ariculo polarizacion circular

8/3/2019 Ariculo Polarizacion Circular

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IEEE -.A.%JsACTIONS O NN TEN N A S AN D PROPAGATION,O L. AP-31, NO . 6, NOVEMBER 1983 949-

i-, ys i s and Optimized Design of Single Feed Circularly Polarized, Microstripntennas..

Absfract-Analysis andptimized gesigwre presented of three types k a 4of singlefeedcircularlypolarized miy ostrip a@ennas, namely, a di -agonal fod nearly quare,aruncated-corners sqb+&and a quare with bmethods are used. The resonant frequencies are .cacuIa&%j:for two or-thogonalodeshichogetherieldircularolarization. 6&$um feed (b)locations are determined for thebest impedance match to a 50 qy a x i a lfeed line. Axial-ratio bandwidths, voltage standingwave ratio


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p refers to the unconn ected ports of the various segmentsy (i.e.. the externa l ports of the circuit y). Subscripts c and

nterconnected ports which are numb ered in suchthat the port ci s con nected to the port di as illustrated

Fig. (d) .Thesubmatr ices in (1 ) are obtained rom he Z-s of the ndividual segments as [151 ,- -

' ='pp -k [zpc-ZpdlZjp- (2 )- -For a electric curren t Ip fed nto he pth port , he voltages

c an d d ports are given by-v c = v d = [ z c p + [ z c c - Z c d ] Z l - p ] I p .- ( 3 )Application ofDesegmen tation Method [ 61Consider the config uration (a) of a runcated-corners square

ntenn a shown in Fig.2(a). This confi guratio n can bep1 and p2 f rom he wo opposite corners of a square

(y-seg men t) as illustrat ed in Fig. 2(b). The nterfacesbe -a- and 6-segments are divided into discrete number of

. These interc onn ected ports are named as c-po rts on cu-seg-andd-p orts on P-segments (Fig.2(b)).Theunconnectedon the a-segm ent are named as p-ports and those on the p-s are nam ed as q-ports. It has been sh own [ 161 that when

num ber of q-ports equals th at of d-po rts (equals th at of c-Z-matrix of thea-seg men t is given in terms of the

3- and y-segments as

L C P zcc1Zppa ZPC= [ ppy z p 9 z ; p . -Zp,-%d 1 (4)-ZdqZ;p - d d , -2dqZbd-2;p = P q q y -Z,,pl- ' Z q p (5 )Zid = [ z q q , -2qq7p] - ' Z q d .zqd ,yqp are submatrices of Zp for 0-segments, andZ p q . ZqP.Zq9, are submatricesof Z, fo ry-segment.

an d Z, are valuated by using the Green's fu nctio ns orisosceles triangle [131 and for a rectangle [121 .For the square patch antenna with a diagonal slot (Fig. 2(c)),

-segment of Fig. 2(d ) is obtained when a rectangular patchto the a-seg men t of Fig. 2(c). In this case

Z p and Z, are evaluated rom the Green's function for aZ, is obtained from (4) an d (5).

As shown in Fig. l(d ), he por ts of the a-segment are termi-d nto radiation esistances. The nput mped anceand helong the radiating edges are evaluated mploying (2 )

adiatiol? CharacteristicsThe radiation haracteristics re valuated in terms of the

magnetic current istribution along the eripheryield at a distance r is given by [ I I ]-E o = qfi0 = jkoF6 = ko( - Fx sin Q + F y cos @)-

q-DOrtSc-portsyL~fportl,f+k

45 C - D O r t S

NetworkD-DOrtS c -ports w o r t s

Feed r-network(a ) (b)


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S H A R M AD 9 5 111 I I I I 1-00

- 0.75E

0.50 ';I

cc0- -c

0xU

--- 0.25

I I I I0.1 0. 2 .3 0 .9

Feed Location (r/AC) 0 . 51 0

Fig. 3 . Variat ions of input VSWR an d axial ratio with feed locat ion fo r adiagonal-fed antenna ( th ickness = 1/8 in , E = 2.52, f requency = 3.101GHz).

