Considerations for Millimeter Wave Printed Antennas

8/3/2019 Considerations for Millimeter Wave Printed Antennas

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740 IEEE TRANSACTIONS ON ANTENNAS AND ROPAGATION, VOL.AP-31, NO. 5 , SEPTEMBER 1983Considerations for Millimeter Wave Printed Antennas

DAVID M . P O U R , MEMBER, IEEE

Abs iruct4 alcula ted data are presented on the performance of printedantenna elementson substrates which may be electrically thick,as wouldhe the case for printed antennas at millimeterwave frequeneies. Prioteddipolesndmicrostrip patchntennas on polytetrafluoroethylene(PTFE), quartz, abd gallium arsenideubstrate are considered.Data aregiven for resonant length, resoriant resistance, bahdwidth, loss due tosurface waves, loss due to dielectric heating, and mutual coupling. A hpresented is an optimizatidn procedure for maximizing or minimizingpower launched into surfacewaves from a multielemerit printed antennaarray. The data are calculated by a moment method solution.

T I . INTRODUCTIONHER E HAS BEEN rapid growth in printed antenna heoryand technology during the last decade [ i ] , [2 ] .Most of thiswork was for ntennasoperating in theUH F o microwavebands 300 MHz to 10 GHz), and characteristics ofprintedantennassuch as ow-cost, low-prof ile,conformability,and ease of manu facture were often ound ooutweigh he

electrical isadvantages, such as narrow andw idth ndow -power capacity, fo r many applications.Currentlyhere is increasing interest inmillimeter wavesystems and applications, such as aircraft-to-satellite communica-tions and imaging arra y ant enn as [3], [4], as well as interest incompletemonolithicsystems which combin eantennaelementsor arrays on the same substrate as the integrated =/IF front-enddete ctor and amplifier circuits. Thus, printed antenn as are beingseriouslyconsidered for use at frequen cies well above 30 GHz,whilepast applica tions were generally below 30 GHz. In theseapplications, substrates are often much hicker and have higherdielectric con stants han at owe r frequencies. I t is the purposeof his pap er opresentperformancedata orand discuss theapplications of printedantennas on these types of substrates.As will be seen , he electrical perform ance of hese ante nna scan be severely degraded, due to surface waves or mutual coupl-ing. Bandwidthand nput mpedance are additionalpropertiesthat aretrongly affected by substrate thickness, ofte n in adesirable way. Othe r factors such asdielectric loss and feedingtechniq ues can also be significantly diffe rent at millimeter wavefrequencies.

This pap er will consider two artic ularypes f r intedantenn as: rectangular m icrostrip patch)elements,an dprinteddipoles. The intrinsicdifferences betw een these twoelementsand heir comp arative electrical performan ces will be discussed.Three ypesof ubstratematerials will be considered: oly-tetrafluoro ethylen e (PTF E), quartz, and gallium arsenide. Thesemater ials represent substrates w hich may be used for millimeter

Manuscript received November 18, 198 2; revised March 15,1 983. Thiswork was supported in partbyGrantsNAG1-163andNAGI-279 be-tween the NationalAeronauticsandSpaceAdministration, Langley Re-search Center, Hampton, VA, and he University of Massachusetts, Am-herst, MA.The author is with the Department of Electrical and Computer Engi-neering, University of Massachusetts, Amherst, MA 01003.

wave antennas, and cover the range of relative Permittivity from2.55 to 12.8. The followingcharacteristics will be presente d inSection 11.

1) General ele ment characteristics.2) Substrate properties.3) Resonant element length.4) Resonant input resistance.5) Bandwidth.6) Losses due to urface waves.7) Losses du e to dielectric.

Section 111 will discuss mutual coupling and surface wave effectsin an array environment and present a procedure for the optimi-zation of array efficiency (minimization or maximization of e =Prad/(Prad -k Psw) , where P rad is the desired adiated powe rand Psw is surface wave power). Alt houg h the results presentedhere are for printed dipole or microstrip patch elements, some ofthe trend s and conclusions will apply to other type s of printedantenna elements.

