ADVANCED ELECTROMAGNETIC METHODS FOR

AEROSPACE VEHICLES

Semiannual Progress Report

(July 1 - December 31, 1991)

by

Constantine A. Balanis

E1-Budawy lE1-Sharawy_

Shahrokh Hashemi-Yeganeh

James T. Aberle

Craig R. Birtcher

Telecommunications Research Center

College of Engineering and Applied Sciences

Arizona State University

Tempe, AZ 85287-7206

Sponsored by

Grant No. NAG-l-1082

National Aeronautics and Space Administration

Langley Research Center

Hampton, VA 23665

(',riz ,a, "u,_,:, -, tlniv.) ":" P L_;CL I l:'
Contents

I. INTRODUCTION 1

II. COMPOSITE MATERIALS

Ao

B.

C.

D.

E.

4

Introduction ............................ 4

Modeling and Measurements of Antennas on High Conductivity Composite Materials ..................... 4

Predicting and Measuring Effects of Low Conductivity Composite Materials on Antenna Patterns .............. 8

Conclusions ............................ 10

Future Work ............................ 11

III. Voltage Finite-Difference Time Domain Analysis of Corona

Discharge Problem

A.

B.

C°

D.

29

Introduction ............................ 29

Voltage Finite Difference-Time Domain analysis of travelling

wave along microstrip transmission line ............ 29

Voltage FD-TD simulation of simplified corona discharge . . . 32

Future work ............................ 34

IV. ANTENNA TECHNOLOGY

A.

B.

C.

D.

E.

41

Introduction ............................ 41

Polarization-Diverse Conformal Microstrip Patch Antennas . . 41

Ferrite-Filled Cavity-Backed Slot Antennas ........... 42

Varactor-Tuned Microstrip Patch Antennas ........... 45

Future Work ............................ 46
I. INTRODUCTION

The Advanced Helicopter Electromagnetics (AHE)-Industrial Associates Program continues its research activities centered on issues that advance technology related to helicopter electromagnetics. The topics of research have been

identified and supported by the members of the program. The Advisory Task

Force of the AHE program reviews the topics of research and recommends

areas of research interest to the group.

This progress report has focused on the following three major topics:

1. Composite Materials

2. Precipitation Static - Corona Discharge

3. Antenna Technology

In Composite Materials the research has focused on the measurements of

the electrical properties of composite materials, and the modeling of material

discontinuities and their effect on the radiation pattern of antennas mounted

on or near material surfaces. Samples of the materials were provided by

Sikorsky Aircraft and AVRADA (through SRI). Measurements of the electrical properties of these materials at microwave frequencies have already

been made, and they have been reported in previous progress reports. These

,properties have been used to model antenna performance when mounted on

composite materials. Since helicopter platforms include several antenna systems at VHF and UHF bands, measuring techniques are being explored that

can be used to measure the properties at these frequency bands. Techniques

are being developed to account for the presence of materials on the performance of the radiation characteristics of helicopter antennas. In particular,

emphasis is placed on the representation and validity of the Green's function

analysis. Separate computer codes have been developed which calculate the

complex surface impedance of a finite size dielectric or composite material

mounted on a perfect electric conductor (PEC). The imaginary part of the

surface impedance accounts for radiation by the discontinuity. The impedance is computed using convolution theory and Green's function techniques.

FFT techniques are used to evaluate integrals included in the convolution

process.
During the second year of the AHE program the effort on corona discharge and precipitation static has been directed toward the development

of a new two-dimensional Voltage Finite-Difference Time-Domain computer

program. Results based on the simplified two-dimensional Voltage FiniteDifference Time-Domain program indicate the feasibility of utilizing potentials for simulating electromagnetic problems in the cases where potentials

become primary sources. For example, the program can successfully predict the propagation constants for the longitudinal wave along a microstrip

structure. In addition, efforts have been made to include the corona discharge mechanism into the two-dimensional Voltage FD-TD for a two-wire

high voltage transmission line. Such a modeling is essential in understanding the discharge process and ultimately corona discharge mechanism by the

sharp edge of an aircraft or helicopter structure.

In Antenna Technology the focus has been on Polarization Diverse Conformal Microstrip Antennas, Cavity-Backed Slot Antennas, and VaractorTuned Circular Patch Antennas. Through the AHE program, numerical

codes have been developed for the analysis of two-probe-fed rectangular and

circular microstrip patch antennas fed by resistive and reactive power divider

networks. These codes can be used to evaluate the overall performance of

polarization diverse conformal antennas in terms of return loss, axial ratio,

cross-polarization level or polarization mismatch. In addition investigation

has been initiated of slot antennas backed by cavities that are partially filled

with ferrite. Experiments to measure the radiation pattern and efficiency of

a prototype cavity-hacked slot antenna have been performed at microwave

frequencies. There is considerable interest in using this type of an antennas

at VHF and UHF frequencies. Computer codes are currently under development to predict the performance of these antennas. These codes utilize

rigorous, fully electromagnetic approaches and should provide us with a good

deal of insight on how to design these antennas for optimum performance.

The narrow bandwidth of conventional microstrip antennas can be overcome

by using a varactor diode to vary its resonant frequency over a fairly wide

bandwidth. By varying the voltage across the varactor, the capacitance of

the equivalent antenna circuit and thus the resonant frequency of the antenna can be changed. The investigation of this type of an antenna has been

started, and it will continue in 1992.

A detailed review of the progress of all of these topics is outlined in this

report. Additional information of the progress of the AHE program during
1991can be found in the previous semiannual progress reports.

3

II. COMPOSITE MATERIALS

A. Introduction

Nonmetallic material are now routinely an integral part of an airframe. However the introduction of such materials to the structure plays a key role on

the performance of the on-board avionics and significantly increases the anMytical complexity of the prediction problem.

In this section, theory and measurements of antennas on composite materials are presented and compared. Two different types of composite materials

are discussed:

1. Materials of high conductivity, such as graphite epoxy and fiberglass

with aluminum screens near the su_a:ce.

2. Materials of low conductivity, such as fiberglass and microwave absorbers.

Measurements of material properties for both types of material have been

performed in our laboratory and presented in our previous progress reports.

The results of these measurements are used to evaluate the surface impedance

of the material. This surface impedance is used to model the composite

material structure as wire-grid and the NEC code is used to model and

predict the radiation patterns of monopole antennas on or near surfaces of

composite material.

B. Modeling and Measurements of Antennas on High

Conductivity Composite Materials

In this section, we first measure the properties of some high conductivity

composite materials. Using the experimental data, we numerically predicted

the effects of the materials on antenna patterns. The computed results finally

compared with measurements.

