)
20 continue
25 continue
c
write (*,*) 'Energy calculated'
esav = enerl(l)
write (*,*) 'esav=',esav
do 40 k = 1, nresp
write (*,*) 'Relative late—time energy of data set ‘,k,‘ =',
& enerl(k) / esav
40 continue
c
return
c
end
c
C _______________________________________________________________________
c
c MINFUNC — Searches for the minimum point of a function.
c
subroutine minfunc
c .
implicit real*8 (a—h,o—z)
c
parameter (mxpts=2048, mxdts=10, mxtkpts=1024)
c

real*8 serr(mxtkpts)

166

common /search/ tkstrt, tkend, tkstep, nsigtk
common /final/ tkmin, smin

c
external sqrtot
c
c Step through tk and locate minimum squared error pt
c
tk = tkstrt
itk = 0
10 itk = itk + 1
serr(itk) = sqrtot(tk)
tk = itk * tkstep + tkstrt
if (tk .le. tkend) go to 10
c
imin = l
smin = serr(l)
do 20 i = 1, itk
if (serr(i) .1t. smin) then
smin = serr(i)
imin = i
endif
20 continue
c
c Locate minimum point
c
if ((imin .eq. 1) .or. (imin .eq. itk)) then
tkmin = tkstrt + (imin—1)*tkstep
smin = sqrtot(tkmin)
else
c
asq = tkstrt + (imin-2)*tkstep
bsq : asq + tkstep
csq = bsq + tkstep
c
c Calculate accuracy from number of significant figures
c
acc = 10.d0**(-nsigtk)
c
smin = golden (asq,bsq,csq,sqrtot,acc,tktmp)
c
c Reassign temporary variable used in call list to common block
c variable
c
tkmin = tktmp
c
endif
c
return
c
end
c
C _______________________________________________________________________
c
c WRRES — Writes results to output files.
c
subroutine wrres
c
implicit real*8 (a—h,o-z)
c
parameter (luna=10, lunal=12, mxpts=2048, mxdts=10, mxnms=20,
& mxnps=42, mxtkpts=1024)
c
character*30 respnm(mxdts), filers, fileep, filefr

167

C

O

charact
charact

real*8

C 0111111011
C ommon
&
C ommon
C ornmon
C ommon
C OITlITlOl'l
C ommon
C ommon
C ommon

create fil

er*30 fname, ftype
er*20 filnam(20)

b(mxnps), hbfs(mxpts), xi(mxpts)

/files/ respnm, filers, fileep, filefr
/system/ nresp, tstart(mxdts), tend(mxdts), nskip
, modes, nptslt
/rtime/ dt, nstart(mxdts), nend(mxdts), npts
/btime/ dtbf, nptsbf(mxdts), nbftot
/harray/ h(mxdts,mxpts), hbf(mxdts,mxpts)
/tarray/ t(mxpts), tbf(mxpts)
/sample/ npulse, dtl, dt2(mxdts), te(mxdts), nmodes
/final/ tkmin, smin
/freq/ x(mxnps)

e names for best fit waveforms

filnam(1) = 'bf1.dat'
filnam(2) = 'bf2.dat'
filnam(3) = 'bf3.dat'
filnam(4) = 'bf4.dat'
filnam(S) = 'bf5.dat'
filnam(6) = 'bf6.dat'
filnam(7) = 'bf7.dat'
filnam(8) = 'bf8.dat'
filnam(9) = 'bf9.dat'
filnam(lO) = 'bf10.dat'
filnam(ll) = 'bfll.dat'
filnam(12) = 'bf12.dat'
filnam(13) = 'bf13.dat'
filnam(14) = 'bf14.dat'
filnam(15) = 'bf15.dat'
filnam(16) = 'bf16.dat'
filnam(17) = 'bf17.dat'
filnam(18) = 'bf18.dat'
filnam(l9) = 'bf19.dat'
filnam(20) = 'bf20.dat'

Write E—pulse waveform data to disk

call ampltd(b)

fn

ftype

50
ds

np

ame

= O

npulse

fileep
'Time'

tkmin / npulse

call

wrdata(fname,ftype,sO,ds,np,b,xi)