All of the data presented in this pap er were calculated using amo men t me thod solu tion of a printed rectangular radiating ele-ment on a grounde d dielectric slab. A detailed description of thismethod,withcomparisonsofcalculatedand measured esultsfor nputan dmut ual impedances, has alreadyappeared in th eliterature [5] , so only a brief descriptio n will be given here.

Importan t factors for antennas on electrically thick substratesinclude surface waves and mutual coupling [6]. The low est ordersurface wave TM,) has a zerocutoff requency,and hus isexcited o somedegree even on very thin ubstrates. AS thesubstrate becomes hicker, more surface wave m odes can exist,and more powe r can be coupled nto these waves. Mutual cou-pling between elements in arrays involves the transfer of powe rf rom one e lement o a nearbyeleme nt via space waves (directradiation) o r by surface waves. Coupling levels greater thanroughly 20-30 dB may have a deleteriouseffect o n array per-form ance , unless specifically ncluded n th e design procedu re.(This asecently been done or rinted dipole arrays [ 7 ] ,where the coupling coefficients were measured.) Thus, it isdesirable for the theoretical solution to account for fields exteriorto th e radiating e lement, i.e., to acco unt for surface wave powerandmutual coupling. The cavity modeland transmission inemod el cann ot do this. In addition, neither of these models haveyet successfully treated he printed dipole eleme nt, and neitherare valid for antennas on thick substrates.The moment method solutionuses th e rigorous dyadic Green'sfunction or hegrou nde d dielectric slab,and so includes heexterior fieldsmaking calculation s or surface wave excitationand mu tual coupling possible. Because of the general natu re ofthemomentmet hod orm ulatio n, rinted dipoles as well asprobe-fed o r mic rostri p line-fed patch es can be han dled . D ielec-tric oss can be easily includ ed by using a comp lex permitt ivityin the solution. The price paid for this versatility is a somew hatmorecomplicated olution, primarily du e o heSommerfeld-

0018-926X/83/0900-0740$01OO 0 1983 IEEE


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A N T E N N A S 741nvolvedn the Green's function.See [5] for

11.PRINTED DIPOLE AND MICROSTRIP PATCHANTENNA ELEMENTSThis section will discuss propertiesofprinted dipoles and

ntenna lemen ts, nd present data nheir electrical

. General Element CharacteristicsPrinted dipole radiating elementsave been extensively studied

e ta i . [8 ] , [ 9 ] , [ lo] , via a s imilar momentprocedure. Fig. 1 shows a typical enter-fedprinted

e element. In practice, the feed ma y tak e the form of a par-el wo-wire ine printed on he substrate. This feed line mayR F er,ergy or, if a detector is placed at the dipole gap, I F

ther case, this type of feed is balanced wit h respectthe ground plane, which can be a serious disadvantage in some

. The use of parallel micr ostrip feed lines to coup leradiating dipole, as in [7], ca n alleviate this difficulty at the

of a mo re com plicate d feeding struct ure, possibly involv-conductorson wosubs trate levels. Advantages ofprinted dipole are that t uses less substra te area com pared

patchelem ents particularly mporta nt n arrays), and hator second resonances without deleteri-s higher order modeeffects.

The microstrip patch antenna, also shown in Fig. 1 ?however,unbalanced with respect to the grou nd plan e. Theprobe from theof the ubstrate. An unbalanced ntenna lement isadvantageous when RF or IF circuitry is t o be com-d with the antenna in a hybrid or mono lithic configura tion.

e disadvantages are tha t he rectangular pat ch uses mo rearea than the dipole, and that a probe-type feed may

to abri cateonmonolithic ubstrates ,or even onubstrate s. A problem also exists withmicrostrip ineince a microstrip line's characteristic impedance determines

efeed inewidth,and is relatively con stan twithfrequency.a resonant patch antenna, however, decreases with

so tha t a given microstrip feed line on ahas an effective upper frequency imit beyond which

would be less than the feed ine width.Finally,one hould realize the ntrin sic differencesn the

ofprinted dipoles andpatches. The firstof a printeddipole , like a half-wave dipole in free

a series-type resona nce, while th e firs t resonance o f aantenna is a paralle l-type anti) resonance In eferenceprinteddipo les, he erm s half-wave and full-wave refer tos in +e effective dielectric me diu m, and so are analogousthe ope rati on of dipoles in free space.). This difference is ae field structure created in the vicinity of the eleme nt

