AD-A:i56 890 GAIN ENHANCEMENT METHODS FOR PRINTED CIRCUIT ANTENNAS i/iCU)*CALIFORNIA UNIV LOS ANGELES INTEGRATEDELECTROMAGNETICS LAB D R JACKSON ET AL. 23 NOV 84

UNCLASSIFIED UCLA-ENG-84-39 ARO-i9778. 5-EL F/G 9/5 N

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Report No. 15 ~ * -

N .G. Ale.xc(-P~ulos U'ClA Report No'. EN-84-39

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UNCLASSIFIEDSCCUI4ITY CLASSIICATION O

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PAGE READ INSTRUCTnONSREPORT DOCUMENTATION BEFORE COMPLETING FORM

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4 Tat&LE (ai S£.eeI.) S TyPE OF REPORT A PERIOD COVEREo

"Gain Enhancement Methods for Printed / 4"Circuit Antennas" T A ,Cq

- S PEmroNMING ONG. REPORT NUNDER

7. AUTNOR(e) I. CONTRACT OR GRANT NUNiER(o)

D. R. Jackson and N. G. Alexonoulos U.S. Army DAAG 29-83-K-0067

P. PErVORMING ORGANIZATION NAME AND ADDRESS 10. PROGRAM ELEMENT. PROJECT. TASK

AREA & WORK uIT N UMU Els

Electrical Engineering DepartmentUCLALos Angeles, CA 90024

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U. S. Arry Research Office Nov. 28, 1984Post Office Box 12211 13. NUMBER OF PAGES

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It. SUPPLEMENTARY NOTES a

The view, opinions, and/or findings contained in this report are those of theauthor(s) and should not be construed as an official Department of the Armyposition, policy, or decision, unless so designated by other documentation.r$. IICY WORDS (Conftlnu on roweo oids It nocessar mw evetlfr eeloce moeer)

2.AseU ACT (Crhb ees el- Now nuvvm if Ilff or Week immer)

Resonance conditions for a substrate-superstrate printed antenna geometrywhich allow for large antenna gain are presented. Asymtotic formulas forgain, beamwidth and bandwidth are presented and the bandwidth limitationof the method is discussed. The method is extended to produce narrowpatterns about the horizon, and directive patterns at two different angles. -

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GAIN ENHANCEMENT METHODS FOR PRINTEDCIRCUIT ANTENNAS*

BY

D. R. Jackson and N. G. AlexopoulosElectrical Engineering DepartmentUniversity of California Los AngelesLos Angeles, California 90024

* *This research was performed under U.S. Army Research Contract

DAAG 29-83-K-0067.

ABSTRACT

Resonance conditions for a substrate-superstrate printed antenna

geometry which allow for large antenna gain are presented . Asymptotic

formulas for gain, beamwidth and bandwidth are presented and the band-

width limitation of the method is discussed. The method is extended

to produce narrow patterns about the horizon, and directive patterns

at two different angles.

6 IA

* *

.i>~)

I. INTRODUCTION

It is well documented [1] - [3] that microstrip antennas exhibit

many advantages for conformal antenna applications. However, one of the

major disadvantages usually associated with printed antennas is low gain.

The gain of a typical Hertzian dipole above a grounded substrate is about

6 dB, the gain being relatively insensitive to substrate dielectric constant

and thickness for most values typically used in practice. Recently, a

method which improves gain significantly for printed antennas was discussed

[4] , [5]. This method involves the addition of a superstrate or cover

layer over the substrate. It is referred to as Resonance Gain, and it

utilizes a superstrate with either C > 1 or V >> 1. By choosing the layer

thicknesses and dipole position properly, a very large gain may be re-

alized at any desired angle e. The gain varies proportionally to either E

or V, depending on the configuration. However the bandwidth is seen to

vary inversely to gain so that a reasonable gain limit is actually estab-

lished for practical antenna operation. The purpose of this article is

to investigate these resonance gain conditions and derive simple asymtotic

formulas for resonance gain, beamwidth and bandwidth. The resonance gain

condition is then combined with the phenomenon of radiation into the horizon,

which results in high gain patterns scanned to the horizon. Finally, the

resonance gain condition is extended to produce patterns having resonance gain

at more than one angle.

