,AD-AL12 607 CALIFORNIA UNIV LOS ANGELES INTEGRATED ELECTROMANET-ETC F/6 9/5ON THE EFFECT OF SUBSTRATE THICKNESS AND PERMITTIVITY ON "~INTE-TC(U)DEC 81 P B KATEI, N 6 ALEXOPOULOS OAABZO-79C0050

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On the Effect of Substrate Thickness and Prit- Technical Laboratorytivity on Printed Circuit Dipole Properties. Report

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Substrate PermittivityPrinted Circuit Dipole

20 ASSTRACT (Ceitlom enUe, si e. it ageewp me EdMotp 1*11Y1 Wol 10mee)

The effect of substrate thickness and relative peritticity on the radiatoproperties of printed circuit dipoles (PCD's) is Investigated. A trade-offbetween substrate thickness and resonant Input resistance, bandwidth andradiation efficiency is presented for a PTF1 glass random fiber substrate. Iis found that for a fixed substrate thickness B, the resonant length anddirectivity decrease with increasing relative dielectric constant t . TheE-plane normalized power pattern Is also examined as a function of 1, and

r

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sSSVUYY OLASSIPI,10CATI011 or THInS PACE(o ~awe sweem

Classification 20. (Continued) 4Vz, ~

N B. It is shown that even for very,!hIn substrates, multiple bean radiationcan result for certain values of e by the excitation of surface waves.

'Multiple bean patterns can also be Sbtalned with Increasing B for a given4_. In fact, as B Increases it is determined that the resonant length,bandwidth and resonant resistance approach the apparent value of a PCD ona dielectric half space. _

IC

I.

On the Effect of Substrate Thickness and Permittivity

on Printed Circuit Dipole Properties.

P. B. Katehi and N. G. AlexopoulosElectrical Engineering Departuent

University of California, Los Angeles, CA 90024

T his work was supported by the U.S. Army under Contract OAAG29-79-C-0050and by the U.S. Navy under Contract N00014-79-C-0856.

Abstract

The effect of substrate thickness and relative permittivity on the

radiation properties of printed circuit dipoles (PCD's) Is investigated.

A trade-off between substrate thickness and resonant input resistance,

bandwidth and radiation efficiency is presented for a PTFE glass random

fiber substrate. If is found that for a fixed substrate thickness B,

the resonant length and directivity decrease with increasing relative

dielectric constant The E-plane normalized power pattern is alsotr

examined as a function of Cr and B. It is shown that even for very

thin substrates, multiple beam radiation can result for certain values

of er by the excitation of surface waves. Multiple beam patterns can

also be obtained with increasing B for a given c . In fact, as B

increases it is determined that the resonant length, bandwidth and

resonant resistance approach the apparent value of a PCD on a

dielectric half space.

Accession For '

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Introduction.

Printed circuit dipoles (PCDs) have been successfully employed

in conformal arrays [1] - [3]. Recently, Elliott and Stern [41 and

Stern and Elliott [5] demonstrated a design procedure for the con-

struction of small arrays consisting of electromagnetically coupled

microstrip dipoles. Implicit in their approach is the accurate

knowledge of mutual coupling and array element optimization. In the

aforementioned applications the dipoles were printed on very thin

substrates (compared to free space wavelength). In the millimeter

and submillimeter frequency range PCOs have been utilized in detector

and imaging arrays with several wavelength thick substrates (see

Rutledge et al. [6) - [8]). The performance characteristics of

PCDs depend in a very crucial way on the substrate thickness B and

substrate relative dielectric constant Cre This is due to the fact

that er and B control the amount of energy coupled into surface wave

modes guided by the substrate [9] - (12]. Consequently, the radiation

efficiency, (i.e., the ratio of energy radiated by the antenna into

free space to that coupled in the substrate), input impedance, radi-

ation pattern and bandwidth need to be investigated as functions of

Cr and B.