Fo r a dipole, the feed couples to the electric field c ompo nentthe dipole axis, while a coax or microstrip line-fed patch

Printe d dipoles andpatches,how eve r, have similarhu sheadiatio n atterns re similar

I 1 > P I .Substrate CharacteristicsThree substratematerials-F'TFE, qu ar tz , an d allium arsenide-

"1 III ----HALF-WAVE O l W L E I--MICROSTRIP PATCH II IP 10 1 2 a

m.Fig. 1 . Resonant lengths o f a printed dipole and a microstrip patch versus

d for cr = 2.55. W = 0.3 h g for the patch. Also shown are the printeddipole and patch geometries.

TABLE IELECTRICAL PROPERTIESO F FfICROWAVE SUBSTRATEStan 6Substrate er X-bmd

F'TFE 2.55 0.001-0.003%As 12.8 0.002Qu- 3.78 0.001

were chosen for comparison in this paper. This choice was basedon the fact that the permittiv ities range from 2.55 to 12.8, andthat these materials are either in use today or are expected t o beused for millim eter wave antenna systems. Because of time andspace considera tions, not all materials available today could becompared here, but it is felt that other typical substrate materialshave propert ies roughly n angeof thoseconsidered.Table Isummarizes the ypical electrical prope rties of the se hree sub-strates.Polytetrafluoroethylene nd elated roductsik eRexoliteand Duro id have been used extensively n th e microwave band.Quartzsubstrate s have very good dimensional stabilityand areoften used in microwave integrated circuits.Gallium arsenideis probably the preferred substrate material for monolithic micro-wave integrated circuits.C.Resonant Frequency

Clearly oneof he irst onsideratio ns in the design of aprinted antenna element is the length L of the element requiredfo rresonance.This ength is a function ofsubstrate hicknessd and dielectric consta nt E , and , in the case of a microstrip patch,a function of the patch width W. Because t he dielectric fills onlypart of the region surrounding the antenna element, the resonantlengthdoesnot scale wi th dielectric con stan tas l/&, as anantenna in a homogeneous medium would.

Fig. 1 shows the required lengths for the first resonance o f aprinted dipole and a rectangular micr ostrip patch elem ent versussubstrate hickness d for a PTFE material. The patch width isW = 0.3 X, (X, is the free-space wavelength). The dipole lengthvaries less than 6 percent for 0 < d < 0.5 b , nd is slightlylonger than the patc h leng th, which varies somew hat more with


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42 IEEE TRANSACTIONS ON ANTENNAS AN D PROPAGATION, VOL. AP-31, NO. 5 , SEPTEMBER 1983

UJ! n lm ! FHALF-WAVE

I II

WAVE-Z SURFACE W SURFACE WAVES-/I

e !0 1 2 d/h. .3 4F i g . 2. Resonantengths for half-wave and fun-wave printed ipoles

versusd or = 3.78.An nteresting eature of the patch antenna is that i t s tops

g for substrate thicknesses greater han 0.11 X,. Withickne ss, the trend s t o an entirely inductivempedance ocus. This effect occursfo rbothprobe-type

ndmicros trip ine-type feeds. This ituation is probably un -mo st cases, and so the use of patches o n thick sub-

may not be practical unless some way of countering thistive rend, by using a capacitive-gap coupling from a feed

for example, is used. The dotted continuation of th e patchonly to show the length chosen for

presented in Figs. 4, 6, and 8. Anease in patch width W can reduce the resonant length by as greater for thicker substrates .

Fig. hows the esonan t engths or half- and full-wave(E , . = 3.78) su bstrate . (The usefulnessis discussed in Section 11-D.)ote that the

value for PTF E, but not by he factor d m , hichif scaling could be appliedwith dielectricFig. 3 shows the equired lengt hsforh alf-an d full-wave printed

GaAs. Again, the patc hnt does not resonate for substrate thicknesses greater thanho .

