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Analysis and design of a resistively coated windshield slot antenna
Torres, Roberto, Ph.D.
The Ohio State University, 1991
UMI 300 N. Zeeb Rd. Ann Arbor, MI 48106
Analysis and Design of a Resistively Coated Windshield Slot
Antenna
A Dissertation
Presented in Partial Fulfillment of the Requirements for
the Degree Doctor of Philosophy in the
Graduate School of the Ohio State University
by
Roberto Torres, B. S. ,M. S.
*****
The Ohio State University
1991
Dissertation Committee: Approved by: Edward Newman ^ /if Leon Peters Jr. Advisor Department of Electrical Ri-Chee Chou Engineering DEDICATION
To my parents. ACKNOWLEDGEMENT
This dissertation is a project that has taken a good portion of my life to complete. Many people have been involved and, directly or indirectly, helped me in finishing this dissertation. Thanking all and every one of them would be an almost impossible task. My supervisor Eric Walton, with his guidance, patience, and excellent suggestions during this project, helped me to learn the difficult art to engineering. He was an excellent teacher. I hope I was a good student. My academic advisor Edward Newman, with his inquisitive mind, made me realized that things are not always what they seem. He saved me from making catastrophic errors in the theoretical portion of this dissertation. My colleague and friend
John Beaver helped me with hardware and software development as well as with measurements and data gathering. His patience and incredible tolerance to my absentmindedness are greatly appreciated. My family has given me unconditional support in all my projects in life. This one was no exception. A very special mention to Chayo who, with all her love and understanding during the final months of this project, gave me enough energy to finish. VITA
October 12, 1960 ...... Born - Mexico City, Mexico.
1982 ...... B.S.E.E. Instituto Tecnologico y de Estudios Superiores de Monterrey, Monterrey, Mexico.
1986 ...... M.S.E.E. The Ohio State University, Columbus, Ohio.
FIELDS OF STUDY
Major Field: Electrical Engineering
Antenna design ...... Eric Walton
Method of Moments ...... Edward Newman TABLE OF CONTENTS
DEDICATION ...... ii
ACKNOWLEDGEMENT ...... iii
VITA ...... iv
LIST OF TABLES ...... viii
LIST OF FIGURES ...... ix
CHAPTER PAGE
I. Introduction ...... 1
1.1 Automotive antenna history ...... 1
1.2 A ntenna P a ra m e te rs ...... 4
II. Theoretical Background ...... 9
2.1 In tro d u ctio n ...... 9
2.2 Monopole on an infinite ground plane ...... 10
2.3 Annular slot a n te n n a ...... 13
2.4 Conclusion ...... 20 III. Measurement Facility Development...... 21
3.1 In tro d u ctio n ...... 21
3.2 Automobile Pedestal ...... 22
3.3 Local Stations Survey ...... 22
3.4 Test transmitter ...... 25
3.5 Impedance measurements ...... 27
3.6 FM Pattern measurements ...... 29
3.7 AM Pattern measurements ...... 34
3.8 Reliability tests ...... 38
IV. Antenna Development...... 42
4.1 In tro d u ctio n ...... 42
4.2 Fender whip antenna ...... 42
4.3 Aluminum Foil A ntenna ...... 47
4.4 Film antennas ...... 53
4.4.1 W eatherm aster antennas...... 56
4.4.2 Sungate a n t e n n a ...... 61
V. Theoretical Problem ...... 73
5.1 In tro d u ctio n ...... 73
5.2 Region 1 Analysis ...... 76
5.3 Region 2 Analysis ...... 77
5.4 Resistive sheet analysis ...... 81
5.5 Method of Moments Formulation ...... 87
5.6 Numerical results ...... 89
5.7 Conclusion ...... 91
vi VI. Conclusions
BIBLIOGRAPHY LIST OF TABLES
TABLE PAGE
1 Commercial radio station locations ...... 24 LIST OF FIGURES
FIGURE PAGE
1 Monopole on a ground plane and its equivalent. (a)Monopole on ground plane, (b) Equivalent dipole ...... 11
2 Monopole elevation patterns ...... 12
3 Monopole impedance, h = 0.8m ...... 14
4 Annular slot ...... 15
5 Annular slot antenna. Elevation pattern ...... 17
6 Annular slot antenna. Azimuth patterns, (a) Equivalent magnetic loop used, (b) Patterns at 8 8 , 100, and 108 MHz ...... 19
7 Photograph of automobile pedestal ...... 23
8 Input signals from radio stations ...... 26
9 Photograph of portable transmitter and antenna ...... 28
10 Antenna impedance measurement ...... 29
11 Sample Smith Chart from instrumentation software ...... 30
12 FM pattern measurement setup ...... 32
13 Software output. FM Pattern Summary ...... 33
14 Software output. FM Pattern Report ...... 35
15 AM pattern measurement setup ...... 36
16 Software output. AM pattern plot ...... 37
17 Variations of signal strength over time ...... 39
18 Multipath environment ...... 41 19 Fender whip antenna. Impedance measurements (normalized to 50C1). 44 20 Fender whip antenna. AM pattern ...... 45
21 Fender whip antenna. FM patterns ...... 46
22 Aluminum Foil Antennas ...... 48
23 AM Impedance of Alpha antennas ...... 49
24 FM Impedance of Alpha antennas ...... •...... 50
25 Aluminum foil antennas. AM pattern ...... 51
26 Aluminum foil antenna. FM pattern ...... 52
27 Plots of signal level as a function of aspect angle for various elevation angles...... 54
28 Test windshield ...... 55
29 Weathermaster antenna. FM patterns ...... 57
30 Weathermaster antenna. AM impedance ...... 59
31 Weathermaster antenna. FM impedance ...... 60
32 Sungate antennas. AM impedance ...... 62
33 Sungate antennas. FM impedance ...... 63
34 Sungate antennas. AM pattern ...... 64
35 Sungate antennas. Feed position studies ...... 65
36 Sungate antennas. Short circuit studies ...... 67
37 Sungate antennas. Short circuit and position studies ...... 6 8
38 Sungate antennas. Bus bar studies ...... 69
39 Sungate antennas. FM patterns ...... 71
40 Signal Strength comparison ...... 72
41 Theoretical Problem. Basic Geometry...... 74
42 General geometry...... 75
43 Equivalence principle applied to region 1 ...... 76
x 44 Region 1 equivalent geometry with ground plane introduced. . . . 78
45 Equivalence principle applied to region 2 ...... 79
46 Equivalence principle applied to region 2 ...... 80
47 Thin dielectric sheet on aperture ...... 82
48 Thin dielectric slab and equivalent sheet impedance ...... 83
49 Magnetic fields close to . (a) in free space, (b) in front of a ground plane ...... '...... 85
50 Method of moments applied to the impedance sheet ...... 87
51 Antenna geometry used in the model evaluation ...... 90
52 Input impedance of geometry shown in figure 51 using a perfectly conducting plate, a 25f!/□ card, and a 200Q/n card ...... 92
53 Efficiency of geometry shown in figure 5 1 ...... 93
54 Final Candidates ...... 96
xi C H A PT E R I
Introduction
This dissertation describes the experimental design of a new windshield an tenna based on the properties of the resistive films to be installed in future wind shields. * In this introduction we will briefly cover the automotive antenna history. We will see why the most common antenna in the market today is the fender whip antenna, and look at the antenna parameters of interest. Chapter II presents study the theory of the fender whip and we will discuss the theoretical concepts used to design the new windshield antenna. Chapter III presents the construction of the measurement facility. Chapter IV covers in detail the experimental development of the antenna. Finally Chapter V presents the theoretical modeling techniques developed to help study this type of antenna problems.
1.1 Automotive antenna history
The traditional way to solve the automobile antenna problem has been to let a metallic rod or wire act as the radiating element, while the automobile acts as a ground plane. Although the ideal place to locate such antenna is at the center of the roof, most modern automobiles locate such antenna on one of the fenders. The antenna is usually tuned to the FM band, which requires the length of the rod to
1 be approximately 80 cm. This antenna is a very good antenna in the FM band and is difficult to improve upon. The fender whip presents the following advantages:
• The antenna design is very simple. All that is needed is a metal rod and a
coaxial cable to connect it to the radio.
• The antenna coverage is approximately omnidirectional in azimuth. This
is desirable since reception should be independent of the direction of the
received signal.
Among the disadvantages of the fender whip are the following:
• The fender whip is not aerodynamic.
• By today’s standards, the fender whip is not aesthetically appealing.
• It is easily vandalized.
• It is easily damaged in places such as an automatic car wash.
• It requires a hole in the chassis and a separate installation step.
An alternate concept is to imbed the antenna in the window glass of the automobile. This method was used in the 70’s. A pair of wires were run in the middle of the windshield from the bottom to the top. Then the wires ran to the extremes of the windshield forming a letter “T”. This simple idea was initially well received but deep directional pattern nulls were a serious problem and the design was eventually discontinued.
Imprinting wires on the windows has become popular again. Some manufac turers are installing TV antennas on the side windows, and the FM antenna on
2 the rear window. Some of the current designs include a complex pattern of im printed wires near the rear window defogger, sometimes configured as a diversity antenna [ 1 ]. Some other manufacturers, have opted for simpler antenna shapes but have installed preamplifiers to boost the weak signals. These active antennas are being used by some Japanese manufacturers in their TV antenna designs. All these concepts have one idea in common: to substitute the wire protruding from the automobile’s chassis by another wire embedded somewhere in the windows of the automobile. Wire antennas imprinted in the rear window come in all shapes and sizes [2],[3]; however, all of them have complex designs and the extra cost of imprinting the wires on the laminated glass.