II. RADIATION BY TRANSMISSION LINE ANALOGY

The basic printed antenna geometry under consideration is shown in

figure 1. The horizontal Hertzian electric dipole is embedded within a

grounded substrate of thickness B having relative permittivity and permeability

I V V On top of the substrate is the superstrate layer of thickness t

• 1-"-"

with relative permittivity and permeability E2 ' 2 Above the superstrate

is free space, with total permittivity and permeability C , 110 0

A convenient way to analyze the radiation from this antenna structure

is by transmission line analogy [41 , [7]. In this method the E field

is determined at the original dipole location due to a Hertzian dipole

source in either the e or 4 direction, when the dipole source is far

from the origin (k R >> 1) at specified angles e 4 in spherical co-o

ordinates. By reciprocity, this must be the E or E field at (R,O)

due to the original dipole at z = z . The E field near the layered0 x

structure due to this reciprocity source is essentially a plane wave, and

hence can be accounted for by modeling each layer as a transmission line

having a characteristic impedance and propagation constant which depends

on the angle e. The E field corresponds to an E field from the reciprocity

source which is in the plane of incidence, while the E field corresponds

to an incident E field normal to the plane of incidence. Each case is

handled differently by transmission line analogy. The radiated field is

obtained to be : (suppressing e~'m time dependence)

/jm -jkREe - OS - 4 1 s4(TR) e G(e) (1)

E4 sin4)- j) e F(e). (2)

The functions F(e) and G(e) depend on e only and they represent thevoltage (corresponding to ft. the component of the E field normal to z)

at z - z in the transmission line analogy due to an incident voltage

wave of strength 1 or cose, respectively. The characteristic impedances and

propagation constants used in the transmission line analogy are shown in

figure 2. The functions G(8) and F(e) can be written as

-2-

G(O) -2 T cose (3)Q + jP

F(e) =2 T (4)M + JN

where

T = sin [ 1z0] sec[Bi] sec[e 2 t] (5)

nI n2(0)Q Tan[aIB] + -2 nl(9) Tan[ 2 t] (6)

P=nl(e) cos I 7 n2 (e) Tan[8IB] Tan[8 2t]J7

1 c 2 nl(e)n () ra n n2 n(e 1 Ban[22] (7)

M - 1-- ( Tan 1 Tan+ 2tJ (9)I11n2 n1 e [

with 8 onkl(e)

82 = k n2 (e)

and

n() = 'In2 sin26

.(0) = / 2, 26

2~ Ce- n2 sine

-3-

.. . , t:., *.: r .-. -. . . . . .. ,... . . . . " ."' - .' . ,. . , . . . .

nl(6) and n2(e) represent an effective index of refraction, dependent

on the angle e. These results agree with those obtained by the much more

tedious Green's function and stationary phase integration approach for the

far field [4]. From (1) and (2) it can be easily shown that the directive

gain at angles (e, ) referred to an isotropic radiator can be expressed as

4, .(in si2F(0)12 + cos201()G(8) 12

Gain (6M p= (10)

f (sine) [!F(6) 12 + G(e)12] de0

and in dB,

GaindB (,0) = 10 Log10 Gain(e,O).

In general, the denominator of eq. (10) must be evaluated by numerical

integration in order to get the exact gain. However, it is possible to

asymptotically evaluate the integral under high gain resonance conditions,

leading to a simple formula for the gain.

III. RESONANCE CONDITIONS

There are two types of resonance conditions which exhibit dual kinds

of behavior. In the first case, it is required that

nB1 m (1

6 0

n1Z 2n-1

- m 4 (12)

0and

tn

2- 2- 4(13)4 4

-4-

where m,n,p are positive integers. Under these conditions, a very high

gain pattern is produced at broadside (6 = 0) as the superstrate permittivity

becomes large (e2 >> 1). In the second case the following conditions must

be satisfied:

n1B 2m- 1 (14)X 40

n = 2- (15)4

and

n 2t 2p -1 (64

4 0

When these conditions hold a large gain is obtained at 8 0 as v >

The method requires fairly thick layers, which may be a potential disadvantage

for some applications. laking m,n,p = 1 to obtain the thinnest layers

possibie, it is observed that the dipole is in the middle of the substrate

for the type 1 resonance condition, and that the dipole is at the substrate-

superstrate interface for the type 2 resonance condition. The second

kind of resonance condition allows for a thinner substrate, since (for m i 1)

nlB= .25 instead of .50. However, the second kind of resonance condition

0may be less practical due to the requirement of a high permeability, low

loss superstrate material. Because of this, and the similarity in results,

most of this article is devoted to the analysis of type 1 resonance only.