In this paper, a trade-off study of er and B on the PCO pro-

perties is carried out. As a specific example of substrate thickness

effect on antenna properties a PTFE glass random fiber substrate

material is considered with Cr a 2.35. The results presented herein

are based on refined analytical and numerical extentions of the

information on printed dipoles contained in [9] - [11].

2

I. Analytical Formulation.

A precise understanding of the effect of substrate thickness

and relative permittivity on the characteristics of printed circuit

dipoles requires the development of integral equation solutions for

the antenna current distribution. The integral equation for the

PCD is given in its general form by (see figure 1)

L 02E(x.y.z) uf L k2 T + vvj • 1(i/?) " (')dr (1)

where L is the length of the dipole, T is the unit dyadic T-

i + 99+ .ff, is the unknown current density distribution and

(TIr') is the dyadic Green's function [91 - (101 for the problem

of interest. For the case of a PCD oriented along the R-direction

and with h - 0 (121 equation (1) simplifies to

E 6 x G+ -G) jldxl (2)

where [101, [12]

a. -" U 01 (-r) o (s l(t.B) (s hu) uxdxlf-nhu) (3)

GXjj=a 1 r fi0 X#B) A,~0 0

G j~tj0 f j(XP)/sinh~uB)N /cosh(u8) uXA 4

r0

fl (k,e) - uo sinh(uB) + ucosh(uS) (5)

f2(A,) -¢r o cosh(uB) + usnh(uB) (6)

o -[(x-x, l* 1~.2] (7)2 ( 2] ()1• 3

and

o [22]I /2 , u [ 2k. 2 (8)

The zeros of f1(x,B), f2(x,e) in the denominator of equations (4),

(5) for ko< x < k correspond to THI, TE surface wave modes (91 - (121

respectively with a TH mode having zero cut-off. The number of

excited surface wave modes depends on the substrate thickness 8

and relative dielectric constant tr* By employing the method of

moments [13] with a basis set of overlapping piecewise-simusoidal

currents the integral equation as given by equation (2) can be

discretized into a matrix form [VI - [ZI [] where the elements of

[Z] can be written as

ZkJ dx dx

xl+iv

In equation (9) 1x -aL/N where N is the total number of subsections

the dipole is divided in. By inversion the current distributions

can be obtined for arbitrary parameters tr' B and L for center-fedin (radius- l0"4 ) dipoles.

4-

Computation of the matrix elements Z i nvolves integration of

Soumerfeld type of integrals along the real x-axis [91, [10] for

which efficient routines have been written [12].

1II. Effect of Substrate Permittivity Variation

The relative permittivity is varied for a fixed substrate

thickness of B - 0.1016AO. For values of cr up to er a 45 and

for the chosen B there are three surface wave modes that can be

excited. The antenna resonant length Lr is shown in figure 2 as

a function of Cr. As more energy is coupled into guided waves

inside the substrate the resonant length decreases with a cusp

discontinuity exhibited at every value of er where the onset of

the next surface wave mode occurs. Figure 2 implies that the

radiation efficiency of the PCD decreases with increasing cr.

The dependence of the input impedance Z1n on Cr is demonstrated

in figures 3 - 5, where Zin is plotted vs. antenna length L for

Cr 2 2, 10, 35 respectively and for B- 0.1016 0 . As er increases

the following effects can be observed: (a) The value of the total

input resistance R decreases. (b) The reactance becomes in-

*creasingly capacitive with a reduced number of resonances.

IV. Substrate Thickness Variation.

A PTFE glass random fiber substrate is selected with

C a 2.35 to analyze the effect of increasing B. The variationrof PCO resonant length vs. B is demonstrated in figure 6 where-

from it is concluded that as B --.-, Lr-+0.375ko which is

anticipated to be the resonant length of a wire dipole of radius

' .. . .

10"a 0 on a dielectric half-space with cr " 2.35. Figure 7

demonstrates the dependence of PCD resonant resistance on B.