An alternate idea is that of using the annular slot antenna concept[4]. The annular slot antenna can be constructed in an automobile by cutting some of the metal in the automobile’s chassis to form a ring shaped gap. The shape of the ring is not critical, but is important that there be no electrical connection between the two areas the ring divides. The idea has been implemented on the roof of a automobile with good results [5]. The metallic roof of the automobile was substituted by a nonconducting material that served as a substrate for the antenna. The antenna was then constructed on top of the substrate.
A new windshield manufacturing technique, which includes depositing a thin metallic layer between two glass sheets, has recently been introduced. Its purpose is to allow the visible part of the spectrum to go through the windshield while blocking infrared and ultraviolet radiation. This film is electrically conducting and as such, it might be used as an antenna.
This dissertation covers the design of a windshield antenna that uses the conducting properties of the metallic film mentioned above. The design approach
3 is experimental and theoretical in nature. Before discussing the antenna design, we will discuss the antenna parameters and their impact on the antenna under development.
1.2 Antenna Parameters
Any antenna has several important parameters [ 6 ] that determine if it is suit able for a particular application. In order to be able to design a good antenna, one has to consider all these parameters. Depending on the application, some of the parameters will be more important than others.
• Input impedance. The input impedance of the antenna is defined as the
ratio of the voltage to the current at its terminals. The resistive component
of the input impedance has two parts: radiation resistance and ohmic loss
resistance. The radiation resistance is used to calculate the amount of power
radiated by the antenna. The ohmic loss resistance is used to calculate the
amount of power lost as heat. These two parts play an important role in the
efficiency of an antenna. It is important to have a good impedance match
between antenna and receiver to minimize losses. It is said that an antenna
is matched to a receiver when its impedance is the complex conjugate of the
impedance of the receiver. This way a maximum energy transfer is achieved.
American automobile radio receivers are typically designed to match to a
fender whip antenna. Any new antenna design should be compatible with
such receivers. Our design goals are to develop an antenna with impedance
similar to the fender whip antenna. • Efficiency. The efficiency of an antenna is a measure of the ability of the
antenna to radiate (or receive) all of the available energy. The efficiency
can be affected by mismatch losses or by conduction and dielectric losses.
Conduction and dielectric losses are difficult to compute and usually are
determined experimentally. Since they depend on the material used to make
the antenna, these losses are not easily reduced once the structure of the
antenna has been set. Mismatch losses can be minimized by adjusting the
input impedance of the antenna until it is matched to the receiver. Fender
whip antennas are usually matched in the FM band. It is very difficult to
match antennas in the AM band because the radiation resistance is very low
and becomes comparable to ohmic losses. For example, a lm dipole operating
at 1MHz has a radiation resistance Rr « 0.00880, while the ohmic losses are
i?ohmic ^ 0*1030, when using a 20AWG wire. These values produce an
efficiency e = 7.9% when the antenna is properly matched. Most of the
energy is wasted as heat. To solve this problem, the radiation resistance has
to be increased. One way to increase the radiation resistance is to increase
the length of the antenna. Since it is not practical to increase the length of
the receiver antennas, the approach has always been to increase the power
of the transmitters and the length of the transmitter antennas, allowing for
smaller and less efficient receivers.
• Radiation pattern. Radiation pattern is defined as the graphical repre
sentation of the radiated power of an antenna as a function of angular space
coordinates. When an antenna is used as a receiving antenna instead of a
radiator, its receiving pattern is the same as the radiation pattern. There
fore the term radiation pattern is used even when the antenna is design as a
5 receiving antenna. The radiation pattern is an important parameter in the
design of an antenna, and it is determined by the particular application. The
automobile antenna should be able to receive a signal from any direction on
the horizon and up to an elevation of more than 20 degrees. Studies made by
Taga [7] show that most of the electromagnetic energy in an urban environ
ment is coming from a range of elevations, having a Gaussian distribution.
The distribution has an average of approximately 20 degrees. It is not de
sirable to receive signal from immediately above (or below), since reception
from those directions will only add to the noise level.
• Directive gain and Directivity. Directive gain is the ratio of the energy
density radiated by the antenna in a particular direction over the energy
density radiated by an isotropic antenna (one that radiates exactly the same
amount of energy in all directions). Directivity is the value of the directive
gain in the direction of its maximum value. These two parameters quantify
the distribution of the radiated energy by the antenna. A high directivity
indicates that most of the energy is going in one particular direction. The
automotive antenna should be omnidirectional in azimuth and have nulls di
rectly above and below. The first requirement tends to push the directivity
down, while the second tends to push it up. The typical fender whip antenna
has a directivity of 1.5, which means that in the direction of maximum radi
ation, the fender whip antenna radiates 1.5 times the energy than a perfectly
isotropic source.
• Gain. The gain of an antenna is defined as its directivity multiplied by its
efficiency. It provides a way of determining how much power the antenna
6 can radiate in the direction of maximum radiation. The higher the efficiency
of an antenna, the closer the gain and the directivity will be.
• Effective aperture. Any electromagnetic wave propagating through space
has certain energy density which is defined as the amount of energy propa
gating per unit area. An antenna is a device used to transform some of that
energy into electrical energy at the terminals of the antenna. If we take the
electrical energy and divide it by the energy density of the electromagnetic
wave incident on the antenna, we obtain the effective aperture of the antenna.
In other words, the effective aperture is the area that contains the electrical
energy available at its terminals if the energy density is the same as the en
ergy density of the incident wave. A higher effective aperture indicates that
the antenna is able to transform more electromagnetic energy into electrical
energy and deliver it to the receiver. Although in some cases the effective
aperture of an antenna is related to its physical area, this is generally not the
case. For example, the fender whip antenna has an effective aperture larger
that its physical area.
• Bandw idth. It is very important that the antenna performance meet certain
minimum specifications throughout the whole frequency range of operation.
In the case of the automotive antenna, there are two bands where the antenna
must perform. In the US the AM band is in the lower part of the spectrum
and covers a 3:1 bandwidth from 540 to 1630 KHz. On the other hand,
the FM band is higher in the spectrum and its bandwidth ratio is 1.23:1
(88MHz-108MHz). These bandwidths are considered large.
7 • Polarization. The AM signals transmitted in the US are vertically polar
ized. The FM signals are horizontally or circularly polarized [ 8 ]. This allows
the fender whip antenna to receive both AM and FM signals.
In this chapter we have briefly discussed the automotive antenna history and the antenna parameters of importance in the design of tin automotive antenna. In the next chapter we will discuss the theoretical principles used in the experimental development of the windshield antenna.
8 C H A PT E R II
Theoretical Background
2.1 Introduction
In this chapter we review the theoretical principles on which the experimental design is based. There are severed low and high frequency techniques that can be used to model antenna designs. However, the modem automobile is a structure that in the FM band is of the order of one wavelength, which makes it difficult to apply any of those techniques to the design of the automotive antenna. High frequency techniques such as PO or GTD are not recommended in this case because after breaking the structure into its components, some of these components would be smaller than A/4, causing these techniques to fail. Low frequency techniques, such as the Method of Moments, would require the structure to be modeled with a high number of modes, specially close to the windshield area, where the location of the feed point is to be determined. In Chapter V we develop a simple model to include the properties of the resistive film into the method of moments. This model can be used for future designs. For the present design, some basic theory is necessary to gain some insight as the experimental design process progresses.
In this chapter we cover the basic theory behind the monopole on an infinite ground plane and the annular slot. The monopole on an infinite ground plane is an approximation to the fender whip antenna. The monopole is the same length as the fender whip, while the ground plane models the automobile chassis. The
9 second antenna we study is the annular slot. This antenna is the basic model for
the resistive windshield antenna. The inner conductor models the windshield and
the outer conductor models the automobile chassis. In section 2.2 we review the
theory for the monopole antenna on an infinite ground plane and in section 2 .3 we
review the theory of the annular slot.
2.2 Monopole on an infinite ground plane
Figure 1 shows a monopole on an infinite ground plane. The conductor has height h above the ground plane and is fed via a transmission line under the plane.
This model is an approximate model for the fender whip antenna. The conductor is the same length as the fender whip and the infinite ground plane is the model for the automobile chassis.
The monopole can be studied using image theory. The ground plane is re moved and the image of the monopole is introduced into the geometry. The result is a dipole of length L = 2h. The fields produced by the dipole are the same as the ones produced by the monopole. The only difference is that the monopole cannot produce any fields for 9 > ir/2. This causes the monopole to have twice the gain and half the impedance of the dipole. The radiation of a dipole has been studied extensively[10]. Assuming a current along the dipole I(z) to be
I(z) = Im sin[fc(| - |*|)] (2.1) where Im is the current at the dipole terminals, k = 2n/X is the wavenumber and z is the distance from the terminals, the far zone electric field is given by
10 Monopole
D ip o le \ Ground plane L = 2h :x
(a) (b)
Figure 1: Monopole on a ground plane and its equivalent. (a)Monopole on ground plane, (b) Equivalent dipole.
11 1 MHz 00 MHz (FM)
ononole
V//////////////////////////////////////////////////////Z 10 dB/div
Figure 2: Monopole elevation patterns.
inlme~ikr cos(k^ cos 8) — cos(fc^) E g = (2 .2 ) 2irr sin 9 where 77 is the impedance of free space and r is the distance from the dipole to the observer. Notice that the electric field does not depend on the azimuth angle
The pattern at 100 MHz is the expected pattern at FM. At both frequencies, the pattern in azimuth is isotropic.