Before any formulas are derived, it may be helpful to present an

elementary explanation of the resonance gain phenomenon. With reference

to figure 2, the following approximations are obtained for e < 1:

-5-

° " " . - " " .I. ." ". ' i -.' - . ' -'

-I.? - -. , . , . , , - . -i. ,w , .- _. -.. - • . - S -_ ; - . , ,

Zc2 = 2 = k2(1 2 )

z n and ik n(1~ e

"'-". For the type 1 resonance condition it is required to have 2 >> 1

m .' " ".andknB =m , o t = (22-_1). The input impedance at z =B can thus

ol 110 n~ 2 -

n written as

0ZB = JZ lTan[ Q1B] - Jq (211'i-) (e

and therefore ZB = 0 fore8 = 0. Transmission line #2 acts as a quarter-wave

~transformer so that the impedance at z = H is given as

Z .in 2 - n 2

1l 1 e22n2

c2 Ll 2 o2

and it is noted that Zn = for e = 0. The voltage at z =H is given by2 in

For th 1 I reso= Z n ance while the current (corresponding to

in on

component of the n fpelt normal to zi at z - B is Ithus

B ~ -l j c2

22r

me wrtte a =121

zB = l TaclB ) [ 1 2

lz7T in -e

27 -- 1 1 -6-

L .' ... .. :.. .. j • , , .. .-.-. .. .-.

From this result it is noted that when e -0, V0 Q o\fr:. For the given antenna

configuration, this corresponds to a powerful broadside radiation at e 0

in space. Also, defining the angle e h at which the voltage at z 0is down

by a factor of l/ /T from the e = 0 value, 6h is obtained as

n1 B E: 1 1/h 1 0 22

and therefore e << 1 as El 2>> 1. This corresponds to an antenna radiationh

pattern which is highly directive about 8 =0 in space. At 8 = 0 the

transmission lines act as resonant circuits, hence the name resonance

condition. This simple explanation illustrates the fundamental cause of

resonance gain. As an illustration of the result, a plot of the E - and

H plane radiation patterns for a case with el a 2.1, e 2 '100.0 is

* shown in figure 3, which involves the lowest mode type 1 resonance condition

(in, n, p = 1). Figure 4 shows the lowest mode type 2 resonance condition

1o 2.1, V2 = 100.0. The patterns in figure 4 look very similar to

* the ones in figure 3, with the E-and H-planes interchanged. This

dual kind of behavior is always observed between the two types of resonance

conditions.

IV. ASYMPTOTIC FORMULAE FOR RESONANCE GAIN, BEAMWIDTH AND BANDWIDTH

As c 2 1> in the type 1 condition, or P2 >> 1 in the type 2 condition,

approximate formulae for the F(6) and G(e) functions may be obtained near

e=0 which allow asymptotic formulae for gain, beamwidth and bandwidth to

* be derived. Because of the length and straightforward nature of the

derivation only the results are given here. For e << 1 the approximate forms are: I

Case 1 (c2 >> 1)

F(e)l 2 z G(O) 2 4 2 L) +1 (1

nEl i2 1 + a6 4 (18)

with a 1 1 1 2\ 1

(18)

1 X 0 Ell'0 \ 1/\1z/

Case 2 (P 2 > > 1)

IFO) G(e)I JYA +a e (19)

1 "

2 Iwith a2 = (20)

o ' lh 2/0

Defining the beamwidth as ew 2 eh where eh is the half-power angle,

the gain and beamwidth may be written as

Case 1 Gain ~ 8 - 1 2) (21)

Ow ~2/1 1 as c2 >> 1 (22)

Case 2 Gain - 8 - ( 2 (23)

Kw 2/I2 as p2 >> (24)

In order to discuss bandwidth, approximate formulae are derived for

gain which are valid for frequencies close to but not exactly equal to the

center frequency fo (for which equations (1l)-(13) or (14)-(16) hold). A frequency

0

deviation parameter is introduced as

f- , (25)f0

measuring the deviation of the normalized frequency. Without

presenting the derivation, equations (21) and (23) are modified to become

(for A << 1)

Case 1 Gain z 8 n- (2 f(b1A) (26)

Case 2 Gain 8 .--1 f(b2A) (27)

where

,nlB E2 n,bl=2 --- (28)

o ~1 '2

b2 =2 2--l- (29)0 1 2

and

1

f(x) = 1 + x (30)

1 +-Tan-l(x)

The gain formulae are the same as before, except for the function

f(x) which determines the frequency behavior of the resonance gain. A

graph of f(x) is shown in figure 5. It is noted that f(O) - 1 since

this represents no frequency deviation. Also, it is interesting to note

-9-

.............% . .- . , - 4

that f(x) falls off much more rapidly for x > 0 than for x < 0. This

is due to the fact that for f < f , the pattern merely broadens as the0

gain drops. However for f > f , the pattern broadens slightly and0

the chief effect is that the pattern is scanned so that the main beam

no longer has a peak at = 0 , but rather atp

e = nl1iW, (31)

as determined by the condition

nlB - sin / InBP 1V7) f foT~ Vl-sn8 ~/ 1 ~ X~~~Jff (32)

