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thesis entitled

A Comparison of Measurement to Simulation
for an Antenna on a Vehicle

presented by
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has been accepted towards fulﬁllment

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M. S . degree in Electrical
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A COMPARISON OF MEASUREMENT TO SIMULATION FOR AN ANTENNA
ON A VEHICLE

By

Michael Robert Markey

A THESIS

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

MASTER OF SCIENCE

Depart of Electrical Engineering

2003

ABSTRACT

A COMPARISON OF MEASUREMENT TO SIMULATION FOR AN ANTENNA
ON A VEHICLE

By

Michael Robert Markey

As consumers require a growing number of information and entertainment
systems in an automobile, the number of antennas integrated into a vehicle increases.
A ﬁrst pass approach to development of these antennas can be done with simulation.
As the antennas operate at higher frequencies, however, simulation can become
computationally expensive since the vehicle itself is part of the antenna. The Method
of Moments (MM) technique is applied for a variety of frequencies ranging from 70
MHz to 1 GHz. Incorporating the Physical Optics (PO) approximation in a hybrid
MM-PO approach can reduce the required RAM. The accuracy of the simulation
results also needs to be veriﬁed with measurement. The measurements are performed
at an advanced facility that allows a full three-dimensional radiation pattern

measurement. These measurement and simulation results are compared.

© Copyright by
Michael Robert Markey
2003

For my parents

iv

ACKNOWLEDGEMENTS

I would like to thank Dr. Rainer Kronberger for his enthusiastic support for
this research. Thanks Rainer for arranging for me to come to Germany for this
research. Your continued interest in the results of this study has been inspirational
to me. Thanks again for coming all the way to East Lansing for the defense.

Thanks to the whole EAA group at FUBA® Advanced Reception Systems
in Bad Salzdetfurth, Germany. Thanks especially to Axel Stephan for your patience
and experience with measurements and your helpful advice with simulation.

Thanks to Dr. Leo Kempel and Dr. Ed Rothwell for your wisdom and

guidance for this project and throughout my academic career. Go Green!

TABLE OF CONTENTS

 

 

 

 

 

 

 

 

 

 

LIST OF TABLES - - -- - -viii
LIST OF FIGURES - - - - -_ - - "mix
CHAPTER 1 - - - - - - - - 1
INTRODUCTION - - - - - 1
1.1 Overview ................................................................................................... 1
1.2 Test Vehicle ............................................................................................... 3
1 .3 Measurement ............................................................................................. 4
1.4 Simulation ................................................................................................. 5
CHAPTER 2
DESCRIPTION OF MEASUREMENTS
2.1 Introduction to the Antenna Measurements .............................................. 6
2.2 The Input Impedance Measurement .......................................................... 8
2.3 Far Field Measurements .......................................................................... 14
2.4 Near Field Measurements ........................................................................ 24
CHAPTER 3 31
SIMULATION METHODS 31
3.1 Introduction to Simulation Methods ........................................................ 31
3.2 The Method of Moments ......................................................................... 33
3.3 Physical Optics ........................................................................................ 37
3.4 Hybrid Methods ....................................................................................... 38
3.5 Simulation with FEKO ............................................................................ 40
3.5.1 Introduction to FEKO ...................................................................... 42
3.5.2 FEKO and the Test Vehicle ............................................................. 45
3.5.3 Hybrid Methods and the Test Vehicle ............................................. 54
CHAPTER 4 - - - -- -- - - 63
COMPARISON OF RESULTS -- - -- -- -- - -- 63
4. 1 Introduction ............................................................................................. 63
4.2 Comparison of Method of Moments and Measurement .......................... 63
4.2.1 Comparison of Input Impedance Measurement with MM .............. 64
4.2.2 Comparison of Far Field Measurement with MM ........................... 70
4.2.3 Transformed NF-FF Measurement with MM Simulation ............... 79
4.3 Comparison of Method of Moments to Measurement and Hybrid
Methods ............................................................................................................... 83
4.3.1 Hybrid I ........................................................................................... 85
4.3.2 Hybrid H .......................................................................................... 87
4.3.3 Hybrid III ......................................................................................... 92
4.3.4 Hybrid IV ........................................................................................ 93
4.3.5 Hybrid V ........................................................................................ 101
CHAPTER 5 -- -- __ . - ‘ - ........ 107

 

vi

CONCLUSIONS - - 107

5.1 Overview ............................................................................................... 107
5.2 MM simulation ...................................................................................... 108
5.3 Hybrid Simulations ................................................................................ 110
5.4 Simulation of an Antenna on a Vehicle ................................................. 113
5.5 Conclusions ........................................................................................... 1 15
REFERENCES .......... -- . - - - - _- 117

 

vii

Table 2.1:

Table 2.2:

Table 3.1:

Table 3.2:

Table 3.3:

Table 3.4:

Table 5.1:

Table 5.2:

LIST OF TABLES

The lengths of monopoles used for each band ....................................... 10
The total time for a near ﬁeld measurement .......................................... 27
The FEKO segmentation rules. From [3] ............................................... 46
The monopole lengths for simulation .................................................... 49
The number of metallic triangles and wire segments in free space as

output by preFEKO ............................................................................ 52
The total memory required and time for simulation .............................. 53
The method of moments computational requirements for all studied

frequency bands ............................................................................... 109

The computational requirements for the hybrid simulations ............... 110

viii

Figure 1.1:
Figure 1.2:
Figure 1.3:
Figure 1.4:

Figure 2.1:

Figure 2.2:

Figure 2.3:

Figure 2.4:
Figure 2.5:
Figure 2.6:
Figure 2.7:
Figure 2.8:

Figure 2.9:

LIST OF FIGURES

The many required communications with a vehicle. From [1] ............... 2
Simpliﬁed vehicle model constructed with wood and brass mesh ......... 3
A typical near ﬁeld scan on a vehicle inside the radome ........................ 4
Simulation model of a vehicle ................................................................ 5

Input impedance on a standard Smith Chart for (a) Band FM 70-120
MHz and (b) Band 3 175-235 MHz ................................................... 11
Input impedance on a standard Smith Chart for (a) Band Own 250-450
MHz and (b) Band 4-5 470-870 MHz ............................................... 12
Input impedance on a standard Smith Chart for Band GSM 800-1000
MHz ................................................................................................... 13
The Radome setup for the far ﬁeld measurement ................................. 16
92 MHz Band FM Far Field Vertical (Normalized Amplitude dB) ..... 19
92 MHz Band FM Far Field Horizontal (Normalized Amplitude dB). 19
205 MHz Band 3 Far Field Vertical (Normalized Amplitude dB) ....... 20
205 MHz Band 3 Far Field Horizontal (Normalized Amplitude dB)... 20

350 MHz Band Own Far Field Vertical (Normalized Amplitude dB) .21

Figure 2.10: 350 MHz Band Own Far Field Horizontal (Normalized Amplitude dB)

........................................................................................................... 21

Figure 2.11: 670 MHz Band 4-5 Far Field Vertical (Normalized Amplitude dB). 22

Figure 2.12: 670 MHz Band 4-5Far Field Horizontal (Normalized Amplitude dB)

........................................................................................................... 22

ix

Figure 2.13: 900 MHz Band GSM Far Field Vertical (Normalized Amplitude dB)

........................................................................................................... 23
Figure 2.14: 900 MHz Band GSM Far Field Horizontal (Normalized Amplitude
dB) ..................................................................................................... 23
Figure 2.15: Illustration of the near ﬁeld measurement .......................................... 26
Figure 2.16: Illustrates the transformed radiation pattern for (top) 350 MHz for
theta polarization with phi = 0° and (bottom) 670 MHz phi
polarization with phi = 90° (Normalized Amplitude dB) .................. 30
Figure 3.1: Scattering Problem ................................................................................ 33
Figure 3.2: The speed-up factor vs. the number of processors ................................ 42
Figure 3.3: The programs and their inputs and outputs ........................................... 45
Figure 3.4: The plane of electric symmetry ............................................................. 47

Figure 3.5: One half of the test vehicle. The other half is generated by symmetry. 48
Figure 3.6: The quarter-wavelength monopole, surface mesh triangles and the
excitation by a voltage across a gap ................................................... 50
Figure 3.7: The test vehicle with MM feed plate and monopole and the rest of the
vehicle considered with P0 approximation ....................................... 56
Figure 3.8: The vehicle as considered with Hybrid IV. The roof edges and the
pillars are considered with MM (shown in black) and the rest of the
vehicle with P0 (White) .................................................................... 61
Figure 4.1: Input Impedance for Band FM 76-108 MHz with MM and

Measurement ...................................................................................... 65

Figure 4.2:

Figure 4.3:

Figure 4.4:

Figure 4.5:

Figure 4.6:

Figure 4.7:

Figure 4.8:

Figure 4.9:

Input Impedance for Band 3 175-235 MHz with MM and Measurement
........................................................................................................... 65

Input Impedance for Band Own 250-450 MHz MM and Measurement
........................................................................................................... 66

Input Impedance for Band 4-5 470-870 MHz MM and Measurement. 66

Input Impedance for Band GSM 800-1000 MHz MM and Measurement

........................................................................................................... 67
Band FM Far Field Measured for Vertical (Top) and Horizontal

(Bottom) Polarization Shown with MM Simulation for 92 MHz and

Vehicle Facing 0° (Shown with Normalized Amplitude dB) ............ 74

Band 3 Far Field Measured for Vertical (Top) and Horizontal (Bottom)
Polarization Shown with MM Simulation for 205 MHz and Vehicle
Facing 0° (Shown with Normalized Amplitude dB) ......................... 75

Band Own Far Field Measured for Vertical (Top) and Horizontal
(Bottom) Polarization Shown with MM Simulation for 250 MHz and
Vehicle Facing 0° (Shown with Normalized Amplitude dB) ............ 76

Band 4-5 Far Field Measured for Vertical (Top) and Horizontal
(Bottom) Polarization with MM Simulation for 670 MHz and Vehicle

Facing 0° (Shown with Normalized Amplitude dB) ......................... 78

Figure 4.10: Band Own Far Field Transformed from Near Field Measured for

Vertical (Top) and Horizontal (Bottom) Polarization Shown with MM
Simulation for 350 MHz at d) = 0° and Vehicle Shown Facing Left

(Shown with Normalized Amplitude dB) .......................................... 81

xi

Figure 4.11:

Figure 4.12:

Figure 4.13:

Figure 4.14:

Figure 4.15:

Figure 4.16:

Figure 4.17:

Figure 4.18:

Band Own Far Field Transformed from Near Field Measured for
Vertical (Top) and Horizontal (Bottom) Polarization Shown with MM
Simulation for 350 MHz at 4) = 90° and Vehicle Shown Facing Into
the Plot (Shown with Normalized Amplitude dB) ............................. 82

The Surface Current Density on the Test Vehicle for the MM
Simulation at 350 MHz ...................................................................... 85

Hybrid I (top) and Hybrid H (bottom) Surface Current Density for 350
MHz ................................................................................................... 88

Band Own Far Field MM, Hybrid I and Hybrid II Simulation for
Vertical (Top) and Horizontal (Bottom) Polarization for 350 MHz at 0
= 85° and Vehicle Facing 0° (Shown with Normalized Amplitude dB)

........................................................................................................... 89

Band Own Far Field MM, Hybrid I and Hybrid H Simulation for
Vertical (Top) and Horizontal (Bottom) Polarization for 350 MHz at ¢
= 90° and Vehicle Shown Facing Into the Plot (Shown with
Normalized Amplitude dB) ............................................................... 90

The Impedance Curves for Measurement, MM and Hybrid II for Band
Own 250-450 MHz ............................................................................ 92

Hybrid IV (Top) and Hybrid V (Bottom) Surface Current Density for
350 MHz ............................................................................................ 95

Band Own Far Field MM, Hybrid IV and Hybrid V Simulation for

Vertical (Top) and Horizontal (Bottom) Polarization for 350 MHz at 0

xii

= 85° and Vehicle Facing 0° (Shown with Normalized Amplitude dB)
........................................................................................................... 96
Figure 4.19: Band Own Far Field MM, Hybrid IV and Hybrid V Simulation for
Vertical (Top) and Horizontal (Bottom) Polarization for 350 MHz at it
= 90° and Vehicle Shown Facing into the Plot (Shown with
Normalized Amplitude dB) ............................................................... 99
Figure 4.20: Band Own Far Field MM, Hybrid IV and Hybrid V Simulation for
Vertical (Top) and Horizontal (Bottom) Polarization for 350 MHz at (I)
= 0° and Vehicle Shown Facing to the Left (Shown with Normalized
Amplitude dB) ................................................................................. 100
Figure 4.2]: Surface Current Density on Side Panel of Vehicle and Monopole
Antenna with Feed Plate all Considered with the Method of Moments
......................................................................................................... 102
Figure 4.22: The Surface Current on the Side Panel of the Vehicle Considered with
P0 (Top) with No Edge Correction and (Bottom) with Edge

Correction on the Top Edge ............................................................. 102

Images in this thesis are presented in color.

xiii

CHAPTER 1

INTRODUCTION

1.1 Overview

Consumers are increasingly demanding multimedia applications for their
automobiles. They are also considering the availability of information and
communications systems when purchasing a vehicle. The growth in demand for these
systems means that the information flow between the vehicle and various sources is of
increasing importance. This has lead to a variety of antennas needed on the vehicle to
allow communication with terrestrial and satellite sources. As illustrated in Figure 1.1
[1], a current automobile could have numerous antennas to handle services such as
AM/FM radio, television, mobile phone, satellite digital audio radio (SDARS), global
positioning satellite (GPS) system, remote keyless entry (RKE), radar systems and
several others. In the near future, vehicles could be equipped with Internet access and
be Bluetooth compatible to allow wireless communications with computers, personal
device assistants (PDA) and other computer and electronic equipment.

These several antennas pose a signiﬁcant design challenge to engineers aiming
to optimize each antenna to meet performance speciﬁcations. Unfortunately, the
vehicle itself often has a large impact on performance since it is part of the antenna.
This requires prototypes of the vehicles and expensive measurement time to determine
how to optimally place the antennas. As design cycle times are reduced, however,
prototypes are becoming more difﬁcult to obtain and measurement time is even more
precious. This has lead automotive antenna engineers to seek another means for

design. Simulation, as a ﬁrst pass approach to design, is a viable means to make some

initial design decisions. Simulating the performance of an antenna with an automobile
requires signiﬁcant computational resources especially for high frequencies. Previous
work [1] has shown that a method of moments simulation for the FM band ranging
from 76-108 MHz on a vehicle compares very well with actual three dimensional
pattern measurements. Many applications shown in Figure 1.1 require much higher
operating frequencies. These higher frequency simulations may be too
computationally expensive for a full method of moments simulation. Therefore, hybrid
methods of simulation need to be explored to reduce the computational expense
required for higher frequencies up to 1 GHz. These hybrid methods need to be
compared with measurement to verify accuracy for a variety of bands of frequencies.
These include BandFM (70-120 MHz), Band 3 (175-235 MHz), Band Own (250—450

MHz), Band 4-5 (670-870 MHz) and Band GSM (800-1000 MHz).

 

Figure 1.1: The many required communications with a vehicle. From [1]

1.2 Test Vehicle

To compare the hybrid methods of simulation with measurement, a model of a
vehicle has been constructed. The model, or “test vehicle,” is constructed in an attempt
to make a realistically sized vehicle that is easy to create in simulation. For this reason,
large, simple geometries and sharp comers are used instead of smooth curves that may
be difﬁcult to create virtually. Additionally, the test vehicle is simpler than the actual
shell of a real vehicle because it does not contain complex materials and numerous
discontinuities such as door hinges, seals and the vehicle interior. The test vehicle is
constructed of wood and covered with brass mesh and conducting materials. It is 3.6
meters long, 1.6 meters wide and 1.56 meters tall. It is elevated from the ground by

0.44 meters. The test vehicle is pictured in Figure 1.2.

 

Figure 1.2: Simpliﬁed vehicle model constructed with wood and brass mesh

1.3 Measurement

In order to completely compare a simulation result with measurement, a full
three-dimensional measurement must be taken. This is performed at the radome. The
radome is a sophisticated range facility that allows a three-dimensional near ﬁeld
measurement. After the measurement is complete, the data is transformed to far ﬁeld
data that can be compared with simulation. A vehicle is shown in Figure 1.3 inside the
radome. The large arm protruding upward is the elevation arm that suspends a
broadcasting antenna at various elevation angles (0). The vehicle containing the
receiving test antenna is rotated on a turntable for various azimuth angles (4)). In this
way, a full scan can be performed. The measurements are discussed in detail in

Chapter 2.