1. Measurements of material properties

Three material samples provided by Sikorsky Aircraft, one fiberglass impregnated with graphite epoxy, one fiberglass with one aluminum screen on the
surface and one fiberglass with two aluminum screens embedded near one

of the surfaces, were tested. Figure 1 shows the geometry and orientation

of all three different material samples. All these samples are symmetric in

the 0° and 90 ° orientations, whereas some anisotropy may exist in the 45°

orientation. To measure the properties of the material in the 45 ° orientation,

other samples have to be cut so that the electric field in the waveguide is parallel to the required orientation. This explains why a single waveguide mode,

with a well known field orientation, has to be used to measure anisotropic

materials. In addition, another fiberglass sample with one aluminum screen

on the surface, made available through SRI (Stanford Research Institute),

was examined.

The surface conductivity versus frequency of the graphite sample is shown

in Figure 2 for two different orientations, 0° and 45 °. As mentioned above,

the structure is symmetric with respect to 0° and 90 ° orientations, as well

as with respect to the 45 ° and 135 ° orientations. As shown in Figure 2, the

conductivity of graphite epoxy is about 1000-1500 S/m in the 45 ° orientation

and about 500-1000 S/m in the 0° orientation. The conductivity increases

with frequency which makes this material a good choice for shielding against

surges due to antenna switching, corona, discharge, etc., where the frequency

spectrum of these transients spreads over a very broad range.

Figure 3a shows the conductivity measurements of the Sikorsky Aircraft

fiberglass sample with one aluminum screen on the surface. The conductivity

is almost isotropic and increases with frequency. The value of conductivity

is less than that of the graphite sample (almost one third). Figure 3b shows

the conductivity measured from the opposite side of the aluminum screen

(dielectric side). The equivalent conductivity in this case is significantly

reduced (by a factor of about 30 less than the front screen conductivity). This

shows the necessity of placing the conducting screen near the outer surface

of the helicopter to get good grounding effects. Similarly, the measured

conductivities the SRI sample are shown in Figure 4.

Figures 5a and 5b show the effective conductivity of both sides of the

fiberglass sample with two aluminum screens embedded near one of the surfaces. First, by embedding the screens inside the material, the conductivity,

similar to the graphite material, became anisotropic. However, contrary to

the graphite, the 0° orientation of this material has higher conductivity. The

conductivity decreases with frequency which does not provide as good of a

shielding against transients. The dielectric side has the lower conductivity,

5
as expected.

Conclusions and recommendations stemming from the above measurements include the possibility of adding aluminum screens to graphite materials to neutralize their anisotropy, if this is of significance. Also, keeping

the aluminum screens at the surface, instead of embedding them inside the

material, can be useful in avoiding reduction of the conductivity versus frequency.

2. Material effects on antenna patterns

The measured data of the high conductivity materials are used to predict

their effects on antenna patterns. The surface impedance used in the computations can be expressed in terms of the conductivity as

(1)

This impedance is used as a load to the segments in a wire grid, representing

a composite material surface, used in the computation of the NEC code.

First, the radar cross section (RCS) of a square sample of graphite epoxy

was computed and compared with measurements made in the EMAC facility

at Arizona State University. The surface of the graphite was modeled as a

wire grid with surface impedance given by Equation 1.

The graphite sample has dimensions of 1.5)_ × 1.5_ at 6 GHz. Initially,

the grid mesh was chosen to be square (Figure 6a). As mentioned above, the

conductivity of this material is anisotropic. To account for this anisotropy, a

denser mesh (as shown in Figure fib) is used to model the graphite surface by

assigning different surface impedance to wires in different orientations. Wires

in the 45 ° orientation are assumed to have lower surface impedance than wires

in the 0* orientation. To save CPU time, the thickness of the sample (0.111

inches corresponding to 0.0564,_ at t5 GHz) was neglected and the sample was

assumed to be infinitely thin. Figures 7 - 10 show predicted and measured

monostatic RCS patterns for two different azimuth angles and two different

polarizations (soft and hard polarizations). The predictions include results

obtained from the square mesh and the denser mesh discussed above, and

for the sake of comparison, results obtained by modeling the graphite as

perfect electric conductor (PEC). Good agreement has been obtained in all

cases with the highest discrepancy of about 2 dB in the endfire direction,

6
probably due to neglecting the thickness of the sample. Using the measured

value of graphite conductivity, instead of assuming it to be a perfect electric

conductor, resulted in a better agreement with measurements in the endfire

direction but gave very similar results to the PEC model in the broadside

direction.

Second, at 6 GHz, radiation patterns of a gold plated A/4 monopole on

a graphite sheet of dimensions 1.5,_ x 1.5,_ were computed, using the surface

impedance given by equation Equation 1 where the conductivity was from

the previous measurements. We also measured the radiation patterns at our

facility as comparisons.

The structure under investigation is shown in Figure 11. The monopole

was placed at the center of the sheet. A coaxial connector was used to connect

the antenna to the test equipment. The thickness of the sheet was 0.111 in

(0.0564,_ at 6 GHz). The modeling of the graphite ground plane is identical to

those used in the prediction of the RCS of this graphite sheet. The monopole

was modeled as an infinitely thin PEC (Zo - 0) wire. We anticipated that

the coaxial connector in the back of antenna will have a minimal effect on

the main beam of the antenna, therefore the connector was not modeled.

The computed and measured results are plotted in Figures 12 and 13 for

two different azimuth angles. Good agreement was observed between theory

and measurements, except for the back portion of the pattern. This may be

due to the absence of modeling of the coaxial connector and the test cable

in the back of the antenna. Neglecting the thickness of the graphite sheet

also may have contributed to some of the discrepancies near and at endfire

directions. The agreement between predicted results based on the actual

surface impedance of the graphite was somewhat better than that assuming

the graphite to be a PEC.

Finally, we built another _/4 monopole antenna on a SRI fiberglass substrate covered with aluminum screen on the antenna side. The dimension of

the ground plane is 2,_ x 2_ and the operating frequency is 4 GHz (the low

end frequency of our ElectroMagnetic Antenna Chamber).

Based on its measured conductivity (_r -- 300 S), the surface impedance

of this material was evaluated, using Equation 1, to be Z, - 5 + j5 _.

The antenna structure, similar to Figure 11 except that the ground plane is

replaced with a fiberglass with aluminum screen facing up, was modeled by a

single layer of wire grids, represent the aluminum screen, and the monopole

antenna. The grid mesh was chosen to be square and the length of each wire

7
was 0.1A. Figure 14 shows the measured and computed radiation patterns.

Good agreement between theory and measurements is indicated except in

the back region. This may be attributed to the fact that the fiberglass at the

back of the antenna, the coaxial connector and test cable were not included

in the model.