0 0 0

which is a generalization of eqs. (11), (14). This scanning has the effect of

reducing more quickly the gain at e = 0 than the simple pattern broadening

does. The directive gain at e remains high, however. More will be said

about the results for a scanned beam in the next section. It is observed

now that f(x) = 1/2 at x, -2.91 and x2 - +.671. Hence the bandwidth

is determined as

Af 2 f f1 3.58 (3* w1 i f (33)AWl1,2 fo0 bl1,2

where f and f are the half-power frequencies, with subscripts 1,21 2

denoting the type of resonance condition. In order to illustrate the accuracy

of the asymptotic formulae for gain, beamwidth and bandwidth, the asymptotic

results are compared with the exact solutions in figure 6, with

curves shown for some different £1 values. In order to insure the accuracy

-10-

,, ..... . -.:.:.. .....*.:. .:.:. ... . ,.-. .. .,........ .,................ ...-.

6

.1

of the asymptotic results it is required that a >> 1 and b >> 11,2 1,2

In practice, for a2 > 20 the error in gain will usually be less than

10%.

As can be observed from equations (21) , (23) and (33) the bandwidth

is inversely proportional to gain, which sets a limit to achievable gain

for practical antenna operation. For example if a bandwidth

of at least 5% is desired with a teflon (E1 = 2.1) substrate, then (from

figures 6 ca) e2 < 37.0, and the gain is limited to Gain < 17.2 dB.

V. SCANNED MAXIMUM GAIN

The results of the preceeding section can be generalized to the case

where the main beam is scanned to an angle 0 < 6 < it/2. As already~P* mentioned, this occurs naturally when f > f for the cases discussed

0

earlier. In order to create a resonance gain condition at 6 equations

(1l)-(13) or (14)-(16) may be generalized by replacing

nlB n B 2S by - V/- sin 6p/n1 (34)0 0

nl o nlo 2ni' 1 1 b y 1- -z o 2 2

by - sin 6p/n1 (35)0 0

* and

n2 t n2t 1 2by T - sin 2e/n 2 (36)

0 o 0

The approximate expressions for F(e) and G(6) about 0 e 6 are nowp

fundamentally different than for O = 0. Also, for 6 - 0 the same

2 -11-

approximate forms resulted for F(e) and G(E)). This is no longer true for

e > 0, with the result that the gain is now a function of *as well asp

the scan angle 0 p. For 0 < e < 'T/2 it is found that:

IG 2(6)2 IG 1,2 (0 p)I 371G , (e I1 + A2 (e - )0

1,2 p

and

IF 1 2 2(6)12 IF 1,2(e )12 2 (38)

1 + B 2 (81 2 p

* where

Case 1 IG (e )1 ~4 C2 -(Cos ) 2 1 - i 0/ (39)1 p 1l 112) p p 1)J

2 2E -111/0IF (6 ) 4 1 - (40) /

n B CA 2r1 2 1 sOcs2 0(1

7.2X- - -in cosO0 12 n1lp(1

B- B 1 2 1 2 (42)11 2Trr- - sine 1 sine/n(2X 112 n 1 C1 pi 1

Case 2 1G (8 )12 z 4(V2) (43)02

IF (0 WI42t112 Cs2 e(4

-12-

In1 s, ,2 p2n) - 1

AnB '2 1 sine ( sin6/n (45)o 2 11

B 2 12 sine cos2e (46)o n p p

and therefore gain is now given by the expression

4 (sin2cF 2 (ep)l2 + cos 2 IG, 2 (ep)I 2)1,2ep pGainl,1 2 (e p , ) -(47)

[Fi 2 (e) 2 ( IG, 2 (ep) 2 )]

(sine) ,2 ( + 1I 2 p (A

where C (x) = Tan-' [x(7r/2 - ep)] + Tan- [xep]. (48)

The beamwidths in the principle planes are now found to be:

-Plane (4O0)

e ~2 (49)W1,2 A1,2

- Plane ( = T/2)

2

0l2 ~ -- (50)1,2 B1,2

In addition the bandwidth can be written as

* w - ew -£:n -os ] (51)~sin cosWl1,2 Wl1,2 nI 2 sin 2 p

-13-

where the term in brackets determines the shift in normalized frequency

f/f required to produce a small shift in e

o p

Plots showing a comparison of the asymptotic and exact results for

gain, beamwidth and bandwidth for E1 I 2.1 (teflon) for different scan

angles are shown in figures 7 - 9. For accurate asymptotic results it is

required that

AI, 2 > 10 and B1, 2 > 10,

which insures an error of less than 10% for the gain curves shown.