GH z, respectively. T he best axial ratio (0.45 dB) is obtain ed at3.101 GHz.B. Optimum Feed Point Location

Although initial experiments were reportedwith ornerfe dantenna, t is found hat hecircu lar polarization can beobtained even when the feed is located elsewhere on the diagonalA C . The variation of he nput VSWR and he axial ratio withfeed location on the diagonal A C is show n in Fig. 3. Th e axialratio degrades from0.45 dB to 0.7 9 dB and he nput VSWRdecreases from 8.1 to1.7 3 as the eed is moved fromcornerA to a point 0.3441 times AC away from the corner. For feedlocation s t distance r greater than0.3441 A C , the nputVSWR increases again. At the optim um feed location where theinput VSWR s minimum (= 1.73), he value of axial ratio is0.77 dB. Further calculations showed that, fo r this o ptim um feedlocation, an axial ratio equal to 0.45 dB is obtained again if th efrequency is shifted to 3.103 GHz (2 MHz higher than the previ-ous value for excitation at th e co rner ) .

The nput mpedance (Zin) at he optimum feed ocation is(62.42 + j28.4) R which is higher than the feed line impedan ceof 50 R. hus nput VSWR could be improved by decreasingZi,. I t may be recalled from he scaling principle of two di-mensional omponents18]hat ,orhe same effective di-mensions of a planar comp onent, he mpedance level (reactivecomponent) reduces to half the original value when the thicknessof the substrate is reduced o half. T herefore? another antennaon 1/1 6 in thick substrate with E, = 2.52 as before was designed.The wid th of he rectangle (a in Fig. 3) was chosensuch thatthe effective width equals the effective widthof he1/8 inthick antenna.Theoptim um atio of lengths of sides of therectangle, for btainin g circular polariza tionwith axial ratioequal o 0.17 dB, is foun d o be 1.026 which is different hantha t or1j8 in thickantenna.Thus he at io b/a is foun d odepend upo n the thickness of the substrate . The minimum inputVSWR. for he antenna on 1/16 in thick substrate: is found tobe 1.33, the corresponding inputmpedance being (53 .3 +j14.2) R. The reactive componentof he nput mpedance isthus reduced to half as compared to thatfor he1/8 in thicksubstrate and the resistive comp onent. representing the radiatedpow er, is reduced from 62.4 2 R to 53.2 R. The optimum feedlocation for minimum inputVSWR is fou nd to be on the diagonal

at a distance 0.3522 times A C . For th is opt imum feed loca t ion,the minimum axial ratio (equal to 0.17 dB) is obtained at 3.1 37 2GHz. As the dielectric constantorhe available substra tewith thickness equal to 1/ 16 in was different (2.49), the antennadesigned was optimized again and theseresults are summarizedin Table I.

The nput VSWR can be reduced further if a 1/32 in thicksubstrate is used. Extrapolating the results, the input impedanceis expected to be around (45.3 + 7 ) R nd the input VSWR islikely to be about1.19.Althou gh he nput VSWR improveswith reduction in the thickness of the sub strate, it has been ob-served that he axial ratio limited ban dwid th also decreases.Thu s a design trade-off is involved in the selection of he sub-strate thickness.C. Bandwidth and Radiation Patterns

Theoreticaland measured values of input VSWR and axialratio as functions of frequency for one of the antennas is shownin Fig. 4. Themeasured values of band width for axial ratioless than 6 dB) is 34.8 MHz (1.12 percent) , he correspondingtheoretical value being 33.7 MHz (1.086percent).The VSWRvariation over this band of frequ encies is small (Fig. 4). Theband width of t he ante nna is therefore limited by the axial ratioand not by the input imped ance. Similar results have also beenobserved for heantenna on 1/16 in thick ubstrate ,but heaxial ratio bandwidth is lower by nearly 40 percent (Table I).

Thexperimentalndheoreticaladiationatternsorthe antenna ( thickness = 1 /8 i n , E , = 2.52) in the 0 = 90' planeare hown in Fig. 5. The eamwidth is calculated romheradiationpattern. Table I gives thesum mary of the result forthe diagonal-fed nearly square patch antenn as investigated.