It is worth mentioning that for B - 1.2ko there exist 6 excited

modes in the substrate. As B -k -, Rr-+ So ohms. Figure 8 shows

the radiation efficiency q . -rr where Rr - Rrr + Rrs, Rrr beingRrs,

the radiation resonant resistance and Rrs the surface wave reso-

nant resistance respectively. The bandwidth of the PCO Is

exhibited in figure 9 vs. B. The bandwidth has been defined

here as

BW ~2Rr10

These curves provide a trade-off analysis for a PCD as e.g. if

we wish to choose a maximum radiation efficiency dipole with

n 3 4 at 8 - 0.2xo, then the resonant length is Lr 0.36934S o,

Rr a 90 ohms and SW a 18%. The corresponding r-plane nor-

malized radiation pattern is shown in figure 10, where it is

observed that the half-power beamwidth Is approximately 70

degrees. On the other hand if an input R. 50 ohms is desired

then B -0.12Xo, OW 8% and n -2.8.

6

V. Radiation Pattern

It is of interest to investigate now the dependence of the far-

field pattern on substrate properties. The far-zone electromagnetic

field can be obtained bya saddle-point method and the electric field

components are given by

Ee 2k;n" (11)

and

E -2k2 ]1 (12)

where

"jk0 R (costko0Sinecos,.- cos(kotx,

.o- O(F_ N e Jo in tcos

[ * e (rBse) + (Cr" 1)siney(er.B'e)] I n

(13)

e-jk 0 R (cos[k°Lxs'necos#]- cOs(kOix)*10 a J00 I- sin k0sin(kox[1 - sin 2 ecos2

N ink 1oxsinecos(*(tr.B'e) n-I I e '(14)

#(t r ,Be)a o.. 1 1 (15)T 1 o r - sn I n

case-___ cot(k sin )

and

7

j ( - j cn :t(k Cr- sn 2e 8)

(16)

Er cose tan(kov r7 sine B)

or

(C rB,e)= taneo(c rB e) A(c rB e) (17)

with

1

A(rgBse) - (1a)i % +J r'sin e r '

Cr + j cose tan(ko/ " s nze B)

An investigation of the expressions given for the far-zone electric

field indicates that the effect of the substrate properties on the

radiation pattern is controlled by the factors o(er.Be) andrrA(c .B,e). Furthermore, it is verified that #(e Be) is a result

of the substrate guided TM modes, while A(erB.e) is due to the TE

modes. A thorough analysis of # and A indicates that o deter-

mines the position of nulls, principal as well as secondary maxima of

the pattern for e - v/2. On the other hand the factor A affects

the sidelobe maxima only and in general it smooths out the pattern.

In summary, the following results can be stated for the dependence

of the radiation pattern on Cr and B.

8

A. Fixed Substrate Thickness.

For fixed substrate thickness B and varying relative dielectric

constant c r we find:

1. I I*()2() n) ~), integer n (19)I r

the radiation pattern consists of one lobe only.

2. If7~) (f) 1 6 r < 1 + (7)2 ( V) , integer n (20)

there may exist more than one beam. Specifically if

2 v-- f 2 47T BLR (21)r 0 o

and

2/U 2 r2/:T -. ++N+a (22)

where [i 11 indicates integer value of, N is an integer and a an arbitrary

real positive number then

I) If N u 0 (a > 0), there exists a single lobe only.

ii) If N > 0, a > 0, there exist 2N + 1 lobes with one of the

maxima always at e - 0.

iii) If N > 0, a - 0, there exist 2N lobes, with a null at 0 0.

B. Fixed Substrate Permittivity.

In this case the following conclusions can be drawn:

I. if ((.I ) 1 (23)

r r

with n an integerthere is always one lobe at most.

9

iI

2. B (24)

r

n an integer there may exist more thar, one lobes.

Again relations (21) and (22) hold. The pattern nulls as determined

by tcre) occur at

n sin [ar - (0%2] 1(25)

n an integer.