 

Figure 1.3: A typical near ﬁeld scan on a vehicle inside the radome

1.4 Simulation

Since the aim of the study is to compare the measurements taken on the vehicle
to simulations, a simulation model must also be constructed. The simulation model is
shown in Figure 1.4 as constructed in FEKO. FEKO stands for “Field Computations
Involving Objects of Arbitrary Shape.” The simulation model has exactly the same
dimensions as the physical test vehicle. It is covered with a triangular mesh to allow
the application of the method of moments and other simulation techniques. The mesh
sizing can be adjusted with frequency. The simulations are discussed in detail in
Chapter 3. The comparison of results from measurement and simulation are shown in

Chapter 4. Chapter 5 includes the conclusions to this study.

 

Figure 1.4: Simulation model of a vehicle

CHAPTER 2

DESCRIPTION OF MEASUREMENTS

2.1 Introduction to the Antenna Measurements

There are many different types of measurements to characterize the
performance of an antenna on an automobile. The automotive industry has an
increased interest in accurate high frequency measurements of many antenna
performance parameters. This interest has been motivated by an increased consumer
demand for automotive electronics that require communication with terrestrial and
satellite antennas under harsh conditions. These electronics include communication
and entertainment equipment that require ever increasing data transfer rates that
operate at higher frequencies. This has led to signiﬁcant design challenges for an
effective antenna on the automobile. Measurements have been a key factor for
assessing the performance of the design. Simulation may point to some new design
solutions, decrease design time, and reduce overall design cost, but it is still necessary
to take thorough measurements to verify the antenna design is within speciﬁcations.

The ﬁrst step in typical high frequency antenna development for a vehicle is to
design the antenna in free space without the vehicle. This is usually done for
frequencies greater than 1 GHz. This design is often modeled using software. Once the
simulated performance is within speciﬁcation then the ﬁrst prototype of the antenna is
constructed. This prototype antenna is tested in an anechoic chamber and a
comparison between the modeled performance and the actual measurements is made.
The prototype then needs to be optimized or redesigned to correlate with simulation if

necessary. After this phase, the antenna is actually mounted on a vehicle and

measured. This is the ﬁnal step in the initial development of a communications
antenna for a vehicle [1]. It is this ﬁnal step in the initial development of the antenna
that will be discussed since the overall goal is to compare the measurement of the
antenna on the vehicle to the simulation of the antenna on the vehicle.

The problem of how to take an accurate three dimensional antenna
measurement on a vehicle has been faced by many automotive engineers. A simple
method for taking a pattern measurement involves driving the test vehicle in circles
around a broadcasting antenna. The irreproducibility of these measurements, in
addition to the susceptibility to outdoor environmental conditions, does not allow for a
good means of measurement [1]. Furthermore, this measurement technique does not
capture a three-dimensional pattern measurement that is necessary to meet
speciﬁcation for many applications, including satellite communications.

The use of a sophisticated range facility leads to more accurate results that are
fast and reproducible. A radome that encloses the vehicle, antenna, and measuring
equipment for the purpose of weather protection is one such facility. The radome
allows far ﬁeld measurements to be taken by rotating the vehicle on a turntable.
Almost full three-dimensional measurements can also be taken by a scanning near
ﬁeld antenna system enclosed in the radome. The near ﬁeld measurements can then be
transformed to far ﬁeld radiation patterns [2]. When the near ﬁeld measurement
antenna is stored below the conducting ground, an accurate impedance measurement
of the antenna mounted on the vehicle can also be made. Despite the flaws, which
every range facility has, the radome provides a good means for taking a combination

of measurements.

With this facility, advances in the use of simulation are possible since there is a
means of accurately benchmarking the antenna simulation performance. The
measurements taken for this investigation are done such that exactly the same test can
be simulated with the software package FEKO [3], which is the basis for this
investigation. The input impedance, far ﬁeld radiation pattern and near ﬁeld scan

measurements will be discussed in the following sections.

2.2 The Input Impedance Measurement

The measurement of input impedance of the antenna on the vehicle is very
important. The antenna input impedance should be closely matched for all desired
frequencies. For this study, the frequencies range from 70 MHz to 1 GHz. Since this is
such a large range, the frequencies are divided into ﬁve smaller bands. These bands
include the FM band deﬁned here as beginning at 70 MHz and spanning to 120 MHz.
Band 3 spans from 175 MHz to 235 MHz. Band “Own” spans from 250 MHz to 450
MHz. Band 4-5 begins at 470 MHz and ends at 870 MHz and ﬁnally Band GSM
begins at 800 MHz and ends at 1 GHz. There are some spaces between the bands
where certain frequencies are not tested.

Since a monopole antenna is easily obtainable but has a relatively small
bandwidth, a reference monopole antenna for each band is used. The system uses a
characteristic impedance of 50 Ohms. The ideal impedance of a monopole is 36 Ohms,
which is near 50 Ohms. Thus, the input impedance should be nearly matched to 50
Ohms for each tested antenna. For this reason a quarter wavelength monopole is the

chosen test antenna, and a different antenna is cut for the center frequency of each

band. The preliminary lengths of the monopoles are cut to N4 since the input
impedance of a quarter wavelength monopole on an inﬁnite ground plane is fairly well
matched to 50 Ohms. Further trimming the monopoles to the proper lengths achieves a
better match for the center frequency for each of the bands as determined by using the
vector network analyzer. Once all the test antennas are matched at the center
frequencies of the different bands, the input impedance is ready to be measured for
each band.

To do this, the vehicle is situated on the center of the turntable in the radome.
The elevation arm, which is used for near ﬁeld measurements, is stored below the
conducting ground to prevent the vehicle antenna from having any mutual impedance
due to coupling with the arm. The network analyzer is then calibrated to the feeding
point on the vehicle to account for additional cable that causes loss and electrical
delay. The input impedance measurements are then performed throughout the
frequency ranges for each monopole mounted on the test vehicle. This measurement
takes a very short time since there are no movements of the vehicle or measuring
equipment. The time to take the measurement is determined only by the network
analyzer and is usually done in less than a second as the analyzer sweeps the desired
frequencies. Table 2.1 shows a list of the tested frequencies with their center
frequency and the length of the quarter wavelength monopole that gives the best match
on the network analyzer. The results are shown on a smith chart for clarity. Figure 2.1
(a) includes the input impedance for the FM band and (b) for Band 3. Figure 2.2 (a)
includes an input impedance plot for Band Own and (b) for Band 4-5 and ﬁnally

Figure 2.3 illustrates the resulting input impedance for Band GSM. Notice the center

of the curve passes through the center of the smith chart due to the monopole being
matched for the center frequency of each band. The input impedance is an important
parameter of an antenna and good measurements are needed to make a careful

comparison to the simulation.

 

 

 

 

 

 

Start Center Stop Mono ole
Band Frequency Frequency Used Frequency Len gthp( cm)
(MHz) (MHz) (MHz)
3 175 205 235 36
Own 250 350 450 21
4-5 470 670 870 l I
GSM 800 900 1000 8'5

 

 

 

 

 

 

 

Table 2.1: The lengths of monopoles used for each band

10

 

(b)

Figure 2.1: Input impedance on a standard Smith Chart for (a) Band FM 70-120 MHz
and (b) Band 3 175-235 MHz

11

450 MHz

r... u""‘o.. ..-

 

  
     
 
    
   

s70 Mir-.1 5?; _

  

LI 5m.

470M"

“ HO... .0..-

    

(b)

Figure 2.2: Input impedance on a standard Smith Chart for (a) Band Own 250-450
MHz and (b) Band 4-5 470-870 MHz

12

 

Figure 2.3: Input impedance on a standard Smith Chart for Band GSM 800- 1000 MHz

13

2.3 Far Field Measurements

The far ﬁeld radiation pattern is a crucial performance characteristic of an
antenna. Since it is so descriptive of antenna behavior, a far ﬁeld radiation pattern is
often given in some manner as a design speciﬁcation. The measured far ﬁeld radiation
pattern is important for this study to verify the accuracy of the far ﬁeld data that is
extracted from the near ﬁeld data. It is also useful to see an additional accurate low
elevation angle measurement. The far ﬁeld measurements are also vital for
comparison with simulation since FEKO computes the far ﬁeld radiation pattern for
the vehicle.

The far ﬁeld radiation patterns are taken with the center of the vehicle situated
at the center of the turntable. The turntable is housed within a weather-protecting
radome. The radome’s hemispherical shell of material allows electromagnetic waves
to propagate through with small attenuation and little dispersion for many frequencies
of interest. The outdoor far ﬁeld antenna is situated 100 meters from the center of the

2

, where D is the maximum

 

radome. The far ﬁeld region begins at dfarﬁeld =

dimension of the antenna and A is the wavelength in free space. The largest dimension
D of the test vehicle is the length of the vehicle (3.6 m). The far ﬁeld region should
also be at least 10?» due to the phase error of 23° that is a result of the non-planar wave
front. This means that the far ﬁeld region ranges from 101 z 42 meters for 70 MHz
and 86.40 meters for 1 GHz. This is well into the far ﬁeld region since the test
frequencies explored are within the range of 70 MHz to 1 GHz. The far ﬁeld antenna

is separated from the vehicle by a distance of roughly 237» for 70 MHz and about 3332.

14

for 1 GHz. The outdoor far ﬁeld antenna is log-periodic and is designed for all tested
frequencies. This outdoor antenna transmits and the vehicle antenna receives after the
wave passes through the radome. The geometry for this measurement setup is
illustrated in Figure 2.4.

A control room beneath the radome sends a transmitting signal to the far field
antenna using a computer and the vector network analyzer. The vector network
analyzer used for all measurements is an HP 8753 ES. The outdoor antenna transmits
and a short while later the device under test (DUT) receives the transmission. The
computer records the received signal strength as measured by the network analyzer
and controls the turntable to rotate a speciﬁed angle. It repeats the transmission,
reception and recording process for the entire 360-degree range. It is important to
align the vehicle on the turntable properly to ensure correct measurements for all
angles.

After a given measurement is taken the control room can rotate the outdoor log
periodic antenna to take a different polarization measurement. The measurement
process is the same for both polarizations except that the outdoor antenna is oriented
vertically for one polarization measurement and horizontally for the other. This allows
the measurements of far ﬁeld vertical (FFV) and far ﬁeld horizontal (FFH)
polarization radiation patterns. Note that this measurement gives the radiation pattern
for only one elevation angle 0 z 85° but all rotational angles 4; taken as speciﬁed by
the controlling computer. Therefore, this measurement alone cannot be used to verify

a simulated radiation pattern but can be useful in verifying one cut.

15

 

Far Field

Antenna
V
V
\_/

A¢°

    
    
   
 

Turntable

 

 

 

  

Radius = 12

DUT
(Receivin

Figure 2.4: The Radome setup for the far ﬁeld measurement

l6

As mentioned above, the control room rotates the turntable a certain angle
between measurements. This rotational or azimuth resolution angle M) is chosen to be
25°. This requires 144 measurement points over the rotation of the turntable. A ﬁner
resolution could be used at the radome facility (about 01° minimal). However, a 25°
resolution is used to allow an easy comparison with simulation and also with far ﬁeld
data transformed from near ﬁeld data which both use a 25° resolution. The elevation
angle of the far ﬁeld antenna has been determined experimentally to be near 85°. This
can be seen by comparing the transformed near ﬁeld to far ﬁeld data to that of the
actual far ﬁeld data. This can be seen in several comparisons of far ﬁeld measurements
with transformed near ﬁeld measurements.

The far ﬁeld measurements are taken for all previously described bands. For
each frequency band the corresponding monopole antenna is attached to the top of the
rear left trunk. The measurement times for the far ﬁeld scan are very small. The
turntable that controls the azimuth direction 4) turns at a rate that allows all 144
measurements to be taken in a few minutes. This time is independent of the frequency
band, but dependent on the bandwidth. If a larger bandwidth is required then the
turntable automatically adjusts the angular velocity resulting in slightly longer
measurement time. The results for these measurements are shown graphically for the
center frequency of Band FM (92 MHz) in Figures 2.5 and 2.6. Figure 2.5 shows the
FFV pattern of the vehicle in normalized dB. The front of the vehicle is aligned with
0° and a maximum in the radiation pattern is normalized to 0 dB. Figure 2.6 illustrates
the normalized FFH pattern of the vehicle in dB. Figures 2.7 and 2.8 show Band 3

normalized FFV and FFH respectively for the center frequency of 205 MHz. Figures

17

2.9 and 2.10 show Band Own normalized FFV and FFH respectively for the center
frequency of 350 MHz. Figures 2.11 and 2.12 show Band 4-5 normalized FFV and
FFH respectively for the center frequency of 670 MHz. Figures 2.13 and 2.14 show
GSM normalized FFV and FFH respectively for the center frequency of 900 MHz.
The rectangular shape in the center of these plots is representative of the vehicle with
the front facing 0°. These results will be used later in the comparison of radiation

patterns to those of simulation.

18

150°, ' '
160° ‘ .-
1705 ‘

 

 

180°

 

190°
2000' '8 .. -.
210° 1 .

 

Figure 2.5: 92 MHz Band FM Far Field Vertical (Normalized Amplitude dB)

110°
120°

 

900
100°. (soa 70°

 

 

 

    

260° 270° 280°29°°

Figure 2.6: 92 MHz Band FM Far Field Horizontal (Normalized Amplitude dB)

19

150?
160°,-
170° ‘

 

 

 

180°

     

25002609 gm» 280°

 

Figure 2.7: 205 MHz Band 3 Far Field Vertical (Normalized Amplitude dB)

11001000. 90° 80°
120° a .

 

150°‘
160°__ '
170° ’

 

 

 

180°

1900-..... ,
200°"
2100'

Figure 2.8: 205 MHz Band 3 Far Field Horizontal (Normalized Amplitude dB)

20

170° ‘

 

180°

 

 

190° ,
200° '1
210°

   
 

............

   

25°°260° 275° 230°
Figure 2.9: 350 MHz Band Own Far Field Vertical (Normalized Amplitude dB)

90°
110,,v100° 00°

 

    

"""""""""""

........

150°
160°

    

170°, -

‘ ’_ . . , .
)4 v, ‘ . . . . , , . ‘u. ,3
>~ \ ' x . . . w 1’ r
' 4 - ' n ‘ . u- I '
- .. - . . _,..- -:., . . .s _ ' .
' 4 ’ . u' - 4,’- . ‘.~ ' o ‘.' - .
‘_ _ . . r 1 o . . .‘ .
.. . ‘ ,' t t 1 , - . .' - ,' . a .
. . 1: , ,' , ‘.' 4 n . ,.
’. . .. . . . . . ,- y . ,.-"
- . , . . . , 3 . . ..~' .
. . . . .
. ~. . .. .11. , °. .. .
-. .‘ . ,.‘ . 1‘ - ’ . .I “.4
. _ ' ._ - , H..-- . l
. __‘ . .-' . .
._. , -~ . .
. , ‘ . 1 ~
. . r v y
,. J 2
.‘ 'l ". '. -. ’m‘zs’ o-
T " . , . w ' .‘ . o'
'2' r ;v' ‘ ‘- .
‘ , . t . . \ '- _. a
. .. ‘ ‘ - - _'.
1 . . x",
r

. I
1 .
. 1
v I
1
. ....... .
'~
. .

 

 

180°

 

.
. .. .-_ . 1 ~'..* . g . ' ~ _ .' ..... '
- _-‘ , ' '. .,.. 4“ . .f ' ° “. .
.' ‘ , . . . . v, ‘
. . - ' > v ~ \ ' 1 ‘,‘ .-
' ' ‘ ‘ 4 ’ . - . . _ .. ‘ . .-‘

,.-‘ t -, .' . L . . . jx .‘ ‘ -.
200° 2 - ,, . :. °~ - .2 . x. 340°
. , 4 - . s ‘. - ‘ ' n .

.‘ ° . ‘. ‘ . °‘ ‘. i i‘

.’ ‘. I ~ "s I p’ ' r ." . . -

. _ ‘ _ . \-. w. u 1 . 1 ' ‘
210° - ' —. » : , - ,- ~ 330°
' . . . : _.‘ .'. .

‘\A' ‘IL. .- . i ‘- . _¢'-~ ."
220° .‘ u. . . a ,, -. 1‘. 320°
' ‘ t‘ 'y . . 'i . . z.....- ‘T . ' ‘ ’ .'

3 ~ ‘ I .' ..
. ~, . . .
230° .- . : ' w- 310°
4 .. a . t.” ' . 1
V ............ ' ‘.

.' E ‘ 3 0
250360, 2700 280,290

Figure 2.10: 350 MHz Band Own Far Field Horizontal (Normalized Amplitude dB)

21

150°

  

170° __ r .

 

 

 

180°

 

210° " ‘71,, ' ‘ 330°
220° 320°
240° .5 ‘~ 300°
2500260° 270° 230°29°°

190°"- ,

Figure 2.11: 670 MHz Band 4-5 Far Field Vertical (Normalized Amplitude dB)

11o,100° 90° 80°

120°.

 
       

70°

.....