IV. TRUNCATED-CORNERS SQUAR E PATCH ANTENNAIn this case (Fig. 2(a)), the woorthogonalmodesof reso-

nance are diagonal mode s which w ould individually yield linearpolarization along the direction s of the two diagonals. Cho ppingof the wo corners makes he resonant f requency of the modealong hisdiagonal to be higher than hat for hemode alongth euncho pped diagonal. The requency of operationand hefeedpoint are hosen uch that he womod es are excitedin phase quadrature.A . Optinzunl Configuration

Th eperipheryof he runcated-cornersantenna (Fig.2(a))is divided into32ports which nclude fourc-portsat each ofthe truncated corners. An addition al port is considered to repre-sent the feed point . Thus, there are 25 p-ports and four d-portsfor each of the 0-segments. The desegn entation metho d is usedto evaluate the Z-matrix of the multi port planar m odel. The an-ten na characterisrics re valuated as discussed in Sec tion 11.It hasbeen found hat or he chosendimensions (2.7 3 cm X2.73 cm) of th e quarepatch, nd1/8 in thick polys tyrenesubstrate ( E , = 2.52 ), he best value of axial ratio (= 0.12 dB)is obtained at 3.175 GHz when b/a = 0.04578 where b is theamount of truncation in cm and a is the length of sides of thesquare patch. The theoretical values of the resonant frequenciesof the woorthogonalmodes, whichcan be excited ndepen d-entally by locating the feed point at the co rners, are 3.134 0 GHzand 3.21 2 GHz , respectively. The frequen cy for the best circularpolarization (axial ratio equ al to 0.12 dB)s 3.1750 GHz.


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8

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I E E E T R A N S A C T I O N S O N A N T E N N A SAND PRO PA G A TI O N , VOL. AP-31 , NO. 6, N O V EM BER 1 9 8 3

TABLE IP E R F O R M A N C E OF D I A G O N A L FE D N E A R L Y S Q U A R E PATCH

A N T E N N A S

ANTENNA I ANTENNA II . Parameters

1 . Thickness, E 1/8", 2.52 1/16", 2.492. W i dt h ' a ' (cm) 2.66 2.803. L e n g t h ow i d t h a t i ob / a ) 1 .0526 1.0296

I I , P e r f o r m a n c ehe ore t ic a lx pe r im e nt a lhe ore t ic a lx pe r im e nt a l1 . B e s t a x i a la t i o ( d B ) 0.45.5 0.17 0.252. Ce nt e rre que nc y fc (GHZ) 3.1030.101.1658.16643. Re sonant f re qu e nc ie s forthogonal modes (GHz) 3.035.032 3.175 3.1694. I n p u t VSWR a tc 1.73.72.33.555. Bandwidth (MHz) f o rx i a l 33.704.80 21.20

3.1223.210.203 3.116

r a t i o c 6 dB (1.086%)0.632%)0.670%)between lE el and IE I

20.00(1.12%)6. Beamwidth fo r 3 dB d i f f e re nc e

0 110"40" 116' 140"

I I I I I

0 3080 3120Frequency (HHz)

1.75=v)>l .M 2n-

1.25

1.00

4 . Theoret ical nd xpe rimental esul ts or x ia l a t io nd nputVSWR for a d iagonal fed antennaon 1 / 8 in th ick subs t r a te (ey = 2.52).

Theory1 , r;,=0' Plone

---- Experiment le = o -

90"OdB -10 -20 -30 -M -20 -10 CdB

5 . Radiat ionpat tern ordiagonal edantenna; h ickness = 1 / 8 i n,E ~ = .52, f requency = 3 .103 GHz.