. esonantResistanceFig. 4 show s the input resistance of a half-wave printed dip ole

patchon a PTFEsubs trate versus thickness.previously poin ted out, he patc h elem ent does not strictly

d > 0.11 A,; the patch resistance shown in Fig. 4r d > 0.11 ho is the real part of he nput mpe dance for alength of 0.270 ho.Since the printeddipole's first resonance

a eries-type resona nce,henput resistance is very smalld, since electrically thin substrates mply highQ reso-

s. The micro strip patch, having aparallel-type resonance,a high inpu t resistance for smalld.Fig. 5 shows the esonan t resistance of half-wave and ull-

dipoles and a microstrip patch on a GaAs substrate.pat ch resistance for d > 0.08 X, s taken as the real

the input.impedance forL = 0.105 ho .The full-wave dipole has a parall el-type resona nce, with highd, similar to a full-wave dipo le in freeelem ent has interestingadvantages in some applica-

--- MICROSTRIP PATCH-.- FULL-WAVE DIPOLE1

4

o ! 1 8' d/x, I0 .05 I 5 .2 .25Fig. 3 . Resonant lengths of half-wave and full-wave printed dipoles and amicrostrip patch versusd for E,. = 12.8. W = 0.15 A 0 for t h e patch.

Fig. 4. Input esistanceofa half-wave printeddipoleandamicrostrippatch versus d for cy = 2.55. The patchis probe fed at a point / 4 fromthe edge, and W = 0.3 ho.


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MILLIMETER WAVE PRINTED ANTENNAS 74 3I I

0 .05 d5 2 .25. dlh.5 . Input resistance of half-wave and full-wave printed dipoles and amicrostrip patch versus d for er = 12.8. The patch is probe fed at apoint L / 4 from th e edge, and I 0.15 ho .. Fir st, ts half-power bea mw idth is significantly less

hat ofa half-wave dipole. Sec ond , if apairof full-wavepoles are arranged b / 2 apar t to for m a subarray element, theand H plane beamwidths will be about equal, and f a detector

ed in the center of t he subarray and conne cted to[3] the X0/4 line

yield an impe danc e inversion from he high in pu tistance of the full-wave dipoles t o a low impedance for match-the diode.All the dipoles are center fed, and all the patc hes are probeat a point L/4 from the (radiating) pa tch edge. Moving the

position toward the end of the dipole or patch will increaseinput resistance, a t the first resonance.

BandwidthBandwidth is defined hereas he half-power width of the

mpe dance response. Fo r a eries-type reso-shown in [101 I this bandw idth (BW) is

2RBW = dX Iw0-w I w o

2 = R + j X is the input impedance at the resonant fre-wo. Fo r a parallel-type resonance ( 1 ) is used with R re-G and X replaced by B , where Y = G + f l is the input

at resonance. T hisdefinition of bandwidth impliesve ratio of ab out 2.4, fo r a ransmission lineofmpedance R or 1/G R. The derivative in (1 )

be evaluated by calculating the nput mpe dance t woresonance and using a finite difference approx-

Fig. 6 show s the calculate d b andw idths of a half-wave printedand a microstrippatch versus substrate hickness or asubstrate. The patch width is 0.3 X, and is fed by a probeL/4 from the pa tch edge, althoug h the feeding me tho d

Fig. 6 . Bandwidths of a half-wave printed dipole ana a microsmp patchversus d for = 2.55. W = 0.3 ho for the patch. The cavity model pre-diction for the patch bandwidths also shown.

or position does not affect he intr insic patch bandwidth. Thebandwidth increases rapidly with increasing substrate hickness,so that bandw idths of 10-20 percent can be obta ined for sub-strate thicknesses in the range of d = 0.1 X to 0 .2 ho . Alsonote that the bandw idth of a patch is significantly greater thantha t of a printect dipo le, at least over the range for whic h hepat ch actually esonates (d < 0.11 ho). These factsar econ-sis tent with the antenna gain/bandw idth relation to antenna size,as discussed by Harrington [11] .The lowe st achievable Q of anantenn a is inversely related to ante nna volu me ; since the patc hantenna encompassesgreater volum e handoes heprinteddipole, ts Q can be lower than the Q of the dipole, hence thebandwidth can be greater. Also shown in Fig. 6 is a bandwidthcalculation for the patc h using the cavity model [ l ] . The cavitymodelapproximation is seen to be useful for ubstrate hick-nesses d