The input impedance of the monopole can be obtained from the dipole also.
The impedance of the monopole is half the impedance of the dipole. Figure 3 shows the input impedance of the monopole calculated using the method of moments.
In this dissertation we use a reference impedance of 50fi. There are several points
12 worth noting here. In the AM band, the input impedance of the monopole is highly capacitive. Since at this frequency band the monopole is electrically very small, there is not much that can be done to change this input characteristic. Any attempts to match the antenna to the receiver are done using a matching network.
The fender whip is expected to have similar input impedance characteristics to this ideal monopole. In the FM band, however, the monopole presents a very different picture. The impedance is close to 5017 and remains in the 2dB circle. More than half of the FM band is inside the 0.5 dB circle.
It is important to remember that these impedance characteristics are calcu lated using an ideal monopole on an infinite ground plane and are calculated at the antenna terminals. Although the AM impedance characteristics are not expected to change dramatically from the model, the FM impedance of the fender whip can be different when we take into consideration that at those frequencies modeling the automobile chassis with an infinite ground plane is less accurate.
2.3 Annular slot antenna
The annular slot antenna shown in Figure 4 is the antenna we use to model the windshield antenna. The center conductor models the film in the windshield and the ground plane models the automobile chassis. As a voltage is applied to the inner conductor, an electric field appears between it and the ground plane.
This electric field radiates into free space and the radiation pattern depends on the distribution of the field along the gap. The effects of the electric field can be modeled using magnetic currents along the gap. This way, we can construct a magnetic loop that radiates essentially the same fields as the annular slot.
13 88.0 MHz
AM band
Normalized to 50 Ohms
Figure 3: Monopole impedance, h = 0.8m.
14 zt
Figure 4: Annular slot.
15 Again, the two frequency bands of interest present different problems. In the
AM band, the annular slot is electrically very small and we can assume that the
magnetic current is constant along its path. In this case, it is straight forward to
find the electric fields radiated from the loop [6]. The electric fields (Eq) radiated
by the loop are given by
kaM e~ikr Eg = ----- Ji(Jfeasin0) (2.3) Z T where a is the radius of the annular slot and M is the magnetic current magnitude.
Notice that the field does not depend on The pattern in azimuth is omnidi rectional. Figure 5 shows an elevation pattern from a magnetic loop with radius
a = 0.7m, at a frequency / = 1.0MHz. Notice that the pattern is essentially the same as the one from the monopole on the ground plane.
In the FM band, we can no longer assume that the magnetic currents are constant along the loop. A common approach to the problem is to assume a cosinusoidal variation along the loop [9]. In this case, the electric fields are given by
* - + i t
°° An + (2.4) (jka)2 + (2n - l)2
• T)l OO Al _ AI
( o° B'( u - B'
(2'5)
{jkaf ± -p2 (2.6)
16 1.0 MHz
10 dB/div
Figure 5: Annular slot antenna. Elevation pattern.
17 where p is any integer. For brevity, the following notation has been used:
An = J2tAz<) [cos ® cos ^ sin(2mu) + sin 8 cos(2nio)]
Bn = J2n(z>) [— cos 0 cos sin(2»tu) + sin 8 cos(2nto)]
Cn = J2n-l(^,) [— cos 0 cos ^ cos(2n — l)u>
+ sin 8 sin(2n — l)u> ]
Dn = J2n—l{z') [c°s 0 cos 0 c°s(2n — l)u>
4- sin 8 sin(2n — l)iu ]
A' = J2n(z ')sin
Bl — J2n-l{z<) sin<^c°s(2n — l)u;
= ka\Jl — sin2 8 sin2 w = arctan( — tan 8 cos Notice that the field distribution is considerably more complicated when the annular slot antenna is large enough that the magnetic currents along the gap cannot be considered constant anymore. In this case, we can no longer expect omnidirectional patterns in azimuth. Figure 6 shows the azimuth pattern for a magnetic loop of radius a = 0.7m, at three different frequencies: 88, 100, 108 MHz. Notice that as the frequency increases, the pattern becomes less and less omnidirectional. Notice that the minimum is less than 10 dB below the maximum. 18 88 MHz 100 MHz 108 MHz Feed p o in t (a) 10 dB/DIV Figure 6: Annular slot antenna. Azimuth patterns, (a) Equivalent magnetic loop used, (b) Patterns at 88, 100, and 108 MHz. 19 2.4 Conclusion In this chapter we covered the theoretical concepts associated with the monopole on an infinite ground plane and the annular slot antenna. By providing a theoreti cal background, these concepts help us understand better the experimental results. We expect the fender whip antenna to have an omnidirectional pattern in azimuth in both AM and FM bands. In the case of the windshield antenna, we expect it to have an omnidirectional pattern in azimuth in the AM band. In the FM band, the difference between the maximum and the minimum might be close to 10 dB. In the next chapter we cover the development of the measuring facility that is used to perform the experimental design of the windshield antenna. 20 CHAPTER III Measurement Facility Development 3.1 Introduction In this chapter we describe the development of the measurement facility built for the purpose of developing the automotive windshield antenna. The facility can be used to measure impedance characteristics and directivity patterns. To measure impedance, it is necessary to have instrumentation and data transfer. To measure patterns, however, it is necessary to rotate the antenna under development 360 degrees. Since the automobile is an integral part of the antenna, it is necessary to rotate the entire automobile. The measurement facility provides the following: • Ability to rotate the automobile 360 degrees. • Test signals transmitted to the antenna with enough power and at the ap propriate frequencies. • Instrumentation to measure signal strength and impedance. A rotating pedestal was obtained to rotate the automobile. This pedestal and its controls are the topic of section 3.2. The input signals are provided by commercial radio stations and a portable test transmitter used on site and are covered in sections 3.3 and 3.4 The methodology and instrumentation necessary to take impedance measurements are discussed in section 3.5. The methodology and 21 instrumentation necessary to take patterns are discussed in sections 3.7 and 3.6. Once the measurement facility was complete, some basic questions needed to be addressed since commercial radio stations are used in the measuring process. Are the signal strengths constant over time? Are there any multipath problems in the measurement facility? These questions are addressed in section 3.8. 3.2 Automobile Pedestal Pattern measurements require the measurement of the signal strength of the antenna under development in all the directions of interest. Since the automobile is an integral part of the antenna, the measurement facility must rotate the auto mobile 360 degrees. Figure 7 is a photograph of the pedestal with the automobile mounted on top. The automobile pedestal used in the project was originally designed for the precision rotation of large antennas and is capable of supporting 20,000 pounds and rotating such a weight to a precise angle. The automobile used in the exper iments is a 1982 Chevrolet Cavalier with no engine. The automobile is attached to the pedestal via two railroad ties that support the automobile and provide the necessary stability to the system. The pedestal is located in the northwest corner of the parking lot at the ElectroScience Laboratory in an area not normally used to park automobiles. 3.3 Local Stations Survey The input signals used in the measurement facility are the local commercial radio stations and a portable test transmitter. We discuss the local radio stations in this section and the transmitter in section 3.4. Table 1 shows the location of 22 Figure 7: Photograph of automobile pedestal. 23 Table 1: Commercial radio station locations. Station id. Latitude (N) Longitude (W) Angle ESL 39 59 56 83 02 45 N/A WOSU 89.7MHz 40 00 59 83 01 09 49 WCBE 90.5MHz 39 57 48 83 00 17 139 WOOL 92.3MHz 39 58 16 83 01 40 154 WSNY 94.7MHz 39 58 15 83 01 39 154 WLVQ 96.3MHz 39 58 16 83 01 40 154 WBNS 97.1MHz 39 58 16 83 01 40 154 WNCI 97.9MHz 39 58 16 83 00 10 132 WXMX 98.9MHz 39 58 16 83 01 40 154 WMGG 99.7MHz 39 58 16 83 01 40 154 the radio transmitters in the central Ohio area that were used in this study. The first column gives the station identification, second and third columns indicate the latitude and longitude in degrees, minutes, and seconds of the transmitter tower location. The last column indicates the angle of the received signal with respect to North. The row marked ESL corresponds to the location of the measurement facility. In the AM band, the directional pattern of the antenna tends to be inherently omnidirectional because the antenna/automobile system is much smaller than the signal wavelength (wavelength is approximately 300 m). The directional pattern of the antenna in the FM band, however, may be quite variable. The wavelength in this case is 3 meters, roughly the size of the automobile. This means that the 24 automobile itself tends to be resonant and that the pattern may have strong lobes and deep nulls if the design is not carefully done. Also in the FM band, there are more reflections from buildings etc., and thus there is more of a multipath problem. As can be seen in Table 1 and-Figure 8 most of the FM signals arrive from the southeast. Figure 8 shows the potential problems that using such signals can cause. Notice that the signal from WOSU is blocked by the ESL building. Any signal received from that source is diffracted by the building. This source, then, is unreliable for measurement of patterns. Six signals come from the same transmitter tower at an angle of 154 degrees. The only difference between these signals are the frequencies of operation and power. Any differences in the patterns for these frequencies can be used to determine multipath problems in the measurement facility. 