Feed Point LocationVariations of the axial ratioand he nput VSWR with heon the line joining the midpoin ts of two opposite

are illustrate d inFig. 6. The npu t VSWR improves fromfor feed location at ( x / a , y / a ) = (0.5, 0.0) to 2.26 for feed( x / a , ria)= (0.5. 0.3 26) and increases again for feed y / a >on the line x /a = 0.5. At the lo cation of th e eed where the

VSWR is minim um the axial ratio is 0.36 d B at 3.175 GHz.

cJ- 0 0.1 0.2 0.3 0.4 0.5-

Feed Locotlon (Y/o)Fig. 6. Var ia t ions o f npu t VSWR a n d axial ratio with f eed oca t ion fo rtmnca ted -co rne r s square antenna thickness = 1 / 8 n , E~ = 2.52, f ie-q u e n c p = 3 .175 GHz).

The axial ratio improves to 0.02 dB when heoperating re-quency is changed to 3 I758 GHz for eedat he ocation ofminimum input VSM7R. For an othe r anten na designed on 1/1 6 inthick substrate ( E , = 2.51) , the minimum input VSWR s foun dt o be 1.6 an d occurs at feed location ( x / a , y / a ) = (0.5, 0.3204) .The input VSWR thus improves when the thickness is reduced.Details of these two antennas are summarized in Table 11.C Bandwidth andRadiation Pattern

The calculated and mea sured values of axial ratio and nputVSWR for one of he runcated -corners square antennas (e , =2.52). su bstrate hickness is 1/8 in) are shown in Fig. 7. Thetheoreticalan dexperimental values ofbandwidth defined foran axial ratio less than 6 dB are 26.4 MHz (0.8 31 percent) and29.4 MHz (0.925percent). The corresponding values for heantenna on the 1/16 in thick substrate (e , = 2.51) are found tobe 1 4.0 MHz (0.44 pe rcen t)and14.4 MHz (0.4535percent) .The eduction in the su bstrate thickness to half reduces thetheoretical axial ratio bandwidth by 4 7 percent and the measuredvalue by nearly 51 percent. The radiationpatterns, t enterfrequencies, have been evaluated and verified experimentally.These are shown in Fig. 8.


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S H A R M A A N D G U P T A : C I R C U L A R L Y P O L A R I Z E D M I C R O S T R I P A N T E N N A ST A B L E I1

P E R F O R M A N C E OF C O R N E R S C H O P P E D S Q U A R E P A T C HA N T E N Y A S

I. P a r a m e t e r s ANTENNA I ANTENNA I II . T h i c k n e s s , g r 1 /a", 2.52 1/16", 2.512. D imens ions a x a cm 2 2.73 x 2.73 2.86 x 2.863 . T r u n c a t i o n b/a 0.04578 0.0573

I I . P e r f o r m a n c e T h e o r e t i c a lx p e r i m e n t a lh e o r e t i c a lx p e r i m e n t a lI . C e n t e rr e q u e n c y f c (GHZ) 3.1758.1750.1756.17532 . R e s on a n t f r e q u e n c i e s f 3.1340o r t h o g o n a l m o d e s (GHz) 3.2155 3.1325.1370.1343 3.2125.2340.22983. A x i a l a t i o t e n t e rf r e q u e n c y (dB) 0.02 0.0 0 . 1 2 0.154 . Bandw id t h (MHz) f o r x i a l 26.4(0.831 2)a t i o < 6 dB 29.4 1 4 .0(0.925%) (0.44%) 14.4(0.45354)5 . I n p u t VSWR a t e n t e rf requency 2 . 26.26 1.6 1 . 86 . B e a r w i d t h o r 3 dBd i f f e r e n c e b etw ee n

IE,I and l E J 1290 152" 129' 138"

X ,

1 c k n e s s 1/8*, E = 2.52 - heoryEweriment1 ' 1 I3160 Frequency (MHz )

VSWR for t runcated-corners square antenna.Fig. 7. Theore t ica l nd xper imenta l results fo r axia l a t io nd i n p u t