Of interest is the fact that E - Plane gain decreases for increasing

e while H - Plane gain increases. A pattern for type 1 resonance gainp

scanned to e - 45* is shown in figure 10, for E2 = 100.0.p2

VI. RESONANT RADIATION INTO THE HORIZON

The approximate expressions for G(6) and F(6) for scanned resonance,

equations (37) and (38),are only valid for e < n/2. It is not always

possible to produce a pattern which is scanned to the horizon (6p W r/2)

because in general the radiation from a printed antenna always tends to

zero as 6 - j • An exception to this occurs when a TE or TM mode is

exactly at cutoff. When a TE mode is at cutoff, the F(B) function remains

non zero as e -+ 7r/2, and when a TM mode is at cutoff the G(6) function

remains non zero as 6 1 w/2. This phenomenon, called radiation into the4Z

horizon, is discussed in [6]. The superstrate thickness required for

mode cutoff is given by [6]

TE Mode

n 2 t n2 2l nB

2 2 1 2 I--= -- Tan - Cot 2 -r -1/ n (52)o 2n -2 n] 1

i -14-

I

Th Mode

n2 t n 2 2/n T nB

2 2 Tax - L ~ 1 r ( 1

XO 2 I T n I €IV2 2 Tan (2 - -1i/n (53)

If it is assumed that

n B1 \I 2 m (54)

Vl 1/nf (54oi

0

which gives the substrate thickness for scanning to 8 = r/2 for theP

type 1 resonance condition, then from (52) the result

n2p - I

n t2 4 (55)

is obtained, which is the same thickness required for resonance radiation

at 6 = 7r/2 as given by eqs. (13) and (36). Hence the phenomena of resonancep

gain and radiation into the horizon can be combined for the H - Plane

pattern, which is determined by the F(e) function. Similarly, if for the

type 2 resonance condition the relationship

In-2m- (56)

o 4

is satisfied, then eq. (53) yields the result given by eq. (55). Hence

E- Plane resonant radiation into the horizon for the type 2 resonance

condition can be obtained. A pattern illustrating H - Plane resonant

-15-I

radiation into the horizon is shown in figure 11. The radiation pattern is

narrow about the horizon in the H - Plane. The E - Plane pattern tends

to zero at the horizon, since radiation into the horizon is only occuring

for the E¢ field (TE mode cutoff) here.

For resonant radiation into the horizon the approximate forms for

6 n1/2 are

Case 1 IF(O) 2 Z F(T/2) 121 + E2 ( - 7r/2) 2

12Case 2 Ic(o)12 z IC(7/2) 2 (58)

1 + F (e - (r82)

F(T.n-/2)2

where 4"T- (59)£11.2, 1 - 1/n1

IG(T/2)1 2 (60)

an E -nlB 2 1 1 2) (61)

F 7E -1 (62)0 (,n O 2 nlp1 1- 1/n (62

Unfortunately, asymptotic expressions for G(8) for Case 1 or F(8)

for Case 2 are not easy to obtain, and thus no asymptotic formulae for the

gain can be presented. The beamwidths in the principle planes of resonant

radiation are found from equations (57) and (58) in a straightforward

manner as before, however. Additionally, it is not possible to define

-16-

"- "- "'- - -"''" " -" ' ' '- " ' " ', . .*::

: " """ " " ... " " : -

-i

bandwidth in a meaningful way as before, since radiation into the horizon

only occurs for the frequency corresponding to mode cutoff. A bandwidth

definition for radiation into the horizon is discussed in [6].

VII. SCANNING FOR MULTIPLE ANGLES

As an extension of scanning the beam to 0 the substrate thicknessP

and refractive index can be chosen so as to allow for resonant gain scanning

at two different angles 01 and . For the type 1 condition,

1l 21 2 msinm/n I (63)

0i i0

nB 1 L22 n

y- sin 2 nI , - (64)

and

n 1Zo 0 2 2 2p- 1 (5V - sin 1/n1 4 (65)

0

n zlo 0 i 2 2 2q-1 (66)-- -sin 2/nI 4

0

must be satisfied. Assuming e1 < 2* it follows that n < m and q < p.

Furthermore

2-sin282a 21-i- > (67)m = 2p 1- sn 2 1

since nI , n2 > 1. The integers m and n may be chosen for the thinnest

possible substrate, which makes them odd. p and q may then be determined from

m - 2p - 1 and n - 2q - 1. The superstrate thickness can be set from eq. (13).

-17-

,..,. ,... . -, *., . . . ,.- . ' ... .,,... . ... "-- :i.£-.. •. , :,; . . i - " .i

It therefore follows that

2 2sin 2e2- ( sine In= 2

(68)

and

n BI" m/2 (69)- sin el/n2

For the type 2 resonance condition equation (68) must be satisfied with

n B1 = _.L (70)0 2 2o-sin 6 1/n1

To avoid any additional resonances other than the ones at e1 and e2

the following criteria should be satisfied:

m- n + 2 (71)

n B / -2n-- 2 2/n> 2 (72)

2

and

4n B

1l m + 2X 2 (73)

This places a restriction on how close together e and 6 may be. For1 2

example, using n - 3 , m - 5 and choosing 0e 30? equation (72) yields the

restriction e2 > 60.