 

 

 

. . 1 . . , - . .
. . . ‘ . . > - "- - a g
I ‘ , - n’ O I; ‘ I V
~ . '. . . \, - -.
. . . _ , \- . i '1‘ 4 u 1 ", '
. . . 1 - .
I ‘ ' l O ‘
— > , \ o a ’
n . ‘. ~ - _‘ ~o .
. - '. .. . .
I . ‘ . I ~ ~ '
» ~ , . . _ . -' , . 9
~ ‘ . . 4- . ~-‘ . - ~ 1 .
. . . . , ._
‘. .‘ i . b .>
. . . . .
1 - l l .' i ‘ 0
. ‘ ’- - ‘ ‘ ‘
. . . . ‘ _. _ .
. . - .
I I .

'v-I. .....

Figure 2.12: 670 MHz Band 4-5Far Field Horizontal (Normalized Amplitude dB)

22

150°. "
160° '

    

 

 

1 80°

 

. iQL ° fi‘ ; a * ; ;

.. " . I .‘f30‘25r,.,,‘_‘5-10 -_5 -
190° ‘. .. ' . r 3500
200° 7.%i ,’ 1', ,fr*:é i v; ‘a. ,._.. 340°
210° ?_‘ .z"l~.’ f i 1 ‘»-\‘ I.“ : 330°
220° ~ . . 320°
230° ' 310°

240 2500 \ é -, 290030?
260° 270° 280°

Figure 2.13: 900 MHz Band GSM Far Field Vertical (Normalized Amplitude dB)

900
1 1 01,1000: 80°

    
  

70°
2 60°
50°

'. 2". . . 710°

 

 

Figure 2.14: 900 MHz Band GSM Far Field Horizontal (Normalized Amplitude dB)

23

2.4 Near Field Measurements

The near ﬁeld measurement is the most important quantity for making a
comparison to simulated results from FEKO. The near ﬁeld scan enables a full three-
dimensional far ﬁeld radiation pattern to be observed through the use of
transformations. These transformations are performed after the near ﬁeld measurement
is complete by software that is associated with the measurement facility. A brief F
presentation of the basic near ﬁeld theory is discussed followed by the measurement
procedure and some typical results.

Near ﬁeld scanning technology has been explored in some fashion as early as

 

the 1950’s [4]. The method of scanning the near ﬁeld is based on scanning over a
known three-dimensional geometry very close to the antenna. Typical scanning
geometries include a plane, cylinder or sphere. While there are some advantages to
using a planar or cylindrical scanning geometry, the spherical system is used in many
cases since it allows the most complete calculation of the far ﬁeld radiation pattern [5].
An antenna on an automobile needs an accurate predication of the far ﬁeld for all
angles whereas a horn antenna, for example, needs only some angles to be predicted. It
is therefore necessary in this study to scan over a spherical geometry to achieve the
most accurate prediction for all angles. The spherical transformation is generally the
most mathematically complicated and requires the most computation time [6]. With
modern computers, however, this is performed easily for most frequencies. Measuring
the magnitude and phase over this minimum geometry at the proper resolution and at
two orthogonal ﬁeld components E¢ and E9 allows for a modal transformation to a full

far ﬁeld three-dimensional pattern.

24

A problem facing the near ﬁeld measurement is that there is a radiation pattern
associated with the transmitting test antenna in addition to the DUT. This means for
some elevation and azimuth angles, low signal strength could be measured where there
is in fact simply a null in the probe’s radiation pattern. This is overcome by using
probe compensation. Probe compensation is based on spherical wave modal
expansion. A spherical wave can be decomposed to represent a superposition of
spherical waves, all monochromatic, traveling in different directions with different
amplitudes. The expansion determines the unknown amplitudes and directions of these
propagating waves through the use of superposition. The probe output is determined as
a function of these expanded ﬁelds. The result is a relationship between the known
ﬁeld-pattem of the probe to the unknown ﬁeld associated with the DUT [2]. This
relationship is speciﬁed by the use of spherical mode coefﬁcients for the probe
antenna contained in the software used to extract the far ﬁeld data. A correction is
made to the pattern and polarization due to the characteristics of the transmitting probe
antenna.

The radome facility achieves a spherical scanning geometry by mounting the
probe antenna on an elevation arm that is 10 m long. It rotates this probe antenna
around the DUT at a constant radius of 10 m for various angles of 0 by moving the
elevation arm. The arm is referred to as an elevation arm since it changes only the
elevation angle; the turntable is needed to change the azimuth angle. Using the

turntable and elevation arm a semispherical geometry can be scanned for nearly all

. xi

1
— d
2 (b+/1) an

 

angles. If the sphere is sampled at a resolution of A6 =

25

 

A¢=

%' (b + ,1) then the radiation characteristics of the DUT are fully extracted in the

transformation [5]. The smallest wavelength of the tested frequency is denoted as A
and b is the radius of the smallest sphere that encloses the body of the vehicle. For the
test vehicle used this is b = 2 m. Note that A0 = A0 and that taking additional data

points at a smaller resolution does not, by the Nyquist sampling theorem, increase the
accuracy of the transformation.

ﬂ

Elevation Angle 0

Near Field
Antenna
(Transmitting)

  
   
  

Antenna
Under Test
(Receiving)

 

 

 

 

 

Figure 2.15: Illustration of the near ﬁeld measurement

This measurement is taken in the radome with the elevation arm as mentioned

above. The setup is illustrated in Figure 2.15 with the vehicle situated in the center of

26

the turntable. The elevation arm hoists the near ﬁeld antenna to the correct elevation
angle 0 and then the turntable is rotated for a changing azimuth 0. The elevation arm
can illuminate the vehicle for all elevation angles between 0 = 0° (towards zenith) and
0 = 88° (near the ground). The probe antenna transmits and the vehicle on the
turntable receives the signal. The elevation arm is then rotated to a new elevation
angle 0 and the process repeats. The polarization of the near ﬁeld antenna is then
changed automatically and again the turntable is rotated while the measurements are
performed. The change in polarization is necessary to capture E4, and E9 over the
minimum sphere. This order of taking measurements is optimized for the time of
measurement since the number of data points required is related to the test frequencies

and the measurement times can be lengthy. See Table 2.2 for the near ﬁeld scan

measurement times for all tested bands.

 

 

 

 

 

 

 

Total
Start Stop Number of Number of Measurement
Band Frequency Frequency P . ts 0 P . ts Time
MHz MHz 0 om om .
(minutes)
FM 70 120 45 11 25
3 175 235 45 11 25
Own 250 450 120 28 90
4-5 470 870 120 30 100
GSM 800 1000 120 30 100

 

 

 

 

 

 

Table 2.2: The total time for a near ﬁeld measurement

27

 

Some resolutions for A0 and A0 shown in Table 2.2 are smaller than they need
to be. This is done to try and make the measurement consistent and simple. For
example, the necessary resolution for band GSM is about 37° and 42° for Band 4-5.
However, a A0 = 3° resolution is used for both GSM and Band 4-5 so that the last
elevation measurement taken would be at the greatest possible angle of 87°. This
requires 29 points and is as close to 88° as possible. This forced the resolution of the
azimuth A0 to also equal 3°. This is a very convenient number since 3° divides evenly
into 360° requiring 120 data points exactly. Though this resolution is unnecessarily
ﬁne for both Band GSM and Band 4-5, it maximizes the measured elevation range and
therefore allows for the best transformation.

The probe antenna for lower frequencies, i.e. the FM band, is a large log
periodic antenna. This large antenna does not allow the elevation arm to scan at very
low elevation angles (near 88°) since the antenna itself would come in contact with the
ground when the polarization is changed to vertical-polarization. For higher
frequencies, i.e. Band 4-5, a smaller log periodic antenna is used in which case the arm
can be lowered to greater elevation angles (up to 88°) without the probe antenna
coming in contact with the ground. The problem with the larger antenna, however,
does not cause major inaccuracies in the extracted far ﬁeld data in most cases. This is
because the scan resolution is determined by the maximum test frequency (minimum
wavelength) and for lower bands the higher elevation angle measurements are not
typically needed anyway. In the case that these measurements are needed for a
transformation, the software has the option to ﬁll any incomplete measurement data

with zeros or, if preferred, with the data taken at the greatest assessable elevation

28

angle. Filling the data with zeroes or the last available data can obviously affect the
accuracy of the transformation and will be discussed later. This measurement data is
then transformed to far ﬁeld data with the use of the software. The transformation
requires the proper discretization in the data points as stated above. The program also
incorporates probe compensation from a ﬁle containing the spherical mode
coefﬁcients for the near ﬁeld scanning antenna. Some far ﬁeld patterns extracted from
near ﬁeld data are included below to give some examples of typical results. The data
has been extracted to achieve a resolution of 25° for 0 and 0. Clearly this amounts to
too many cuts to be displayed here. Figure 2.16 (top), for example, shows the radiation
pattern for 350 MHz with theta polarization taken at phi = 0°. Figure 2.16 (bottom)
includes the radiation pattern for 670 MHz with phi polarization taken with the vehicle
rotated 90°. The vehicle is shown in gray in the center of the radiation pattern in
Figure 2.16. These are just sample cuts and will be used to make comparisons later to

the simulated results.

29

 

 

 

 

170° 130° 190°200°

20010° 0° 350°

 

 

 

 

Figure 2.16: Illustrates the transformed radiation pattern for (top) 350 MHz for theta
polarization with phi = 0° and (bottom) 670 MHz phi polarization with phi = 90°
(Normalized Amplitude dB)

30

 

CHAPTER 3

SIMULATION METHODS

3.1 Introduction to Simulation Methods

As a vehicle begins to require a larger number of antennas at different
frequencies for a variety of applications, simulation becomes a sensible means to
verify the antennas are within their performance speciﬁcations. For antennas operating
at higher frequencies, the placement of the antenna on the vehicle may be critical to its
functionality. Additionally, antennas mounted on a vehicle perform quite differently
than in free space. As designers look to lower design costs and cycle time, simulation
becomes a viable approach for predicting this performance and determining the proper
placement.

In most automotive scenarios, the performance of an antenna needs to be
analyzed with the antenna in close proximity to other electrical bodies. In this study,
for instance, an antenna is mounted on a vehicle that has sharp edges, pillars and other
distinct regions. The vehicle geometry itself has a signiﬁcant impact on the overall
performance of the antenna. Since the vehicle plays such an active role in the radiating
system, the vehicle geometry needs to be carefully considered in simulation to ensure
an accurate solution for the characteristics of the antenna.

There are several different techniques used in computational electromagnetics
to ﬁnd this solution. A few of these techniques include the Method of Moments (MM),
Physical Optics (PO) and the Uniform Theory of Diffraction (UTD). Each method has
its own advantages and practical applications while also having unique drawbacks.

Choosing the correct method to ﬁnd the solution is important to help ensure

31

computational errors and approximations will be reasonable and controlled. The type
of problem, the available computational resources, and the difﬁculty of formulating a
computer program to ﬁnd the answer, all govern the best choice of technique.

The MM analysis is a well-known and fairly reliable means of characterizing
the performance of an antenna for lower frequencies. This approach is often used as a
reference for comparing other simulation results from different techniques. Many
antenna geometries are conducive to using the Method of Moments [16]. The method
of moments can be applied to complex geometries where electrical bodies are in close
proximity to the antenna. However, the MM is usually used only for electrically small
systems due to the computer resources required to perform the simulation. A test
vehicle that has dimensions on the order of several wavelengths poses a considerable
computational challenge in terms of both memory and computation time.

Using multiple methods of simulation on one system has brought about
“hybrid” simulation techniques. Hybrid techniques, in the general sense, implement a
particular method to solve one part of a problem while using another method to solve a
different part. The solutions are then brought together to try and accurately represent
the actual system. In this way, a technique that is more accurate can be used where
accuracy is needed while a technique that is less computationally expensive can be
used at different locations that would otherwise require too many resources. There are
numerous software packages and computer codes that use a wide variety of methods to
simulate an electromagnetic system. A few of these include, NBC [7], ESP [8], WIPL

[9], MOM3D [10], JUNCTION [l l], FEKO [12], FASANT [l3], EMC-2000[14] and

32

 

HEMCUVI [15]. For this study, because of its versatility and availability, FEKO is the

software package used.

3.2 The Method of Moments

By the MM technique, an approximation of the current induced over the
vehicle is obtained as the numerical solution of an integral equation. This is done in
the form of a series of known basis functions [16]. The fundamental idea behind the

method will be described to give background for the theory of using hybrid methods.

    

. . \ Wire
Excrtatron:
( Ei , Hi ) Perfectly

conducting body

Figure 3.1: Scattering Problem

The theory of MM is widely understood among computational

electromagnetics engineers. This particular development and notation is based on [17]

33

since those authors have played some role in the implementation and formulation of
the M in FEKO.

Consider a wire attached to a perfectly conducting surface as shown in Figure

3.1. An incident plane wave is formed by the ﬁelds (El. ,Hl.) and acts as an excitation

to the system. This plane wave induces electric current both on the wire segment (I)
and along the perfectly conducting surface in the form of surface currents (.7 ). These 1
currents are in return responsible for the resulting scattered ﬁelds is and HS.

Superimposing the incident and resulting scattered ﬁelds gives the total ﬁelds in the

 

region Etotal and H

total
Etotalel-‘I'Es, (3.1)
Hmml = Hi +115. (3.2)

The scattered ﬁelds resulting from the induced current on the wire and surface current

on the perfect electrical conducting body (PEC) can be represented by taking the linear

integro-differential operator on the surface current i and the line current I. This is

accomplished by using the operators

IZJ{]’}=;’—V [[(v:4 -j(?’))-G(?,'r")dA’— jw-‘f— j j(?’)-G(F,F’)dA’, (3.3)
A; 4EA’

47:20)
”H "' _ 1 " '° -I - «I I
LJ{J}—Z—ﬂ—Vx‘{jl(r)°0(r,r)dA, (3.4)
£f{1}=’—JV [m—(CZ.G(7,F’)dz’- jwi [1(7’).i'-G(7,r’)dz’, (3.5)
47220 Ll BI 44th

34

II? {I} = -—l—Vx II(F’)-f’-G(F,'r”)dl’. (3.6)
471' L!

The unit vector f’ denotes the direction of current flow I along the wire segment. The

vector i" denotes the location of the observation point. The surface divergence over

the primed coordinate system is denoted by VA, and 6(7, 7’) is the free space

Green’s function deﬁned as

21%02-71
2

G(?,F’) = e

 

l7- F1 (3.7)

When these operators are applied in the proper form, they yield the scattered ﬁelds due

to the line and surface currents:
ES=Z§{]’}+Z§{I}, (3.8)

-.

H =Z§I{j}+i.7{1}. (3.9)

S
In the moment method, the current .7 is expanded into a series of basis functions

f1, f2 ,...fN J on the perfect conducting surface. The current I is expanded into a

series of basis functions g1, g2 ,...g NI on the wire. When these basis functions are

superimposed and weighted by the complex coefﬁcients an and ,6” they yield an

expansion of the currents [18]:

N
1= iﬂn '81:, (3.10)

n=l

35

N
j=ian'fn- (3.11)

n=l

In FEKO, the geometry is divided into triangular patches to form a mesh. This

allows the choice of the surface current basis functions in developed by Rao,Wilton
and Glisson [19]. A separate basis function is usually chosen for the linear current
basis function 8n and is taken here to be a triangular function. FEKO uses special
basis functions to transition between the wire segment and the surface. The choice of
coefﬁcients an, and ,6" is determined by considering the boundary conditions to
satisfy Maxwell’s equations. The vanishing tangential electric ﬁeld on perfect

electrically conducting surfaces is one such condition that can be used [17]:

15tan :0 (3.12)

Using this boundary condition, an electric-ﬁeld integral equation (EFIE) can be

derived from

:0. (3.13)

Here, I? is the unit normal vector to the surface in Figure 3.1.Substituting equation

(3.1) into (3.8) yields
ﬁxlEi+Lf{i}+LIE{1})=o. (3.14)

Inserting equations (3.10) and (3.1 1) into (3.14) results in

N} "E NJ *E _. _.
":1 [1:1

36

This formulation can be used to solve for the scattered electric ﬁeld by ﬁnding the

proper weighting coefﬁcients an and ,6" . These linear equations have a total number

ofunknowns Ntotal = N1 +NJ.

3.3 Physical Optics

Physical Optics is another commonly employed method for simulation. It is
based on the idea that certain areas in a structure are illuminated while others are
shadowed. In the illuminated region the PO approximation for currents can be made.
In the shadowed regions, only diffraction terms are used. An operator for the PO can
be made just as for the MM. Using these approximations allows the basis functions
chosen to represent the currents to be greatly simpliﬁed and can also reduce the
number of unknowns. This reduction, since it is based on an approximation, can affect
the accuracy of the calculated ﬁelds, so it must be used carefully.