V. SQUARE PATCH ANTENNA WITH A DIAGONAL SLOTFor a square patchantennawitha diagonal slot Fig. 2(c))

also, the woorthogonalmodesare diagonal modes.The dif-ferenc e in the resona nt freque ncies is caused by the rectangularslotwhich disturbson emodemore han heother.Thede -segmentationmeth od is used to evaluate the2-matrix of themu ltip ort planar m ode l as explained in Sec tion 11-C. The out erperiphery has been divided into 24 portswhich constitutep-ports.The number of q-ports needed (and hence that of e-ports andd-ports also) is 27. Equatio n (4) is used to evaluate the 2-m atri xof the multiport model.A . Optimum Configuration

The thickness and dielectric constantof he ubstrate are1/8 in and 2 .52, respectively. The ou ter dimensions of the squareare 2.602 cm X 2.602 cm. The optim um dimensions of the slotare 2.89 cm X 0.47cm. Theseyield an axial ratioof0.198dB at3.130 GHz. The woorthogonally spaced modes of th eantenn a tructure can be excited ndependently by feeding atpoints 1 and 2 (Fig. 2(c)) respectively. The measured values of

90'

9 53

2 , 52

90 'Od B -10 -20 -3030 -20 -10 Od BFig. 8. Radia t ionpa t te rn or runca ted-corners qu are n ten na ; th ick-

ness = 1/8 in , er = 2.52, f requency = 3.176 GHz).

resonant requencies of the woorthogonalmodes are 3.060GHz and 3 .210 GHz. The respective theoretical values are 3.063GHz and3.212 GHz. As before theoperating requency orcircular polariz ation lies in between the tw o values.The variation of axial ratio and input VSWR with feed loca-tion on the line joining hemidpointsof woopposite sides(x/a = 0.5) is shown n Fig. 9. The optim um feed location isfound o be a t (x/a, y/a) = (0.5, 0.1636)where nput VSWRis 2.3 and axial ratio equals 0.2 dB. Fory /a > 0.1636 on the linex/a = 0.5, the npu t VSWR improves furtherbut axial ratiostarts degrading.B. Bandwidth and Radiation Pattern

The axial ratioand nput VSWR as functions of frequencyareplotted in Fig. 10. Input VSWR and axial ratio have beencalculated for two feed locations. The theoretic al values of axialratiobandwidthsare same for he wo eed ocation s. VSWRvariations in the wo casesare show n in Fig. 10.Experimentshave been conducte d or eed ocationat @/a, y/a) = (0.5.0.064). The theoreticalan dexper imen tal values ofbandwidths(for axial ratio to be less than 6 dB) are 35.5(1.134percent)and 38.0 MHz (1.214perc ent) , respectively. The variation ininpu t VSWR over this reque ncy range is small as comparedto he variations in axial ratio values. The heoret icalan dex -perimental radiation patterns are illustrated in Fig. 1 1. Table111 summarizes the perform ance of this antenna.


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4

3CL

w

1

IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. AP-31, NO. 6, NOVEhlBER 1983

0 0.1 0.2 0.3Feed Locotlon Y/a)

Fig. 9. Variations of i n p u t VSWR a ndaxia l a t iowi th feed loca t ionsfor square an tenna wi th a d iagonal s lo t ( th ickness = 1 / 8 in, E~ = 2.52,f r e q u e n c y = 3.130 GHz).

0. 4

- heory4

0.0 I I I I I I I I3100 3120 3140 3160 3180Freauency (MHz)Fig. 10. Theore t ica l and exper imenta l resu l t s for square an tenna wi th ad iagonal s lo t ( th ickness= 1/8 n, el .= 2.52, f requency = 3.130 GHz).

,@= 0' Plane

---- Experiment

Fig. 11. Radia t ion a t te rn fo r a quare n tennawi th diagonal s lo t(thickness = 1/8 in , sr = 2.52, f requency = 3.130 GHz) .TABLE I11

PERFORMANCE O F SQUARE PATCH ANTENNAWITH A DIAGONAL SLOT~

~ ~~

T h e o r e t i c a lx p e r i m e n t a lI. t e n t e r f r e q u e n c y fc (GHZ) 3.130.1302 . Resonance f requencyfrthogonal modes ( G H d 3.0633.212 3.0603.2103. A x i a l a t i o t fc4. B a nd w id th f o r x i a l a t i o e s s h a n 6 dB

0.19835.5 MHz(1.134%)

0.238.0 MHz(1.214%)

5. I n p u t VSWR a t c h os en f e e do c a t i o n 2 .9 2.96. Be a nw idt h f or 3 dB d i f f e re nc ebetween IE , I an d IE I0 116"24"

Subs t ra te th ickness = 1 /8 in, c y= 2.52. Dimensions of square pa tch = 2.602 X 2.602 em .Dimensions of t h e s l o t= 2.89 X 0.47 em .