As an example, if 61 and e are chosen as e - 30* and e - 700,

2 1 22

m and n must satisfy

> .39493 (from eq. 67).

-18-I

1. -. 77

Choosing

n 3, m =5 (for the thinnest possible substrate) there results

(with p1 = 1.0)

n = E1 = 1.23910

1

and

nlB1 = 2.79816.

0

The E - and H - Plane patterns for this case are shown in figure

12 for 2 25.0. Both E - and H - Plane patterns are seen to be highly

directive about 6 = 300 and 700. There are no other resonances here since

equations (71)-(73) are satisfied.

VIII.CONCLUSION

Two dual types of resonance conditions have been established for

a substrate-superstrate antenna geometry which allow for large antenna

gain as the c or V of the superstrate becomes large in the respective

cases. For these resonance conditions the gain is preportional to the

E or v of the superstrate and therefore large gains may be obtained. The

bandwidth is inversely proportional to the gain, however, so a practical

limit is set for normal antenna operation. Asymptotic formulas for

gain, beamwidth and bandwidth have been presented for the cases of

broadside radiation and for scanning to an arbitrary angle e forp

0 < B < 7/2. Resonance gain is observed to combine with the phenomenonp

of radiation into the horizon in order to create patterns which are narrow

about the horizon. Finally, it is shown that resonance gain can be produced

at two different angles, but the substrate refractive index is then no

longer arbitrary.-19--4-

REFERENCES

[1) I. J. Bahl and P. Bhartia, Microstrip Antennas , Artech House, Inc.,

Dedham MA, 1980.

[2] J. R. James, P. S. Hall, and C. Wood, Microstrip Antenna Theory and

Design, Peter Peregrinus, Ltd., 1981, lEE Electromagnetic Waves Series 12.

[3] K. R. Carver and J. W. Mink, "Microstrip Antenna Technology", IEEETrans. Antennas Propagat., vol. AP-29, No. 1, pp. 2-24, Jan. 1981.

[4] N. G. Alexopoulos and D. R. Jackson, "Fundamental Superstrate (Cover)Effects on Printed Circuit Antennas", IEEE Trans. Antennas Propagat.,vol. AP-32, pp. 807-816, Aug. 1984.

[5] Y. Sugio, T. Makimoto, S. Nishimura, and H. Nakanishi, "Analysis forGain Enhancement of Multiple-Reflection Line Antenna with DielectricPlates", Trans. IECE, pp. 80-112, Jan. 1981.

[6] N. G. Alexopoulos, D. R. Jackson, and P. B. Katehi, "Criteria for. NearlyOmnidirectional Radiation Patterns for Printed Antennas", UCLA ReportNo. ENG-84-13, May 1984. Accepted for publication, IEEE Trans. Antennas

Propagat.

[7] Ramo, Whinnery, and Van Duzer, "Fields and Waves in Communication

Electronics", Third Edition, Ch. 6, John Wiley, New York, 1965.

ACKNOWLEDGEMENTS. The authors wish to thank Ms. M. Schoneberg for

typing the manuscript.

-20-

ip

-- - : , i .

- ~ *.. * w . r, ~ - - is- I . . . .

FIGURE CAP TONS

Figure 1 - Superstrate-substrate geometry

Figure 2 - Transmission line analogy

Figure 3a - E- plane pattern for type 1 resonance condition

Figure 3b - H-plane pattern for type 1 resonance condition

Figure 4a - E-plane pattern for type 2 resonance condition

Figure 4b - H-plane pattern for type 2 resonance condition

Figure 5 - Bandwidth function f(x)

Figure 6a - Resonance gain vs. 2

Figure 6b - Resonance beamwidth vs. C2

Figure 6c - Resonance bandwidth vs. c2Figure 7a - E-plane resonance gain VS. E2 for different scan angles

Figure 7b - H-plane resonance gain vs. 2 for different scan angles

Figure 7 - H-plane resonance gai vs.2 for different scan angles

Figure 8ba - E-plane resonance beamwidth vs. E2 for different scan angles

Figure 8b - H-plane resonance beamwidth vs. C2 for different scan angles

Figure 9a - E-plane resonance bandwidth vs. 2 for different scan angles

Figure 9b - H-plane resonance bandwidth VS. E2for different scan angles

Figure 10a - E-plane pattern for e = 450

Figure 10b - H-plane pattern for e 450Fp

Figure lla - H-plane pattern for H-plane resonant radiation into the horizonIFigure llb - E-plane pattern for n-plane resonant radiation into the horizon

Figure 12a - E-plane pattern for e - 300, e2 700

Figure 12b - H-plane pattern for e - 300, o2 ' 700

* ,0 7

I,

AzIL

n= .