The dependence of the 1-plane normalized radiation power pattern

on Cr and B is now investigated. We consider again the PTFE

substrate with er a 2.35. For the optimum radiation efficiency of

figure 8 the substrate thickness is B - .2Ao. In this case equation

(22) is satisfied for N - 0 and a - 0.613 i.e. the radiation pattern

consists of a single lobe as shown in figure 10. In light of equations

(21) and (22) it can be verified that for 6 - 0.-2 O, 0.975xo and 1.OSXO

the r-plane normalized power pattern will have respectively one, two and

three lobes as shown in figures 11 - 13.

If the substrate thickness B is fixed, e.g. at B - 0.1016xo then

the E-plane normalized power pattern is shown in figures 14 - 16 for

Cr - 2,10,35 respectively. With increasing er we observe that the PCD

directivity is decreased because more energy is radiated close to the

o - v/2 direction along the length of the antenna as the number of modes

guided in ths substrate Increases. It is further observed In figure 17,

that when er - 25 and for 8 - 0.1016X, there exist three lobes and

according to equation (25) the nulls are at e - ± 62.1110. This last

case is of special interest since for the given Cr and B values there

20

exist three guided modes in the substrate. The zero of f1(u,B) pertaining

to the dominant TH mode can be shown to occur near the branch point ko.

This explains the nature of the pattern near e - w/2, i.e. a strong

surface wave mode is launched along the ends of the dipole and it pro-

pagates as a cylindrical wave on the substrate interface (141.

Conclusions.

It has been demonstrated in this paper that it is possible to make

a precise trade-off analysis for the design of optimum printed circuit

dipole elements. This has been achieved by determining the dependence

of the antenna element properties on substrate thickness and relative

dielectric constant. For a substrate chosen with Cr = 2.35, an optimum

design for a center fed dipole has been determined to require a substrate

thickness of 0.2x . This yields an optimum radiation efficiency n a 4,

i.e. the power radiated in free space is four times that which is coupled

in guided modes in the substrate. This design also gives an optimum band-

width of 18% and an input resonant resistance of 90 ohms for a resonant

length of Lr 0 O.369345xo.

11J

References

[1] H.G. Oltman, "Electromagnetically coupled microstrip dipoleantenna elements," presented at the Proc. 8th European MicrowaveConference, Paris, France, Sept. 1978.

(2] D.A. Huebner, "An electrically small microstrip dipole planar array,"presesnted at the Proc. Workshop on Printed Circuit Antenna Technology,New Mexico State Univ., Las Cruces, N.M. Oct. 1979.

[3] H.G. Oltman and D.A. Huebner, "Electromagnetically coupled micro-strip dipoles" IEEE Trans. Antennas Propagat., vol. AP-29, pp. 151-157, Jan., 1981.

[4] R.S. Elliott and G.J. Stern, "The design of microstrip dipole arraysincluding mutual coupling, part I: Theory," IEEE Trans. AntennasPropagat., vol. AP-29, pp. 757-760, Sept., 1981.

[5] G.J. Stern and R.S. Elliott, "The design of microstrip dipole arraysincluding mutual coupling, part 1I: Experiment," IEEE Trans. AntennasPropagat., vol. AP-29, pp. 761-765, Sept., 1981.

[6] D.B. Rutledge, S.E. Schwartz and A.T. Adams, "Infrared and sub-millimeter antennas," Infrared Phys., vol. 18, pp. 713-729, 1978.

[7] T.L. Hwang, D.B. Rutledge and S.E. Schwartz, "Planar sandwltch antennasfor submillimeter applications," Appl. Phys. Lett., vol. 34, pp. 9-11,1979.

[8] D.B. Rutledge, S.E. Schwartz, T.L. Hwang, D.J. Angelakos, K.K. Mei,and S. Yokota, "Antennas and Waveguides for Far-Infrared IntegratedCircuits" IEEE J. Quantum Electron., vol. QE-16, pp. 508-516, May 1980.