Open file for summary output

open(luna,file=filers)

open (lunal, file='mode.dat',status='unknown')
write (luna1,*) nresp,nmodes

write (luna,*) 'results —————————————————————————— '
write (luna,*) 'tk = ',tkmin

write (luna,*) 'squared error per pt = ',smin

do 30 k = 1, nresp

write

(luna,*) ‘data set ',k

168

20
c

C
C

40

50

do 10 j = 1, nbftot
hbfs(j) = hbf(k,j)

jdc = 1

tstemp = tstart(k)

tetemp = tend(k)

ntmp = nmodes

dttemp = dtbf

call linear (x,ntmp,jdc,tstemp,tetemp,hbfs,tbf,dttemp,b)

do 20 j = l, nmodes
eng = ener(b(2*j—1),x(2*j—1),x(2*j).b(2*j),tstemp,tetemp)

write (luna,*) 'mode no. ',3
write (luna,*) 'sigma = ',x(2*j—l)
write (luna,*) 'omega = ',x(2*j)
write (luna,*) 'amp = ',b(2*j~1)
write (luna,*) 'phase = ',b(2*j)
write (luna,*) 'energy = ',eng
continue

write (luna,*) 'dc = ',b(2*nmodes+1)

write out modal info

do 25 j=1, nmodes

ar = b(2*j—1)*cos(b(2*j))

ai = b(2*j-1)*sin(b(2*j))
write (luna1,*) ar,ai,x(2*j—l),x(2*j)
continue

write (luna1,*) b(2*nmodes+1)

continue

Close(luna)
close (lunal)

open file for best fit data

do 60 k = 1, nresp
open (luna,file=filnam(k),status='unknown')

do 35 j = 1, nbftot
hbfs(j) = hbf(k,j)

tstemp = tstart(k)

tetemp = tend(k)

ntmp = nmodes

dttemp = dtbf

call linear (x,ntmp,jdc,tstemp,tetemp,hbfs,tbf,dttemp,b)

do 50 i = nstart(k), nend(k)
ti = tbf(i)
f = b(2*nmodes+1)
do 40 j = 1, nmodes
f = f + b(2*j-1)*exp(x(2*j—1)*ti)*cos(x(2*j)*ti+b(2*j))
write (luna,*) ti,hbf(k,i),f
continue
close (luna)
continue

open file for complex natural frequency output
open(luna,file=filefr)

do 70 i = 1, nmodes

169

70 write(luna,*) x(2*i—1), x(2*i)

0000

0

0000000000

Close(luna)
return
end

ENER - Calculates energy in a single mode waveform between
t = t1 and t2

real*8 function ener (amp,sigma,omega,phi,t1,t2)

implicit real*8 (a—h,o—z)
complex*16 s, jphi

jphi = dcmplx(0.,phi)
s = dcmplx(sigma,omega)

if (sigma .eq. 0.d0) then
term = 2.d0*(t2-t1)

else
term = (exp(2.d0*sigma*t2) — exp(2.d0*sigma*tl)) / sigma
endif
ener = (amp*amp/4.d0)*(term + dreal(exp(2.d0*(s*t2+jphi))/s) -
& dreal(exp(2.d0*(s*t1+jphi))/s))
return
end

————_~—---—-—-————————-—-o———-—-—o—a-—.-—-—-—_——_—————.—_—.—————————__———_———_—

SQRTOT — Calculates the squared error per point between the actual
data and the data constructed from extracted natural frequencies
for a given E—pulse duration. The E—pulse method is used to extract
the natural frequencies. This function is minimized to find the
optimum fit between actual and reconstructed data. This should
yield the optimum E—pulse.

real*8 function sqrtot (tk)
implicit real*8 (a-h,o—z)

parameter (luntk=11, mxpts=2048, mxdts=10, mxnms=20,
& mxnps=42)

logical dpsw, szsw, dcsw, irsw

real*8 sg(mxnps-l), om(mxnps—l)
complex*16 zc(mxnps), zr(mxnps), zz
real*8 hbfs(mxpts), b(mxnps)

common /switch/ dpsw, szsw, dcsw, irsw

common /system/ nresp, tstart(mxdts), tend(mxdts), nskip
& , modes, nptslt

common /search/ tkstrt, tkend, tkstep, nsigtk

common /rtime/ dt, nstart(mxdts), nend(mxdts), npts
common /btime/ dtbf, nptsbf(mxdts), nbftot

common /harray/ h(mxdts,mxpts), hbf(mxdts,mxpts)

common /tarray/ t(mxpts), tbf(mxpts)