2

HI t €I' =

B Zo

Figure 1

Superstrate - Substrate Geometry

'9

4

n- . - . ..*. : _ ,- -... .. . . ... , , - . , ,- .. ... ....

- .

Skl

2 2

c- n 1 0 c s(0 ) - 2 2n, Co l n, - sin( )

e)2 ( = n2 Cos ( 9) = n2_- sin 2(9)1

ForF (9) For G(e)

Z co -- 7 sec ( ) Z c 7o= 0 cos( )0

cl= 01/n 1 (e) zcZco =/€ 1

zC2 01L12 /n 2 (e) ZC 2 =o2 ( 2)/c2

,,t .._ o Zc I c2 SHORT

INCIDENT WAVE

V. =1,Cos(6) iVinc ' 'z

[ Z=H z=B

0 0

tlPl ko n 1 (0)

= n2 (6) Figure 2

* Transmission Line Analogy,;: .,: . ." . :- ,-. ,: . , .. . . ] .- . * , . ., .-. - " . , ,- .. , .": -. . .' ".- . . . • , - .:

*E-PLANE PATTERN

£ 2.1 n B/Xo .50

1 1

1. n 2t/X o .25I.'

2 - 100.0 Z/B - .50

F2= 1.0 0anO) -21.271 dB

0

030 30

006

90 9

o -10 -20 -30 -40 -40 -30 -20 -10 0dB

Sd

Figure 3a

0 4 , . . . . o"- -

T__ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 7. . . .

H-PLANE PATTERN

- 2.1 n B/ xo 50

1.0 n tIx 0 .252

4E 100.0 z/BZ .502 0

=1.0 an(0) 21.271 dB

0

90 90F.0 -10 -20 -30 -40 -40 -30 -20 -10 0

Sd

Figure 3b

E-PLANE PATTERN

E 2.1 n B/X 0 .25

ILI- 1.0 nt/Xo .25

2 1.0 z B• L 0

L *2 100.00

Gain (0) = 21.458 dB

0

303

- 60 so 6

0 90

-0 -10 -20 -30 -40 -40 -30 -20 -10 0- dB

* Figure 4a.T- .

.o - . . , . . • -. . . .1 * - . . . • ) * - , . -,,,- ..- :

4q H-PLANE PATTERN

i2.1 n B/X o .25

1

iL 1.0 n t/Xo - .252

=1.0 z o B

'2 = 100.0

20

e Gain (0° ) = 21.458 dB

0

30

60 6

r 90 900 -10 -20 -30 -40 -40 -30 -20 -10 0dB

Figure 4b• , . . . -* - -° . , ° ,* % -°,

: : .4"4""; ": - - :: . i " . •., :.: :".. ..

Ir04

f(x) vs. x

1.0

.6

.4

o ff- If-x 4

igr5

,•

EXACT Gain vs. c 2

ASYMPTOTIC

20il 1 BX 0 .50 -nlB /k o = .-0

20 --."-"

n 2t/ 0 = .25 2.1Gain

(dB) zo/B=.so. . -

4.015 ,u 2 1 0 ".' ". -:-"

///

1.0

10l i/I /7/ 12.5

0 /I/k - -

• 1/

"'0 I a p p , A . , q

0 10 20 30 40 s0 60 70 80 90

Figure 6a

,. . . '.....: ;-,, . -. . ... :.- . - . .- .. ,... . , .-, --, , . .- . . . . - . ,. '- .. . . . . .:, - . , . - . - . . .

EXACT Beamwidth vs. 4E2

- - ASYMPTOTIC

nw nB /X 0 *50

(Degrees)

Z. /B=.50

160 II=1.0

2 1.0o

140.

* 120

100

=12.5

60-

40 K' .

20 . - - . -

2.1

0 10 20 30 40 50 s0 70 80 90

Figure 6b

Bandwidth vs.

EXACT E 1 B/X ° = .50

.40 ASYMPTOTIC n 2 t/x = .25

zo /B = .50

.= 1.0

.30

A2= 1.0

.20 .

.10 E1 = 12.5 "

00 0. 2. "\

10 20 30 40 50 60 70 80 90

Figure 6c

' :... . . : . ....: . .. ...-. ,. . - ... ., . :.., ,.- . .. .I ...