In the illuminated region, the PO approximation can be made for the current

-0

density J P0 ﬂowing on the surface. This approximation is based on the Physical
Optics current in the radiation integral [20]

JP0=2rixHi. (3.16)
Here, r“: is the unit normal vector from the surface and Hi is the incident magnetic

ﬁeld. The radiation integral can form an operator just as in the MM case. PO,
however, cannot be applied to line currents I as successfully as the MM can.

Therefore, a linear integro-differential operator is used only for the surface current

37

jPO' This operator is the same as in the MM case (e.g. equation 3.3 and 3.4) but it is

used on the currents approximated by (3.16).

3.4 Hybrid Methods

Hybrid methods use one simulation technique at one location while using
another technique at a different location. There are several hybrid techniques
employed in a variety of software applications [7-15]. The techniques described here
are the ones that are most applicable to those used in FEKO. The exact means for
implementation of the methods in FEKO are proprietary to the developers so a general
description is given.

It is desired, by the use of these techniques, to reduce the total number of

unknowns N = N I + N J . By making a signiﬁcant reduction in the number of

total
unknowns, the size of the system of equations can be reduced. Reducing the size of the
system of linear equations can greatly reduce the computational cost expended to form

a solution. A reduction using PO can only be applied to N J since the PO

approximation cannot be applied to the line currents. Many authors have explored the
reduction of computational cost by hybrid methods, including [15].

Using the conventional MM solver, the computational cost in terms of memory

requirements is on the order of the total number of unknowns squared, N totalz . The

cost in terms of solution time can be as large as on the order of N total3 . If the hybrid

method is used then a region is designated as using the MM technique and thus has

unknowns N MM and a region is designated as using the PO approximation with

38

 

unknowns N p0 . The number of unknowns, N total , can be expressed as
N MM + N p0 . The P0 region is typically much larger than the MM region so
N MM << N 130 . This is because it is recommended that only the regions containing

the antenna, near regions, discontinuities and electrically small objects be considered
with the MM [15]. The remaining geometry can be considered with P0. The number

of PO unknowns can be broken into two separate unknowns N 590 and N unlit

P0
_ lit unlit
NpO—NP0+NP0 . (3.17)

These unknowns are associated with the areas that are illuminated or in a

shadow in the PO approximated region. Since N MM << N p0 , the number of
unknowns can be approximated by N total z N p0 . The computational cost associated
with the system in terms of storage can be approximated as being on the order of

N MM wﬁ’o [15]. The relative cost of the MM-PO hybrid compared to a full MM

simulation can be represented as the ratio of MM unknowns to the number of PO

unknowns:

C05thybrid x N MM
CostMM N p0

 

(3.18)

The hybrid method expresses the PO approximated surface current as a

superposition of basis functions in :

_, NMM +NP0_,
JP0 = 27,, 'fn- (3.19)

nzNMM +1

39

Here, 7n is the coefﬁcients that are based on the approximation of PO on the surface.

Applying the Electric Field Integral Equation as in equation (3.14) but this time

including the PO approximated surface current yields equation (3.20).
ﬁx(L§{i}+Lf{I})=-ﬁx(§i+L§{ip0}) (3.20)

By applying the proper weighting functions, as in the MM, this equation can be
converted into a system of equations that can be solved by back-substitution or any
other computationally efﬁcient method. This is the fundamental idea for how a PO-

MM hybrid method is implemented in FEKO.

3.5 Simulation with FEKO

The program FEKO, which will be discussed in the following sections, is
installed on two Hewlett-Packard (HP) 17000 UNIX Workstations. These workstations
each have 8 Gb of RAM and four processors that operate at a clock speed of 440
MHz. The FEKO program is a parallel version in that it can coordinate both machines
to work together to make computations. This allows a total RAM allocation of 16 GB
and a total number of processors in use to be eight. Of course, not all 16 GB of RAM
can be allocated in this system since memory is necessary to run the operating system
and other incidental applications that may be in use. Realistically, the largest RAM
that can be allocated for solving a problem in this system is 13 GB. A larger allocation
is possible, but doing so slows the system down so much that the computational cost is
too large and a solution cannot be found in a reasonable amount of time. This is
believed to be mostly due to the operating system as well as the program itself

requiring some additional memory to perform the operations. A problem that requires

40

a very large RAM allocation, that is greater than the available RAM on the computers,
can be solved “out of core.” An out of core solution writes memory to the hard disk
and treats it as virtual memory. Since a hard disk has a very slow read and write
ability, it is difﬁcult to ﬁnd a solution by this method in a reasonable amount of time.
An in-core solution is the most practical to solve. This is because an in-core solution
only allocates memory to RAM. The RAM has the fastest write and read abilities.
Since MM solutions are very memory-intensive, most of the time required for a
simulation is due to the movement of memory. For most simulations, if a problem
needs to be solved out of core than it is deemed impractical to solve. For all the
simulations used in this study, an in-core solution was used.

A small geometry Method of Moments simulation is used to test the parallel
processing capabilities of the two HP J7000 computers. The test simulation has 3,100
metallic triangles that form the mesh and 4,506 metallic edges that form these
triangles. The total number of basis functions necessary is 4,514 (4,506 edges + 8 wire
segments for the monopole). The problem in total requires 350 MB of RAM. The
results are shown in the form of the speed-up factor in Figure 3.2. Here t(n) represents

the time it takes to complete the same simulation using n processors.

41

 

Speed-up Factor vs Number of Processors

 

4

3.5 /—

 

 

 

 

 

 

 

Speed up factor t(n) / t( 1)

 

 

 

l 2 3 4 5 6 7 8

Number of Processors (n )

 

 

 

Figure 3.2: The speed-up factor vs. the number of processors
The t(l) term represents using just one processor to complete the job. Using all 8
processors, however, does not allow the problem to be solved 800% faster as might be
expected. It is shown that using 8 processors t(8) / t(l) yields a speed up factor of
roughly 3.5. This is due to overhead in handling the memory on the 1.3 Gb/s

maximum throughput bus and managing the processors to work together.

3.5.1 Introduction to FEKO

FEKO [3] is a software package based on the Method of Moments. The word
FEKO is formed from the German acronym for words that translate to “Field
Computations Involving Objects of Arbitrary Shape.” FEKO is referred to as a
software package because it contains multiple programs that are used to take an input
from a user, perform a simulation, and view the results. These subprograms are

editFEKO, preFEKO, winFEKO, the FEKO solver and graphFEKO. The user steps

42

through the programs to take a problem from the speciﬁcation to the ﬁnal results.
Taking these multiple steps helps the user realize any errors in the geometry,
excitation, or requested ﬁelds before an erroneous simulation is committed to run for a
long period of time. Since there are 5 programs and about 40 different ﬁle types
associated with FEKO, only the fundamentals of the programs as well as a few of the
important ﬁle types will be discussed.

The program editFEKO is used to simplify the creation of an input ﬁle. This
input ﬁle is of the type *.pre and is based on text entries. The *.pre name represents
that the “*” could be an arbitrary name. For example the ﬁle could be named
vehicle.pre. This program has many useful tools to insert commands and organize the
text-based input. The program’s inputs are all based on “cards.” There are only two
classiﬁcations of cards in editFEKO. These are the geometry cards and the control
cards. The geometry cards, as the name implies, are used to specify the geometry of
the problem. The control cards are used to specify the excitation, requested ﬁelds and
other control-type operations. For example, it is also necessary in the program
editFEKO to specify the maximum length of a segment in the geometry. This is done
through a geometry card since this impacts the geometry of the problem. The
maximum length of a segment should be less than N 10. According to the FEKO
manual, a maximum segment length could be as large as MS to M6. However, this
could lead to severe inaccuracies in the MM solution and should be checked with a
smaller segment length anyway. Instead of using many geometry cards to specify a

complex geometry such as an automobile, editFEKO can input a variety of geometries

43

from other computer aided design (CAD) programs. Once the problem is completely
speciﬁed in editFEKO, it is necessary to run preFEKO.

The program preFEKO takes the *.pre ﬁle created in editFEKO and prepares it
to be viewed as a geometrical problem with an excitation in winFEKO. This is done
by the creation of a *.fek ﬁle. The software preFEKO also checks the geometry,
excitation and requested ﬁelds for errors or inconsistencies that would not allow the
solver to function properly. The program also summarizes the total number of
triangles formed by the segments, the total number of wire segments, and other useful
information pertaining to the problem. Once preFEKO is run and the *.fek ﬁle is
created, the problem is ready to be viewed in winFEKO.

The program winFEKO is a graphical program that allows the problem to be
viewed. A veriﬁcation of the geometry, as well as the proper direction of the normal
vectors can be made. It is important for the normal vectors to all face outward on a
closed body, for example, since this allows other methods of simulation, such as PO,
to be easily applied. The program does not have the ability to change the geometry
however since this can only be speciﬁed in editFEKO. Once the geometry has been
viewed and veriﬁed to be correct, the FEKO solver is run which actually performs the
simulation. The solver creates the ﬁnal output in a *.out ﬁle. When this is complete
the results can be displayed in winFEKO as a three-dimensional radiation pattern.
Other outputs of interest, such as current density, can also be displayed in winFEKO.
The results can also be interpreted in graphFEKO when it is necessary to compare
only certain angles, polarizations, or how well the antenna is matched. In this way, any

problem can be speciﬁed and the proper steps can be taken to move the problem

through the software package to gain a solution. Figure 3.3 illustrates the basic ﬂow of

the problem from user input to the program output that is interpreted by the user.

User in ut *. re *.fek *.out Output to user

editFEKO i—> preFEKO _’ winFEKO 4 graphFEKO
FEKO solver

 

 

 

 

—v

 

 

 

 

 

 

 

 

 

 

 

 

Figure 3.3: The programs and their inputs and outputs

3.5.2 FEKO and the Test Vehicle

The ultimate goal of this study is to compare the measurements that are taken,
as described in Chapter 2, to the simulated results. To do this, the diagram in Figure
3.3 needs to be followed when developing an accurate simulation using FEKO. The
ﬁrst step is to specify the problem in editFEKO. This is a very important step and
needs to be done with care. Since a vehicle is a large and fairly complex geometry it is
difﬁcult to create this in editFEKO through the use of cards. This is true especially
since the geometry needs to be broken into triangular patches that need to share edges
and vertices in addition to aligning properly to the measured location on the actual test
vehicle. Using another program called Concept, this complicated construction of the
vehicle is more easily completed. Concept is simply a CAD program that allows the
construction of triangles to be easily manipulated. The data is then formatted for
editFEKO and imported. The vehicle is thus constructed only with numerous triangles
and no other geometrical shapes such as rectangles. These triangles have a very course
segmentation length. In fact, the lengths of the edges of the triangles are probably too

large. This is because the vehicle was drawn in Concept to be simulated for a variety

45

of frequencies. Additionally, the triangular area formed by the inside of the edges is
probably too large for most frequencies. This is because the amount of current on a
segment is assumed to be constant in the MM. If this segment is too large then this
assumption may be grossly incorrect. It is therefore necessary to further break the
course triangles created in Concept into ﬁner triangles that have some frequency

dependence so the constant current assumption can be valid. FEKO states, as

. . . xi .
mentioned before, that the maxrmum length of a segment can be rs — where 21 rs the

wavelength in free space. Additionally, FEKO recommends that the area A of a

2
triangle formed by these segments be less than 37%. The segmentation rules that are

recommended by FEKO are adhered to by all of the simulations unless otherwise

stated. These rules are summarized in Table 3.1.

 

 

 

 

 

FEKO Segmentation Rule Warning Error
Ratio of the segment length l to _l_ L
the wavelength xi ,1 > 0'3 ,1 > 0'5
Ratio of the segment radius ,0 to B B
the segment length l ,1 > 0'3 ,1 >1'0
Ratio of the area of the triangles A > i A > i
A to the wavelength squared 112 r 22 30 ,{2 10

 

 

 

Table 3.1: The FEKO segmentation rules. From [3]

Many times, a problem is further simpliﬁed due to symmetry. FEKO also has

the ability to consider magnetic, electric and geometric symmetry to aid in solving a

46

 

problem faster and more efﬁciently. A plane of electrical symmetry is a plane that can
be replaced by an electrical wall without changing the ﬁeld distribution. Electrical
symmetry can play a very large part in reducing computational cost to a problem. It
should be used whenever possible to make a problem easier. A plane of electrical
symmetry is illustrated in Figure 3.4.

This plane of electrical symmetry is representative of the inﬂuence the perfect
electrically conducting ground has on the system. The outer shell of the test vehicle is
symmetric. However, a plane of electric symmetry cannot be used since there is only
one monopole antenna on the vehicle and symmetry would create two. Instead,
geometrical symmetry can be used for the car body without mirroring the monopole
antenna. This can be done down the center from the front of the vehicle to the back.
Unfortunately, geometric symmetry does not reduce the number of unknowns in the
current basis functions as electrical symmetry does. It does, however, lead to a
reduction in computation time when the matrix is determined. This symmetry is
illustrated in Figure 3.5. The model is created to be of the exact size of the actual test
vehicle (1 :1 scale). It is a total of 3.6 meters long and 0.44 meters from the perfect
electric ground plane that is below the vehicle, but not pictured in Figure 3.5. After

symmetry is applied, the total width is 1.6 meters.

5 d
H
_Ti_ﬁ_ _________________

Figure 3.4: The plane of electric symmetry.

47

The antenna used in the simulation model is a quarter-wavelength monopole
with the same length as that of the actual monopole used in measurement. There are
ﬁve different bands of frequencies for this study. A different quarter-wavelength
monopole is used for each frequency band and the lengths are summarized in Table

3.2. Band “Own” has been created speciﬁcally for this study.

 

(""F

Plane of geometrical symmetry x_

 

 

 

   

Figure 3.5: One half of the test vehicle. The other half is generated by symmetry.

 

 

 

 

 

 

 

Start Center Stop
Band Frequency Frequency Used Frequency Monop; :01": ngth
(MHZ) (MHZ) (MHz)
FM 70 90 120 85
3 175 205 235 36
Own 250 350 450 21
4-5 470 670 870 1 1
GSM 800 900 1000 8.5

 

 

 

 

 

Table 3.2: The monopole lengths for simulation
The FEKO solver uses a full MM technique on the vehicle unless another
technique is speciﬁed by the use of a geometry card. For instance, a surface area could
be considered using P0 or UTD. Triangular basis functions are used on the quarter-
wavelength monopole. The solver thus requires the monopole to have some

segmentation that would allow the use of these basis functions. The segmentation for

. . 2 .
the monopole antennas rs the same for the surface mesh and is E unless otherwrse

speciﬁed. Once the geometry has been properly represented, the type of excitation
needs to be selected.

The program FEKO has 13 different ways of exciting the system. These
include excitation by a plane wave, a voltage gap between wire segments, a magnetic
current, a voltage along a wire segment and many others. For these simulations, the
chosen excitation is by a voltage gap between wire segments. This is most
representative of the actual phenomenon that occurs when taking the measurements

and is done for all the same frequencies that were measured. Illustrated in Figure 3.6 is

49

 

a screenshot from winFEKO of the geometry at the feed location. The monopole
antenna shown is of length 21 cm and is used for Band Own. Since both the quarter-
wavelength monopole and segmentation size both depend on frequency, the
monopoles for all ﬁve bands each have 8 segments (7 for Band 3). The excitation
location is shown as a small hemispherical shell between the antenna and the surface

mesh triangles.

 

/ \ V3.2

Wee Mesh Triangles
/ _ /
V

Quarter-Wavelength
Monopole (8 Segments)

\/ V

 

 

 

 

 

\

Excitation

Figure 3.6: The quarter-wavelength monopole, surface mesh triangles and the
excitation by a voltage across a gap

50

The triangular mesh must have a vertex at the point where the monopole is
attached as can be seen at the location of the excitation. Once the geometry is correctly
veriﬁed and the excitation is speciﬁed, the ﬁnal step in setting up the simulation is to
identify the “requested ﬁelds.” This means commanding the software to compute the
far ﬁeld values at all requested locations for all requested frequencies. Again, since the
ultimate goal of this study is to compare the measurement to simulation, the requested
ﬁelds are calculated at the exact locations with the exact frequencies as with the
measurements. This is done in spherical coordinates over the entire hemisphere 0° < q)
< 360° and 0° < 0 < 90°. It is not necessary to calculate the ﬁeld points below the
perfectly conducting ground plane since the ﬁeld values at those locations are zero.
The chosen resolution of 25° is the same as with the measurements. This means the
ﬁelds are calculated at 144 points in the 0 direction and 37 points in the 0 direction.
This amounts to a total of 144 - (37 - 1) +1 = 5185 locations where the far ﬁeld values
are calculated for both horizontal and vertical polarizations.