170

 

common /enerlt/ enerl(mxdts)
common /sample/ npulse, dtl, dt2(mxdts), te(mxdts), nmodes
common /freq/ x(mxnps)

c
c Calculate start of late time, and fining out the
c biggest end time
c
tendb = tend(l)
C
do 5 i = 1, nresp
if ( tendb .le. tend(i) ) tendb = tend(i)
te(i) = tstart(i) + tk
dt2(i) = (tend(i)-te(i)) / (nptslt—1)
5 continue
c
dtl = tk /npulse
c
c Calculate pulse function amplitudes for E—pulse
c
call ampltd(b)
c
c Calculate complex zero's of E—pulse. These correspond to the
c natural frequencies of the response.
c
do 10 i = 1, npulse
10 zc(i) = b(i)
c
ndeg = npulse - 1
call zroots (zc,ndeg,zr,.true.)
c
c Calculate complex frequencies
c
do 30 i = 1, ndeg
22 = (-1.d0/dt1) * log(zr(i))
sg(i) = dreal(zz)
30 om(i) = abs(dimag(zz))
c
if (irsw) then
do 40 i = 1, ndeg
40 write (*,*) 'sg = ',sg(i),' om = ',om(i)
endif
c
c Identify complex conjugate pairs
c
nmodes = 0
ndegml = ndeg — 1
do 60 j = 1, ndegml
iflag = 0
jpl=j+l
c
do 50 i = jpl, ndeg
c
if (om(j) .eq. 0.d0) om(j) = 1.d—5
test = abs(om(i) — om(j)) / om(j)
if (test .1t. 1.d—4) iflag=1
50 continue
c
c test for multiple frequency
c
if (nmodes .ge. 1) then
do 45 i = l, nmodes
test = abs(om(i) - om(j)) / om(j)

if (test .1t. 1.d—4) iflag = 0
45 continue

171

endif

c
if (iflag.eq.1) then
c
if ((sg(j) .gt. 0.d0) .and. (szsw)) then
nmodes = nmodes + 1
om(nmodes) = om(j)
sg(nmodes) = 0.d0
if (irsw) write (*,*) 'set sigma = 0.0'
else if ((sg(j) .gt. 0.d0) .and. (dpsw)) then
if (irsw) write (*,*) ’discarding +sigma term'
else if (sg(j)*tendb .gt. npts*dt) then
if (irsw) write (*,*) 'discard large +sigma term'
else
nmodes = nmodes + 1
om(nmodes) = om(j)
sg(nmodes) = sg(j)
endif
endif
60 continue
c
do 70 i = 1, nmodes
x(2*i-1) = sg(i)
x(2*i) = om(i)
70 continue
c
sqrtot = 0.d0
c
do 120 k = 1, nresp
c
do 110 j = 1, nbftot
110 hbfs(j) = hbf(k,j)
c
jdc = l
c
c Assign temporary variables for call list instead of using
c common block variables
c
tstmp = tstart(k)
tetmp = tend(k)
ntmp = nmodes
c
call linear (x,ntmp,jdc,tstmp,tetmp,hbfs,tbf,dtbf,b)
c
if (irsw) then
write (*,*) 'data set # ',k
do 100 i = 1 ,nmodes
write (*,*) 'sg = ',x(2*i—l),' om = ',x(2*i)
100 write (*,*) 'am = ',b(2*i—1),' ph = ',b(2*i)
' write (*,*) 'dc = ',b(2*nmodes+l)
endif
c
c calculate squared error for data set k
c
serror = 0.d0
c
do 90 i = nstart(k), nend(k)
ti = tbf(i)
f = b(2*nmodes+1)
c
do 80 j = 1, nmodes
80 f = f + b(2*j—l)*exp(x(2*j—1)*ti)*COS(X(2*j)*ti+b(2*j))
c

serror = serror + (f—hbf(k,i))*(f—hbf(k,i))

0

continue

sqrerr = serror/nptsbf(k)

sqrtot = sqrtot + sqrerr/enerl(k)
continue
write (*,*) 'tk = ',tk,‘ sqrtot = ', sqrtot