3.4 Test transmitter In addition to the signals from commercial radio stations, a portable trans mitter was used. A ground plane antenna tuned to 100 MHz is connected to the output of the transmitter. The location of the portable transmitter antenna should satisfy the following requirements: • The antenna must be far enough from the automobile to be considered as being far away from it. The minimum distance to achieve this is given by 2D2/A where D is the maximum dimension of the automobile. In our case this distance is approximately 15 m. 25 ESL building WOSU (89.7) Automobile WCOL (92.3) WNCI (97.9) WSNY (94.7) WLVQ (96.3) WBNS (97.1 HXMX (98.9) WMGG (99.7) WCBE (90.5) Figure 8: Input signals from radio stations. 26 • The antenna must close enough to have a clear signal in the instrumentation. This distance depends on the power of the transmitter. In our case this distance is approximately 24.4 m. • The transmitter must be located where no reflections from any nearby objects reach the receiver. This transmitter cannot generate low frequencies in the AM band. It is used to generate FM signals only. The typical signal strength is about 30 dB below the signal strength of the commercial stations. However, the signal is also about 30 dB above the noise level, providing a good signal-to-noise ratio. 3.5 Impedance measurements Having completed the description of the components of the measurement fa cility, we proceed now to discuss the different measurement setups used to mea sure the antenna parameters. We begin with the impedance measurements. The impedance measurement setup is shown in Figure 10. The antenna, installed on the automobile, is connected to the network analyzer through a directional coupler. The network analyzer provides a reference signal, which is applied to the antenna through the directional coupler. At the same time, a sample of the same signal is applied back to the network analyzer reference channel (channel R). Any reflected energy from the antenna goes to channel A. The system then is able to determine the impedance of the antenna. The data is transmitted to a computer, which in turn processes and stores it for future analysis. In this case no external sources are used. 27 Figure 9: Photograph of portable transmitter and antenna. 28 Network Analizer oc OUT RET A B □ lo VAX QQQO Computer proc*»»ing Antanna V Directional Coupler A ttenuator CZZh Antenna Impedance Measurement Figure 10: Antenna impedance measurement. The data gathered by the computer is then processed and a final impedance plot is obtained. A sample of the processed data is shown in Figure 11. One of the most popular ways to represent an impedance is in the form of a Smith chart, such as the one shown in Figure 11. 3.0 FM Pattern measurements The general setup to measure the radiation pattern of the antenna is shown on Figure 12. The antenna is connected to a spectrum analyzer, which in turn is connected to a computer using an IEEE-488 interface. The computer will store 29 Frequency: 1: 86.0 MHz 2: 107.9 MHz Normalized to 50 Ohms alpha-1. No gap. Line ** 29 in. 2nd run, after removing extra items. Input file: z0830i.plz Output file: z0830i.tda Figure 11: Sample Smith Chart from instrumentation software. the data for future analysis. The automobile is mounted on the rotator. The input signal is provided by the commercial radio stations in the Columbus area. As the automobile rotates, the spectrum analyzer measures the signal strength over the FM band and the computer saves the data for further analysis. Knowing the locations of the radio stations, it is possible to determine the relative direction of arrival with respect to the automobile. The amount of data gathered on each run includes one full frequency scan per angle measured. In a typical run, the band is measured every three degrees. At 481 points per scan, we have 57,720 points per run. It is important to compile all the information and show it in a way suitable for study. Figures 13 and 14 show the two basic outputs of the instrumentation software. Figure 13 shows a summary of the gathered data. The information in this figure serves to show any possible errors in the measurement. The time vs angle graph located on the left top serves to calibrate the actual angle information with the one calculated by the computer. The straight line is the function calculated by the computer, while the small circles indicate the actual measurements. These two curves should agree to have a reliable angle measurement. The equations for the two curves are shown to the right of the figure. The lower part of the figure shows a typical output presentation from the spectrum analyzer. The two text lines are taken from the instrument at the time the measurements were taken. The curves shown are the maximum and minimum indicated during the measurement. It is possible to see the variation of signal strength from this figure. The plot is calibrated in dBm. Figure 14 shows the patterns generated by the instrumentation software. The data computer collects the information for each frequency of interest and plots the strength of the signal with respect to angle of incidence relative to the automobile. 31 mW/MMM/W/MM/to R otator oO 0569B Spoctrua Anallxar Rotator Control Antenna Pattern Measurement Figure 12: FM pattern measurement setup. 32 SUMMARY Fila: plll6a.raw ( 11-16-1990 13:12:07) w-1 w/ cabla at 102M Hz Raaolutlon “ 3 dagcaas Resolution >3.00 dagcaas Dalta - 1.93 aaconds Hin pH Measurement curva: Tina - 0.642 angla + 0.00 aaconds Calculatad curva: O Tine - 0.640 angla + -0.36 saconds 0 ieo 360 ANGLE CTR 98.0 MHz SEAN 2 MHz/ RES BN 100 kHz VF .01 10 d B/REF -10 dBm 10 dB/REF ATTEN 0 dB 8HP AUTO — 4- . L J__ I 1 Figure 13: Software output. FM Pattern Summary. 33 The location of each radio station is used to adjust the plots so they all show the same orientation. The frequency is indicated in each plot together with the maximum power. This reference is the same as the maximum registered in the summary figure. The last two polar plots correspond to the portable transmitter (102MHz) and noise level (103MHz). Notice how the power received from the portable transmitter is considerably less than the average radio station signal; however, it is still 34 dB above the noise level. 3.7 AM Pattern measurements AM signals are found in a low frequency band from 0.56 to 1.63 MHz. Since the spectrum analyzer used in the FM pattern experiments cannot be used at such low frequencies, a new method of obtaining the patterns was designed. Figure 15 shows the AM pattern measurement setup. This setup is very similar to the FM pattern measurement setup. The automobile pedestal and rotator control are the same. There is no portable transmitter in this case. The method used to read the signal strength is different. Instead of connecting the spectrum analyzer to the antenna, a commercial radio is connected. The automatic gain control (AGC) voltage in the radio is a function of the signal strength at the input of the receiver. By measuring the AGC voltage of the radio and using a calibration table to translate the voltage into signal strength, we are able to process the data and obtain patterns. This technique has the advantage that the input impedance of the radio is typical of that of most manufacturer installed automotive radios in use today. This is particularly important in the AM band because most automotive radios have compensation for the highly capacitive impedance of the whip antenna, while most radio frequency instruments are designed to match the coaxial cable 34 File: pi116a.raw, ( 11-16-1990 13:12:07) CM1: w-1 w/ cable at 102M Hz 09.7 MHz (ref - -19 dB) 90.5 MHz (ref - -27 dB) 9 2 .3 MHz ( r e f - -1 5 dB) 94.7 MHz (ref - -17 dB) 96.3 MHz (ref - -17 dB) 97.9 MHz (ref - -17 dB) 90.9 MHz (ref - -29 dB) 9 9 .7 MHz ( r e f - -1 5 dB) CAR FRONT t s 102.0 MHz (ref » -40 dB) 103.0 MHz (ref - -74 dB) Figure 14: Software output. FM Pattern Report. 35 V7?, R otator xoc HOC to (SB Rotator Control AM Pattern Measurement Figure 15: AM pattern measurement setup. impedance of 50fl or 75fi. Comparison of signal levels provided by different types of antennas is thus very realistic. The main limitation of this system is that only one frequency can be measured at a time. This makes this method much slower than the FM measurements, where the entire band was measured in one scan. Figure 16 shows a sample of an AM pattern. It is important to notice that the maximum power reference shown on the output is the power relative to the maximum power the radio is able to receive before saturation. This is not an absolute reference as in the FM patterns. Two signals can be compared against each other using this reference, but there is no absolute reference value used in this method. 36 UvwUm • J/XX Fender whip antenna. AM p a t t e r n 10 d B /D IV Max = -10.00 dB Figure 16: Software output. AM pattern plot. 37 3.8 Reliability tests Since the measurement facility is located outdoors, it is subject to interference and weather conditions. Before taking any measurements, it is reasonable to ask if the measurements are reliable. To address this problem, a series of tests were performed in the facility. These tests covered the following problems: • Time deviations. If the power from the commercial radio stations is not constant over time, it is not possible to take any reliable measurements with out the use of a reference antenna. A reference antenna connected during measurements unnecessarily complicates the process. • Multipath. If the antenna is not receiving a single input signal, a significant effort is required to determine patterns accurately. To determine if the commercial radio stations transmit a signal with constant power, the equipment was tuned to one station and the signal level was measured during a 5 minute period, the average time it takes to measure one pattern, at a rate of one sample every few seconds. The results are shown in Figure 17. It can be seen from the figure that the variation in signal power is ±0.5 dB, well within margin of error. This measurement was repeated on different dates and the power received from the stations in the various measurements was the same. This important feature was used to compare measurements taken on different dates. Multipath problems can arise when the signal from the commercial station reflects from a large object. The reflection from such a large object can reach the measurement facility simultaneously with the original signal. The two signals usually are not in phase and when they combine to form the total received signed, they add constructively in some cases and destructively in others. The result is 38 Number of Samples iue 7 Vrain fsga teghoe time. over strength signal of Variations 17: Figure 20 10 - 5 1 -- 5 2 -- 5 — - - inl