[9] N.K. Uzunoglu, N.G. Alexopoulos and J.G. Fikioris, "Radiation propertiesof microstrip dipoles," IEEE Trans. Antennas Propagat., vol. AP-27,pp. 853-858, Nov. 1979.

[10] I.E. Rana and N.G. Alexopoulos, "Current distribution and inputImpedance of printed dipoles," IEEE Trans. Antennas Propagat., vol.AP-29, pp. 99-105, Jan. 1981.

[11] N.G. Alexopoulos and I.E. Rana, *Mutual Impedance computation betweenprinted dipoles," IEEE Trans. Antennas Propagat. vol. AP-29, pp. 106-111, Jan. 1981.

112] P.O. Katehi, "Printed circuit dipole characteristics for microwave,millimeter wave and submillimeter wave applications," UCLA Master'sThesis, 1981.

12

[13] R.F. Harrington, Field Computation by Moment Methods Macmillan, NewYork, 1968.

(141 P.B. Katehi and N.G. Alexopoulos, "On the nature of the electromagneticfield radiated by a printed antenna on a grounded substrate" UCLAIntegrated Electromagnetics Laboratory Report No. 3, 1981.

13

Acknowledgements:

The authors wish to thank Professor N.J. Orchard for helpfull discussionson bandwidth definitions.

z

zZO

Figure I Wire Dipole Embedded In a

Grounded Dielectric Slab

R

4000

2000

x

200

Folo

II I I I I. I

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Figure 2 : Input Impedance for a Printed

Dipole with 4E= 2 and b=0.1O16ko

Resonant Length Lr=O.3Sko

Zin(ohms)

-5001

0.1 02 03 0.4 0.5 0.6 0.7 0.8 OL9L(OO

Figure 3 :Input Impedance for a Printed

Dipole with e,=1 and b=O.1O16~o

Resonant Length LirwO.2OSko

zin(ohms)

.1 2 3 .A

Figure 4 .:Input Impedance for a PrintedDipole with e,=3 5 and b =.10 16k 0

Resonant Length Lr=OtO025Xo

LrA.)0.4- II

i 0.2-

0.1I

IIIIII

• . I I1 , 1 1 _

Figure 5 Resonant Length vs. Relative

Dielectric Constant a. for thePrinted Dipole with b=0.1016ko

I: On* Surface Wave

II: Two Surface Waves

III: Three Surface Waves

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Figure 10

E-Plane Normalized Power Pattern

(frn2.35,B=O.20A* *L=0.36934 5X,

90

cis 0 -10 -20 -20- -10 0 dB

Figure I1I

E-Plane Normalized Power Pattern

(Cr2.35,B30.2A. .L=0.3k*.)

-0'

dB 0 -10 -20 -20 -10 0 dB

Figure 12

E-Plane Normalized Power pattern

C4Er=2.36.BuO.9 ?5A* ,L=0.3k,)

000

-90* 0d1B 0 -10 -220 d

Figure 13

E-Ptane Normalized Power Pattern

(Crn 2 . 3 6 .B=I O5A. ,LvO.3k,)

0

d0 -10 -20 -20 -10 0 dB

Figure 14

E-Plane Normalized Power Pattern

(Er=2.35.B=O. 101 A. L=0.3),.)

-900 900dB0-10 -20 -20 -10 0 dB

Figure 15

E-Plane Normalized Power Pattern

(frinl 0.0,8=0.101 SA. ,L=0.3A.)

90*1

dG 0 -10 -20 2CI

Figure 16

E-Plans Normalized Power Pattern

f (s35 .0 8=0. 10 1ISA.* L=.3k*SA)

000

dB 0 -10 -20 -20 -10 0 dB

Figure 17

E-Plane Normalized Power Pattern

(Er m25,BzO. 1016X. .L=0.3A&)