Write squared error data to disk

write(luntk,*) tk, sqrtot
return

end

---————_—————-—————————--——-————_-———-——-————————-——————————————————n——

subroutine ampltd (b)
implicit real*8 (a-h,o-z)
parameter (mxpts=2048, mxdts=10, mxnps=42)

logical dpsw,szsw,dcsw,irsw

Solves for E—pulse pulse function amplitudes

real*8 b(mxnps)
real*8 a(mxnps,mxnps)
real*8 diag(mxnps)
real*8 save(mxnps)
integer ipvt(mxnps)

common /switch/ dpsw, szsw, dcsw, irsw

common /system/ nresp, tstart(mxdts), tend(mxdts), nskip
, modes, nptslt

common /search/ tkstrt, tkend, tkstep, nsigtk

common /rtime/ dt, nstart(mxdts), nend(mxdts), npts

common /btime/ dtbf, nptsbf(mxdts), nbftot

common /harray/ h(mxdts,mxpts), hbf(mxdts,mxpts)

common /sarray/ slope(mxdts,mxpts)

common /tarray/ t(mxpts), tbf(mxpts)

common /enerlt/ enerl(mxdts)

common /sample / npulse, dtl, dt2(mxdts), te(mxdts), nmodes

fill matrix

npl = npulse — 1

do 10 n = 1, npl
do 5 m = 1, npl
a(m,n) = 0.d0
continue
b(n) = 0.d0
continue

do 50 k = 1, nresp
energ = enerl(k)

do 40 m = 1, nptslt

173

tm = te(k) + dt2(k)*(m-1)

c
do 30 n = l, npulse
c
tln = (n—1)*dt1
t2n = tln + dtl
c
t1 = tm - t2n
tu = tm — tln
ml = 2 + int((tl — t(l)) / dt)
mu = 1 + int((tu — t(l)) / dt)
deltal = t1 - t(ml - 1)
deltau = tu — t(mu)
c
suml = 0.d0
sum2 = 0.d0
iend = mu - 1
c
do 20 i = ml, iend
suml = suml + slope(k,i)
sum2 = sum2 + h(k,i)
20 continue
c
temp = (dt—deltal)*(O.5d0*slope(k,m1—1)*
& (dt+deltal)+h(k,ml-1)) +
& deltau*(0.5d0*slope(k,mu)*dt+h(k,mu)) +
& dt*(0.5d0*dt*suml+sum2)
save(n) = temp/energ
c
30 continue
c
do 12 kk = l, npl
do 11 jj = 1, npl
a(kk,jj) = a(kk,jj) + save(jj)*save(kk)
11 continue

b(kk) = b(kk) + save(kk)*(-save(npulse))
12 continue

c
40 continue
c
50 continue
c
c fill in for dc e—pulse
c
if (dcsw) then
do 60 kk = 1, npulse
a(kk,npulse) = 1.d0
60 continue
c
do 70 jj = 1, npulse
a(npulse,jj) = 1.d0
70 continue
c
a(npulse,npulse) = 0.d0
b(npulse) = -l.d0
endif
c
c solve matrix problem
c

if (dcsw) then
nsolve = npulse
else
nsolve = npl
endif

174

call decomp (nsolve,a,ipvt,diag)
call solve (nsolve,a,ipvt,b)

c
b(npulse) = 1.d0
c
return
end
c
C _______________________________________________________________________
c
c LINEAR — Peforms linear regression (least squares) to obtain
c amplitudes and phases + dc
c
subroutine linear (x,nmodes,jdc,tstart,tend,h,t,dt,b)
c
implicit real*8 (a-h,o-z)
c
parameter (mxpts=2048, mxnps=42)
c
real*8 a(mxnps,mxnps), diag(mxnps)
real*8 b(mxnps), x(mxnps)
real*8 h(mxpts), t(mxpts)
integer ipvt(mxnps)
c
pi = 4.d0 * atan(l.d0)
c
nstart = 2 + int(tstart / dt)
nend = 1 + int(tend / dt)
nmodt2 = 2*nmodes
nmodp = nmodt2 + 1
c
c fill B vector
c
do 20 i = l, nmodp
b(i) = 0.d0
20 continue
c
do 100 i = nstart, nend
hi = h(i)
ti = t(i)
n = 1
do 50 j = l, nmodes
ex = exp(x(n)*ti)
b(n) = b(n) + hi*ex*cos(x(n+1)*ti)
b(n+1) = b(n+1) + hi*ex*sin(x(n+1)*ti)
n = n + 2
50 continue
b(nmodp) = b(nmodp) + hi
100 continue
c
c fill a matrix
c
do 120 i = 1, nmodp
do 110 j = 1, nmodp
a(i,j) = 0.d0
110 continue
120 continue
c
do 200 i = nstart, nend
ti = t(i)
n = 1
do 150 j

1, nmodes
(

exn = exp x(n)*ti)