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S H A R M A 955VI. CONCLUDING REMARKS

A technique employing impedance Greens functionsorsegments with magnetic wall boundary is used for analysis anddesign of three types of single feed circularly polarized microstrippatch antennas. The dimensions of the hree ypes of antennasare ptim ized or btaining he best axial ratios.The inputVSWR and axial ratio variations with feed locations are investi-gated in an att em pt o achieve abetter nput VSWR withou tusing an externalmpedancematching etwork. t has eenobserved that for the three types of anten nas investigated, per-fect matching with a 50 s1 feed line is not practical unlessanimpedance matching network is used. Better input VSWR can berealized b y using a hinne rsubstrate,but he axial-ratio band-width is reduced by nearly 40 to 50 percent when the thicknessof hesubstrat e is halved.Among the hree ypes of antennasrepo rted , the square pa tch antenn a with a diagonal slot has thelargest axial ratiobandwidth, whereas theminimum VSWR isobtainedwith diagonal-fed early quare patch ntenn a.Thetruncated-corners ntenna xhibitshe best axial ratio (0.02dB) buthas he leastaxial-ratio bandwidth.The i npu t VSWRvalues of the same order as the square antenn a with a diagonalslot. The heoreticalan dexperimental results are fou nd o bein a reasonable agreement.

REFERENCESK. R. Carver and J . W. Mink, Microstrip antenna technology, I Trans . Antennas Propaga t .. vol. AP-2 9, pp. 2-24, Jan. 1981.J . R . J a m e s et a l . . Micro str ip Antenna Theory and Design. Steven-age , UK: Peter Peregrinus, 1981.1. J . Bahl and P. Bhartia. MicrostriD Antennas. Dedham. MA: ArtechH o u s e , I 9 8 I .J . Q. Howell , Microstrip Antennas, I Trans. Antennas Propa-gar.-. v o l . A P - 2 3, p p . 9 6 9 3 . J a n . 1 9 7 5 .H. D. Weins chel, A cylindrical array of circularly polarized micro-str ip antenna s, in 1975 Antennas Propagat . Soc. Inr. Symp. Digest ,pp. 177- 180.C . M. Coloi, Corner fed electric microstrip dipole, Naval MissileCenter , F t . Mugu, CA: Mar . 1978 .J . L. Ken. Micros t r ip an tenna deve lopments , . in Proc.WorkshopPrintedCircuitAnrennas. New Mex ico State Univ., pp. 3.1-3.20, Oc t.1979.IEEE Tran s. Antennas Propaga t . . v o l. A P - 29 . p p . 9 6 9 4 , J an . 1 9 81 .L . C . Shen , Elliptical microstrip antenna withcircular-polarization,S. A . L o n g e t a i . , An experimental study of the circularly-polarizedell iptical printed circuit antenna, I Trans. Antennas Propagat . ,vol. AP-29, pp. 95-99, Jan. 1981.R . E . Munson,Conformalmicrostripantennasand arrays. l E ETrans . Antennas Propaga t .. vol. AP-22, pp. 74-78, Jan. 1974.K . R . Carver and E. L. Coffey, Theoretical Investigations of Micro-str ipAntennas,MexicoStateUniv. .Tech .Rep.PT-00929. an.1 9 7 9 .T. Okoshi ndT .Miyoshi , Theplan ar circuit-An approach tomicrowaventegrated ircuitry, IE Trans.MicrowaveTheoryTe c h . , vol. MT T-20 , pp. 245-252. Apr.1972.R. Cha dha an d K. C. Gupta , Greens func t ions for r iangular seg-ments in planar microwave circuits , I Trans. Microwave TheoryTe c h . , vol.MTT-28,pp. 1139-1143, Oct.1980.