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4 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. AP-31,NO. 5 , SEPTEMBER1983

0

I I- ALF-WAVE DIP01MICROSTRIP PATCI

.OS - 4% .15 .2

rEi

A.25

Fig. 7 . Bandwidths of a half-wave printed dipole and a microstrip patchversusd for er = 12.8. W = 0.3 X0 or the patch.1 SURFACEAVE 2 SURFACEAVES

IIItII

00> ? -Y -

I I

I---HALF-WAVEDIPOLE III0tp.- -MICROSTRIP PATCH

9- I i f i OsL 1r=2.55 -II IIII

0 , , , I I0 1 .2 .3 .4%

Fig. 8. Loss due to surfacewaves or a half-waveprinted dipole and amicrostrip patch versusd for er = 2.55. W = 0.3 ho for the patch.

P r a d is th epow er adiate d via space wave (directmainm power), and Psw s the power coupled into surface waves.+ Psw is then he otalpow er delivered to heprinted

elem ent. Dielectric oss is ignored here.Theeffectofinite-sized subs tratewoul d be to diffract he surface waves

he ubst rate edges, possibly causingundesirable effectsevel, polarization,ormain beam shape.Surface

byorcouple d o eed lines o ron the substrate.In he mo me nt met hod form ulat ion surface wave fields andfields are easily separated from the Sommerfeld-typeexpression for he otal fieldsof an elementalcurrent

on a groun ded dielectric lab-the urface waves comehe residuesof thecontour integral.Since themomen tmatrixelements areexpressed n termsofof the fields from the expan sion mod es, these elem ents

broken up asZ m nZ m n mn,c a d + zsw (4)

Z , , represents hematrixelement using the otal fieldnd Z E : and Zzn represent thedirect adiatio n (space wave)if In repre-

currenton he n th expansionmode, he otal nputcan be written as

n m

and the radiated pow er can e written asPrad= Re I : ZE t Im . ( 6 )Fig. 8 shows efficiency (3 ) versus sub strate hickn ess d fo r

a half-wave printed dipole and a microstrip patch, for E , = 2.55.Observe that e + 1.0 as d + 0, sincesurface wave exc itati onis negligible for very thin substrat es. As d gets larger the TMosurface mode becomes stronger, reducing e. However, the a-diated pow er becomes greate r as d increases, so tha t e levels offand starts to increase for d > 0.1 ho. A t d = 0.2 ho, the nextsurface mode (TE,) start s to prop aga te, causing a slope discon-tinuity in e and adecrease in e as this mode becomes morestrongly coupled. This type of slope d iscontin uity is also seen inrelated dielectric covered antenna problems [121.

An interesting eature of Fig. 8 is the similaritybetween efor the dipole and the patch. Also, e does not depend on the feedlocation of the dipole or patc h, or on the patch widthW.Fig. 9 shows he efficiency e fo r half-wave and full-wavedipoles and a microstrippatch on GaAs substrate.Note hatsurface wave power accounts fo r over half of he otal nputpower for d > 0.045 A,.G. Losses Due to Dielectric

Power loss due to dielectric heating can be calculated by usingth e loss tangent nd omplexpermittivity or heparticulardielectric material. For the half-wave dipole(aseries-type reso-


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74 5r an s= .003ALF-WAVE DIPOLE

MICROSTRIP PATCHFULL-WAVE DIPOLE

,=12.8 --_- -.3 SURFACE -I -

AVESIIIIIIIIII1

0 .os 1 .15 .2 .25a09. Loss due to surface waves for half-wave and full-wave printed d&poles and a microstrip patch versus d for E , = 12.8. W = 0.15 h g fort h e patch.