From the above examples, we believe that the NEC code can predict accurately high conducting material discontinuities. However, with the extensive

use of nonconductive material in modern helicopter platforms, it is necessary

to examine the capability of the NEC code in handling low conductivity or

nonconductive materials.

C. Predicting and Measuring Effects of Low Conductivity Composite Materials on Antenna Patterns

In the first year of this work, we developed a solution for dielectric c6ated

surfaces. This solution was validated only for very large surfaces. The accuracy of this solution degrades as the dimensions of the dielectric surface

decreases. Furthermore, the analysis was not successful in predicting the

impact of composite materials on the antenna efficiency (refer to our previous annual report on the radiation patterns of _/4 monopole on a 2_ x 2_

partially-coated surface). Later on, we initiated an attempt to use a Green's

function analysis for dielectric discontinuities using equivalent source techniques. With this technique, the effect of the discontinuity is introduced by

a source of electric or magnetic fields to represent the difference in the fields

with or without the dielectric coating. We explored two different approaches;

the spectral domain and the spatial domain. We found the spatial domain to

be difficult to apply to more than one discontinuity or to use for composite

materials.

In our previous reports, we presented an iterative technique to calculate

the surface impedance of a perfect conductor partially coated with a composite material. We found that this iterative technique will be extremely

slow and computationally inefficient. So, we worked on the derivation of a

closed form solution for the surface impedance of a partially covered perfect

electrically conductor. We also extended this expression to include magnetic

materials and material losses. For a partially covered perfect electric conductor as shown in Figure 15, the effect of discontinuity can be modeled, as
mentioned above, by a fully covered ground plane and equivalent sources.

Using convolution theory, it is possible to prove that the surface impedance

Zo as a function of coordinates can be expressed as:

t (4_'(e.- 1)'TE(k_-,8.,-_,t-z) x_,.'ZT(k.-_.,-_v,z)dzdk_' _

fO t471"(ft r -- l)_T(k z -- t_x --_lt, t -- Z) X Id._j(kx - _ffi,-fl,,z)dzdk=/

" CO

.. .,,

, (4_'(,, - llYr(k_ - _,-f/,,t - z) x _,.'ZT(kx-- 13_,-j6,,zldzdk_)

+ J--£ eJJ',_sin(k_w_)

27r oo

fo ,4,(_- _)_(-_,_-_,,-_)× f/._(-_,_-_,_)a_d_, ]

-1

(2)

where

_ = _o_(0)_o,(¢) (3)

_ = _osi,_(o)si,_(¢,) (4)

and Zr,_r, Tg,TJ are the transmission matrices of the composite material.

It is clear from the above equation that the value of the surface impedance

depends on the incidence angle 0 as shown in Figure 11. This makes it

necessary to run the NEC code for different angles. We wrote a computer

9
program to calculate the surfaceimpedance for different values of 0 and

(azimuthal angle). At the present time this code uses regular inverse Fourier

transforms to calculate Zo. We plan to use IFFT in the future to save CPU

time.

To verify our theory, we built a _/4 monopole antenna at 10 GHz on a

2_ x 2_ ground plane. The ground plane was partially covered with a lossy

material of er = 10 - j3.8 and pr = 2.12 - jl.5, as shown in Figure 16. In

our computations, three values of the surface impedance at 0 = 15 °, 45 ° and

75 ° were used. The computed versus measured radiation pattern are shown

in Figure 17. The calculated radiation pattern for the antenna on a perfect

electric conductor (without the lossy material) is also displayed. The effect

of the lossy material is to reduce antenna efficiency. The calculated pattern

using our new theory was somewhat higher (by about 4 dB in the main lobe)

than the measured value. The reasons for this discrepancy may be:

. Material properties are not known accurately. We plan to build another

antenna on a material with well known properties, such as Teflon or

Duroid.

. More values of the surface impedance at different angles are required.

This will require running the NEC code several time and is expected

to consume a lot of CPU time.

D. Conclusions

This section presented measurements and predictions of composite materials

on antenna patterns. Two categories of composite materials were examined.

The first type are materials of high conductivities, including graphite

epoxy and fiberglass with an aluminum screens. Their conductivities were

measured and then used in pattern computations with the NEC code. The

predicted results showed good agreements with measurements. Thus, we

conclude that the surface impedance given by Equation 1 can be used, as

loads in the NEC wire grid model, to successfully predict the effects of the

structure discontinuity if the composite materials have high conductivities.

The second type are materials with low conductivities, such as microwave

absorbers. We developed computer codes to calculate the complex surface

impedance of a finite size dielectric or low conductivity composite material.

10
We built and tested a monopole antenna on a partially covered ground plane.

Although predictions of the radiation pattern of such an antenna show the

same trend as the measured pattern, the computed pattern was higher than

the measured pattern.

E. Future Work

Including the effects of material discontinuities on the radiation patterns of

antennas is a most challenging problem. Our efforts so far have shown that it

is possible to include these material discontinuities in our analytical models.

However, there are a number of issues need to be addressed. First, the code

has to be validated by carrying out further radiation pattern measurements

and computing the complex surface impedance for many values of the incidence angle (we used only three angles in the above theoretical work). The

theory will also be used to study the scattering from simple structures such

as plates and cubes. We have plans to further improve the accuracy and the

computational efficiency of our code by implementing IFFT techniques in

our calculations. Finally, complex structures, such as helicopters and other

complicated platforms will be investigated.

11
0

90

0

O.

I m

I oven

Fibers

t= 0.I I 1 In for graphite

t---0.058 in for fiberglass with one screen

t--0.062 In for fiberglass with two screens

Figure 1: Geometry of the composite material samples.

12
2.5

.

t.S

o

Figure 2: Conductivity of the graphite in kS/re.

13
*,ljil_li,jllll,I I,l,i,',,lli_Jlllllll'll 1.500.

200.- K

Io 100.

O. ,i,,,I,,,,,,I,,,,,,I,,,,,,I,I,I,,I,,,,,,-

8.2 8.9 9.6 10.3 II. 11.7 12.4

FREQUENCY (GHz)

(a)

50"[-IJllJillllliili_'_'"_lllll_ll'_lVtl'il_ll/it50"_

49. --_40.

_'_ 20. -- 20.

_ -

b t0. _ ....... -............. _ tO.

o.,,,,,,,1,,,,,,1,,,,,,I,,,,,, I,,,,,, I,,,,,,-io.

8.2 8.9 9.fi 10.3 it. lt.7 12.4

FREQUENCY (GHz)

(b)

Figure 3: Conductivity of the Sikorsky fiberglass with one Aluminum screen,

where Solid line: 45°; Dotted line: 0°. a. Screen side, b. Dielectric side.