[ I41 K . C . G u p t aandP.C .Sharma,Segmentationan ddesegmentationtechniquesornalysis of planarmicrostripntennas, in 1980[ 151 R. Chadha and K . C. Gupta . Segm entation metho d using impedanceAntennas Propagar. Soc. lnr. Symp. Diges t , pp. 19-22.matrices oranalysis of planarmicrowave ircuits, IEEE Trans.Microwave Theory Tech. , vol. MTT -29, pp. 71-74, Jan. 1981.[ 161 P. C . S h a r m a a n d K . C. Gupta. Desegmentation method for analysisof wo-dimensionalmicrowave ircuits . IEEE Trans.MicrowaveTheory Tech. , vol. MTT -29, pp. 109&1098 , Oct. 1981.[ 171 H. Pues and A. Vande Capelle,A simpleaccurate ormula or heradiation onductance of a rectangularmicrostrip ntenna. I n t .

Antennas Propagar. Soc. Svmp. Diges t . pp . 23-26. June 1981[ 1 81 K . C . G u p ta et a l . , Comp uter Aided Design of MicrowaveCircuits.Ded ham , MA: Artech House, Dec. 1981. pp. 256-258.

P. C . Sharma (S79-M82) was born in Bhensola,Ujjain, India, on August I . 1947. He received heB.E. an dM . E .deg rees in electrical ngineeringfrom Shri Govindram Seksaria Insti tute of Tech-nology and Science Indore (Universi ty of Indore)in 1969 and 1972, respectively. and he Ph.D . de-gree in Electrical Engineering from Indian Instituteof Technology. Kanpur, India. in 1982.He worked with MilitaryCollege of Telecom-municationngineeringMhow.ndia,uring1971. In 1972 he joined S .G .S . Insti tute of Tech-nology and Science, in the Departm ent of Electri-cal Engineering. and is at present employed as Reader in the Department ofElectronics and Telecommunication Engineering there. His f ields of interestare systems engineering, networks. electromagnetics and microstrip anten-nas .

Kuldip C . Gupta (M62-SM74)was orn in1940.He eceived heB.E.an dM.E.degrees inelectricalommunicationngineeringrom theIndian nstitute of Science,Bangalo re. ndia, in1961 and 1962. respectively, and the Ph.D . degre efromBirla nstitute of Technologyan dScience,Pilani, India, in 1969.H eworkedtunjabngineering ollege,Chan digarh , India, from 1964 to 1965. the CentralElectronics Engineering Research Institute. Pilani,India, rom1965 to 1968,an dBirla nsti tute ofTechnology from 1968 to 1969. Since 1969 he hasbeen with the Indian Insti tute of Technology, Kanpur, India, and has been aProfessorof ElectricalEngineeringsince1975. On leave rom he ndianInsti tuteofTechn ology. he wasaVisitingProfessor at the University ofWaterloo,Canada rom 975 to 1976.EcolePolytechniqueFederale eLausan ne, Sw itzerland, in 1976, Technical Universi ty of Denmark from 1976to 1977, and Eidgenossische T echnische Hochschu le, Zurich, Switzerland. n1979.From 1971 to 1979he was Coordinator or hePhased Array RadarGroup of Advanced Centre for Electronic Systems at the Indian Insti tute ofTech nolog y. He is currently a Visiting Professor at the University of Col-orado. Boulder. He has published four books: icrowave Integrared Circuits.WileyEastern ndHalstedPress,1974, MicrosrripLiner ndSlotlines,

Artech House, 1979. Micronaves , Wiley Eastern, 1979 Halsted Press. 1980,a n d Computer -Aided Des ign o fMicrowave Circui t s . Artech House, 1981. Heholds one patent in microwaves areas.Dr. Gup ta is a fel low of the Institution of Electronics and Telecommunica-t ion Engineers, India.

ariculo polarizacion circular

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