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,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
UNCLASSIFIED UCLAENG81-40 ARO-15965. 10-EL HL
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REPORT DOCUMENTATIONI PAGE READ SN3?UCT1O.%5
I REPO'RT NUMBER 4 2. OOVT ACCESSION No: S. RECIPIENT'S CATALOG MUMMER
0 T:T7LZ E an Subljiei) *. TYPE of REPORT a PtgmOC COVERED
On the Effect of Substrate Thickness and Prit- Technical Laboratorytivity on Printed Circuit Dipole Properties. Report
a. P9111ORUING ORG. REPORT MUNGER
7. AU?#qOR(aj# a. CONTRACT ON GRANT NUMMSERVO)P. B. Katehi and N. G. Alexopoulos
DAAG 29-79-C-0050NO 14-79-C-0856
9 PERFORMAING ORGANIZATION NAME AND ADDRESS I0. PROGRAM ELEME1NT. PROJECT. TASKAREA a WoRkUNIT NUmNERS
Electrical Engineering DepartmentUCLALos Anteles, CA__90024_______________
I I CON.TROLLING OFFICE NAME AMC ADDRESS 12. REPORT DATE
Dr. James Mink December 1981AMo - P 4800-C-8i IS. 3IjIM89R Of PAGES
14 MONITORING AGENCY NAME A A0ORCSSI'l EUlemI Mwgu Cuunt~lida Office) It. SECURITY CLASS. (et able repeat)
Army Research OfficeResearch Triangle Park UnaclassifiLedNorth Caroline I.DECLASSIFICATIONi DOWNGRADING
I. DIST ISuTION STATEMENT (of this Itepe) T , )MID L
Awsov~d fo, public release;Diaftibution Unlimited
17. DIST RIDUTION STATEMENT (of me siboo,.cI entee.da ineek ".0 0=, k1efl ROP..)
1S SuPPLEMENTARY NOTES rc/r P!n?4r rC'TAI" r-., p. T*H!? REPOR'THE VIEW, OIIIA11RA
AN OFFICIAL rjaPAaht'j.?-T .r~.2 -... R0
cLiON, WNLES~i SO EI)A1D 61 ~ i~2
IS. KEY WORDS (C801IauO 00 10V 0080 Sde J1 #W00840Y Old ld"t"& SW Week 8W*bo)
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
DD M, 1473 EItToN or 1 NOV as3 isNO A~Te
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 '
DTIC TAB [Unan nounced 0'
Distribution/
Availability Codes
Avail and/or
DTIC Dist Special
C PY1N8P'ECT.
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
2 .4 A6 L8!L(X,)
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
I I
* So* -
U.S
* 0o
U.'
S*5~
S C* *
SI. C)
I-
* 60*
U5* I..
Ua
2
* 0
0* h,. * 0
@2 C~I
US - UIL~ q~
0S.. 0
- - C0
* 4' -'* 0S
- CU
* C4S~
S0
SS
.3 -S
a0
I U -
-L n I I I I l I n
-. U"_)rI 'U•
S
I *S
0,-
o a
0 ."S. C
t m 0
' , i ' .. -h.
C )~ c=
I.P
- - ,
m* . .. . . I I I S -- .- .......
0,,
.iE 4
SO
o 0
I' SmC
- UU,
a-. a
i n i - " I n ...
0-C
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* 01
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0IL
CS
* Co* C
I-
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-
IL. ~0
aSQa 0 6
S..
*2 'II
C
S.
0S
Sm3
£U.
dB-10 -20 -20 -10 0 dB
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&)