Once the geometry is created, the excitation is chosen, and the ﬁelds are
requested, the simulation is ready for the preFEKO program that creates the *.fek ﬁle
to be input to the FEKO solver. The preFEKO program also outputs useful

information pertaining to the size of the problem. The information for the ﬁve bands is

summarized in Table 3.3 for a 1% maximum segment length. The 14;- segmentation

uses the shortest wavelength (highest frequency “ fupper”) within the band.

51

 

 

 

 

 

 

 

Band Number of Metallic mm"? °f Wm
(f ‘ f upper) Triangles in Free Space Segments in Free Space
lower (from the Monopole)
FM
(70 — 120 MHz) 2,744 8
3
(175 — 235 MHz) 7,600 7
Own
(250 — 450 MHz) 17.366 3
4-5
(470 — 870 MHz) 56-054 8
GSM
(900 — 1000 MHz) 70,698 8

 

 

 

Table 3.3: The number of metallic triangles and wire segments in free space as output
by preFEKO

Once the *.fek ﬁle is created, it is important to visually inspect the geometry in
winFEKO to ensure that it is correct and the normal vectors are facing in the correct
direction. After the visual check in winFEKO, the *.fek ﬁle is ready to be processed
by the FEKO solver. The FEKO solver uses the MM to compute the surface currents
and then uses the integro-differential operators to ﬁnd the ﬁeld values at the requested
ﬁeld locations and produces the *.out ﬁle. The MM technique has a large RAM
consumption and requires signiﬁcant processor time. The full MM simulation is run
for all bands of frequencies with a 25° resolution for 51 frequencies. This will allow
an exact comparison to measurement. Table 3.4 shows the number of unknowns and

the average time per frequency point to run the simulations using all 8 processors.

52

 

 

 

 

 

 

 

 

Number of Average
. Number of RAM Simulation
Metalllc . . .
Band Ed Basrs Required Time per
ges .
Functions (MB) Frequency
(MM)
(hours)
PM 3,972 3,980 258.150 0.032
3 1 1,256 1 1,263 1,961.420 0.336
Own 25,882 25,890 10,373.720 3.07
4—5 83,786 83,794 1 12,042 ~30
GSM 105,706 105,713 178,818 ~90

 

 

 

 

 

Table 3.4: The total memory required and time for simulation

Table 3.4 includes the RAM required for these simulations. In the case of Band

4-5, the RAM is larger than the two HP computers can realistically handle. This

. . . xi .
Simulation takes an unreasonable amount of time to run at the T0 segmentation and

therefore ls not permrtted to ﬁnlsh. For thls reason, it IS decrded to use a g maxrmum

segmentation length to lower the computation cost. This is at the largest boundary for
acceptable segment lengths according to FEKO and probably does not yield very
accurate results. This very course segmentation still has 24940 metallic edges and
24948 basis functions. This requires almost 10 GB of memory and nearly the same

amount of time as the Band Own simulation. For Band GSM, there is no way to use

even the greatest allowed segmentation of 351 since the required RAM is still too large.

is used. This requires 26422 metallic edges

 

So, a maximum allowed length of ’1
4 525

53

 

and 26429 basis functions. To accomplish this, roughly 10 GB of memory is required
and a simulation time of nearly the same as Band Own. Since this simulation exceeds
even the coarsest allowed segmentation rules it is expected that these results will be

less accurate than a properly sampled simulation.

3.5.3 Hybrid Methods and the Test Vehicle

The results shown in table 3.4 illustrate the problems associated with
simulations that are electrically large using MM. For the given computational abilities,
a simulation of the test vehicle for Band FM and Band 3 are indeed quite practical.
They require a reasonable amount of RAM (less than 2 GB) and can be completed in
about one hour (maximum) for 51 frequency points while maintaining the
recommended segmentation lengths. Band Own, however, is nearing the peak of the
computing abilities for the HP machines. It requires 10 GB and a full 3 hours to
simulate a frequency point. Additionally, Band 4-5 and Band GSM cannot be
simulated using the MM in FEKO with the proper segmentation lengths. They are
simply too large and require extreme amounts of RAM and computation time. This
has brought about the need for a hybrid method of simulation. A hybrid method could
incorporate the P0 with the MM to reduce the RAM required and hopefully speed up
the calculations while maintaining relatively good accuracy. This could ideally allow
the Band GSM and Band 4-5 simulation to be possible in addition to making the Band
Own simulation less computationally expensive.

A hybrid approach is accomplished in the geometry speciﬁcation of the

simulation process in editFEKO. FEKO has the ability to selectively solve some areas

54

of the geometry with the accurate but computationally expensive MM while using the
PO approximation on other areas. As stated in the theory section for P0, the Physical
Optics approximation for currents on the body of the vehicle should only be applied to
certain areas. First of all, the wire quarter-wavelength monopole antenna must be
considered with the Method of Moments since the PO approximation is best applied to
surfaces. Additionally, a small plate below the wire antenna should use the MM so the
accuracy of the input impedance can be maintained. Often, antenna engineers
recommend that the size of the MM region be 2}» or larger to allow a sufﬁcient area
for the surface wave on the vehicle to maintain accuracy. However, in the case of the
largest frequency of Band Own, the feed plate would need to be 2)» = 1.4 meters. This
is nearly as large as the entire rear trunk (1.8 meters). There are also many parts of the
vehicle within a distance of 27» from the antenna such as the pillar and roof.
Considering all of these, or even just the entire trunk, with the MM would not allow a
sufﬁcient reduction in RAM requirements. Thus, the feed plate is chosen to be much
smaller than 2). with the anticipation that there will still be relatively good accuracy.

The feed plate is roughly 20 cm by 13 cm.

55

    

Rest of vehicle
considered with P0

Full MM area: Feed
Plate & Monopole

Figure 3.7: The test vehicle with MM feed plate and monopole and the rest of the
vehicle considered with P0 approximation

Since Band Own is the highest frequency band that can be simulated with a
full MM approach on the available computers, it is used most extensively in the
approach for hybrid methods. Additionally, due to the very large computation times,
simulations here are often done only at a single frequency as opposed to all 51
frequencies. This allows a quick inspection to see if the results appear reasonable, and
if so, a more thorough simulation can then be examined. The results are discussed in
detail in Chapter 4. The ﬁrst step in exploring the feasibility of hybrid methods is to
consider the entire test vehicle with P0 while using the MM on just the wire quarter-

wavelength monopole antenna and a small feed plate below the antenna. The area

56

surrounding the MM feed plate and antenna on the driver’s side rear trunk and the rest
of the vehicle is considered with P0. This is shown in Figure 3.7.

The P0 card in FEKO has several options that must be considered. For the ﬁrst
trial, the entire vehicle with P0 is used with only the most basic options selected. This
is done with “full ray tracing” and “decoupling with moment method.” The full ray
tracing option traces out the path of a ray from its origin, through any reﬂections that
may occur, and out to the far ﬁeld. The reﬂections occur by encountering electrical
conducting bodies such as the side, any of the six pillars, or roof of the vehicle [21].
Additionally, as in the full MM simulation, there is an inﬁnite PEC ground below the
vehicle. This simulation is denoted here as “Hybrid 1” since later it will be easier to
reference the simulation results. This is done for the center frequency of Band Own at
350 MHz and is simulated with full ray tracing and decoupling with moment method.
Additionally, it is decided that since the computational cost is so low with this PO

approximation, that the segmentation length can be further reduced at very little
. . . 2. . .
expense. For this reason, a maxrmum segmentation length of only -]—5 is used m an

attempt to maintain accuracy. For this simulation, 86 metallic edges are considered
with the MM while 53,362 metallic edges use the PO approximation. Therefore, 94
MM basis functions and 53,362 PO basis functions are used. This corresponds to a
total of 101.236 MB. This is two orders of magnitude smaller than a full MM
simulation requirement of 10 GB and represents a remarkable savings. The simulation
requires 0.208 hours to complete one frequency point.

The goal of this exploration is to ﬁnd a reasonable balance between simulation

time, accuracy, RAM consumption and practicality. The simulation, taking 0.208

57

hours per frequency point, when approximated for a full 51 points takes roughly 10
hours. The actual results of the radiation pattern and input impedance of this
simulation will be discussed in detail in Chapter 4.

The next step is to consider again the whole vehicle with P0, but this time
including coupling the MM region with the PO region. This may be a better

assumption since currents in the feed plate certainly affect surface current on the rest
. . . . . l
of the vehicle. Again, the maxrmum segmentation length 18 decreased to I5 to

maintain some accuracy. This simulation is denoted as Hybrid II and is run for 350
MHz just as Hybrid 1. The simulation requires the same edges and basis functions as
Hybrid 1. However, there is a much larger memory requirement to handle the coupling
of the PO to MM regions. This simulation requires a total of 798 MB. This simulation
takes 0.24] hours for the one point. Multiplying this time by 51 gives an approximate
total simulation time of about 12 hours.

So far, all the simulations are run with a perfectly electrical conducting ground
that is inﬁnite. The Radome, as discussed in Chapter 2, has a conducting ground that is
only 24 meters in diameter. Outside the Radome, there is earth ground that is mostly
non-conducting. Therefore it is attempted in Hybrid [[1 to model the conducting
ground of the vehicle with P0, the entire vehicle with P0 and the feed plate and
monopole antenna with the MM. The coupling with the MM and PO regions is
considered and full ray tracing is used. A large circular conducting disc is used to
model the Radome ground. This disc has an extremely large area however, and
reducing the radius from 12 meters to 10.2 meters reduces the number of triangles

from 288,296 to 222,400. This is a very large number of triangles but a radius of 10.2

58

meters is used to save on memory. Also, the PO ground uses a maximum
segmentatlon length of §.Th18 Simulation is mainly run for experimentation to see if

there is an impact on the input impedance due to the PEC. The number of basis
functions for the PO region is 332,811 and the number of MM basis functions is 64.
This simulation takes a total of 3592 MB of RAM and 0.780 hours to perform for 350
MHz. The far ﬁeld radiation pattern is not calculated since this experiment is for input
impedance and the far-ﬁeld radiation pattern would take an extremely long time to
compute.

After examining the current density on the vehicle for a full MM simulation,
the hybrid currents are compared in Chapter 4. This comparison is valid since the MM
simulation is often considered as a benchmark for other simulations. This will also be
validated in Chapter 4 also. As for now, the current density acquired by Hybrid I, II,
and III is insufﬁcient to yield the proper radiation pattern or the proper input
impedance. These are the two most important aspects of this study. Therefore a more
advanced hybrid method is employed that is intended to compensate for this
inaccuracy. The areas on the vehicle where there are sharp discontinuities yield a lot of
current activity as will be seen in the upcoming MM current density results. The
density is rapidly changing on the roof edges and at and around the pillars. This
rapidly spatially changing current density is not well simulated by the PO
approximation. Therefore, it is decided to expand the MM region to include the roof
edges and the pillars. Note that part of the roof is also considered with the MM region.
This is an attempt to use the more accurate MM approach where there are lots of

changes in current density and use the PO approximation where current is less volatile.

59

This is shown in Figure 3.8 and is represented by Hybrid IV. Hybrid IV uses the 1%

segmentation since the number of MM basis functions is increased. The number of
triangles is 17,378 and 1,946 metallic edges are considered with MM. There are
23,954 edges that use PO. This requires 6576 MB to complete this simulation. This
simulation does consider the far ﬁeld calculation for ﬁve frequency points and takes a
total time of 51.830 hours. That makes roughly 10 hours per point and represents a
signiﬁcant increase in computation time.

FEKO has some geometry correction cards that can be used to compensate for
inaccuracies with certain canonical geometries for the PO approximations. These cards
can, for example, compensate for surface current on two sides of a wedge. Or, the
current on the sharp edge of a plate can be better approximated. Since the test vehicle
is composed of sharp PEC plates that are interconnected these correction cards can be
placed at a variety of locations. For instance, there is a wedge formed by the front
bumper of the vehicle and the side panel. This is an example of one of about twenty
corrective wedges that are implemented in the vehicle to try and further improve the
simulation of the current density and ultimately the far ﬁeld pattern and input
impedance. The other correction card implemented is the current on the edge of a
plate. The roof edge and pillars are all simulated using the full MM. This leaves only a

few edges that need to be considered with this correction card.

60

 

Considered with
P0 (white)

Considered with
MM (black)

Figure 3.8: The vehicle as considered with Hybrid IV. The roof edges and the pillars
are considered with MM (shown in black) and the rest of the vehicle with P0 (White)

The driver side door is one example of a location of this corrective edge. There

are a total of ﬁve corrective edges implemented on the test vehicle simulation model.
Thls srmulatlon uses the 10 segmentatlon as m Hybrid IV smce the same areas are

considered with MM. The only difference is the corrective cards. This simulation has
similar memory requirements as Hybrid IV since the same areas are considered with
P0 and MM. The simulation time, however, is different. The total computation time to

compute the far-ﬁeld data at three frequency points is 39 hours. This means a

61

simulation time of roughly 13 hours per point. This represents a 30% increase in time
from the simulation Hybrid IV.

The comparison of these simulation results will be explored in detail in
Chapter 4. There are many decisions to be made regarding which region to choose as
MM and which to use the PO approximation. Additionally, the use of corrective cards
to compensate for edge effects has a distinct impact on the overall solution. A few
different simulation approaches were discussed here to gain an understanding of how
using a hybrid method through the implementation of a surface current approximation

can impact the simulation time, RAM requirements, and overall accuracy.

62

CHAPTER 4

COMPARISON OF RESULTS

4.1 Introduction

Now that the measurements have been described in Chapter 2 and the
simulations in Chapter 3, the goal of comparing the separate results can be met. From
this comparison some conclusions will be drawn here, and others will be discussed
later in Chapter 5. The ﬁrst comparisons are between the full Method of Moments
simulations and measurements. This is because the MM is typically the most accurate
means of simulation and is most likely to best match the measurement. Once the MM
simulations are compared, the hybrid results will be explored. Since there are three
different types of measurements, each will be looked at independently. First, the input
impedance will be compared. Next, the far ﬁeld radiation patterns will be examined

and, ﬁnally, the transformed far ﬁeld data will be explored.

4.2 Comparison of Method of Moments and Measurement

The MM simulations, as discussed in Chapter 3, are compared to measurement
for all bands including FM, Band 3, Band Own, Band 4-5 and Band GSM. Once a
correlation between the MM and measurement has been established, the results of the
hybrid methods will be explored. They will be compared with the MM and with actual

measurement.

63

4.2.1 Comparison of Input Impedance Measurement with MM

The input impedance is compared ﬁrst since it is the most simple, has the least
amount of data, and is the most simple to compare. Recall that the impedance is both
measured and simulated for the appropriate monopole antenna attached to the top of
the left rear trunk of the vehicle. The details concerning the measurement is included
in Chapter 2 and the simulation is discussed in Chapter 3. The input impedance is
shown on a standard smith chart for all bands. Figure 4.1 includes a comparison of
measured impedance for Band FM with M simulated. The frequency range for this
band has been truncated here to 76-108 MHz. This is because this smaller range is
used in simulation even though 70-120 MHz is used for measurement. There are still
data points at the same frequencies within the 70-120 MHz set and a reasonable
comparison can be made. Figure 4.2 shows a comparison for Band 3 between MM and
measurement for 175-235 MHz. Figure 4.3 shows the input impedance for Band Own
250-450 MHz. Figure 4.4 shows the input impedance for Band 4-5 from 470-870
MHz. Figure 4.5 illustrates the impedance for Band GSM spanning 800 -1000 MHz.

A very good correlation between the measured and simulated impedance on
the test vehicle can be seen for Band FM in Figure 4.1. The simulation impedance
curve follows the measurement data with the exception of a very slight shift. A small
clockwise rotation in the simulation would allow a better accordance with
measurement. However, the curve includes the same general features in simulation
and measurement. Additionally, many points are nearly perfectly aligned for

frequencies between 95-108 MHz.

 

[-~--Measured -- Method of Moments ]

 

   

Figure 4.1: Input Impedance for Band FM 7 6-108 MHz with MM and Measurement

 

[,.4- Measured —-— Method of Moments I

 

Figure 4.2: Input Impedance for Band 3 175-235 MHz with MM and Measurement

65

 

Measured -—Method of Moments ]

 

 

Figure 4.3: Input Impedance for Band Own 250-450 MHz MM and Measurement

 

{- Measured + Method of Moments I

   

   

.' 470MHz}

     

,...od.-.‘.-...‘o-t_.

  
  

  
   

. l
. I
.

.
t.
.I
I
o.