200.

iO0.

O.

14
NEASURENENTPERFO_ED 6/2B/91

ftber7nfur.rep fjberTnbur.rep

B:

500.

400.

cn 300

Io

C 200.

,el

.J

lO0.

O.

500.

400.

300.

200.

t00.

O°

U1

tO

f-

.J

Figure 4: Conductivity of the SRI fiberglass sample with one aluminum

screen at the surface.

15
2.5

.

"_" t.5

b

.5

.

50.

40.

30.

_" 20.

"_ t0.

"_.', l,,,,i J,,,, ii,,, ,,,I I,,,,,I,,,,, I I J,,,, L

q,_,,l_,,t,,l,,,,lll,,,,,llJliilll,,,,,,-

8.2 8.9 9.5 10.3 tt. tt.7 t2.4

FREQUENCY (GHz)

(,0

m

m

m

O.-lli,IIIIl'''ill'li,'l'lltlll'lII'il'll'i1'

8.2 8.9 9.6 t0.3 1t. tt.7 t2.4

FREQUENCY (GHz)

(b)

Figure 5: Conductivity of the Sikorsky fiberglass with two Aluminum screens,

where Solid line: 45°; Dotted line: 0°. a. Screen side, b. Dielectric side.

2.5

.

t.5

t.

.5

Oo

50.

40.

30.

20.

t0.

Oo

16
Z_y Incidentbeam

_X

(-0.7,5,0.75)

i

i

t

(-0.75,-0.75)

I

I

I

)

I

liy

&,, 0.1 _ 411osegment8

(0.75, 0.75)

I :

' i

(0.75,-0,75)

X (a).

(b)

o(o)=eo_n_mlm=ddlk=_mny

Figure 6: Wire grid representing a composite material sheet, a. Square

mesh. b. Denser mesh.

17
phi- 0.0

irephite, raqular mash

graphite, denser mesh

pea. reqular mesh

........ measurement

m

b

_0

1o

-10

-2o

-30

f

I I I 1 I ;

0 60 1_0 160 P.40 :}00 :SeO

(Degrees)

Figure 7: Principal elevation plane(0 °) scattering pattern of a 1.51 x 1.5t

plate(soft polarization).

18
ph/,-45.0

|rapl-tte. reqular mesh

liraphJte, denser mesh

pec. reqular mesh

measurement

m

t_

2O

10

-10

--2O

--3O

Figure 8: Oblique elevation plane(45 °) scattering pattern of a 1.SA x 1.SA

plate(soft polarization).

19
pbJ,,= 0.0

graphite, requJs0r roesh

graphite, denser naesh

....... pec, requ.lay mesh

........ measurement

20

10

m

Figure 9: Principal elevation plane(0 °) scattering pattern of a 1.5_ x 1.5_\

plate(hard polarization).

20
phi-45.0

graphite, reqular mesh

..... _raphite, denser mesh

pec. requJar mesh

........ measurement

b

o 8o 12o 18o

(Degrees)

Figure 10: Oblique elevation plane(45 °) scattering pattern of a 1.5_ x 1.5_

plate(hard polarization).

21
I I

composite material sheet

_V4 monopole antenna

Graphite material

Coaxial connector

Figure 11: Geometry of a monopole antenna on a graphite material ground

plane.

22
llraph/te, requtlecr mesh

........ graphite, denser mesh

....... pec, reqular mesh

......... measurement

gO

150 150

180

Figure 12: Principal elevation plane(0 °) radiation pattern of a _/4 monopole

on a 1.5,_ x 1.,5_ ground plane(co-polarization).

23
phl=45.0 3O

graphite, reqular me3h

........ graphite, denser mesh

....... pec, requdetr mesh

......... meastwement

30

9O gO

120 120

150 150

180

Figure 13: Oblique elevation plane(45 °) radiation pattern of a _/4 monopole

on a 1.5)_ x 1.5)_ ground plane(co-polarization).

24
30

0

3O

60

6O

9O

9O

120

150

180

150

Figure 14: Radiation pattern of a quarter-wavelength monopole on a 2_ by

2_ plate. Impedance = (5 + jS).

25
composite material

air

ground plane

Equivalent source of discontinuity

_mposite material

I II I I II II I I II I I

-,,,.

ground plane

Figure 15: Analysis of discontinuities using the equivalent source.

26
_4 monopole antenna

Partially covered ground plane

Figure 16: Geometry of a monopole antenna and partially-covered ground

plane.

27
Computed(Coated)

........ Measured(Coated)

Computed(PEC)

0

30 30

gO gO

180

Figure 17: Radiation pattern of a quarter-wavelength monopole on a 23, by

2_ coated plate.

28

III. Voltage Finite-Difference Time Domain

Analysis of Corona Discharge Problem

A. Introduction

In the previous quarterly report, a simplified two-dimensional Voltage

Finite-Difference Time-Domain code was developed to analyze TE-wave propagation in an infinitely long microstrip line structure, as shown in Figure 18.

The program was limited since longitudinal propagation of the wave (Zdirection) had not been taken into consideration. Nevertheless, the general

behavior of the fields and the surface current on and around the upper strip

conductor were found to be reasonable. In the present report both longitudinal and transverse wave propagations are considered.

The report consists of two parts. In the first part, we are concerned with

the extension of the longitudinal wave propagation in the Voltage FD-TD

code for the microstrip line, and the dependency of its propagation on the

operating frequency. The result obtained will be analyzed and verified by a

different analytical method. In the second part, the Voltage FD-TD will be

modified to determine radiation of a high voltage transmission line, shown

in Figure 19, with and without air chemistry formulation [1] for the corona

discharge, and the subsequent electromagnetic interference.

B. Voltage Finite Difference-Time Domain analysis

of travelling wave along microstrip transmission

line

In the absence of the dielectric substrate between the two conductors of a

microstrip transmission line, the propagation constant of the wave travelling

along the line is that of free space, and the characteristic resistance (assuming zero loss for the conductors) is independent of frequency. Inclusion of the

dielectric substrate creates non-linear effects in the the propagation constant

where it is no longer proportional to the frequency, and the characteristic impedance does not remain constant as a function of frequency. The non-linear

effects are due to higher order TE (transverse electric) and TM (transverse

magnetic) modes along the microstrip structure. To take into account the

higher order modes and the longitudinal propagation constants, one needs to

29
include the E and/_ six components into the Voltage FD-TD program while

they propagate along Z-direction.