tegh (dB) Strength Signal -22 39 7"S[7A -21 -20 a pattern that may have deep nulls in it. Figure 18 shows a possible scenario where multipath is involved and a typical pattern that results from the multipath environment. This null is not related to the antenna characteristics. It is difficult to find a location where there are no multipath problems. In an urban area there are many large structures such as buildings, water tanks, etc., that provide a very complex multipath environment. Commercial radio transmitters usually are located within large urban areas and the signals that reach the rural areas are relatively free from multipath interference. Fortunately, when there are several commercial signals present at the measurement facility, it is possible to separate the multipath problems from the antenna patterns. The multipath nulls are very frequency dependent. If the pattern shows a null or a characteristic that is common in all frequencies, then we can Bafely assume that such characteristic is part of the antenna pattern. However, if a null appears in only one or two of the frequencies under analysis, then one may suspect that such nulls are part of the multipath environment. The problem is not easy to solve, the nulls might be due to frequency dependency of the pattern. It is important to note that the direction of the nulls is independent of the direction of the main or secondary signals. The simplest way to eliminate the multipath problem is to locate and test the transmitter where there are no reflections that reach the antenna under study. The portable transmitter discussed in section 3.4 is used for this purpose. Locating the transmitter close enough to the antenna to minimize any possible reflections, but in the far field where R > 2D2/A, and locating the antenna on the ground to avoid any reflection from the ground, it is possible to minimize the multipath problem. The commercial radio stations will be used to compare measurements taken at different times. 40 B u ild in g Reflected signal Automobile from building Typical multipath effect Figure 18: Multipath environment. 41 C H A P T E R IV Antenna Development. 4.1 Introduction In this chapter we describe the experimental design of the automotive wind shield antenna. In Chapter II we covered the basic theoretical principles on which the experimental design is based. In Chapter III we covered the experimental fa cility developed to help in the design process. The first step in the design process is to measure the characteristics of the commercial fender whip antenna. Both impedance and patterns are measured and the results are compared to the theo retical results shown in Chapter II. The second step is to test different antenna configurations using aluminum foil to simulate the resistive film. Again, impedance and pattern measurements are taken as a function of antenna under test (AUT) parameters. The last step is to test the concepts developed on the resistive film. Several test windshields were built for the purpose of measuring realistic antenna characteristics. Two different film types are tested in the measurement facility, Weathermaster and Sungate. 4.2 Fender whip antenna As explained in the introduction, the most common automobile radio antenna is the fender whip antenna. When it is matched in the FM band, this antenna retains good reception in the AM band. In this section we will present and analyze 42 the experimental results obtained when measuring the fender whip antenna in the measurement facility described in Chapter III. Figure 19 shows the impedance characteristics of the fender whip in the AM and FM bands. The impedance in the AM band is highly capacitive. This com pares very well with the theoretical model studied in Chapter II. In the FM band the antenna is fairly well matched to a 50fl load. The impedance is almost com pletely inside the 0.4 dB loss circle. The typical automobile radio input circuitry is designed to match to these antenna impedance characteristics. It is important that the windshield antenna have similar impedance characteristics. This way the windshield antenna will be compatible with the large majority of automobile radios available in the market today. Figure 20 shows a typical AM directional pattern. As expected, this pattern is practically omnidirectional. Practically all the patterns taken in the AM band were omnidirectional. Since the shape of the pattern satisfies the requirements in all cases, signal strength becomes the most important parameter to consider. Figure 21 shows a set of patterns taken in the FM band. The first nine frequencies correspond to commercial radio stations in the Central Ohio area, the tenth (102 MHz) corresponds to the portable transmitter used in the facility, and the last frequency (103 MHz) corresponds to a part of the band with no signal, therefore reflecting the noise level of that particular measurement. The pattern obtained from the portable transmitter is nearly omnidirectional as expected. The patterns obtained from the radio stations 6how the multipath effects present in the measuring facility. The average signal-to-noise ratio is 56.3 dB. 43 Normalized to 50 Ohms Figure 19: Fender whip antenna. Impedance measurements (normalized to 50fi). 44 A Fender whip antenna. AM pattern 10 dB/DIV Max = -10.00 dB Figure 20: Fender whip antenna. AM pattern. 45 File: plll6a.raw, ( 11-16-1990 13:12:07) CM1: w-1 w/ cable at 102M Hz 89.7 MHz (ref - -19 dB) 90.5 MHz (ref - -27 dB) 92.3 MHz (ref - -15 dB) 94.7 MHz (ref - -17 dB) 96.3 MHz (ref - -17 dB) 97.1 MHz (ref - -14 dB) 97.9 MHz (ref - -17 dB) 98.9 MHz (ref - -29 dB) 99.7 MHz (ref - -15 dB) CAR FRONT 102.0 MHz (ref - -40 dB) 103.0 MHz (ref - -74 dB) Figure 21: Fender whip antenna. FM patterns. 46 4.3 Aluminum Foil Antenna In this section we will study different antennas built using aluminum foil. Before studying the prototype film antenna, it is important to determine first the suitability of the design. Using aluminum foil to simulate the resistive film is a good approximation provided the resistive film has low enough resistivity. The aluminum foil antenna is expected to be slightly more efficient than the film antenna. As it will be seen in future sections, the use of the aluminum foil i6 a good approximation to the resistive film antenna. Figure 22 shows different antennas that were measured in the experimental facility. The most attractive of all the designs is the antenna named alpha-2. The antenna is simple and the feeding is at the bottom center, very close to the radio. Figure 23 shows the input impedance of a typical alpha antenna in the AM band. Notice that the antenna presents a highly capacitive load just as the fender whip does. Figure 24 shows the input impedance of different alpha antennas in the FM band. In this case, the situation is slightly different. Most of the antennas remain close to the 2dB loss circle. One of the exceptions is alpha-4, with half the band outside the 2dB loss circle. Figure 25 shows the AM band pattern for the alpha-2 antenna. Notice that the antenna is practically omnidirectional, as expected. Figure 26 shows the FM patterns for the alpha-2 antenna. Notice that the pattern has no deep nulls and the minimum is just 5dB below the maximum. The average signal-to-noise ratio is 58.6 dB which is more than 2 dB better than the fender whip antenna. This indicates that, although the signal strength is slightly lower than that from the fender whip, the signal quality is better due to the lower noise level. 47 Alpha antennas Car chasis• p Aluminum f o i l Alpha-1 Alpha-4 Alpha-2 Alpha-5 3 =9=3 Alpha-3 A lpha-6 Figure 22: Aluminum Foil Antennas. 48 50 Ohms 7.96 pH 25 Ohms 100 Ohms 3.98 pH 15.9 pH 200 Ohms 10 Ohms 31.8 pH 1.59 #»H A, 500 Ohms 79.6 pH -500 Ohms 318 pF -10 Ohms 15.9 nF 200 Ohms 796. nF -25 Ohms Ohms 6.37 nF 1.59 pF -50 Ohms 3.18 nF Normalized to 50 Ohms Figure 23: AM Impedance of Alpha antennas. 49 50 Ohms 796 nH 25 Ohma 100 Ohma 398 nB 1.59 >iB 500 Ohma 7.96 fiB Alpha-3 25 Ohma 637 pF -50 Ohma 318 pF Hormallzad to 50 Ohma Figure 24: FM Impedance of Alpha antennas. 50 p0507 foil am 3.pll Antenna Pattern measurements. Tin foil antenna antenna. AM band. 10 dB/DIV Max = -50.00 dB Figure 25: Aluminum foil antennas. AM pattern. 51 File: p0924g.raw, < 09-24-1990 16:50:01) CM1: Alpha-2. No shorts. Cable-PW. 1st run. 89.7 MHz (ref - -21 dB) 90.5 MHz (ref - -29 dB) 92.3 MHz (ref - -20 dB) CAR FRONT Figure 26: Aluminum foil antenna. FM pattern. 52 Since most of the commercial radio signals arrive from an angle between zero and 20 degrees from the horizon, it is important to take measurements where the elevation of the transmitter can be changed. Figure 27 shows a comparison be tween the fender whip antenna and the aluminum foil antenna alpha-1 at different elevations. Notice that there are two nulls in the alpha-1 pattern. These nulls still exist at zero degrees, even though there are many measurements that show that there are no reed nulls there. The only remaining explanation is that these nulls are caused by the interaction between the direct path and reflections from the ground. 4.4 Film antennas In this section we will study the film antennas that resulted from the designs using the aluminum foil. We will begin by measuring the resistivity of the avail able samples to determine the conducting properties of the films. These properties are important from the point of view that the lower the resistivity of the film, the more accurate the modeling with aluminum foil would be. Following a similar procedure to that for the aluminum foil antennas, we will consider different con figurations. We will measure the impedance characteristics and the patterns for all the configurations. Once we find a suitable design we will proceed to optimize the design. Several test windshields were studied to design the film antenna. Figure 28 shows a typical test windshield. The windshield approximates the final design windshield as much as possible. The film, which usually covers all the glass sur face, is deleted at the edges of the windshield to provide the needed gap for the 53 Fender whip A lp h a -1 Figure 27: Plots of signal level as a function of aspect angle for various elevation angles. 