Do Not Excite Surface Waves

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1026 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 41, NO. 8, AUGUST 1993

Microstrip Patch Designs ThatDo Not Excite Surface Waves

D. R. Jackson, J. T. Williams, Arun K. Bhattacharyya,

Absh.act--Two variations of a circular microstrip patch designare presented which excite very little surface wave power. Bothof the proposed designs are based on the design principle thata ring of magnetic current in a substrate (which models thepatches) will not excite the dominant TM o surface wave ifthe radius of the ring is a particular critical value. Numericalresults for radiation efficiency and radiated field strength froma ring of magnetic current are shown to verify this basic designprinciple. The proposed patch designs are chosen to have a radiusequal to this critical value, while maintaining resonance at thedesign frequency. These patch designs excite very little surface-wave power, and thus have smoother radiation patterns whenmounted on finite-size ground planes, due to reduced surface-wave diffraction. These new patch designs also have reducedmutual coupling, due to the reduced surface-wave excitation.Measured results for radiation patterns and field strength withinthe substrate are presented to verify the theoretical concepts.

I. INTRODUCTIONCOMMON property of most microstrip antennas is thatA he antenna element launches surface wave modes, inaddition to the fields radiated into space. The power launchedinto the surface waves is power which will eventually belost, at least for the case of an infinite substrate; hencethe excitation of surface waves lowers the overall radiationefficiency of the antenna. For finite-size substrates, the surfacewave power will diffract from the edges of the substrate,resulting in a disturbance of the radiation pattem. Furthermore,the excitation of surface waves also results in increased mutualcoupling between distant antenna elements, since the surface-

wave fields decay more slowly with radial distance than dothe space-wave fields. For these reasons the excitation ofsurface waves is generally undesirable. Since the dominantTMo surface wave of a grounded dielectric layer has a zerocutoff frequency, a microstrip antenna will, in general, alwaysexcite some surface-wave power. One exception has beennoted in [l], for a horizontal antenna element in a particularsubstrate-superstrate combination. One disadvantage of themethod in [ l ] is that a superstrate layer is required, andalso the substrate layer must be electrically thin, at least fornonmagnetic superstrates.

Manuscript received July 20, 1992; revised February 3, 1993. This workwas supported by the Texas Advanced Research Program and the U.S. ArmyResearch Office under contract DAAL03-91-G-0115.D. R. Jackson, J. T. Williams, R. L. Smith, S. J . Buchheit, and S . A. Longare with the Department of Electrical Engineering, University of Houston,

Houston, TX 772044793 ,A. K. Bhattacharyya is with the Department of Electrical Engineering,University of Saskatchewan, Saskatoon, Canada SN7 OWO.IEEE Log Number 921 1791.

Richard L. Smith, Stephen J. Buchheit, and S . A. Long

In the present work, two novel types of microstrip antennasare presented for which surface-wave excitation is greatlyreduced. The surface-wave excitation is avoided by specificdesign of the radiating element, rather than design of the layergeometry, as in [11. These patch designs are both variations ofa standard circular microstrip patch and have a common designprinciple-a ring of magnetic current in a substrate will notexcite the TMo surface wave, provided the radius is chosen tobe a particular critical value. According to the equivalenceprinciple and the cavity model, a circular microstrip patchcan be modeled as a ring of magnetic current, for computingexterior radiation. Hence, a circular patch having the samecritical radius as the magnetic current ring will not excitethe TMo surface wave. If the substrate is thin enough sothat only the TMo surface wave is above cutoff, then such apatch will not excite any surface wave power, except for thatexcited by the probe feed and the higher-order modes on thepatch. This result was first discovered in [2]. In addition to thereduced surface-wave excitation, the space-wave field near thesubstrate that is radiated by the patch is also reduced, at leastfor thin substrates for which the TMo propagation constant isclose to ko . However, a conventional circular patch havingthis critical radius will not be resonant. In order to makethe patch resonant, the standard circular patch design mustbe modified to change the resonant frequency, while keepingthe radius of the radiating aperture constant. Two differentways of accomplishing this are illustrated by the proposeddesigns.