To begin with, consider the most general three dimensional problem for/_

and H fields. They can be derived via auxiliary potentials V (scalar electric

potential) and A (vector magnetic potential):

£=_¢v_ °Xat (5)

/_=1_×_ (6)

Both V and A are solutions to non-homogeneous second order partial differential equations

v_ 02A

-_-_- =-_£ (7)

02V Pt

V2V _ _¢-8-f_-= --[

In addition, the pairs (V, .4), and (,_/_) are related by

(8)

OV

_.X+._-_ =o (9)

J-a/_ (10)

and fit can be external impressed sources that produce electromagnetic

fields and/or internal response sources produced by the electromagnetic fields

in the conductors (equation 10).

It is easily verified that any twice differentiable function of (t - _) or

(t + _) can be the solution to homogeneous forms of equations (7) and (8)

for a wave traveling in the positive or negative Z-directions, respectively.

u = _7 is the velocity of wave propagation in the medium with e and tt as

its permittivity and permeability, respectively. For the microstrip line the

1

phase velocity lies between the speed of the light in free space (--'_00) and

the unbounded dielectric 1

(_). Assuming the fields, the currents, and the

potentials can be represented by the following general separable function

30
Co(x,y,z,t) = C(x,y,t)f(t- z_) (11)

u

the three-dimensional problem can be reduced to a two-dimensional one,

further minimizing the complexity of the analysis. For example,the FD-TD

form of the electric field components become

E.+1⁄2,. 1

(z + _,j) =

V"+1⁄2(i + 1,j)- V"+1⁄2(i,j)

Az

A_(i + 1⁄2,j)- a'_-a(i + 1⁄2,j)

At

(12)

1 Vn+1⁄2(i,j + 1)- Vn+1⁄2(i,j) (13)

E_+12(i'J + 2) = - Ay

1 n--1 "

Av(*,3 n. • + 5) - Ay (z, J + 15)

At

1 ,,+_ . . A'_(i,j)- A z,_-a (z,j) •

E2 +1⁄2 (i,j) = -V 2(z,3)- (14)

u At

Based on these equations a Voltage FD-TD code was developed to determine

the propagation constant and characteristic resistance of the microstrip line

structure shown in Figure 18. The flow chart used in this development is

similar to the chart in the previous report. Figure 20 shows the characteristic resistance versus frequency for w = 2ram, d = 2rnrn, and er = 2.5. As

it can be seen the characteristic resistance is a non-linear function of frequency which is due to the higher order TM modes propagating along the

line. Figure 21 displays the normalized propagation constants versus normalized thickness for the TE and TM waves. /3 and k0 are the propagation

constants of the microstrip line and free space, respectively; and 3,0 is the

wavelength in free space. TMv and TEv lines correspond to the values of

d

versus E resulted from the Voltage FD-TD simulation. They are obtained

from two different values of u computed by imposing the continuity of tangential electric field at the interface between the free space and the dielectric

d

substrate. TMT and TET lines present theoretical allowable _ versus

values for the higher order TE and/or TM modes in the dielectric substrate

31
without the upper strip conductor, which is often referred to as slow wave

structure. These theoretical plots are obtained using the following iterative

equations [2]:

for TE waves, and

1

=- (_/ko)_- 1

(15)

1

= _0 (_/_0)- (/_/k0)2 (16)

for TM waves. As it can be seen, the computed normalized propagation

constants by the Voltage FD-TD, and the iterative equations (15) and (16)

are in good agreement.

C. Voltage FD-TD simulation of simplified corona

discharge

In this section an attempt is made to implement a simplified version of corona

discharge mechanism, using air chemistry formulation [1], into the Voltage

FD-TD code, and to simulate the interference produced by the discharge.

The model used for the simulation consists of an infinitely long two-wire

transmission line immersed in an ionized medium, while a high potential

gradient exists between the two wires. Furthermore, the wires are assumed

to be square in their cross sectional view, as shown in Figure 19. There are

two reasons for selecting this model. First, the elongated sharp corners of the

wires can approximate some of the sharp edges on the body of an aircraft,

where high electric fields are more prevalent. Second, the two-dimensional

set up of the model simplifies the program and its running time when the

additional air chemistry formulation is implemented.

To observe the effect of the simplified corona discharge on the radiated

wave from the transmission line two different conditions were simulated using

the Voltage FD-TD program. In the first condition Voltage FD-TD was

used to determine the radiated electric and magnetic fields without the air

chemistry formulation. This is similar to first half of the present report

32
without the dielectric substrate. In the secondsituation, the air chemistry

formulation was used to modify the Voltage FD-TD code to find the radiated

electric and magnetic fields.

The three-species air chemistry formulation for n, electron density [J-_],

n_ negative ion density [J--_], and n+ positive ion density [_-_] is given by

the following differential equations:

a,,,(t)

dt + + e(IE(t)l)- he(t) =Q(t) (17)

dt

+ = (18)

dn+(t)

dt

-- + [/_n,(t) + "rn_(t)]n+(t) = Q(t) + G(lffT,(t)l)n_(t) (19)

= noCt)+ n_(0 (20)

a = q(tt_n_ + p_n_ + p+n+) (21)

where/3 is the lumped electron-ion recombination [ cm--Za ] et_ is the lumped

t sec J'

electron attachment rate [--_] as a function of electric field, 7 is the lumped

ion-ion neutralization coefficient tfc"---2_ ls,c J, G is the avalanche rate [7_7] as a func-

[ ion-pairs ]

tion of electric field, and Q is the ionization rate t cm_ J" a is the air

rmhosl conductivity t-_--_ ,,/*_, #-, and/z+ are the electron, the negative ions, and

positive ions mobilities, respectively. Figure 22 displays the flow chart that

was used to develop the modified Voltage FD-TD program. The steps in the

flow chart are similar to the previous report flow chart with the additional

variable conductivity at every point (except the conductors) to be computed

and used at every cycle of the program. Figure 23 shows the radiated electric

field at some point between the conductors of the transmission line. Solid

line presents the variation of the electric field as a function of time without

the air chemistry formulation. The frequency of the excitation was set to

2.5 GHz. The line indicates smooth variation of the electric field as a sinusoidal potential difference are excited on the transmission line. Dashed line

represents the electric field as a function of time with the air chemistry formulation. High oscillatory variation of the dashed line shows interference due

to variable conductivity, or change in the electron and ion densities (equation

33
21), in the areasurroundingthe wires which indicates the corona discharge.

This is an important result since spectrum analysis of the electric field can

reveal some of the possible electromagnetic interference (EMI) frequencies

produced by the air chemistry formulation, or the corona discharge.