, for exam ple, the radiation efficiency based o n dielectriccan be calculated as

RrRr +-RI

q =-, ( 7 )R, is the radiation resistance at he nput erminals and

l is th e loss resistance. Rr and RI can be found from two cal-ons of input impedance; one with tan 6 = 0, and one withn 6 # 0. The radiation resistance is R, = Re(&) for tan 6 = 0,

loss resistance is fou nd from R, +RI = Re @in) wi thn 6 # 0. This is an accu rate procedu re for small losses. F ormicro strip atches (anti-resonances), thein (7). Note hat

(7) does not includepower loss t owaves (alt hou gh t does includ eheating loss fromsur-

fields).Efficiency based on dielectric loss for a half-wave dipole and

micr ostrip patch versus d is show n in Fig. 10 fo r E , = 2.55.engths of the dipole andpatchar echosenfo rresonance,W = 0.3 A,-,. Loss tangents of 0.001

nd 0.003 were used.It is seen that the patch efficiency is greater than the dipolehat efficiencymprovesapidly as substrate

of heseeffects can be explainedbyng hat, or a given power evel, the fieldsare morecon-for hin substrates or narrow antennaelements, hus

power is lost to dielectric heating than in cases of thickerwider elements.

111. PRLNTED ANTENNA ELEMENTS INANARRAY ENVIRONMENTThis section will discuss som e aspects of the printed antenna

in an array configuration-in particular, mutual couplingn surface wave power.. Mutual Coupling

When printed antenna elements are in an array environment,e mutu al coupling levels can degrade idelobe levels, mainshape , and possibly cause array blindness. Forek now ledge

couplingbetweenarrayelementsandproper inclusion

t a n b . 0 0 3- ALF-WAVE DIPOLEMICROSTRIP PATCH0

Er=2.55

- ALF-WAVE DIPOLEMICROSTRIP PATCH0

Er=2.55

0 .05 1 .1s .2 .254J-aFig. 10. Loss due to dielectric orahalf-wave dipole and a microstrippatch versusd for E = 2.55. W = 0. 3 X0 or the patch.

4

Fig. 11. E-planeandH-planemutualcouplingmagnitudebetween half-wave dipoles andbetween microstrip patches versusd for E , = 3.78.intohe rray design procedure an minimizehese effects

The calculationof mutualcoupling as two-p ort ransferimpedanceby hemomentmethod is describedn [SI. Themethod yields magnitudes as well as phase,an dcomparisonswith measured data for patches are shown in [5].Mutual cou-pling between arallel an d collinear half-wave dipoles versusseparation is shown in [9]. Calculations fo r full-wave dipoles havealso been ma de, with the result tha t full-wave dipole coupl ing isabou t 10 dB less tha n he half-wave dipo lecoupling orbothparallel and collinear configurations. (These data are not show nhere for ack of space.)Fig. 11 shows the coupling between parallel half-wave dipolesand patchesand collinear half-wave dipoles andpatcheson aquartz ubstrate versus substrate hickness.The lements reresonan t, and he spacing between elements is 0.5 io.or hinsubstrat es he coup ling levels are very low but increase apidlywith increasing thicknessand hen end to oscillate for hick-nesses greater than about 0.5 Xo .

The domin ant coupling mechanism for the parallel configura-tion is via space wave fields; since these fields are stronge r in thebroadsidehan in the ndfire irections,he oupling levelsbetween parallel dipolesare airly large for close spacings, bu t

~ 7 1 , 131.


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746 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, V O L . A P - 3 1 , NO. 5 , SEPTEMBER 1983

direction nd so have mostcollinear configuration.

.A m y Efficiency-an Optimization ProcedureSection 11-F discussed printed ntenna leme nt efficiency, based on pow er lost to surface waves. This section will discuss

happens to e whenelements are combined in anarray,t will be seen tha t e can be increased or decrea sed, de-on the elem ent excitatio ns, from he efficiency of an

An example will be given for wo collinearf-wave dipoles spaced h o/2 apa rt on a quartz substrate. Micro-

patches can be treated in the same manner, and the proce-can be pplied to arrays with more than two elements .