175

exn*cos(x(n+1)*ti)
exn*sin(x(n+1)*ti)

cen
sen
m = 1

do 140 k = 1, nmodes

exm = exp(X(m)*ti)
cem = exm*cos(x(m+1)*ti)
sem = exm*sin(x(m+1)*ti)
a(n,m) = a(n,m) + cen*cem
a(n,m+1) = a(n,m+1) + cen*sem
a(n+1,m) = a(n+1,m) + sen*cem
a(n+1,m+1) = a(n+1,m+1) + sen*sem
m = m + 2
140 continue
a(n,nmodp) = a(n,nmodp) + cen
a(n+1,nmodp) = a(n+1,nmodp) + sen
n = n + 2
150 continue
m = 1

do 160 k ='1, nmodes

exm = exp(x(m)*ti)
cem = exm*cos(x(m+1)*ti)
sem = exm*sin(x(m+1)*ti)
a(nmodp,m) = a(nmodp,m) + cem
a(nmodp,m+1) = a(nmodp,m+1) + sem
m = m + 2
160 continue
200 continue
c
a(nmodp,nmodp) = a(nmodp,nmodp) + dfloat(nend-nstart+1)
c
nmat = nmodt2
if (jdc .eq. 1) nmat = nmodp
c
call decomp (nmat,a,ipvt,diag)
call solve (nmat,a,ipvt,b)
c
c put into phase-amplitude form
c
n = 1
do 250 i = 1, nmodes
an = sqrt(b(n)*b(n) + b(n+1)*b(n+1))
phin = atan(-b(n+1)/b(n))
if (b(n) .lt. O.d0) phin = phin + pi
b(n) = an
b(n+1) = phin
n = n + 2
250 continue
c
return
end
c
c _______________________________________________________________________
c
c DECOMP - Decomposes matrix A to triangular form.
c From: Linear Algebra by Gilbert Strang
c
subroutine decomp (n,a,ipvt,diag)
c
implicit real*8 (a—h,o—z)
c
parameter (mxnps=42)
c

integer n,ipvt(mxnps)
integer nm1,i,j,k,kp1,m

176

real*8 a(mxnps,mxnps)
real*8 diag(mxnps)

c
ipvt(n) = 1
if (n .eq. 1) go to 70
nml = n—l
c
do 60 k=1,nm1
kpl = k+1
c
c find pivot p
c
m = k
do 10 i=kp1,n
10 if (abs(a(i,k)) .gt. abs(a(m,k))) m=i
ipvt(k) = m
if (m .ne. k) ipvt(n) = -ipvt(n)
p = a(m,k)
a(m,k) = a(k,k)
a(k,k) = p
diag(k) = p
if (p .eq. 0.0d0) go to 60
c
c compute multipliers
c
20 do 30 i=kp1,n
30 a(i,k) = -a(i,k)/p
c
c interchange rows and columns
c
do 50 j=kp1,n
t = a(m,j)
a(m,j) = a(k.j)
a(k.j) = t
if (t .eq. 0.0d0) go to 50
do 40 i=kp1,n
a(i,j) = a(i,j) + a(i,k)*t
40 continue
50 continue
60 continue
c
70 diag(n) = a(n,n)*dfloat(ipvt(n))
c
return
end
c
C _______________________________________________________________________
c

c SOLVE — Solves matrix eqn Ax = B with a decomposed dy DECOMP

subroutine solve (n,a,ipvt,b)

c
implicit real*8 (a—h,o-z)

c
parameter (mxnps=42)

c
integer n,ipvt(mxnps)
integer nm1,k,kb,kp1,km1,m,i
real*8 a(mxnps,mxnps)
real*8 b(mxnps)

c

c forward elimination

c

if (n .eq. 1) go to 30

177

nml = n—l
do 10 k=1,nm1
kpl = k+1
m = ipvt(k)
s = b(m)
b(m) = b(k)
b(k) = 5
do 10 i=kp1,n
10 b(i) = b(i) + a(i,k)*s
c
c back substitution
c
do 20 kb=1,nm1
kml = n—kb
k = km1+l
b(k) = b(k)/a(k,k)
s = -b(k)
do 20 i=l,km1
20 b(i) = b(i) + a(i,k)*s
c
30 b(l) = b(1)/a(1,1)
c
return
end
c
C ———————————————————————————————————————————————————————————————————————
c