-1

Figure 4.4: Input Impedance for Band 4-5 470-870 MHz MM and Measurement

66

 

 

j... Measured + Method of Moments I

 

 

Figure 4.5: Input Impedance for Band GSM 800-1000 MHz MM and Measurement

Figure 4.2 illustrates that there is a fairly good correlation between
measurement and MM simulation for Band 3. The points near the upper and lower
boundaries of the frequency band (175 MHz and 235 MHz) are close in value. The
center frequencies, around 205 MHz, are not as well correlated. There is also a higher
concentration of measured data points near the center frequency than in the MM
simulation. The simulation has the impedance data points closer together near the
outer boundaries of the frequency band. This means that the MM simulates a greater
change in impedance with respect to frequency near the center frequency than is
shown by measurement. Additionally, the simulated curve is slightly shifted upward

from the measured curve for the higher frequencies within Band 3. Thus, the curves

67

share the same basic features and shape, but the actual measurement and simulation
points have some small discrepancy.

Figure 4.3 shows a good general comparison of the input impedance between
the MM and measurement for Band Own. This comparison is especially important
because many of the hybrid methods are also developed in this band of frequencies.

Because of the extreme computational requirements to simulate Band Own, only 21 re

-- 1' . "l’l-rki

data points are used from 250-450 MHz instead of the measured 51 data points. This is
decided since there is not a lot of detail in the measurement curve (no resonance is ,-

apparent) and less data points can be used to adequately describe it. As in Band 3, a

 

slight clockwise rotation in the simulated data would allow a very good correlation to
the measured data.
Figure 4.4 depicts the impedance curves for Band 4-5. As stated in Chapter 3,

the simulation for this band could not be run with the proper segmentation length of
xi . . . . . . . xi
1—()-. This Simulation is run wrth a maxrmum segmentation length of only g and thus

the impedance results are not considered to be accurate. Despite this large
segmentation, there is still a fairly good accordance with measurement. The lower
frequencies, near 470 MHz, appear to have an especially good correlation to

measurement. This is probably because the segmentation is chosen for the maximum

frequency of 870 MHz. Using a % segmentation length with A solved from the upper

bound (870 MHz) yields a maximum length of 0.0689 meters. This length is nearly the

same as 1110 for the lower bound (470 MHz), which yields 0.0638 meters. Therefore,

68

the proper segmentation length is nearly satisﬁed for 470 MHz but is not for 870
MHz.

Figure 4.5 illustrates the Band GSM impedance curves for measurement and
simulation. The measured results are interesting because of the resonance in the curve.
This is usually difﬁcult to accurately simulate. Again, however, the MM segmentation

rules cannot be satisﬁed. The memory required for this simulation is simply too great F
and a segmentation length of even greater than 331- is used, as described in Chapter 3.

Therefore it is determined that the simulation results are mostly meaningless for Band

 

GSM. This again points to the need for hybrid methods to allow higher frequency
simulations to be run.
Overall, the impedance results between the MM and measurement are very
good. This is especially true when the segmentation rules can be properly satisﬁed.
There is a trend of a slight rotation and shift between the measured and simulated
curves. Though it may be difﬁcult to determine the exact cause of this shift, one
possibility could be some small electrical delay that is not accounted for in
measurement. This could have allowed a phase error. The network analyzer is
calibrated before any measurements are taken but the use of a small adapter that could
not be accounted for may be a reason for this shift. This would assume that the MM

simulation is indeed more accurate than the measurement itself. The possibility that
. . xl . . .

the maxrmum segmentation length 1—0- is not small enough is not very llkely to be a

cause for this error. This is indicated because the same simulation for Band FM and

Band 3 with a 2:10 maximum segmentation length is run and the results yield nearly

69

the exact same impedance curve. So, since the presumably more accurate 20
. . . . xi .
segmentatlon length Simulation ylelds the same results as the E segmentation length

Slmulatlon, it can be assumed that the 1—0 Slmulatlon lS accurate. Another possrblllty is

that FEKO needs a different choice of basis functions for transitioning between the
wire segments and the surface. This is the area with the most current activity and
where the impedance is actually determined. This would assume that the measurement
is more accurate than the simulation. The impedance results in general are very good.
When the segmentation rules are properly satisﬁed, it would be relatively safe for an
automotive engineer to assume that the MM simulated impedance is very close to

measurement.

4.2.2 Comparison of Far Field Measurement with MM

The far ﬁeld radiation measurements and simulations are very important for
this study. Recall from Chapter 2 that the far ﬁeld measurements are taken by rotating
the vehicle 360° while a signal is broadcasted from an antenna 100 meters outside the
radome. This is done for only one elevation angle but for both horizontal and vertical
polarization (FFH and FFV). The elevation angle is estimated to be about 85°. This is
decided because the 85° cuts of both the horizontal and vertical polarization radiation
patterns from simulation best match the measurement patterns. The scale for the
ﬁgures shown for these plots is a normalized amplitude scale from 0 to —40 dB. This is

because the received voltage in measurement may not be in the same range as what is

70

1",. n.

. :- ." ..".I¥1'-

 

simulated. However, the relative received signal strength may be proportionally
equivalent to simulation if the results are normalized so that the peak measured signal
strength is set to 0 dB for both measurement and simulation. The horizontal
polarization plots usually have more detail (numerous nulls) than the vertical
polarization plots. This is especially true for the lower frequencies. This is because the
antenna on the vehicle is vertically aligned and receives horizontally polarized
components through coupling with the vehicle.

Shown in Figure 4.6 are the full MM simulation results for the FM band center
frequency of 92 MHz with the far ﬁeld measured results for both vertical and
horizontal polarizations. Only the center frequency is shown to save space but this
measurement and simulation are performed for many other frequencies in the band as
previously described. Note that the front of the vehicle is facing 0° and is depicted in
gray in the plots. There is an excellent accordance between measurement and
simulation for this frequency for both polarizations. The general shape of the FFV plot
is followed but this has very little detail for 92 MHz. The FFH plot shown in the
bottom of Figure 4.6 is more interesting since it has a few nulls at 30°, 85°, 150°, 325°
and some detail near 255°. Not only does the simulation accurately capture the
measured locations of these nulls, but also properly represents the depths. The other
frequencies in this band show similar results. This ﬁgure is a good representation of
the entire frequency band so only 92 MHz is shown.

Shown in Figure 4.7 are the full MM simulation results for the center
frequency of band 3 (205 MHz). This ﬁgure also includes the far ﬁeld measured

results for both vertical and horizontal polarizations. As in the FM band, there is a

71

very good correlation between the measured and simulated results. The general shape
of the vertical polarization curve is the same in both measurement and simulation. The
horizontal plot contains a lot more detail. There are several nulls in the simulation that
are similar to the measured results. The depths of the nulls are slightly deeper in
simulation than in measurement however. For instance at about 330° there is a null in
simulation that has a normalized magnitude of —20 dB and the measured value is —10
dB. The location of the null itself is consistent however. Both the horizontal and
vertical polarization plots show a good match between measurement and simulation.

Figure 4.8 illustrates the FFV and FFH plots for the center frequency of band
Own at 350 MHz. Again, the results are fairly good between measurement and
simulation. It can be seen that the number of nulls is starting to increase as higher
frequencies are investigated. The FFV plot includes some nulls in the ﬁrst quadrant 0°
< q) < 90°. These nulls are captured in measurement and simulation. The angles
between 300° < (p < 345° seem to have some slight discrepancy in amplitude but the
general features are similar. This may be a difﬁcult region to make the results match
since the antenna is mounted on the rear left trunk top and these angles are the front
right side of the vehicle. Thus, the vehicle itself is partly shadowing the antenna.
Overall, however, there is a good enough correlation for an engineer to rely on the
MM simulation. The results for other frequencies in this band are similar.

Figure 4.9 contains the FFV and FFH for band 4-5. This includes simulation
and measurement. At 670 MHz, there are quite a few nulls in the radiation patterns for
both vertical and horizontal polarizations. The simulation for this band however uses

the lower bound for the acceptable maximum segmentation length. Therefore, it is

72

assumed that the many discrepancies between measurement and simulation are largely
due to the lengths of the triangle edges being too large. Using some imagination, if the
nulls in simulation were less deep, then the measured results would start to look
similar for the FFV plot. The simulation nulls are slightly too deep for the FFH

scenario but there is a much smaller error between measurement.

73

 

[... Measured —Method of Moments I

105°

 

 

 

 

 

|~-~Measured — Method of Moments ]

105°.

 

 

 

 

255° 2 700 [285°

Figure 4.6: Band FM Far Field Measured for Vertical (Top) and Horizontal (Bottom)
Polarization Shown with MM Simulation for 92 MHz and Vehicle Facing 0° (Shown
with Normalized Amplitude dB)

74

 

|~-- Measured —Method of Moments I

105°

 

 

 

 

 

L- Measured —— Method of Moments]

      

105° 90° 75°

 

 

 

Figure 4.7: Band 3 Far Field Measured for Vertical (Top) and Horizontal (Bottom)
Polarization Shown with M Simulation for 205 MHz and Vehicle Facing 0° (Shown
with Normalized Amplitude dB)

75

 

[~--- Measured — Method of Moments I

       

110°100° 90° 80°

 

 

 

 

L- Measured — Method of Moments I

105°

 

 

 

 

Figure 4.8: Band Own Far Field Measured for Vertical (Top) and Horizontal (Bottom)
Polarization Shown with MM Simulation for 250 MHz and Vehicle Facing 0° (Shown
with Normalized Amplitude dB)

76

T7-
-

 

Using some imagination, if the nulls in simulation were less deep, then the
measured results would start to look similar for the FFV plot. The simulation nulls are
slightly too deep for the FFH scenario but there is a much smaller error between
measurement. The overall features of the FFH plots are similar for most frequencies
within this band. At the higher frequency range of 870 MHz, there is not a very good
correlation between measurement and simulation because the triangle segment lengths
are getting larger with respect to the frequency at that point and a good representation
of the surface current is not made.

The band GSM plots for FFV and FFH are not shown here since the
segmentation rules are violated in the MM simulation. This yields a radiation pattern
that is mostly meaningless. A comparison cannot be accurately made and no
conclusions can be drawn from this plot so it is not included.

The comparison of FFV and FFH measurements to the method of moments
simulation results shows that the MM is a very good means to estimate the
performance of an antenna. This has only been shown here for the elevation angle of
85° but demonstrates that the measured far ﬁeld radiation pattern is consistent with
simulation and can be used later to compare with the transformed near ﬁeld to far ﬁeld

data.

77

 

Measured —Method of Moments |

 

 

Measured —Method of Moments I

    

105° 99” 75°

Figure 4.9: Band 4—5 Far Field Measured for Vertical (Top) and Horizontal (Bottom)
Polarization with MM Simulation for 670 MHz and Vehicle Facing 0° (Shown with
Normalized Amplitude dB)

78

4.2.3 Transformed N F-FF Measurement with MM Simulation

The comparison of the MM simulation is now done with the far ﬁeld results
that are transformed from near ﬁeld data. This near ﬁeld measurement and
transformation is described in Chapter 2. This comparison is very extensive since it
involves more than just one 360° rotation at a single elevation angle. The NF-FF
transformed data contain 74 different elevation angles and 144 azimuth angles. There
are clearly too many plots to include here. Therefore, cuts are chosen that are
representative of the performance of the simulation with respect to the measurement.
This comparison will focus on the results for band Own. This is because band Own is
the highest frequency range that can be simulated with the proper segmentation of the
vehicle and antenna with the given computational resources. This will also allow the
study of the hybrid methods results to be an easy extension of this comparison.

Shown in Figure 4.10 is the vertical and horizontal polarization plots of the
radiation pattern for 0 = 0° for the center frequency of band Own (350 MHz). It can
be seen that for this angle the MM simulation does fairly well at representing
measurement. The most noteworthy discrepancy is at the angle 0 = 65° for the
horizontal polarization. There, a deep null in simulation and only a slight null in
measurement can be seen. A null is also evident at 0 = 40° in the vertical polarization.
It is common that the measurement null depth is not as sharp as the simulation depth.
This could be due to reﬂections and noise in the radome. This would allow some
signal strength to be measured when it is not from the actual test antenna. Of course,
this would not be simulated, allowing the simulated null depth to be much more

profound. The transformation from near ﬁeld data to far ﬁeld data uses the values last

79

measured to approximate the immeasurable points down near 0 = 85°. The choice to
use the last values measured as opposed to just ﬁlling these measurements with zeros
is governed by observing that the simulated results show a peak at the vertical
polarization plot of about —1 dB at 0 = —90° (270°). The simulation for horizontal
polarization shows that there is a value of —10 dB at 0 = —87.5°. Using the last
measurable values for the extreme near ﬁeld measurements allows the best correlation
to simulation. The last values will be used for the rest of the comparisons unless
otherwise stated.

Figure 4.11 illustrates the radiation pattern for the vehicle facing into the plot
((1) = 90°). The horizontal polarization, shown in the bottom plot, shows a good
consistency between measurement and simulation. The null depth at about 0 = 45° is
quite different. The measurement is actually deep (-40 dB) while the simulation is
only -10 dB. The vertical plots show a good correlation except that simulation ﬁnds a
null at 0 = 80° and 0 = 280° while measurement does not show this.

Figures 4.10 and 4.11 show just a few plots of the radiation pattern for the
antenna on the vehicle for only one frequency. There are numerous other possible
angles and frequencies that a curve could be generated at. Many plots at different
angles and frequencies have been examined that are not included to save space. It can
be concluded from these plots and Figures 4.9-4.11 that the MM simulated radiation
pattern results are very similar to the far ﬁeld pattern that has been transformed from
near ﬁeld data. There are some errors but it is reasonable to assume that the MM

results yield a far ﬁeld pattern and impedance curve that closely match measurement.

80

 

[— Method of Moments ----- Measurement ]

0
020°1°°. ° . 340°

 

 

 

 

 

[.-.Measured —Method of Moments ]

30° . *.

   

 

 

 

Figure 4.10: Band Own Far Field Transformed from Near Field Measured for Vertical
(Top) and Horizontal (Bottom) Polarization Shown with MM Simulation for 350 MHz
at 0 = 0° and Vehicle Shown Facing Left (Shown with Normalized Amplitude dB)

81

 

Method of Moments

 

---------- Measured Near Field Transformed to Far Field

 

 

 

 

      

‘ '- 210°
160$70" 180° 1902000

 

Method of Moments
Measured Near Filed Transformed to Far Field 7

 

 

 

20.,1o° 0° 350340..
30° -. ‘

 

 

 

 

Figure 4.1 1: Band Own Far Field Transformed from Near Field Measured for Vertical
(Top) and Horizontal (Bottom) Polarization Shown with M Simulation for 350 MHz
at 0 = 90° and Vehicle Shown Facing Into the Plot (Shown with Normalized
Amplitude dB)

82

4.3 Comparison of Method of Moments to Measurement and Hybrid Methods
Now that it has been shown that the Method of Moments simulations are
usually very close to measurement, hybrid methods can be explored. First, however,
an important visual comparison can be made to determine if a hybrid method will
yield a good match to a full MM and measured radiation pattern. Looking at the
surface currents on the vehicle allows an estimate for how well the radiation pattern E:
will match. This is true because the radiation pattern itself is computed from the
surface and line current. There is no way to actually measure the surface current on the

vehicle so the MM results are used. This can be justiﬁed because the MM radiation

 

pattern is so similar to measurement that the surface currents must also be similar.
Shown in Figure 4.12 is the surface current density for the method of moments
simulation for 350 MHz on the test vehicle. The vehicle is oriented with respect to the
small axes enclosed in a box in the upper right side of the ﬁgure. Looking carefully at
this ﬁgure, the monopole antenna can be seen on the left rear trunk top. The amount of
current on the monopole is indicated by various shades of gray as indicated in the
legend on the left side of the ﬁgure. This scale is titled “Log Line Cur [A]” and shows
the logarithm of the line current on the antenna. This current is usually about the same
on all the simulations because the line current always uses the MM. So, the surface
current on the vehicle is the most important for comparing simulation results and the
line current will not be discussed. The scale titled “Log Surf Cur [A/m]” indicates the
amount of surface current on the vehicle itself. The scale goes from the largest at Log
(0.0269 A/m) = —1.57 to the smallest at Log (0.00331 A/m) = ——2.48. The most surface

current density is seen near the antenna on the left rear trunk. The entire left rear

83

comer in fact has the most current density on the entire vehicle. The front part of the
vehicle is mostly very dark because there is not much current density there. This is
because the rest of the vehicle mostly shadows the front. A large current density can
be seen on the pillars and the roof edges. These areas are very crucial since small
changes in their geometries can have profound impacts on the resulting current

densities all over the vehicle.

84

 

LogL‘neCu [A]

.< 2.48000 g
I 238900
I am
n 2.20700
I 2.11800
I 2.02500

 

 

 

  
  

Figure 4.12: The Surface Current Density on the Test Vehicle for the MM Simulation
at 350 MHz

4.3.1 Hybrid I

The ﬁrst hybrid simulation to be compared is “Hybrid 1” as described in
Chapter 3. This simulation considers a small feed plate on the trunk and the monopole
antenna with MM and the rest of the vehicle with P0. This simulation does not
include a coupling between the MM and the PO regions. Hybrid 1 only requires about
100 MB of RAM and 0.20 hours per frequency point. This is about the same

computation time as the MM simulation because the segmentation lengths have been

85

reduced to %. Recall that the MM segmentation length is I20 for the results shown in

Figure 4.12. The Hybrid I simulation is a good starting point and will be looked at for
350 MHz.