D. Future work

For the future, our effort will be directed toward more accurate and complex

modeling of the air chemistry formulation for the sharp wedge near an infinite

ground plane where there is high electric potential between the wedge and

ground plane. The high electric field intensity near the sharp wedge can

be considered to be an excellent model to the high electric field near the

sharp wedges of the wings of an aircraft or the rotary blades of a helicopter.

Hence, EMI predicted by the model will give some indication on the frequency

spectrum generated by the sharp edges of the aircraft, and how this spectrum

will interfere with on-board communication systems.

34
by

................... 0°.°..o. ° o .,° °°..o,o...o.°,°.°. i!i!!i!ii!Jiiiiiiiiiiiii!iiiii!iiiiC iii!iii

iiilii

.................. I I I I I I i I I ..........

._--- W ---_

×

v

Figure 18: Microstrip transmission line excited by sinusoidal voltage source.

35
absorbing bounOary.

Figure 19: Two-wire transmission line used in the corona discharge analysis.

36
300.

_" 225,

E

tO

0

150.

75.

0° ' ' ' I ' ' ' ' i .... i .... I

5. 10. 15. 20.

('1E9 GHz)

Figure 20: Characteristic resistance of the microstrip transmission line as a

function of frequency for w =3.91 ram, d =1.27 mm, and e, = 2.2.

37
O

c_.

1.36

1.27

1.18

1.09

1.00

0.00 0,80

,,/'"" ........ "_.,/ #@' .,.*°" ,,,,-.°

I MT// TET....'"',,../

/ " F._. /,,'TM.. ..";:" "TE,

// - V .."/ V

// / /

I/ .." .I

// .." ./

I ."

/ ..."/"

I/ .-" /

,/" ../" .11

// ,/-/

// /

/,/, , . _ .i' , . , I .... i • ' '

0.20 0.40 0.60

d/X.

Figure 21: Normalized TE wave and TM wave propagation constants of the

Microstrip Transmission Line and Dielectric-Clad ground plane as functions

of normalized dielectric thickness.

38
START

I

a = 0 everywhere except in the conductors.

Using modified Voltage FD-TD program (variable or) to determine V, A,

E, and H everywhere.

Using finite difference approximation

to solve the three-species air chemistry formulation for n,, n, and n+

From new ne, n, and n+ compute new

values of cr everywhere (except in the

conductors)

Figure 22: Flow chart for the modified Voltage FD-TD analysis of the corona

discharge.

39
1500.

-750.

Figure 23: Computed X-directed electric field at x=D/4, where the dashed

line represents the formulation with the air chemistry and the solid line is

that without the air chemistry.

40
IV. ANTENNA TECHNOLOGY

A. Introduction

Microstrip and cavity-backed slot antennas are widely used at UHF and above

in aerospace applications such as helicopters because they are conformal to

the vehicle surface as well as light weight, low cost and easy to manufacture.

During the past year, significant progress has been made in three areas of

conformal antenna technology: polarization-diverse microstrip antennas_ ferrite-loaded cavity-backed slot antennas and varactor-tuned

microstrip patch antennas. In this section, progress to date in each of

these areas is discussed, and plans for future work are outlined.

So Polarization-Diverse Conformal Microstrip Patch

Antennas

During the first two years of the AHE program, we developed numerical

codes for the analysis of two-probe-fed rectangular and circular microstrip

patch antennas fed by resistive and reactive power divider networks. These

solutions utilize a rigorous full-wave Green's function/Galerkin approach,

and thus model all of the effects of the dielectric substrate (including surface

waves) as well as feed-to-feed coupling. Such a rigorous approach must be

used if the models are to be accurate for patches printed on thick and/or

high dielectric constant substrates. Another important consideration is the

fact that the frequency performance of these patch radiators depends on the

characteristics of the specific network chosen to feed the element. Hence,

a rigorous analysis that accurately treats both the patch radiator and its

feed network is imperative. These codes can be used to evaluate the overall

performance of polarization diverse conformal antennas in terms of return

loss, axial ratio, cross-polarization level or polarization mismatch.

Figure 24 illustrates the geometry of two-probe-fed circular microstrip

patch antenna. The antenna was fabricated at ASU using our newly developed printed circuit fabrication facility. The antenna parameters are

e,. = 2.33, rand = 0.0012, d = 0.21844 cm, R = 2.0 cm, xpl = 0.7 cm,

ypl = 0, xp2 = 0, yp2 = 0.7 cm, r0 = 0.045 cm. The start frequency is 2.0

GHz, the stop frequency is 3.0 GHz, and the frequency step is 25 MHz. The

measured scattering parameters ($11 and $21) for the antenna are compared

41
in Figure 25 to results calculated using the numerical model. The calculated

data was obtained using 326 seconds of CPU time on ASU's Cray X-MP/18se

supercomputer. Measurements were made in ASU's ElectroMagnetic Anechoic Chamber (EMAC) facility. As can be seen, the agreement between

theory and experiment is quite good.

C. Ferrite-Filled Cavity-Backed Slot Antennas

We reported our efforts on the cavity-backed slot antennas in the previous

semiannual progress report. Since then, further progresses have been made

and they are represented in this progress report.

Narrow bandwidth is a major disadvantages of conventional microstrip

and cavity-backed slot antennas. This disadvantage precludes their use in

a number of applications that could benefit from antennas possessing their

many desirable characteristics. In this and the next section, we discuss some

of the efforts underway to develop tunable conformal antennas. The basic

concept is to start with an inherently narrow-bandwidth antenna and somehow vary one of its parameters allowing the antenna to be tuned over a

fairly wide bandwidth. In many applications, it is actually more desirable to

use such a tunable, inherently narrow-bandwidth antenna than an inherently

wide-bandwidth antenna because of the ability of the narrow-bandwidth antenna to reject out-of-band interference.

The use of magnetized ferrite to control radiation and scattering characteristics of antennas is a promising yet relatively undeveloped technology.

One can conceive of a cavity-backed slot antenna that could be used to cover

several different frequency ranges if materials of different constitutive parameters were substituted into the cavity backing. In practice, this concept can

be realized by partially (or completely) filling the cavity with ferrite and then

varying the permeability tensor of the ferrite by application of an external

magnetic field.

An example of the type of structure we are considering is shown in Figure 26. A radiating slot is etched in the ground plane of a printed microstrip

feed network and backed by a cavity which contains both ferrite and dielectric layers. We have fabricated a prototype antenna with the following

parameters:

• CAVITY: 0.60 in × 0.40 in x 0.25 in.

42
FERRITE:

41rM, = 3400 Gauss

e, = 15.5

linewidth = AH = 600 Oe

thickness = 0.025 in.