54 Deleted film R esistive film ^ Connecting tabs Figure 28: Test windshield. annular slot. Several tabs are connected from the film to the outside of the wind shield. These connections are located along the border of the windshield at regular intervals. There are two different windshield types that are being considered: Sun- gate and Weathermaster. The Sungate windshield is designed to filter undesirable IR solar radiation. The Weathermaster windshield is an electrically heated wind shield (EHW). This presents the problem of isolating the antenna from the heater system. This dissertation deals with the design of a general antenna for the Sun gate windshield. Although this general design will work for the Weathermaster antennas, a special DC decoupling circuit will have to be designed in that case. 55 4.4.1 Weathermaster antennas. The first film antenna studied is the Weathermaster windshield. This film has a higher resistivity than the Sungate and is expected to have more losses than either the Sungate or the aluminum foil antennas. Since the film in this windshield is connected to external DC sources, a separate coupling network will be needed. This section covers the antenna characteristics only. The coupling needs are addressed in preliminary tests only. Studies with the aluminum foil antenna show that one of the best antenna candidates is the antenna with the feed at the bottom center of the windshield. This configuration is the one used in the Weathermaster experiments. Figure 29 shows the patterns obtained from the Weathermaster windshield with the feed at the bottom center. The first nine frequencies shown correspond to commercial FM stations. The frequency 102 MHz corresponds to the portable transmitter, and 103 MHz corresponds to the noise level. Notice that the pattern due to the test transmitter is not very different from the pattern using the aluminum foil antenna. Also notice that the signal strength has gone down a few dB. The average signal-to-noise ratio in this case is 58.3 dB, about 0.3 dB worse than the aluminum foil antenna. This signal-to-noise ratio is 2 dB better than the one from the fender whip antenna. The pattern has narrowed slightly. The fender whip and the aluminum foil antenna showed a maximum to minimum ratio of about 5 db, the Weathermaster antenna shows a maximum to minimum ratio of 10 dB. Since the typical radio has a dynamic range of more than 50 dB, it has the capacity to compensate for such maximum to minimum ratios. Figure 30 shows the impedance of the Weathermaster antenna in the AM band. There are no surprises here. The input impedance is highly capacitive 56 File: pll29a.raw, ( 11-29-1990 14:15:49) CM1: pi-1 at 102M Hz 69.7 KHz (ref - -23 dB) 90.5 HHz (ref - -32 dB) 92.3 MHz (ref • -21 dB) 94.7 HHz (ref > -20 dB) 96.3 HHz (ref - -23 dB) 97.1 HHz (ref - -21 dB) 97.9 HHz (ref - -25 dB) 96.9 HHz (ref - -35 dB) 99.7 HHz (ref - -21 dB) CAR FRONT 102.0 HHz (ref - -46 dB) 103.0 HHz (ref - -61 dB) Figure 29: Weathermaster antenna. FM patterns. 57 through the entire band. This input impedance is essentially the same as the one measured from the aluminum foil antenna. Figure 31 shows the input impedance of the Weathermaster in the FM band. There are two curves in the figure. The one labeled direct connection corresponds to the input impedance of the antenna when the feed is directly connected to the film at the center bottom of the windshield. Notice that the impedance is inductive and all the curve is inside the 2dB loss circle. This is a good enough match, representing a loss of about 2 dB. By attaching a small conducting strip to the outside wall of the windshield, we can form a capacitor between it and the film inside the windshield. By connecting the feed to the strip instead of the film, we are effectively connecting a capacitor in series with the antenna. The size of the strip determines the capacitance between the film and the feed. Since the antenna is slightly inductive, a capacitor in series can be used to compensate for the inductance and match the antenna. The curve denoted “capacitive coupling” in Figure 31 shows the input impedance of the Weathermaster antenna when using a small conducting strip on the outside of the windshield. The strip is 14.5cm long by 2.0cm wide. By using this capacitive coupling, the input impedance is now inside the 0.4 dB loss circle. Capacitive coupling is a promising technique for this type of windshield. Since there is no direct connection to the film, the DC power can be connected without affecting the input circuitry of the radio. However, this would affect the patterns and input impedance of the antenna. The DC connections appear as short circuits at higher frequencies. In section 4.4.2 we study the effects of different short circuit configurations on the patterns of the windshield antennas. 58 Normalized to 50 Ohms Figure 30: Weathermaster antenna. AM impedance. 59 Frequency: 1: 86.0 MHz 2: 107.9 MHz Direct connection* Capacitive coupling Normalized to 50 Ohma Figure 31: Weathermaster antenna. FM impedance. 60 4.4.2 Sungate antenna Figures 32 and 33 show the input impedance of the Sungate antenna for different configurations. The impedance shown is the impedance at the feed point of the antenna and not at the end of the transmission line as was the case for the earlier impedance measurements. The reason for this is that the input at the feed is important to determine the type of matching to use in the antenna. Notice that in the AM band all the configurations present a highly capacitive load. This input impedance characteristic is shared by the fender whip. As will be seen, the transmission line losses will be of primary importance in this case. Figure 33 shows the input impedance of the Sungate windshield antenna using direct connection at two different feed points. Notice that the impedance shifts and the reactance changes from slightly inductive to slightly capacitive. Both curves remain inside the 2dB loss circle. The AM patterns obtained were all similar in magnitude and shape. Figure 34 shows a typical AM pattern obtained from the Sungate antenna together with the pattern from the fender whip antenna. For all practical purposes, both patterns are omnidirectional in azimuth. A high impedance (1250) transmission line was used to limit the coupling losses of the Sungate antenna in this band. The pattern for the Sungate is within 3 dB of that for the fender whip antenna. The FM patterns are more sensitive to changes in the antenna configuration than the AM patterns. Several studies were made to determine the best configu ration. Figure 35 shows the effects of changing the feed point on the lower edge of the windshield. There are two patterns shown for each windshield. The first one is the pattern as measured using the portable transmitter. The second one is a typ ical pattern measured using a commercial radio station. The first one is useful to 61 Frequency: 1: 0.6 MHz 2: 1 .6 MHz Normalized to 50 Ohms Figure 32: Sungate antennas. AM impedance. 62 Fraquancia*: 1 - 86.0 KHz 2 - 106.0 KHz Faad point B Nozaalizad to 50 Ohaa Figure 33: Sungate antennas. FM impedance. determine the pattern characteristics and the second one is useful to determine the overall power received by the antenna. Remember that the portable transmitter is not reliable in terms of providing constant power between measurements, while the commercial radio stations provide constant power that can be used as reference. Notice that the pattern is relatively insensitive to changes in feed location. The maximum point shifts together with the feed point. As the feed point gets closer to the corner, the reception from the back of the vehicle is reduced by about 5 dB. Notice that the general reception of the commercial signal i6 slightly reduced as the feed point moves off center. Figure 36 shows the effects of a series of shorts connected to the antenna. These configurations can be used as models for the Weathermaster antenna and its coupling to the DC power bus. A short circuit is connected between the antenna 63 test.pll test2.pll HLR antenna. Fender whip antenna. AM pattern AM pattern dB/DIV Max = -10.00 dB Figure 34: Sungate antennas. AM pattern. 64 LOCAL ANTENNA PATTERN STATION Ground c o n n e c tio n 92.3 MHz ( r e f - -12 dB) Ground c o n n e c tio n 9 2 .3 MHz ( r e f » -12 dB) G round c o n n e c tio n 92.3 MHz (ref -15 dB) Ground c o n n e c tio n 92.3 MHz (ref » -15 dB) Figure 35: Sungate antennas. Feed position studies. 65 film and the automobile chassis. The location of the shorts is changed a6 indicated in the figure. The feed point is not changed. Notice that the pattern suffers when ' the short is located on top of the windshield. A6 the shorts are connected lower around the edge, the pattern improves. The last two cases 6how two excellent patterns. Notice that the power received from the commercial radio station has gone down about 7 dB when compared to the power received when there i6 no short circuit connected to the antenna, as shown in Figure 35 Figure 37 shows another effect of short circuits connected between the antenna and the automobile chassis. In this case, however, only one short circuit was connected and its location was moved along the upper edge of the windshield. The feed point was moved accordingly to maintain the two gap segments that ran from the feed point to the short circuit of equal length. Notice that the pattern presents deeper nulls in the last two cases. Although the power received is larger than the one in the last figure, the presence of the short circuit affects the reception significantly. The final study is shown in Figure 38. A copper tape was connected to all the tabs in the lower edge of the windshield making an electrical connection among all these points. The feed was changed from the center to the corner and the effects of these changes recorded. The basic antenna with the feed at the center of the windshield is included as reference. Notice that the patterns are not isotropic and the power received is reduced by 8dB. Figure 39 shows the FM patterns obtained from a Sungate windshield an tenna using the capacitive coupling described in section 4.4.1 and a 0.8 m long 125Q transmission line. This is the result of a compromise between the AM and the FM reception problems. At low frequencies, 6uch as the ones in the AM band, 66 ANTENNA LOCAL PATTERN STATION Ground c o n n e c tio n G round , c o n n e c tio n 9 2 .3 HHt ( r e f - -19 dB) Ground connections Ground c o n n e c tio n 92.3 MHz ( r e f - -20 dB) Ground connections G round ^ c o n n e c tio n 9 2 .3 MHz ( r e f - -1 9 dB) Ground connections Ground r < c o n n e c tio n 9 2 .3 MHz ( r e f - -1 9 dB) Figure 36: Sungate antennas. Short circuit studies. 