c ZROOTS - Calculates complex roots. From Numerical Recipies.
c
subroutine zroots(a,m,roots,polish)
implicit real*8 (a-h,o-z)
parameter (eps=1.d—6,maxm=101)
complex*16 a(m+1),roots(m),ad(maxm),x,b,c
logical polish
do 11 j=1,m+l
ad(j)=a(j)
11 continue
do 13 j=m,1,—1
x=dcmplx(0.d0,0.d0)
call laguer(ad,j,x,eps,.false.)
if(abs(dimag(x)).le.2.d0*eps**2*abs(dreal(x)))
2 x=dcmplx(dreal(x),0.d0)
roots(j)=x
b=ad(j+l)
do 12 jj=j,l,-l
c=ad(jj)
ad(jj)=b
b=x*b+c
12 continue
13 continue
if (polish) then
do 14 j=1,m
call laguer(a,m,roots(j),eps,.true.)
14 continue
endif
do 16 j=2,m
x=roots(j)
do 15 i=j—l,1,-l
if(dreal(roots(i)).le.dreal(x))go to 10
roots(i+l)=roots(i)

15 continue

i=0
lO roots(i+1)=x
16 continue

178

return

end
c
C ———————————————————————————————————————————————————————————————————————
c
c LAGUER — From Numerical Recipies
c
subroutine laguer(a,m,x,eps,polish)
implicit real*8 (a-h,o—z)
complex*16 a(m+1),x,dx,xl,b,d,f,g,h,sq,gp,gm,g2,zero
logical polish
parameter (zero=(0.d0,0.d0),epss=6.d-8,maxit=100)
dxold=abs(x)
do 12 iter=l,maxit
b=a(m+1)
err=abs(b)
d=zero
f=zero
abx=abs(x)
do 11 j=m,l,-l
f=x*f+d
d=x*d+b
b=x*b+a(j)
err=abs(b)+abx*err
11 continue
err=epss*err
if(abs(b).1e.err) then
dx=zero
return
else
g=d/b
92=g*g
h=g2—2.d0*f/b
sq=sqrt((m-l)*(m*h—g2))
gp=g+sq
gm=g—sq
if(abs(gp).lt.abs(gm)) gp=gm
dx=m/gp
endif
x1=x-dx
if(x.eq.x1)return
x=x1
cdx=abs(dx)
if(iter.gt.6.and.cdx.ge.dxold)return
dxold=cdx
if(.not.polish)then
if(abs(dx).le.eps*abs(x))return
endif
12 continue
pause 'too many iterations'
return
end
c
c _______________________________________________________________________
c
C GOLDEN - From Numerical Recipies
c

real*8 function golden (ax,bx,cx,f,tol,xmin)
implicit real*8 (a—h,o—z)

r=.61803399d0

c=l.d0-r

x0=ax

x3=cx

if(abs(cx-bx).gt.abs(bx—ax))then

179

 

 

 

00

000000000000000

x1=bx
x2=bx+c*(cx—bx)
else
x2=bx
x1=bx—c*(bx—ax)
endif
fl=f(xl)
f2=f(x2)
if(abs(x3—x0).gt.tol*(abs(x1)+abs(x2)))then
if(f2.lt.f1)then
x0=x1
xl=x2
x2=r*x1+c*x3
f0=f1
f1=f2
f2=f(x2)
else
x3=x2
x2=x1
x1=r*x2+c*x0
f3=f2
f2=f1
fl=f(x1)
endif
goto 1
endif
if(f1.lt.f2)then
golden=f1
xmin=x1
else
golden=f2
xmin=x2
endif
return
end

 

RDDATA — This subroutine reads in a data set that has uniform
sampling.
The first line of the data set contains the filetype
Time
Frequency
S—Pulse
If file contains S-Pulse data then the next line has the
sigma and omega of the mode associated with that S—Pulse.
The following lines contain:
start time. nS or Ghz
sampling interval nS or Ghz
sampled data points (# for time, # # for frequency and S—Pulse)
(S—Pulse = Cosine, Sine pulses)

 

 

subroutine rddata(fnm,ftype,sO,ds,np,sigma,omega,x,y)
implicit real*8 (a-h,o~z)
parameter (luna=10, mxpts=2048)

character*30 fnm, ftype
real*8 x(mxpts), y(mxpts)

open(unitzluna, filezfnm)