Since all mutual coupling terms between array elements would(5) and (6) apply to the total inpu t power and totalpower, respectively, for an array of printed elem ents.

array fficien cy, based on power lost to surface, can then be written in matrix form as

[Z] is theotal (square) impe dancematrix, [&ad] isecontr ibut ion o he ad ia ted ie ld , [I] is a column vectornsion mode currents, and the superscript t denote s trans-

[R] = Re [Z ] and [&ad] = Re [&d l , then) can be written as

To illustrate the method an example of two printed dipoles,expansionmodes on eachdipole, will be discussed.he [Z] an d [R]matrices are then 6 X 6 , and [I] is a six-element

f he expansion modes are numbered consecu-vely dow n each center-fed dipole, the terminal currents for the

secon d dipoles will be I , and I , , respectively. If VIthe port) voltageapplied to dipole1and V 2 is the port)age applied to dipole 2, the n

Now et [ I l0 ] [ I ] for V I = 1, V , = 0 and et [I o ] =I] for VI = 0, V2 = 1. Then by superposition he dipole cur-

caused by ort xcitation voltages V I and V 2 can e

[ f l = [SI [VPI 1 (1 1)[VI is a two-elementport voltage vector nd [SI =

[ I l o ] , [ I o l ] is a 6 X 2 matrix . The array efficiency can the nessed in te rm s of the por t oltages as

Note hat (12) expresses the performance ndex e as a ratiotwo quadra tic forms. Thus, (12) can be optimized by solving

1I0 , I I0 .05 1 .15 2 2 5

d h -3

Fig. 12. Optimizedfficiency e for two collinear half-wave dipolesh0/2 apart versus d for E,. = 3.78. L s chosen from Fig. 2 for resonance.

..-

the eigenvalue pro blem ,[ A l [ V P l = e [ B l [ V P l , (13)

where [A ] = [S*][&ad] [s] and [B ] = [S*] [R]SI areHermitian2 X 2 matrices. A similar procedurehas beenusedfor free-space array optimiza tion [14]. If the dipoles are identi-cal th en, by symm etry, i t can be shown tha t [A] and [B] havethe form

with a ] , a 2 , b l , b2 real. The eigenvectors, rep rese ntin g hefeed voltages for optimum e , are then either even or odd:

The corresp ondin g eigenvalues are then the efficiencies resultingfrom the above excitations:

Generally the even modeproducesmaximum e while theoddmode produces minimume .The optimized efficiency e for two collinear half-wave dipoles&,/2 apart versus substrate thickness (er = 3.78) is shown in Fig.12, for even and odd mode excitations. Also shown is th e effi-ciency of an solated dipole. As can be seen, the efficiency canbe improved by as much as 30 p ercent for even mode excitation.A similar calculation for tw o parallel dipoles results in a 10 per -cent improvement for even mode excitation. For the data shownhere,maximummprovement ccursor ophasal xcitationof the rray elements-a very practic al result fo r broadsidearrays. Odd- mode excitatio n generally produces a reduced effi-ciency,whichmeansmorepower isbeing coupled to surfacewaves-a result whic h may be of inte rest for surface wave ante n-nas. In Fig. 12 the e , and eo curves cross at abo utd = 0.19 ho.

The change n efficiency for printed antenna elements in anarray can be partially explained in terms of the phasings of the


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POZAR: MILLIMETER WAVE PRINTED ANTENNASsurface wave fields. Surfac e waves, launc hed endfire from eachdipo le, are significantly ou t of phase (because of the ho/ 2 dipolespacing) a nd tend to cancel. It is hypo thesized that an elementspacing exists such that maximu m cancellat ion occurs ande -+ 1 ,at least forsubstrate thicknesseswhere onlyone surface wavemo de exists. This ituationwouldprobablynotoccurwhenmore than one surface mode is present, since the different phaseconstants would preclude totalcancellation.