67 ANTENNA PATTERN LOCAL STATION Ground c o n n e c tio n G round . c o n n e c tio n „ Ground c o n n e c tio n G round . c o n n e c tio n Ground c o n n e c tio n G round . c o n n e c tio n Ground c o n n e c tio n Ground . c o n n e c tio n 9 2 .3 MHz ( r e f - -11 dB) Figure 37: Sungate antennas. Short circuit and position studies. 68 LOCAL ANTENNA PATTERN STATION Ground c o n n e c tio n 9 2 .3 MHz ( r e f « -12 dB) Conducting a t r i p Ground c o n n e c tio n 92.3 MHz (ref - -20 dB) Ground c o n n e c tio n 92.3 MHz (ref - -22 dB) Ground c o n n e c tio n 9 2 .3 MHz ( r e f - -23 dB) Figure 38: Sungate antennas. Bus bar studies. 69 short transmission lines behave less than transmission lines and more like capac itors in parallel. If the antenna is capacitive, as in our case, the signal at the input of the radio is the result of a voltage division between the antenna and the transmission line capacitances. The loss due to this voltage division can be min imized by reducing the capacitance of the transmission line, therefore increasing its impedance. On the other hand, a higher transmission line impedance causes impedance mismatches at the FM band. In our case, those mismatch losses are approximately 2 dB. Neither the commercial radio station patterns nor the pattern using the trans mitter have sharp nulls. The average signal-to-noise ratio is 58.4 dB which is prac tically the same as the aluminum foil antenna and almost 2 dB better than the fender whip. Figure 40 shows the signal strength for the Sungate antenna, the fender whip antenna, and the commercial “T” windshield antenna measured using the spectrum analyzer and a 5017 system. Notice that the signal from the Sungate antenna is consistently better than that from the “T” antenna. The fender whip provides stronger signal across the band; however, the noise is increased also. Since the dynamic range of the typical FM receiver is more than 40 dB, the signal strength differences are not critical. 70 File: p0115b.rawf ( 01-15-1991 14:00:22) CM1: capacitive coupling (inside) 89.7 HHc (ref - -25 dB) 90.5 MHz (ref - -34 dB) 9 2 .3 MHz ( r a f • -23 dB) 94.7 MHz (raf - -21 dB) 9€.3 MHz (ref - -24 dB) 9 7 .1 MHz ( r e f - -21 dB) 9 7 .9 MHz ( r a f - -2 6 dB) 98.9 MHz ( r e f > -36 dB) 99.7 MHz (ref > -21 dB) CAR FROHT t 0 1 0 2 .0 MHz ( r e f > -50 dB) 103.0 MHz ( r e f - -80 dB) Figure 39: Sungate antennas. FM patterns. 71 SIGNAL STRENGTH COMPARISON STATION Fender whip HLR antenna "T" antenna D ifference 69.9 MHz -20 dB -25 dB -36 dB 11 dB 90.5 MHz -27 -34 -41 7 92.3 MHz -14 -23 -23 0 94.7 MHz -16 -21 -30 9 96.3 MHz -17 -24 -30 6 97.1 MHz -14 -21 -27 6 97.9 MHz -17 -27 -40 13 98.9 MHz -29 -37 -38 1 99.7 MHz -15 -21 -25 4 CTR 97.9 MHz SPAM 2 MHz/ RES BW 100 kHz VF .03 REF -10 dBm 10 dB/ ATTEN 0 dB SWP AUTO Fender whip HLR antenna T antenna Figure 40: Signal Strength comparison. 72 C H A PT E R V Theoretical Problem 5.1 Introduction In this chapter we discuss a theoretical development that will help to model resistive film antennas in presence of a perfectly conducting ground plane. Wind shield antennas such as the ones developed in Chapter IV can be studied using this model. Once this model is implemented, we will be able to predict the input impedance and radiation patterns of different windshield antenna configurations. We will be able to see the effects of changing the shape of the windshield or the width of the gap, and the effects of the feed position or the resistivity of the film. This model does not include the effects of any capacitive coupling such as the ones described in Chapter IV. In this chapter we discuss the mathematical formulation of the problem. The geometry is shown in Figure 41. There is a perfectly conducting ground plane with a rectangular aperture. The aperture is covered with a resistive sheet and there is a small gap between the sheet and the ground plane. This is a highly idealized case of the antenna proposed here. The resistive sheet simulates the windshield and the ground plane simulates the car’s body. To analyze this geometry it is better to first analyze a more general geometry and then consider our problem as a particular case. Figure 42 shows such a gen eral geometry. There is a perfectly conducting ground plane with an aperture A. 73 Perfectly conducting ground plane Resistive sheet m m m Figure 41: Theoretical Problem. Basic Geometry. 74 Obstacle Impressed current Region 1 * n, r- Ground Plane £ _ ♦ n2 Aperture Region 2 Figure 42: General geometry. The perfectly conducting ground plane divides space into two regions: the upper region (region 1) contains the impressed currents and a dielectric obstacle. The lower region (region 2) is empty. h\ is the unit vector normal to the plane facing region 1 and n 2 is the unit vector normal to the plane facing region 2. The im pressed currents are located in region 1 and are denoted by i. The obstacle has a dielectric constant e and is confined to volume V. The total electric and magnetic fields produced in region 1 are ( E\,H\) and the total electric and magnetic fields produced in region 2 are (F 2 ,# 2 )• 75 Obstacle c \ _ . . Impressed n eo)Ei curren t ( 5 Region 1 (vj[° J Mi=-r\xl^ i » . y ’n2 Aperture Region 2 . ( 0 , 0 ) Figure 43: Equivalence principle applied to region 1. 5.2 Region 1 Analysis Figure 43 shows the geometry of Figure 42 once the equivalence principle [10] has been applied. According to the equivalence principle, the electric and magnetic fields in a region will not change if we substitute the original sources and obstacles by equivalent sources in free space. In our problem, region 1 has the obstacle and the ground plane to be replaced by equivalent currents. The obstacle can be replaced by free 6pace and the equivalent current f = ju>(e - cq)E i (5.1) 76 and the ground plane can be removed by replacing it by free space and the magnetic and electric currents M \ = Ei x ni = —ni * Ei in A (5.2) and Jl = ni x Hi (5-3) Since the product &i x hi is zero on the ground plane, the current Mi exists only in the aperture region A. The fields produced in region 1 are the total fields (E i,H i) while the total fields produced in region 2 are zero. Since the fields in region 2 are zero, we can put a perfectly conducting ground plane a very small distance below the plane that divides region 1 from region 2. The ground plane will short the electric currents, and thus they can be eliminated, as seen in Figure 44. 5.3 Region 2 Analysis A similar procedure can be followed to analyze region 2. As illustrated by Figures 45 and 46, the fields in region 2 can be produced by the equivalent currents M 2 = E 2 x 7X2 in A (5-4) and J2 = A2 x j? 2 (5-5) located just below the ground plane. The fields in region 2 will be the total fields (jE?2>#2) while the fields in region 1 will be zero. Again, we put a ground plane just above the equivalent currents. As before, the electric currents are shorted out and can be removed. 77 t -Arsfe f \r Impressed e„ (Ei ,H ,) _^J-goi(e-e 0)E. current s /- N Region 1 ( £ 0 > n,A L. n, Ground plane Region 2 ( 0 , 0 ) Figure 44: Region 1 equivalent geometry with ground plane introduced. 78 ( 0 , 0 ) Region 1 A J2 = n2xH2 Region Figure 45: Equivalence principle applied to region 2. 79 ( 0 , 0 ) Region Ground plane n, Region (E2 ,U2) Figure 46: Equivalence principle applied to region 2. 80 Since the total electric field is continuous across the aperture, we have the following relationship M 2 = E 2 x n2 = —Mi (5-6) To simplify notation, let us define the following terms n = h\ = -n2 (5.7) and M = M i = - M 2 (5.8) Let (E l,H l) be the fields produced by (Jl,M l) in presence of the ground plane. Let { E ^ be the fields produced by M in presence of the ground plane. If we apply continuity of the magnetic fields across the aperture we find that n x Hi = h x & 2 in A (5-9) and nx{H M +HJ + Hi) = nx (-H M) in A (5.10) -H{ - 2 H tM =H} in A (5.11) where the subscript t means the tangential component in A. 5.4 Resistive sheet analysis Consider the particular case where the dielectric is electrically thin and is located just above the aperture. As shown in Figure 47, the dielectric has a 81 Dielectric Sheet Ground Plane Figure 47: Thin dielectric sheet on aperture. 82 Thin dielectric slab. e„ ji = jo;(e-e0)T Equivalent sheet admittance Figure 48: Thin dielectric slab and equivalent sheet impedance.. thickness T and a dielectric constant e. Since the dielectric is electrically thin, we can neglect the vertical component of J. Using equation (5.1), J can be replaced by the surface current J s = J T = jw{e - eQ)E iT = Y E lt (5.12) where Y = ju(e — cq) (U/O) is the sheet admittance of a thin dielectric slab. As shown in Figure 48, we are substituting the dielectric slab with thickness T with a sheet impedance with no thickness and admittance V. can be treated as a dependent unknown, since it depends on the electric field in the aperture, which is the same field used to calculate the magnetic current M = E\ x h\. M is given by the tangential component of the field E\. At the same time, the surface current density J depends on the tangential component of the field E\. Knowing M automatically determines J^. Equation (5.11) becomes - J5Tts - 2 = H} in A (5.13) where is the magnetic field produced by J ^ and the subscript t means the fields are tangential in A. We need to find H ^ in terms of . Figure 49a shows an electric current in free space. Applying the boundary conditions to the magnetic fields just above and just below the current J ^ we have hx{HB - Ha ) = Xs (5.14) Due to the symmetry of this geometry, HB = —HA. Therefore, the magnetic field just below the electric current is given by « a a = (5.i5) In our case, the current is not in free space, it is located just above the perfectly conducting ground plane. Using image theory, we can determine the magnetic field H § right on the plane of the aperture. Figure 49b shows the current and its image. On the image plane, the magnetic field produced by the current is reinforced by the magnetic field produced by its image. The result is a field with twice the strength than the field produced by the current in free space H S = n x J S (5.16) 84 H B O O Q Q Q O O O O 0 s H. (a) C u r r e n t CT GOO 0(6)0 ...00 0 0 Image of Jk (b ) Figure 49: Magnetic fields close to J^. (a) J^ in free space, (b) in front of a ground plane. 