DIELECTRIC:

e_ = 10.8

thickness = 0.050 in

Figure 27 shows the return loss and insertion loss seen by the microstrip

line. There are three distinct response regions: the first from 5 GHz to 7

GHz, the second from 8.5 GHz to 9.5 GHz, and the third from 10 GHz to

10.5 GHz. The first region is due to complex air-guided magnetostatic surface

waves which occur at frequencies above the resonant frequency

47rM_. (22) L = (Ho + -7)

which for this material is 4.76 GHz. The second region is due to complex

ground-guided magnetostatic surface waves which occur at frequencies below

the resonant frequency

fg = _(Ho + 4_'M,) (23)

which for this material is 9.52 GHz. The resonance of the cavity itself which

occurs at 10.25 GHz is the dominant mechanism in the third region. For this

ferrite material, the first two regions are not very useful for antenna purposes

as there is very little radiation loss and measured patterns are quite poor.

This can be attributed to the large line-width (600 Oe), which results in large

loss near the resonant frequencies. Low loss materials have linewidths of 50

Oe or less, and can be as low as 1 Oe. On the other hand, the third region

seems to be somewhat more useful for these purposes. Figure 28 shows the

H-plane co-polarized radiation pattern of the antenna at l0 GHz. While the

H-plane pattern is reasonably symmetric, measurements have shown that the

E-plane pattern is substantially worse. Additional work needs to be done in

this area.

It is expected that the development of analysis software for the structure

will greatly enhance our ability to successful implement this novel antenna

43
concept. As a first step in the analysis of these types of antennas, fullwave numerical models for two-dimensional free-space-filled cavity-backed

slot antennas have been developed. These models allow evaluation of the

scattering width as well as the input admittance per unit length and radiation

pattern of the antenna.

Figure 29 shows the geometry of a two-dimensional cavity-backed slot

in an infinite, perfectly conducting, zero thickness ground plane. Full-wave

Galerkin solutions for determining the scattering width and input admittance per unit length of this radiating structure have been developed. These

solutions utilize the Green's function for a magnetic line current element radiating in the presence of an infinite, perfectly conducting ground plane. To

facilitate the analysis, this Green's function is derived in the spectral domain.

In addition, the Green's function for a magnetic line current element radiating into a two-dimensional cavity comprising perfectly conducting walls is

also required.

To evaluate the scattering width, a plane wave is assumed to be incident

upon the structure. The equivalence principal is used to close off the aperture and replace it with a magnetic surface current just above the ground

plane and its negative just below the ground plane. This ensures continuity of the tangential electric field across the slot. The unknown magnetic

surface current is obtained by formulatingan integral equation statement of

the boundary condition that the tangential magnetic field must be continuous across the slot. The integral equation is discretized by expanding the

unknown magnetic surface current in a set of known basis functions with

unknown coefficients and following Galerkin's procedure.

Two different sets of basis functions are considered. The first comprises a

set of sinusoidal functions which do not explicitly exhibit the proper behavior near the knife edge. The second set of basis functions comprises Chebychev polynomials modified by an appropriate edge factor. Conveniently, the

Fourier transforms of functions in both basis sets can be found in closedform. Numerical studies have found that while both basis sets yield identical

results, the basis set with proper edge behavior converges much more rapidly,

and is thus the preferred basis set. However, the spectral domain integrations for the admittance matrix elements that arise from this basis set require

convergence acceleration for accurate calculation to avoid unreasonably long

calculation times.

Figure 30 shows the calculated scattering width of the slot in decibels

44
relative to one meter for both hard (TMz) and soft (TEz) polarizations.

The antenna parameters are W = 5.0 cm, e = 2.0, rnr = 1.0, a = 35.4 cm,

c = 17.7 cm, 0 i = 30 degrees. Notice the peaks in the scattering response

which correspond to the cavity resonances.

Figure 31 shows the calculated input admittance per wavelength of the

slot. The parameters are the same as in Figure 30. For this calculation, the

plane wave excitation is replaced by a current sheet in the aperture. Each

of the curves in Figure 30 and the two curves in Figure 31 were calculated

using about 220 seconds of CPU time on the Cray X-MP/18se.

We are currently extending our existing computer codes to allow treatment of a three-dimensional slot antenna backed by a cavity that is filled

with arbitrary dielectric and ferrite layers.

D. Varactor-Tuned Microstrip Patch Antennas

The principle of the varactor-tuned patch antenna can be qualitatively explained as follows. Consider the equivalent circuit of a conventional circular

patch based on the cavity model as shown in Figure 32. The R-L-C tank

circuit represents the dominant mode of the patch with R representing all

loss mechanisms (including radiation), and the series inductance represents

higher order (non-radiating) modes of the patch as well as the effect of the

probe feed. By mounting a varactor diode between the patch conductor and

the ground plane, we effectively couple a voltage-controlled capacitance in

parallel with the R-L-C tank circuit. By varying the voltage across the varactor, we change the capacitance of the tank circuit and thus the resonant

frequency of the antenna.

The geometry of the varactor-tuned circular patch antenna that was fabricated is shown in Figure 33. A high Q silicon hyperabrupt tuning varactor

(part number MA4ST556_31) was denoted by M/A-COM and used in the

prototype. The probe feed position is chosen such that the patch has an input impedance close to 50 Ohms at resonance, and the position of the diode

is near to where the maximum electric field occurs under the patch in order

to maximize the amount of tuning. The DC bias supply is connected through

the HP-8510 network analyzer. The input return loss versus frequency for

several bias voltages is shown in Figure 34. As can be seen, in changing the

bias voltage from 0 volts to 15 volts, we are able to tune the antenna from

1.575 GHz to 2.64 GHz, which corresponds to a 50% bandwidth.

45
A comparisonof measuredand calculated input return loss versusfrequencyfor bias voltagesof 4 and 20 volts is shownin Figure 35. The calculated data isgeneratedusingthe computerprogramfor two-probe-fedcircular

microstrip patch antennasmentionedearlier. The varactordiode is modeled

as a lumped load at the base of a perfectly conducting pin whose radius

is equal to the actual diode radius. The load impedance is evaluated from

the equivalent circuit for the varactor diode shown in Figure 36. As can be

seen, the agre4ment between theory and experiment is good. Tolerances in

the dielectric constant of the substrate and patch dimensions combined with

an inability to exactly specify the diode packaging parasitics are the likely

causes of the slight deviations between theory and experiment.

E. Future Work

During 1992, work will continue on the topics discussed above. Using our

rigorous models, it has been found that two-probe-fed circular and rectangular microstrip patch array elements which are designed to radiate and receive

circular polarization exhibit axial ratios at boresight which are on the order

of 1 to 2 dB. In many systems, these performance levels are unacceptable.