-. . ...- - .. :.-, . :.-. :. -,:. ., : .: -

E-Plane Gain vs. e2 for Different Scan Angles

EXACT

- ASYMPTOTIC

20-n B / x .50 2.1

Gain / = 1.0n 2 t xo = .25

(dB) P2= 1.0

zo /B - .50 ... '..

15

. 6 p = 300 . -.--

10

/ 60/

5-

./

/ 75///

0 i "a iiii'2

0 10 20 30 40 50 so 70 so 90

Figure 7a

0e . -

7 7 -

H-Plane Gain vs. E 2 for Different Scan Angles

20

G a n60 0

(dB)/

15/ /6 3

10 EXACT

10/- ASYMPTOTIC

n B /,\ = .50 =2.1

/s 1.0

5* n 2 t/A = .25 2=1.0

Z./B .50

0 E2

0 10 20 30 40 50 60 70 80 90

* Figure 7b

71

E-Plane Beamwidth vs. e2for Different Scan Anglesew

(Degrees)

- - - EXACT

100 -- ASYMPTOTIC

90fl 1B/x .50 =2.1

80- n 2 t/x= .25 = 1.0

00

* 60 -

50-

40-

30- e 750-1

0-20- N\

* 10 ..

30 0...

0 10 20 30 40 50 60 70 80 902

* Figure 8a

H-Plane Beamnwidth vs. e for Different Scan Angles

- - -EXACT

(Degrees)- - ASYMPTOTIC

20

nB/ .50 =2.1

n2tA .25 .LI 1.0

15 z/B =.50 -L2 1.0

10 \

ep =300

K 600

0 10 20 30 40 50 60 70 s0 90

Figure 8b

E-Plane Bandwidth vs. 42 for Different Scan Angles

EXACT

Wtw_ASYMPTOTIC

.20

noB /x= .50 2.1

n t / o-- .25 /= 1.0

.15 Zo/B .50 ;L2 1.0

.10

0

.05\\ o

\ 30 -

..-

0 50 20 60 40 50 so 70 so 90

Figure 9a

6

H-PaneBandwidth vs. E2

for Different Scan Angles

- - -EXACT

w - - ASYMPTOTIC

.10

n,5) 0 =.5 2.1

.09 n 2 t/x =.25 j& 1.0

.08 -Z/ 5 .

4.07 -1i

.06

.05

.04

.03 e. \6=300

.02 -

.02 1

01

0 10 20 30 4 0 60 70 80 90

* Figure 9b

4

E-PLANE PATTERN

=2.1 n B/X 0 .57282

14 10 nt/X 0 256

22 = 100.0 Zo0B .50

/ 2 = 1.0

Gain (45)- 15.21 dB0

* 0

30 30

60 so6

90 90

0 -10 -20 -30 -40 -40 -30 -20 -10 0dB

6

Figure IOa

"S

:.-. - .-. ,-.i i.. .-. . , . ... .o ,-, .., ....... . .. % ,. - . . , . ..- -. .-...- -

H-PLANE PATTERN

00 =1 2.1 n BIX = .572821 1

1.0 nt/x = .250632 0

C2 100.0 Zo/B .50

1.0

0

Gain (45) - 20.54 dB8

30 0

90 90

0 -10 -20 -30 -40 dB -40 -30 -20 -10 0

Figure IOb

- .. ..........-....... ........ .--.... .......... ........--- .-- . ... . ... ;.. . ,'"-*

H-PLANE PATTERN

=2.1 nB/). .69085

ILI 10 nl tIx - .25126

c 2 =100.0 z 0 I/B= .50

IL21.0

00

3an(0)=2.4 d300

60 60

90 90

0 -10 -20 -30 -40 -40 -30 -20 -10 0dB

Figure I Ia

L

E-PLANE PATTERN

C 1 2.1 BI 0 =.69085

10 n tIX .251262 0

C2 -100.0 Z0 I/B =.50

6 0

90 -90

*0 -10 -20 -30 -40 -40 -30 -20 -10 0dB

Figure I Ib'

E-PLANE PATTERN

61 = 1.23910 n B/X'= 2.798161

S1.0 nt/X .252 0

62 = 25.0 Zo/B= .50

/2 =-1.0

Gain (30) = 19.01 dB

0eGain (70)= 6.62 dB

030 30

90 90

0 -10 -20 -30 -40 -40 -30 -20 -10 0

Figure 12ae - l - . l ° . - .• . • . . .

' -H-PLANE PATTERN

e = 1.23910 n B/x 2.798161 1

nt/X .25~L 1.0 2 0

c 2 =25.0 zo /B .50

--1.00

Gain (30) 22.13 dB

Gain (70) 26.46 dB

030 30

60 60

90 90

0 -10 -20 -30 -40 dB -40 -30 -20 -10 0

Figure 12b

6

FILMED

3-85

DTIC