85 Using the equation above, and equation (5.12), equation (5.13) becomes - j f - 2HtM = HI in A (5.17) Y E UT - 2 = Hf in A. (5.18) Noting that M = Ei x n, we get the following integral equation - 2 H + Y M t = Hi in A. (5.19) This integral equation is the one to be solved using the Method of Moments. So far, there has been no restrictions concerning the dimensions of the problem. This formulation is valid in 2D as well as in 3D geometries. In this investigation, we in tend to apply the Method of Moments to solve the more general three-dimensional case. Equation (5.19) is the dual of the problem of scattering by a resistive plate [11 ]. Equation (5.19) is the general integral equation for the scattering of an aper ture covered by a resistive sheet. It is important to remember that the magnetic current Mt radiates in front of a perfectly conducting ground plane. If the aperture is not covered by a resistive card, i.e., Y = 0, the integral equation (5.19) becomes - H f = Hi in A. (5.20) where H ^ is the scattered field on the aperture. This equation i6 essentially the same as the equation for the scattering of a perfectly conducting plate. In the case of a perfectly conducting plate the equation relates the incident and scattered electric fields, while equation (5.19) relates magnetic fields. This is consistent with Babinet’s principle [13]. 86 Resistive Sheet —H W. Figure 50: Method of moments applied to the impedance sheet. 5.5 Method of Moments Formulation The method we will use to solve equation (5.19) is similar to the one used in [11]. What follows is a formulation of the problem in two dimensions. The Galerkin method will be used where basis and weighting functions are identical. Figure 50 shows the resistive sheet divided in N expansion modes. The equivalent magnetic current will be approximated by N M = ' £ l nM n (5.21) n=l 87 where the In are the N unknown coefficients of the expansion function, and the M n are the N pulse basis expansion modes, i.e., 1/W n, w ithin Rn M n = (5.22) 0, otherwise By applying Galerkin’s method with identical basis and weighting functions, the integral equation (5.19) reduces to the following matrix equation [Z + AZ)I=V (5.23) where [Z + A Z] is the N x N impedance matrix, V is the N element source vector, and I is the coefficients vector composed by the N unknown coefficients In. Typical elements of the impedance matrix are given by Zmn — —2 f HinM mdx (5.24) Jm where Htn is the tangential component of the magnetic field radiated by M n in presence of the ground plane, and the integral is over the region m. A typical element of the [A Z] matrix is given by AZmn = / y M mM ndx (5.25) Jm Since we are using a pulse basis function, this matrix reduces to a diagonal matrix whose elements are given by AZrnn = JnY(x)dx (5.26) A typical element of the source vector is given by 88 Vm = [ M mdx (5.27) Jm The final solution is found when Equations (5.24),(5.26), and (5.27) have been evaluated and substituted in (5.23). The elements In are found by inverting the m atrix [Z + A Z) in Equation (5.23). Once we know the elements In the approx imate magnetic currents on the sheet can be determined and all the quantities of interest, such as radiation or scattering patterns and input impedance can be evaluated. 5.6 Numerical results Using the solution obtained by the implementation of the Method of Mo ments, several useful parameters can be calculated. In this section we discuss some numerical results obtained using such formulation. Figure 51 shows the an tenna geometry used to calculate impedance and efficiency. There is a perfectly conducting ground plane with an aperture with length L and width W. Inside the aperture there is a resistive card with resistivity R which covers the aperture leaving a gap g between the card and the ground plane. The dimensions used in these calculations are L = 31mm (5.28) W = 31mm (5.29) g = 1mm (5.30) and the frequency band of operation is 2.5-3.2 GHz. The total gap length at this frequency band is 1.0 to 1.28 A, which is the approximate gap length of the 89 Feed w point Figure 51: Antenna geometry used in the model evaluation, windshield antenna. The antenna is fed at the bottom center of the resistive card. Figure 52 shows the antenna’s input impedance for three different cases: R = 0.0, 25.0, and 200.0 fl. The numerical results using the Method of Moments are plotted together with experimental results. There is good agreement between the measured results and the theretical prediction. The measurements were obtained by cutting a 31x31 mm aperture on a 90x90 cm aluminum plate. The measure ments were taken with a HP 8510 network analyzer. The perfectly conducting plate was made with aluminum and the resistive cards were cut from epoxy fiber glass cards with resistive film on one side. The theoretical values agree with the measurement results well within experimental error. Figure 53 shows the efficiency of the antenna as a function of resistivity. Notice that up to a resistivity of 100ft/D the antenna is relatively efficient. After that point, however, the efficiency decreases dramatically. The numerical results are shown together with two measurements obtained using the Wheeler Method [14] using a 23x23x23 inch Wheeler cap. 5.7 Conclusion In this chapter we have discussed the theoretical development that will enable us to model windshield antennas that use resistive films. This formulation can be used to predict the input impedance and radiation pattern of different resistive film antennas. Changes in windshield size, gap size, feed position, or film resistivity are all included in the formulation. This model does not include the curvature of the windshield or any capacitive coupling such a6 the one described in Chapter IV. In Chapter VI we present the final antenna candidates that are proposed for this dissertation. 91 2 0 0 Measurements T h e o r y Perfectly conducting 25 Ohms/sq 200 Ohms/sq -100 300 Perfectly conducting 25 Ohms/sq ■r. •H 200 Ohms/sq 5 0__ 2500 3200 Frequency (MHz) Figure 52: Input impedance of geometry shown in figure 51 using a perfectly conducting plate, a 2511/□ card, and a 20011/□ card. 92 Efficiency (%) 100 20 40 80 60 1 iue 3 Efcec o emty hw n iue 51. figure in shown geometry of Efficiency 53: Figure Theory — Measurement § sti ty (Ohms/sq) y it iv t is s e R 10 100 93 1000 10000 C H A P T E R VI Conclusions This dissertation has covered the analysis and design of a windshield antenna based on annular slot principles. The antenna is built using resistive films imbed ded in some modern windshields. The design process began with the study of a model for the fender whip antenna and the annular slot as the model for the an tenna under development. The second step was to develop a measurement facility to measure the parameters of interest in this particular design. The measurement facility included impedance and radiation pattern measurement capabilities. The experimental design was then executed and two final candidates were finally selected. As shown in Figure 54, the transmission line is connected directly to the resistive film or capacitively coupled using a conducting strip attached to the glass. The dimensions of the strip depend on the size and shape of the windshield and are adjusted to match the antenna to the receiver. In both designs, a 125fi coaxial transmission line is used. Both of these configurations are excellent AM/FM antennas. Signal ampli tudes are only 3 to 6 dB less and the signal-to-noise ratio is nearly identical to that of the fender whip antenna. Their directional patterns and impedance characteris tics are designed to be equivalent to that of the fender whip antennas. These new antenna designs can provide the automotive industry with a modern alternative to 94 the fender whip antenna with no need to redesign the radio or install external am plifiers. They are inherently compatible with modern infrared heat load reduction films and electrically heated windshields. To further understand the different mechanisms involved in this type of an tenna, a simple model was constructed and solved using the Method Of Moment. The theoretical study has shown that the resistivity of the film imbedded in the windshield affects the efficiency of the antenna. As long as the resistivity is less than 100fl/n the efficiency is larger than 80 %. Any resistivity greater than lOOfl/D, would dramatically reduce the efficiency of the antenna. Although the antenna designed in this dissertation is an AM/FM antenna, the same principles can be used to design other antennas that are currently being used in automobiles, such as the cellular phone and TV antennas. The design of such antennas is a logical extension to the work presented in this dissertation. 95 Final Candidates Conducting Strip Ground Connection Capacitive coupling Ground . Direct Connection Connection Direct coupling Figure 54: Final Candidates. 96 BIBLIOGRAPHY [1] K. Kurita, “Present and Future of New Technology for Automotive Glasses,” Jou. of JSAE Vol. 42, No. 9, pp 1224-1230, 1988. [2] P. T. Boaz, “Radio Antenna for Automobile Windshield,” U.S. Patent No 4,141,011. Feb. 20, 1979. [3] K. Sakurai, “Windshield Glass for a Vehicle Having Heating Conductive Wires and Antenna Wires,” U.S. Patent No 4,736,206. Apr. 5, 1988. [4] L. Nagy, “A New Generation of Antennas for Automobile Use,” SAE Technical Paper Series, Paper No 870092, Warrendale PA, 1987. [5] L. Nagy, “Vehicle Roof Mounted Slot Antenna with Lossy Conductive Mate rial for Low VSWR,” U.S. Patent No 4,707,700. Nov, 17, 1987. [6] C. Balanis, Antenna Theory. Analysis and Design, New York: Harper and Row, 1982. [7] T. Taga, “Analysis for Mean Effective Gain of Mobile Antennas in Land Mo bile Radio Environments,” IEEE Trans. Veh. Technol., Vol. VT-39, No. 2, pp. 117-131, 1990. [8] H. Jasik, Ed., Antenna Engineering Handbook, New York: McGraw Hill, 1984., sec. 28-1. [9] J. E. Lindsay, “A Circular Loop Antenna with Nonuniform Current Distribu tion,” IR E Trans. Antennas Propagat. Vol. AP-8, pp. 439-441, July 1960. [10] R. F. Harrington, Time Harmonic Electromagnetic Fields, New York: Mc Graw Hill, 1961. [11] E. Newman, “TM Scattering by an Impedance Sheet Extension of a Parabolic Cylinder,” IEEE Trans. Antennas Propagat. Vol. 36, pp. 527-534, April 1988. [12] R. F. Harrington, Field Computations by Moment Methods, New York: M acmillan, 1968. [13] R. E. Collin, Field Theory of Guided Waves, 2nd Ed. IEEE Press, New York, 1991. [14] E. H. Newman, P. Bohley, C. H. Walter, “Two Methods for the Measurement of Antenna Efficiency,” IEEE Trans. Antennas Propagat. Vol. AP-23, pp. 457- 461, July, 1975. 97