During 1991, we began to investigate some techniques for improving the axial

ratio. One approach is to use balanced pairs of probes to create a perfectly

symmetrical radiator. This approach has the disadvantage of requiring a

more complicated feed network, which may no longer be achievable using a

purely planar structure. It is also possible to compensate for the element

asymmetry by adjusting the amplitude and phase of the feed excitation by

suitably designing the feed network. Another very interesting approach to

be investigated during 1992 is the use of an gyromagnetic (ferrite) superstrate to achieve high-quality circular polarization from an element with an

intrinsically poor axial ratio or even from a linearly polarized element.

Investigation of some stacked microstrip patch antenna configurations

will also begin during the next quarter. By stacking patch antennas, one

can improve the impedance bandwidth of the antenna and/or provide for an

antenna which can operate at two widely separated frequencies.

During the past year, we began to investigate slot antennas backed by

cavities that are partially filled with ferrite. Experiments to measure the

radiation pattern and efficiency of a prototype cavity-backed slot antenna

have been performed at microwave frequencies. The ferrite material that

46
wasused in our experimental work has a line width of 600 Oe, and is thus

not suitablefor magnetostaticapplications. There is considerableinterest in

using this type of antennaat VHF and UHF frequencies.We havecontacted

Trans TechCo., and they haveagreedto donatehigh quality ferrite materials

suitable for operation in magnetostatic modes. In particular, we will be

receivingTTVG-800 with a line width of 10 Oe,which will enableoperation

at UHF (1.1 GHz). Another material we will be receivingis G-1009with a

line of 50Oe, which will enableoperation at VHF (250 MHz).

Computer codesare currently under developmentto predict the performanceof theseantennas.Thesecodeswill utilize rigorous,fully electromagnetic approachesand should provide us with a good deal of insight on how

to designtheseantennasfor optimum performance. Both experimental and

theoretical efforts will continuethrough 1992.

Work will alsocontinueoncharacterizingvaractor-tunedmicrostrip patch

antennas.Weareparticularly interestedin investigatingthe possibility of developingsuchantennasfor the UHF rangeaswell asenhancingour computer

model with the ability to predict the radiation patterns of suchantennas.

47
_'_ (:pl,Ypl)

(xp_,Yp2)

Figure 24: Geometry of a two-probe-fed circular microstrip patch antenna.

48
• TillS TIIEORY

t EXPERIMENT

Figure 25: Measured and calculated $11 and $12 for a two-probe-fed circular

patch antenna with the probe feeds positioned to provide unbalanced circular

polarization.

49
Coax connector

He

\

®

Microstrip line

\

Slot antenna

Ferrite

Hiahdielectric

constant material

Cavity

Figure 26: Cross-section of a slot radiator that is backed by a cavity containing a ferrite layer.

5O
E

512

REF 0.0 dE)

5.0 dB/

1 -3.9116 dB

hp

MAR <ER 1

log MAG $22

REF 0.0 dB

1 5.0 dB/

V -3.2313 dB

log MAG

START 2.@0@@@@@@@ GHz

STOP 12.@00@@00@0 GHz

Figure 27: Return loss and insertion loss seen by the microstrip feedline of

the prototype cavity-backed slot antenna.

51
_avity-ba_ked slot, no bias, horizonta] orientation

aOgOB0|.rep

A:vv (i)

FBEOUENCY = 10 BHz

D

-JO.

-20.

_-30.

:E

{3 -40.

.J

-$0.

_,,,,,'j,, , ,, I, ,,i, l, ,,,, iJ',,,',l,,, ,,

-,,,,,I,,,,,1,,,,,1,,,,, I,,,,,!,,,,,

-IB0. -120. -60. 0. 60. JE0. iB0.

AZIMUTH (deg)

Figure 28: H-plane co-polarized radiation pattern of the prototype cavitybacked slot antenna.

52
w--_

Er, _tr C

v×

Figure 29: Geometry of a two-dimensional cavity-backed slot antenna.

53
E

cn

"(D

ZIZ

£Z3

(_.9

Z

rY

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ty3

20.00 I I

10.00

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0.10 0.20 0.30 0.40 0.50

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HARD POLARIZAT/ON

SOFT POLARIZA T/ON

0.60

I I I

#

I

1

0.90 1.00

FREQUENCY (OHz)

Figure 30: Monostatic scattering width of a two-dimensional cavity-backed

slot antenna for hard and soft polarizations.

54
-1-

I,-...-.

0

Z

L._,_.I

._J

LJ

>

<:_

L/3

0

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FREQUENCY (GHZ)

Figure 31: Input admittance of a two-dimensional cavity-backed slot antenna.

55
©

©

Figure 32: Equivalent circuit of a microstrip patch antenna based on the

cavity model.

56
diode|ocafi_

0.157 cm

Figure 33: Geometry of the prototype varactor-tuned circular microstrip

patch antenna.

57
C

D

Sil

REF 0.0 dB

5.0 dB/

I=g MAG

'hp

M,_,RKER 1'

1. 575 GHz

I ,, ,

MARKER 2

2.6;4 GF-Iz

,. \,, //

'_ Vi j

OV 2.5V

5.0V

START 1.000000000 GHz

STOP 3.000000000 BHz

IO.OV

Figure 34: Measured input return loss of the prototype varactor-tuned circular microstrip patch antenna versus frequency for various bias voltages.

58
£I3

6Eb

Or)

C/3

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Z

b----

!,1

£15

0.00

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Vbias = 20 V

I I I I

2.20 2.40 2.60 2.80 3.00

FREQUENCY (GHZ)

Figure 35: Measured and calculated input return loss of the prototype

varactor-tuned circular microstrip patch antenna versus frequency for bias

voltages of 4 and 20 volts.

59
LI, Rs

cp cj

0

Cp - package capacitance = 0.15 pF

L.p = package inductance = 0.40 rtH

Rs = series resistance = 2.27 Y2

Cj =junction capacitance = 2.402 pF @ Vblas " 4 V

0.558 pF @ Vbias = 20 V

Figure 36: Equivalent circuit of the M/A-COM MA4ST556_31 varactor

diode.

60
References

[1] W. A. Radasky, "An examination of adequacy of the three-species air

chemistry treatment for the prediction of surface burst EMP," Mission

Research Corporation, prepared for Defence Nuclear Agency, AD-A025

280, Dec. 1975.

[2] R.S. Elliott, "Antenna Theory and Design," Prentice-Hall, Inc., Englewood Cliffs, New Jersey 07632 1981, Ch 9, Sec. 4.

[3] C. A. Balanis, "Antenna Theory: Analysis and Design", John Wiley &

Sons, Inc., pp. 733-734, 1982.

61