Figure 4.13 includes the surface current density for Hybrid I (top picture). This
is a screen shot from FEKO with the same scale for current density as the MM shown
in Figure 4.12. It can be seen that the surface current density of Hybrid I is lacking
some of the detail that the MM simulation has. This deﬁciency most importantly
displays a lack of activity on the pillars and the roof edges in addition to the front of
the vehicle’s edges having almost no current. It can be expected that the radiation
pattern may be inaccurate for this curve because of the inconsistencies of the current
density.

Figure 4.14 and Figure 4.15 show just two radiation patterns that include both
the method of moments simulation and the Hybrid I simulation result. It can be seen
that there are some differences between Hybrid I and the MM results for the FFV
pattern in the top plot of Figure 4.14. These differences are up to 15 dB in some cases
and the general pattern only very loosely follows the MM result. The horizontal case is
much different in that major nulls are completely missed by the Hybrid I simulation.
Figure 4.15 shows the plots for (l) = 90°. The general features of the M are followed
for the vertical polarization plot 0° < 0 < 90°. However, for —45° (315°) < 0 < 0°
neither the features nor the amplitudes of the patterns match very closely. Many other
cuts have been examined for Hybrid I and the results are similar.

Hybrid I and Hybrid II have extremely similar impedance plots. These are shown in

Figure 4.16 (only Hybrid H is shown). The impedance curves have the same general

86

shape but the Hybrid I-II curve is larger in “radius” than the measured and MM
curves. The impedance is one of the most important parameters of the antenna and it is
imperative to make a reasonable correlation between simulation and measurement.
Hybrid I is thus insufﬁcient to properly model the vehicle surface current, input

impedance and the far ﬁeld radiation pattern.

4.3.2 Hybrid II

Hybrid H is a very similar simulation to Hybrid I except that the coupling
between the MM and the PO region is considered. This has a signiﬁcant impact on the
RAM consumption and computation time. For this simulation, roughly 800 MB and
0.24 hours per frequency point are required. The bottom plot of Figure 4.13 shows the
surface current density for 350 MHz. There are clearly some major differences
between the bottom plot on Figure 4.13 and the current shown on Figure 4.12 by the
MM. In Figure 4.13 many parts of the vehicle do not show a high enough current
density. This is especially true on the roof and sides of the vehicle. It appears that the
area around the MM feed plate may be properly modeled but the surrounding areas are

grossly incorrect.

87

 

Log Surface
Current

-<-3.078
-2.964
-2.85
-2.735

-2.621
-2.507
-2393
, -2279
-2.164
‘ -205

 

Figure 4.13: Hybrid I (top) and Hybrid 11 (bottom) Surface Current Density for 350
MHz

 

— Method of Moments---Hybrid | ----- Hybrid || |

150°
160° 20°
170° . 10°
160° 0°
190°\ 350°
200° 5 ‘ 340°
\ j .
210° ' 330°

  

270°

  

6-
260°

 

—Method of Moments- t-Hybrld | Hybrid II I

 

Figure 4.14: Band Own Far Field MM, Hybrid I and Hybrid H Simulation for Vertical
(Top) and Horizontal (Bottom) Polarization for 350 MHz at 0 = 85° and Vehicle
Facing 0° (Shown with Normalized Amplitude dB)

89

 

[— Method of Moments- - » Hybrid l ----- Hybrid ll 1

20°‘°°

 

 

 

 

 

[— Method of Moments - - Hybrid I Hybrid II I

10° 0° 350°

 

20°

 

 

 

Figure 4.15: Band Own Far Field MM, Hybrid I and Hybrid II Simulation for Vertical

(Top) and Horizontal (Bottom) Polarization for 350 MHz at q) = 90° and Vehicle
Shown Facing Into the Plot (Shown with Normalized Amplitude dB)

90

Figure 4.14 shows that for the vertical polarization, the Hybrid H simulation is
mostly similar to the Hybrid I simulation. No signiﬁcant improvements from Hybrid I
can be seen. For the horizontal polarization, the Hybrid H plots show only some
correlation to the MM region. There may be some small improvements here in that the
overall amplitudes appear to better match the MM. The largest inaccuracy of Hybrid II
is the null at 135°. This null is not found in the simulation with Hybrid II but is in the
MM results. Figure 4.15 illustrates some improvements for Hybrid II. For the vertical
polarization (top plot) there is a better correlation to MM than Hybrid 1. This is
especially true for angles 315° to 270° (-45° to —90°). In the horizontal polarization
plot in the bottom picture in Figure 4.15, there are some distinct improvements with
Hybrid II. The null at 0 = 315° (-45°) in simulation is found with Hybrid II but not
with Hybrid 1. Overall, the Hybrid II curve is closer to MM than Hybrid I.
Additionally, the impedance plot of Hybrid II is shown in Figure 4.16. This plot shows
an inconsistency between measurement and simulation as discussed earlier with
Hybrid I. Many other plots of Hybrid II have been compared to the MM solution and
they appear to be similarly slightly inaccurate despite the marginal improvements from

Hybrid 1.

91

 

[-- Measured --~- Method of Moments —- ~ Hybrid II I

 

Figure 4.16: The Impedance Curves for Measurement, MM and Hybrid H for Band
Own 250-450 MHz

4.3.3 Hybrid III

The simulation for Hybrid [H is devised largely as an experiment of interest.
The impedance plot for Hybrid II is nearly the same as Hybrid 1. So, only Hybrid H is
shown in Figure 4.16. It is clear that there are some differences between the Hybrid
curve and the measured and simulated with MM. The Hybrid HI simulation has been
developed to try and match the impedance better for the 250-450 MHz range and see
how the current ﬂows on the ground. An attempt has been made to model the ground
of the radome as discussed in Chapter 3. The ground is modeled as a 10.2 m radius
circular disc and is considered with P0. This simulation, however, has too many

unknowns (roughly 220,000) to solve for the impedance at multiple frequency points

92

so no results are shown for Hybrid III. It is expected that this will not largely affect the
input impedance anyway since the MM feed plate at the antenna feed location is
largely responsible for this aspect of the simulation. This is because impedance is the
ratio of the excitation voltage to the current at the feed location that is considered by

the accurate MM.

4.3.4 Hybrid IV

It can be seen from Hybrid I and Hybrid H that the surface current densities on
the vehicle are not close enough to the MM solution to allow a very good correlation
between their radiation patterns. There is an especially large discrepancy on the pillars
and roof edges. These areas are insufﬁciently modeled with P0 and should be
considered with MM. Considering these areas with MM will increase the
computational cost of the solution. This is necessary, however, since Hybrid I and
Hybrid II are simply too inaccurate for certain angles. Considering the edges and
pillars with MM and the rest of the body with P0, as illustrated in Figure 3.8, yields
some interesting results. This simulation requires 6576 MB of RAM and about 10
hours per point. This is a signiﬁcant increase in computation time and RAM from both
Hybrid I and Hybrid II.

The surface current density on the vehicle is shown in the top image in Figure
4.17. Looking at this picture, and comparing it to Figure 4.12, it can be seen that there
are some improvements from Hybrid I and Hybrid II. The surface current density on
Hybrid IV in Figure 4.17 depicts more current activity on the pillars and roof region

than Hybrid I and 11. Hybrid IV also shows a fairly good correlation for the rear trunk

93

surface current. This is just a preliminary comparison to see if the hybrid simulation
has modeled the surface currents roughly as well as the MM simulation. There are still
some differences but this will hopefully allow a more accurate radiation pattern.

Though the Hybrid IV surface current densities appear to be more similar to
the MM simulation than Hybrid I and Hybrid H, the radiation patterns are the most
important comparison. It may be useful to additionally reference Figure 4.14 for this
part of the discussion. Figure 4.18 shows a comparison between the MM simulated
and Hybrid IV results for 0 = 85° for both vertical and horizontal polarizations. Hybrid
V is also included in these plots and will be discussed in the next section. The Hybrid
IV simulation for vertical polarization is depicted in the top part of the ﬁgure. There is
a very good correlation between MM and Hybrid IV for the angles —90° (270°) < (l) <
15°. This is much more accurate than Hybrid 11 especially since the amplitudes and
general features of the curve are not included with Hybrid II.

For the horizontal plot, shown in the bottom plot of Figure 4.18, it is very
difﬁcult to determine if Hybrid IV shows improvement since there is little correlation
to the MM simulation. Hybrid IV shows two additional nulls in the area 255° < 0 <
315° for a total of three nulls. The MM and Hybrid H curves show only a single null.
Realistically, however, this curve is mostly inconclusive. The 0 = 85° plots for
horizontal polarizations typically show the worst correlation between curves. This is
probably because the extreme low elevation angles represent a wave encountering the
lowest part of a side of the vehicle with the polarization orthogonal to the receiving
monopole. The received signal strength is thus due mostly to reﬂections and coupling

that are difﬁcult to model with the PO approximation.

94

  
 
   

Log Surface
Current

-<-3.078
-MM
2%
-m5
2&1
-um
-m%
_-mw
-mm
2%
eww

Illa-Ila.-

Figure 4.17: Hybrid IV (Top) and Hybrid V (Bottom) Surface Current Density for 350
MHz

 

 

 

 

 

 

[— Method of Moments- ~ ~ Hybrid 1v ----- Hybrid v |

 

 

 

 

 

Figure 4.18: Band Own Far Field MM, Hybrid IV and Hybrid V Simulation for
Vertical (Top) and Horizontal (Bottom) Polarization for 350 MHz at 0 = 85° and
Vehicle Facing 0° (Shown with Normalized Amplitude dB)

96

Figure 4.19 depicts vertical and horizontal plots for 0 = 90°. The vehicle is
shown facing into the plots. The null depths at 60° and 45° are more accurate than
Hybrid H. There is also more distinct detail for the angles 320° (-40°) < 0 < 290° (-
70°). The null depths at i 80° are much too deep using Hybrid IV, but generally it
could be concluded that Hybrid IV is more accurate for this cut.

The horizontal polarization plot, depicted in the bottom image in Figure 4.19,
shows some improvement over the previous hybrid approaches. The overall amplitude
of the curve is more consistent with the MM simulation. There is not a signiﬁcant
improvement for this angle, however, considering the increase in computational cost
for Hybrid IV.

Since Hybrid IV has shown some improvements over the previous simulations,
an additional cut will be looked at here. Figure 4.20 depicts horizontal and vertical
patterns for (b 2 0° at 350 MHz. The vehicle is shown facing to the left. From the
angles -90° (270°) < 0 < -50° (310°) there is an excellent correlation between the MM
and Hybrid IV. This is probably because those angles are accurately simulated with
the MM since that area faces the rear trunk that has the MM feed plate. On the other
side of the vehicle, the null depth at about 0 =40° is not as deep as the MM simulation.
However, this is actually closer to the measured null depth as shown in Figure 4.10.
The only other signiﬁcant inaccuracy is the large beam amplitude at 0 =25°. The MM
simulation has amplitude of —12 dB while Hybrid IV computes the amplitude to be
about —-5 dB. Overall, the vertical polarization Hybrid IV compares quite well with

MM simulation.

97

The horizontal polarization plot, shown in the bottom of Figure 4.20, depicts
the Hybrid IV curve loosely following the MM curve. There is a fairly large
discrepancy at the angle 0 = -35° (325°). Hybrid IV computes a null there (~40 dB)
while the MM simulation computes only a depth of around —12 dB. Also, at
approximately 0 = 5° there is a beam height of 0 dB in MM but a null in Hybrid IV of
nearly —7 dB. At 0 = 65° the MM simulation ﬁnds a null depth of —40 dB. Hybrid IV
computes a depth of —25 dB at approximately the same location (0 = 70°). Hybrid IV
compares quite well with the MM simulation for the horizontal polarization in

addition to the vertical polarization.

98

 

 

 

 

 

 

 

 

 

 

.

 

70° 180° 1903“”

Figure 4.19: Band Own Far Field MM, Hybrid IV and Hybrid V Simulation for

Vertical (Top) and Horizontal (Bottom) Polarization for 350 MHz at q) = 90° and
Vehicle Shown Facing into the Plot (Shown with Normalized Amplitude dB)

99

 

 

L— Method of Moments- --Hybrid iV ----- Hybrid v I

  

0
200 1 0° 0 3500340

 

 

 

 

 

[— Method of Moments- --Hybrid IV ----- Hybrid V ]

 

20°1°° 0°, ..... 35°°340°

......
.‘..

 

 

 

Figure 4.20: Band Own Far Field MM, Hybrid IV and Hybrid V Simulation for
Vertical (Top) and Horizontal (Bottom) Polarization for 350 MHz at q) = 0° and
Vehicle Shown Facing to the Left (Shown with Normalized Amplitude dB)

100

 

4.3.5 Hybrid V

The Hybrid V simulation is the most advanced hybrid simulation developed in
this study. This simulation, as discussed in Chapter 3, implements FEKO’s correction
cards for edge currents on plates. The same areas are considered with P0 and MM on
the vehicle. The P0 areas use the correction cards to account for fringe wave currents.
Since most of the vehicle is still considered with P0, using this correction on all edges
could allow a signiﬁcant improvement in the surface current density and ultimately the
radiation pattern. Figure 4.21 shows the full MM surface current density for the driver
side panel of the vehicle (left side) alone. The rest of the vehicle is not included in this
simulation. The monopole antenna is included with the feed plate that is also
considered with MM. The feed plate and monopole are difﬁcult to see in the image
since they are directly behind the side panel. The surface current density can be seen
to be changing a lot over the entire area of the panel. There is plenty of detail on the
top edge of the panel where current density is changing along the edge.

The top picture in Figure 4.22 shows the exact same side panel with the
monopole antenna and feed plate. In this ﬁgure, the side panel is considered with P0
as in Hybrid I through Hybrid IV. There is no correction for the top edge. It can be
seen that the top edge is not very similar to the MM density picture in Figure 4.21. The
bottom picture in Figure 4.22 shows the exact same panel as Figure 4.21 but the
correction on the top edge is included. This not only makes the current density around

the top edge similar to the MM but also corrects the currents in the middle of the panel

101

as well. All the edges of the vehicle that don’t form a comer are corrected in Hybrid

V. Log Surface

.<-3.078
-MM
2%

+-mu
2&1
-um
-m%
,-um
-mm
2%

.>-1.936

IIZIIIIII

 

Figure 4.21: Surface Current Density on Side Panel of Vehicle and Monopole Antenna
with Feed Plate all Considered with the Method of Moments

IIIEIIIEII
b
b)
8

>-l.936

 

Figure 4.22: The Surface Current on the Side Panel of the Vehicle Considered with P0
(Top) with No Edge Correction and (Bottom) with Edge Correction on the Top Edge

102

The plates that form a comer use a separate wedge correction feature that
corrects the surface current density on both sides of the wedge. A wedge correction is
implemented at all locations where is a wedge on the vehicle formed by combining
two plates. This will hopefully improve the radiation pattern since the current density
on the surface of the vehicle should be drastically improved.

The surface current density on the vehicle for Hybrid V is shown in the bottom
image of Figure 4.17. Comparing this to the full MM surface current density in Figure
4.12 reveals that there are some improvements over Hybrid IV. First of all, the rear
trunk and rear “bumper” have a much higher current density in Hybrid V. This is more
consistent with the MM simulation. Also, the base of the front left pillar is more
illuminated than Hybrid IV. This is more consistent with MM. Many edges show a
slight improvement over Hybrid IV and appear more like the MM simulation. This
should lead to some improvements in the accuracy of the radiation pattern.
Implementing these many corrections to the wedges and edges of the vehicle have no
impact on the required RAM. In fact the required RAM is the same as Hybrid IV.
However, since there are additional computations the total time is increased by 30% to
a total of approximately 13 hours per frequency point.

The resulting radiation patterns are compared with Hybrid IV in the previous
ﬁgures. The top image in Figure 4.18 shows the vertical polarization for 0 = 85° for
the MM, Hybrid IV and Hybrid V. Hybrid V has no noticeable improvements over
Hybrid IV in this cut. In fact Hybrid V completely misses the null at q) = 45°. This cut
is probably mostly similar in accuracy to Hybrid IV. The bottom image in Figure 4.17

for the horizontal polarization at 350 MHz shows some improvement over Hybrid IV.

103

This is indicated for angles 255° < (l) < 315° since the nulls are more closely matched.
There are also some improvements in the area of 115° < (11 < 210° where the
amplitudes more closely match MM. This is probably because for low elevation
angles, with the incorrect polarization, reﬂections are important. The induced currents
on the vehicle are critical when considering reﬂections and are more closely modeled
when corrections are used in Hybrid V.