Read in filetype

180

 

read(luna,1) ftype
l format(a)

if (ftype.eq.'Spulse') then
read(luna,*) sigma, omega
endif

read(luna,*) sO
read(luna,*) ds

c
c Read in the sampled values.
c
i = 1
if (ftype.eq.'Time') then
10 read(luna,*,end=99,err=999) x(i)
y(i) = 0
i = i + 1
goto 10
else if (ftype.eq 'Spulse') then
20 read(luna,*,end=99,err=999) x(i), y(i)
i = i + 1
goto 20
endif
c
99 np = i—l
c
Close(luna)
c
return
c
999 write(*,*) ' *** Error in subroutine rddata ***'
Close(luna)
stop
c
end
c
c _______________________________________________________________________
c
c WRDATA - This subroutine writes uniformly sampled data to a file.
c The first line of the data set contains the filetype
c Time
c Frequency
c S—Pulse
c If file contains S—Pulse data then the next line has the
c sigma and omega of the mode associated with that S—Pulse.
c The following lines contain:
c start time. nS or Ghz
c sampling interval nS or Ghz
c sampled data points (# for time, # # for frequency and S—Pulse)
c (S—Pulse = Cosine, Sine pulses)
c
subroutine wrdata(fnm,ftype,sO,ds,npts,v,x)
implicit real*8 (a—h,o—z)
parameter(luna=10, mxpts=2048)
c
real*8 v(mxpts), x(mxpts)
character*30 fnm, ftype
c
open(luna, filezfnm)
c
c Write out sampling interval.
c

write(luna,5) ftype
5 format (a)

181

write(luna,*) sO
write(luna,*) ds

c

c Write out sampled values.

c
if (ftype.eq.'Time') then
do 20 i = 1, npts

20 write(luna,*) v(i)

endif

c
if (ftype.eq.'Frequency') then
do 30 i = 1, npts
write(luna,*) v(i), x(i)

30 continue

endif

c
Close(luna)

c
return

c
end

c

182

A.4 Radiated Emissions Program

The program Vomefor was written to take the input file res.dat generated from the
program ep. for and extracts the natural frequency information. Impedance data is also
inputted from an impedance measurement data file. Worst-case voltages are computed
for each natural frequency. From these voltages and impedances, worst-case conducted
emission currents are calculated at the natural frequencies and outputted to a data file.
Worst-case radiated electric fields are computed for a variety of typical harness lengths

found in automobiles and outputted to a data file.

183

A.5 Source Code for Vome.for

The following is the source code for Vome. for.

Program Vome

c
c
C ********************~k****************************************
C * it
c * Program Vome *
C it *
c * Written by Matt Feusse *
c * Last updated: March 21, 2001 *
C * *
c * This program reads in data from res.dat and the *
c * impedance files for each motor, and computes the *
c * radiated E-fields and conducted emission currents at *
c * the natural frequencies. *
‘k *
g **'k**********************************************************
c
c
Implicit none
Integer nummodes,ierror,I,mode(10),II,K,KK,LL,N
Real*8 pi,d,L,latetime
Real*8 sigma(10),omega(10),amp(10),phase(10),energy(10)
Real*8 natfreq(10),freq(10000),imp(10000),ome(10000)
Real*8 ratio(10),natimp(10),v(10),current(10)
Real*8 totcurrent(10),beta(10),f(10),efield(10),dbuvefield(10)
Character*80 motor,res,imped,newfile,newfile2
pi=3.14159265359
d=10.0
c
C**************************************
c Acquiring User defined info
C**************************************
c
Write(*,*) "Which Motor are you testing?"
Read(*,*) motor
Write(*,*) "Enter the name of the results data file:"
Read(*,*) res
Write(*,*) "Enter the name of the impedance data file:"
Read(*,*) imped
Write(*,*) "Enter the name of the current output file:"
Read(*,*) newfile
Write(*,*) "Enter the name of the e-field output file:"
Read(*,*) newfile2
Write(*,*) "How many modes?"
Read(*,*) nummodes
Write(*,*) "What is the beginning of the late time (ns)?"
Read(*,*) latetime
latetime=latetime*l.Oe—9
2*************************
c Open the files
C*************************
c
Open(Unit=l,File=res,Status='Unknown',Actionz'read',
& Iostat=Ierror)
Open(Unit=2,Fi1e=imped,Status:'Unknown',Action='read',
& Iostat=Ierror)
Open(Unit=3,Fileznewfile,Statusz'Unknown',Action='Write'.
& Iostat=Ierror)

184

OmaHUnitz4,File=newfile2,Statusz'Unknown',Action='Write',

 