IV. CONCLUSIONThis paper has presented data on resonan t length , input resist-ance, ban dwidth , surface wave po wer, dielectric loss, and mu tual

couplingor rinted dipoles andmicrostrip atch ntennas.Emphasishas been on th eeffect of thesubstrate ,whichm ayhave a igh ielectric co nst an t ndma y ot be electricallyth in a tmillimeter w ave frequencies.Many other configurations of array elements could be studiedfor mu tual coupling effects and surface wave power optimization.It is conceivable that for an array with many elements surfacewave power can be made negligible for particular eleme nt spac-ings and excitations.

A very im portan t need is t o verify mo reof he heoreticalcalculationswithmeasurements, particularlyfo rprinteddipolein pu t resistance and surface wave losses for dipoles and patch es.Some type of modified Wheeler cap method [ 151 may work forthe lat ter measurement.

ACKNOWLEDGMENTThe auth or wo uld like to than k Professor Yngvesson of th e

University of Massachusetts for his interest in the mplicationsof thiswo rk, nd Professor Schau bert of the University ofMassachusetts for a critical review of the manuscript.

747REFERENCES

[ I ] , K. R. Carver andJ. W . Mink, Microstrip antenna technology, IEEETrans. Antennas Propa gat. , vol. AP-29, pp. 2-24, Jan. 1981.[2] R. J. Mailloux, J . F. McIlvenna, and N . P. Kernweis, Microstriparray technology, IEEE Trans. Antennas P ropag at. . vol. AP-29, pp.25-37, Jan.-1981.[3] K. S . Yngvesson, T. L. Korzeniowski, R . H. Mathews, P. T. Parrish,an d T. C. L. G. Sollner,Planw millimeter wave antennas withapplication to monolithic receivers, Proc. SPIE, vol. 337, (Milli-meter Wave Technology), 1982.[4] D. B.Rutledge and M. S . Muha, Imaging antenna arrays, IEEETrans . Antennas P ropoga t. , vol. AP-30, pp. 535-540, July J982.[5] D . M. Pozar,1nput .impedance and mutual coupling of rectangularmicrostrip antennas, IEEE Trans. Antennas Propagat., vol. AP-30,[6] J. R. James, P. S . Hall, ahd C. Wood, Microstrip Antennas: Theoryan dDesign. Stevenage, U.K.: Peter Peregrinus, 1981, pp. 51-64.[7] R. S . Elliot, and G . I. Stem, The design of microstrip dipole arraysincluding mutual.coupling, Part 1: Theory; Part 11: experiment, IEEETra ns. Antennas Propaga!.. vol. AP-29, pp. 757-765, Sept. 1981.[8] I . E. Rana. and M. G.A exopo ulo s, Current distribution and inputimpedance of printed dipoles, IEEE T rans. Antennas Propagat., vol.[9] N: G . Alexopoulos and I . E. Rana, Mutual impedance computationbetween printed dipoles, IEEE Tra ns. Antennas Pro pag at., vol. AP-29, pp. lO&lll, Jan. 1981.[lo] N. G . Alexopoulos,P. B . Katehi, and D. B . Rutledge, Substrateoptimization for integrated circuit antennas, IEEE Trans. MicrowaveTheory Tech. , vol. MTT-31, pp. 55C-557, July 1983.[ l l ] R . F. Harrington, Time-Harmoniclectromagneticields. NewYork, McCraw-Hill, 1961.1121 M. C. Bailey and C. T . Swift, Input admittnce of a circular wave-guide aperture covered by a dielectric slab, IEEE Tra ns. AntennasPropagat . , vol. AP-16, pp. 386-391, July 1968. .[13] M. C. Bai!ey and F. G . Parks, Design of microstrip disk antennaarrays , NASA Tech. Mem. 78631, Feb. 1978.[ 141 R. F . Hamington, FieldCompwation by Moment Methods. NewYork, MacMillan, 1968.

[I51 E. H . Newman, P. Bohley, and C. H. Walter, Two methods for hemeasurement of antenna efficiency, IEEE T ra ns . A n t e k s P r op a-g a t . , vol. AP-23, pp. 457461, July 1975.

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David M. Pozar (S74-M80); for a photograph and biography please seepage 350 of the May 1982 issue of this T RANSACT I ONS.

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Considerations for Millimeter Wave Printed Antennas

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