The vertical polarization results for (l) = 90° are depicted in the top image in
Figure 4.19. The vehicle is shown facing into the plot. For this out there are certainly
some improvements over Hybrid IV. This is evident for all the angles to the left of the
vehicle 0° < 0 < 90° where there is a much better correlation to the MM simulation.
The amplitudes and null locations match very well. For the angles —45° (315°) < 0 <
0°, both Hybrid IV and Hybrid V fail to accurately represent the pattern. However, for
the remaining angles Hybrid V is slightly superior to Hybrid IV in accuracy. The
horizontal plot is in the bottom of Figure 4.19. Here, it can be seen that the null at 0 =
315° is well captured in Hybrid V. The angles 0° < 0 < 90° show a better following of
the MM features but the amplitudes of Hybrid IV are closer to the MM simulation. It
is evident that Hybrid V, despite the slight inaccuracies in the horizontal plot is
generally more accurate than Hybrid IV for this cut.

The vertical polarization results for (ll = 0° are depicted in the top image in
Figure 4.20. The vehicle is shown facing to the left. For this cut there are some
improvements over Hybrid IV. For the angles -90° (270°) < 0 < 0° Hybrid V is
somewhat more accurate than Hybrid IV. For the angle 0 = 10° the null depth is more

accurate with Hybrid V than Hybrid IV. However, the beam amplitude at 0 = 25° is

104

 

less accurate. There is slightly more detail in the remaining angles but the correlation
to M is not signiﬁcantly better. The horizontal polarization shown in the bottom
image of Figure 4.20 illustrates that there is one major improvement in that the
erroneous null simulated by Hybrid IV at 0 = 315° is no longer existent. In fact, that
angle now shows the proper beams and nulls that are found in the MM solution.
Hybrid V shares with Hybrid IV the same minor error at 0 = 10° of simulating a null.
The remaining curve follows the MM solution fairly well without many signiﬁcant
errors.

It is shown in Figures 4.18 through 4.20 that the overall performance of Hybrid
V is superior to Hybrid IV. Of course, there are several other cuts that can be explored.
After looking at many other angles, it can be concluded that there is a general trend of
Hybrid V being more accurate for some angles. Hybrid V is usually not less accurate
than Hybrid IV as is evident in looking at just three cuts at both polarizations. It can
thus be concluded that overall, Hybrid V is the most accurate simulation model
developed for the test vehicle. Its current density shows the best correlation to the MM
simulation and the radiation patterns are very close indeed. The input impedance has
been simulated for only three frequency points and does not generate a smooth curve.
This is because of the high computation cost of Hybrid V. However, it is expected that
the impedance looks at least as good as the Hybrid H impedance curve in Figure 4.16
if not better. This is because Hybrid V has more MM regions and should have an
overall accurate representation of the full MM surface current density. Also, Hybrid V
uses the same MM feed plate as Hybrid H and since the impedance is the ratio of the

excitation voltage to the current at that location it is reasonable to guess that the

105

impedance curves are similar. All three simulated points with Hybrid V are very near
points on the Hybrid H impedance curve. This shows that Hybrid V is a reasonably

good means for approximating the computationally expensive MM simulation.

106

 

CHAPTER 5

CONCLUSIONS

5.1 Overview

As vehicles begin to require a larger number of antennas operating at higher
frequencies, the shape of the vehicle itself impacts the optimum design and location of
these antennas. For frequencies greater than 1 GHz the challenge for automotive
antenna engineers is to ﬁrst design the antenna in free space. Then, the correct location
on the vehicle to mount the antenna must be determined. Engineers then need to take
numerous measurements to ensure that the antenna on the vehicle is performing within
speciﬁcation. The antenna design may need to be changed along with the location in
order to meet the rigorous speciﬁcations of, for instance, satellite radio. This poses a
signiﬁcant problem to engineers as they attempt to reduce design cost and cycle time.
For this reason, simulation is looked at as a means to decrease the need for expensive
measurements. The proper simulation technique needs to be applied to achieve a
reasonable result. The results of the simulation need to be veriﬁed with comparison to
measurement to ensure simulation is a viable means to make design decisions.

A model of an automobile has been constructed with wood, metal and ﬁne
brass mesh. This model is fairly representative of a small vehicle and has a length of
3.6 m, a height of about 1.5 m and a width of 1.8 m. This vehicle has been constructed
because it is easier to model in simulation than an actual automobile that has
discontinuities, a variety of materials, and smooth curves. This physical model is

composed of simple geometrical shapes that have made it easy to model in simulation.

107

 

Having an actual test vehicle and a simulation model with exactly the same
dimensions allows a thorough comparison between measurement and simulation. The
measured and simulated ranges of frequencies have been discussed and begin at 70
MHz and end at 1 GHz. This range of frequencies includes the previously discussed
band FM, band 3, band Own, band 4-5, and band GSM. The choice of test antenna is a
quarter wavelength monopole.

The method of moments technique is an accurate, but computationally
expensive, means for simulating the radiation pattern of an antenna on the vehicle.
Band 4-5 and band GSM can’t be accurately simulated with the MM due to the large
RAM requirements. Hybrid methods have been explored as a possible remedy for this
while maintaining reasonable accuracy. These simulations have been compared to

measurement in Chapter 4.

5.2 MM simulation

The method of moments technique is explained in Chapter 3. The simulations

for Band FM, Band 3 and Band Own have been run with a 110 maximum
segmentation length in FEKO. Band 4-5 is run with a maximum segmentation of i

and Band GSM has segmentation lengths even greater than i so that the simulation

can ﬁt in the available 16 GB of RAM. This is beyond the bounds of acceptable
segmentation lengths as speciﬁed by the software package FEKO as discussed in

Chapter 3. The results for these simulations are considered inaccurate.

108

Chapter 4 discussed the comparison between the impedance measurement and
simulation. An excellent correlation is made for Band FM, Band 3, and Band Own.
Simulation is shown to nearly match measurement for these bands. Band GSM and
Band 4-5 did not show the correct results for impedance, but the general features of
the impedance curves are consistent. The far ﬁeld patterns for Band FM, Band 3, and
Band own also show an excellent match to measurement. It has been concluded, due
to the closeness of measurement and simulation for the impedance and far ﬁeld
radiation patterns, that the method of moments simulations are quite close to

measurement.
Table 5.1 shows the number of metallic edges in simulation with a %

maximum segmentation length. This includes the estimated time requirement if the
simulation could actually run for Band 4-5 and Band GSM. The time per frequency
point of the simulation is related to the frequency raised to the third power. The time
for Band 4-5 is estimated to be roughly 30 hours per frequency point. The computation

time per frequency point is about 90 hours for Band GSM.

 

 

 

 

 

 

 

Number of Metallic . .
Ban d Edges (MM) with 3110 RAM Ayerage Simulation
. Required Time per frequency
(MHz) Maxrmum (MB) point (hours)
Segmentation Length
FM (70 - 120) 3972 258.150 0.0019
3 (175 - 235) 11256 1,961.420 0.0196
Own (250 - 450) 25882 10,373.720 3.0758
4-5 (670 - 870) 83786 112,042 2 30
GSM (800 - 1000) 105706 178,818 2: 90

 

 

 

 

Table 5.1: The method of moments computational requirements for all studied
frequency bands

109

 

 

As can be seen in Table 5.1, there is a large computational cost associated with

the required RAM. Additionally, the estimated simulation time per frequency point is

fairly large for Band 4-5 and Band GSM. This would require a long simulation time if

multiple frequency points are needed. This makes the method of moments the most

accurate of all the simulations studied here but also the most expensive in terms of

Storage space.

5.3 Hybrid Simulations

The hybrid methods discussed in Chapter 3 are one possible way to ﬁnd results

at a reduced computational cost. Tabulated in Table 5.2 are the computational

requirements for Hybrid I through Hybrid V for Band Own only. This band is used

only because it is the highest frequency that can be completely simulated with the

accurate method of moments. Additionally, the center frequency of 350 MHz is most

 

 

 

 

 

 

 

often used.
. Average
Hy bud Maximum ‘ Number of Number of Simulation
For Band . RAM .
Own Segmentation Unknowns Unknowns (MB) Time per
Length MM PO frequency
350 MHz .
pornt (hours)
I M15 94 53362 101.236 0.208
H M15 94 53362 798.225 0.241
Ground M5
IH Vehicle M15 94 222400 3592.506 -
IV M10 1954 23954 6576.008 10.02
V M10 1954 23954 6576.008 13.10

 

 

 

 

 

 

Table 5.2: The computational requirements for the hybrid simulations

110

 

 

 

 

 

The results from these simulations are compared for some typical cuts to the
MM solutions in Chapter 4. Hybrid I through Hybrid IH all use a maximum
segmentation length of M15. This is because the RAM requirements for a M 10
simulation are so low that a smaller segmentation length is used to try to maintain a
good accuracy. Hybrid I considers the entire vehicle with P0 and the monopole with
the small feed plate just below the monopole antenna on the left rear trunk top with

MM. The results from Hybrid I show in Chapter 4 that the accuracy of the radiation

 

pattern is quite different from the MM simulation.

Hybrid H has the same maximum segmentation length and thus has the same
number of PO and MM unknowns. The RAM required is larger (798.225 MB) because
a coupling between the MM regions and PO regions is now considered. There is an
increase in computation time related to this increase in RAM: Hybrid H takes 0.241
hours to complete. Hybrid II is shown in Chapter 4 to also be deﬁcient in accurately
capturing the correct radiation plot. Additionally, the impedance plot of Hybrid H is
slightly shifted from the MM and measured curves.

Hybrid IH has a ﬁnite circular ground plane that is considered with P0 instead
of as an inﬁnite PEC. This model attempts to simulate the condition in the radome
since the radome has a ﬁnite ground plane. However, this simulation has too many
unknowns to solve. Also, it is very difﬁcult to estimate the computation time per
frequency point. This is because the ground plane uses a maximum segment length of
M5 and the vehicle uses M15. It can be assumed that the computation time is much

greater than 20 hours per frequency point.

111

Hybrid IV considers the roof edges, all four pillars, the feed plate, and
monopole antenna with MM and the rest of the vehicle with P0. Since Hybrid H
shows better results than Hybrid 1, the coupling between the PO and MM regions is
considered. This simulation is run because the radiation patterns resulting from Hybrid
H and I are too inaccurate to draw any certain conclusions about the antenna
performance on the vehicle. Many null depths are inaccurate and occasionally, as
described in Chapter 4, the general shape of the radiation pattern is not correct. As the
amount of area containing MM regions increases, the computational cost increases
also. The RAM required is 6,576 MB and requires 10 hours per frequency point to
complete. From the MM solution in Table 5.1, this is a 64 % savings in RAM but a
325% increase in computation time. The simulation represents a possible solution for a
computing system that has only half the available RAM but three times the computing
power. This simulation should run well on a system with 8 GB of RAM and with two
3 GHz processors. This solution could possibly be computed with a PC cluster with
only two machines with modern computing abilities. The accuracy of this simulation
is still lacking for some cuts. The surface current density on the test vehicle does not
match the density from the MM simulation as shown in Chapter 4. Since the surface
current is integrated to ﬁnd the far ﬁeld values, an improvement of the surface current
density will impact the radiation patterns. For this reason, the simulation model
Hybrid V is developed.

Hybrid V incorporates exactly the same geometry as Hybrid IV. Again, the
roof edges, pillars, monopole antenna, and feed plate are all considered with the

method of moments. The rest of the vehicle is considered with P0. For this

112

simulation, special correction calculations are performed on the boundaries of PO
regions. These corrections are aimed at improving the surface current density
accuracy. This will ideally improve the far ﬁeld radiation pattern. Since the geometry
is the same as Hybrid IV, the RAM required is also 6576.008 MB. The computation
time is slightly larger however due to the increase in calculations. The computation
time of 13 hours per frequency point represents a 433% increase in the calculation
time. This is a signiﬁcantly longer time than the MM solution but represents a 64%
savings in RAM. Hybrid V is the most advanced simulation model developed in this
study. The accuracy of the solution is discussed in Chapter 4 and is slightly better than
Hybrid IV. The surface current has shown some deﬁnite improvements over Hybrid
IV. Additionally, many cuts show a better correlation to the MM simulation. There are
still some details in the general pattern shapes that are left out in Hybrid V however.
These discrepancies could be reduced by further increasing the areas considered with
MM. This will increase the accuracy of the solution. However, this will also further
increase the computational cost of the solution and defeat the purpose of exploring
hybrid methods, which is to reduce the computational cost and allow high frequency

simulations.

5.4 Simulation of an Antenna on a Vehicle

The overall goal of this study is to allow the simulation of high frequency
antennas on vehicles. It has been shown that for the available computing resources the
method of moments simulations cannot be run for frequencies greater than Band Own

(250 — 450 MHz). This necessitates the use of hybrid methods. Though there are a

113

 

variety of hybrid methods one could apply, the P0 with M method has been
explored here. These hybrid methods are used only for Band Own since it is the
highest frequency for which a full MM simulation can be run. From this study, a
general algorithm could be applied to set up a simulation using the hybrid PO - MM
method.

First, a simulation model of the vehicle needs to be constructed in FEKO.
Irnportin g a CAD drawing of the vehicle can accomplish this. Once the three
dimensional CAD drawing is imported into FEKO, a triangular mesh can be applied to
the vehicle. The mesh should obey the segmentation and triangular criteria as speciﬁed
by FEKO. A M10 maximum segmentation length of an edge on the triangle is
typically sufﬁcient.

If possible, a full MM simulation of the vehicle needs to be run. A full
simulation of the vehicle with the method of moments will allow a very accurate
solution for the radiation pattern and input impedance. Also, the surface currents on
the vehicle will be accurately simulated with the MM. Once this simulation is
complete, the vehicle should have a new mesh created that has a variable segmentation
length. Areas that have a very low surface current density can have a larger triangle
segment length so as to save in RAM consumption. Surface areas near the antenna
feed point, at high current density locations or at discontinuities should maintain the
M10 maximum segmentation length. Once this is complete, the model can be further
modiﬁed to have some areas considered with P0 and others with MM. Flat areas that
have low current activity away from the feed location are best considered with P0.

Full ray tracing should always be performed. This requires additional computational

114

time but is essential to maintain any accuracy. Coupling between the MM regions and
PO regions should certainly be considered. This is proven through an increase in
accuracy in Hybrid H over Hybrid I. Corrective wedges, as applied in Hybrid V are
unlikely to be applicable to an actual vehicle model. This is because most actual
vehicle models don’t have sharp comers formed by the intersection of large planes like
the test vehicle in this study. The application of the corrective edges in FEKO could,
however be applied in some cases depending on the location of the PO and MM
regions.

Once the PO region is applied, the hybrid simulation should be compared with
the full MM simulation to ensure it maintains the desired level of accuracy. Some
additional modiﬁcation could be necessary if the hybrid simulation accuracy is
unacceptable. The P0 hybrid model should represent a signiﬁcant savings in the RAM
requirements. However, it may also require a larger computation time. It is therefore
recommended that this model be applied to computer systems that have faster

processing and RAM bus speed with less RAM.

5.5 Conclusions

In this thesis, an advanced antenna measurement facility is presented. This
measurement facility allows the three-dimensional far ﬁeld radiation pattern of an
antenna mounted on a vehicle to be measured. With use of this facility, measurements
are performed on many frequency bands ranging from 70 MHz to 1 GHz on a test
vehicle with a quarter wavelength monopole. Simulation is also a very important

means for engineers to make design decisions about the antenna on the vehicle. The

115

 

test vehicle is modeled in FEKO, a MM based software package, and is simulated for
the various bands. Frequencies greater than 450 MHz, however, require too many
computational resources for an accurate simulation. For this reason hybrid methods
are discussed. These hybrid methods are developed for the center frequency of 350
MHz of Band Own. A variety of methods are explored and ultimately Hybrid V yields
the best results. This method features a 64% savings in RAM but a 425% increase in
computation time. Though the entire simulation is not run for other frequency bands,
using Hybrid V allows Band 4-5 (670 MHz to 870 MHz) to run with only 7,860 MB

as opposed to the MM requirement of 112,042 MB. This is a 90% reduction in RAM.

 

Though there will be a longer run time, at least this simulation can now be run with E
the available resources. Hybrid V allows Band GSM (800 to 1000 MHz) to run with

11,360 MB instead of the 178,818 MB required by the full MM. This is also a 90%

reduction in RAM requirements. For faster computers with less available RAM, new

antenna ideas can be explored in simulation without taking the time to build numerous

prototypes and measure the antenna on the automobile. Once a design concept is

functioning in simulation, however, it is necessary to take thorough measurements to

ensure the proper functionality. In this way, simulation and measurement can be

mutually beneﬁcial to antenna development.

116

[ll

[2]

[3]

[4]

[5]
[6]

[7]

[8]

[9]

[10]

[11]

[12]

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