& Iostat=Ierror)
Vhite(3,*) "Output Data File for the",motor,"Motor"
Write(3,*) " ————————————————————————————————————————————————————— "
Write(3,*) " ----------------------------------------------------- "
c
C**************************************************************
c This section reads the res dat file and identifies
C the natural frequencies
C**************************************************************
c
Read(l,*)
Read(l,*)
Read(l,*)
Read(l,*)
I=l
Do I=l,nummodes
Read(1,lO) mode(I) -r!:,
10 Format(20X,IlO) :
Read(l,20) sigma(I)
20 Format(12X,E25.l6)
Read(l,30) omega(I) F
30 Format(12X,E25.l6) !
Read(1,40) amp(I) g
40 Format(12X,E25.l6) E
Read(l,50) phase(I) .
50 Format(12X,E25.16)
Read(1,60) energY(I) L ..
60 Format(12X,E25.l6) “‘**

sigma(I)=sigma(I)*l.0e9

omega(I)=omega(I)*l.Oe9

natfreq(I)=omega(I)/(2*pi)
Enddo

C
C****************************‘k********~k************************

This section grabs the impedance and frequency data.

c
C*****‘*********************'************************************
c

Read(2,*)

Read(2,*)

II=1

Do While (.not. EOF(2))
Read(2,70) freq(II),imp(II)
7O Format(FlS.8,F20.8)
freq<II)=l.0e6*freq(II)
ome(II)=2*pi*freq(II)
II=II+l
Enddo

C
C*********************************************************************

This section computes the impedances at the natural frequencies

c
c using linear interpolation.
Ci-~k*'k‘k****************************************************************
c
Do K=l,I-l
KK=1
Do while ((KK.LT.II-2).and.(natfreq(K).GT.freq(KK)))
LL=KK
KK=KK+1
enddo
ratio(K)=natfreq(K)*2/(freq(KK)+freq(KK-l))
natimp(K)=ratio(K)*(imp(KK)+imp(KK-l))/2
enddo
c

185

 

C*********************************************************************

c This section takes the voltages due to each natural frequency

c and calculates the currents due to those natural frequencies.

c A radiated electric field is computed for a range of wire

c harness lengths. This information is written to an output file.

C********************'k*******************************‘k****************

C

Do K=l,I—l
Do N=l,20
L=N*0.05
v(K)=amp(K)*eXp(sigma(K)*latetime)
current(K)=v(K)/natimp(K)
beta(K)=2*pi*natfreq(K)/(3.0e8)
f(K)=1.0—cos(beta(K)*L/2)
efield(K)=(abs(f(K))*120*abs(current(K)))*l.0e6/(d)
dbuvefield(K)=20*loglO(efield(K))
Write(4,lOO) natfreq(K)/l.Oe6,L*lOO,dbuvefield(K)
Enddo
100 Format(F6.2,5X,F6.2,5X,F8.3)
Enddo
c
C*******************************************************************
c This section writes the frequency, impedance,voltage and
c current data associated with each natural mode to a file.

C*******************************************************************

c
Do K=l,I-l
Write(3,*) "Natural Mode #",K
Write(3,*) "Frequency (MHz): ",natfreq(K)/l.0e6

Write(3,*) "Impedance at Natural Frequency: ",natimp(K)
Write(3,*) "Maximum Voltage: ",V(K)
Write(3,*) "Maximum Current: ",current(K)
Write(3,*) " ———————————————————————————————————————————————
Enddo
End

186

[1]

[2]

[3]

[4]

[5]

BIBLIOGRAPHY

C. R. Paul, Introduction to Electromagnetic Compatibility. New York: John
Wiley & Sons, Inc., 1992.

International Electrotechnical Commission, Geneve, Suisse, CISPR 25: Limits
and Methods of Measurement of Radio Disturbance Characteristics for the
Protection of Receivers Used on Board Vehicles, first ed., 1995.

Daimler Chrysler, DC C EMC Test Specification and Laboratory Procedures,
November 19, 1999.

Edward, J. Rothwell, Kun-Mu Chen, Dennis P. N yquist, Weimin Sun,
“Frequency Domain E-Pulse Synthesis and Target Discrimination,” IEEE
Transactions on Antennas and Propagation, vol. AP-35, pp. 426—434, April
1987.

E. J. Rothwell, K. M. Chen, “A Hybrid E-Pulse / Least Squares Technique for

Natural Resonance Extraction,” Proceedings of the IEEE, vol. 76, pp. 296-298,
March 1988.

187