In order to numerically verify the concept of reducedsurface-wave excitation by a ring of magnetic current withthe critical radius, the space-wave and surface-wave powerradiated by a magnetic current ring in a substrate is for-mulated. Results show that the surface-wave excitation iseliminated when the ring radius attains the proper value.Numerical results are also presented showing the field am-plitude versus radial distance from the magnetic current ring.The results show that the field decays much more rapidlywhen the radius is chosen to eliminate the surface-waveexcitation. This result may have practical importance in thedesign of large phased arrays, where mutual coupling dueto surface-wave excitation results in undesirable scan blind-ness.

Measured results showing field amplitude versus radialdistance from the patch are presented to verify experimentallythat the radiated fields decay away from the new patch designsfaster than from conventional circular patches. Measured radi-ation pattems are also presented to demonstrate that reduced

0018-926)3/93$03.00 0 993 IEEE


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JACKSON et al.: MICROSTRIP PATCH DESIGNS 1027

diffraction at the edges of the ground plane does result insmoother radiation patterns.11. DESIGNPRINCIPLE

In order to understand the operation of the proposed patchdesigns, a conventional circular microstrip patch antenna isconsidered first, shown in Fig. l(a). The patch is shown witha probe feed, although other feeds could be used equallywell. According to the cavity model, the magnetic field onthe radiating aperture p = U is zero, as is the current onthe top surface of the patch. Using the equivalence principle,an exterior equivalent model for the patch is the well-knownmagnetic current model shown in Fig. l(b). Assuming auniform probe current (no z variation), the magnetic current atthe patch edge is due to all possible cavity modes of the formTM,,o, where the indices n, p , and q in TM,,, specify thevariation in the 4 , p, and z directions, respectively. Neglectingall higher-order modes, the 4 variation of the magnetic currentis chosen as the corresponding dominant TMllo cavity modefield variation, so that, for a feed probe at $ =0,

MS(4 )=Jcos4. (1 )By superposition, the radiation from this ring current sheetcan be constructed from the radiation from a single loopof magnetic current K(4 ) at a variable height zo above theground plane, with K(4 ) = COS^. This current ring modelis only approximate because the aperture is not in reality aperfect magnetic conductor. Furthermore, the simple currentfunction of (1) neglects all higher-order modes with n # 1.Although a simple cavity model can account for the excitationof higher-order modes, it cannot account for the nonidealaperture boundary condition (which results in fringing fields).The approximate model becomes more accurate, however, forthinner substrates. More accurate results for a general casewould require a full-wave solution such as a spectral-domainmethod to model the effects of the fringing fields at theaperture.Consider now the radiation from d single Hertzian dipoleof magnetic current, oriented in the z direction, at a heightzo above the ground plane. This infinitesimal dipole willexcite a T M o surface-wave field. If II, denotes any particularcomponent of this surface-wave field, the general form of thefield will be

(2)where ,BTM~ s the propagation constant of the TMo surfacewave, which must be determined numerically [3]. The ampli-tude factor A ( z , zo ) depends on the height of the source andthe observation point above the ground plane. This factor maybe determined from the residue of the surface-wave pole in aspectral-domain solution [3], although the exact value is notneeded for the present discussion.Next, consider the surface-wave excitation from a ringof magnetic current K($) , shown in Fig. 2. The surface-wave fields from the ring may be found from the fields ofthe Hertzian dipole, integrating over the ring current. If theobservation point is sufficiently far from the ring, a far-field

+=~ ( 2 ,~ ) H , ( ~ ) ( P T M ~ P )in4,

z t

1.I + x-(b)

Fig. 1. (a) Geometry of a conventional circular patch antenna, showing thefeed probe. (b) The magnetic current model for the exterior fields of thepatch, based on the cavity model.

approximation for the phase of the radiated surface wave fromeach point on the ring may be used, yielding the factor (seeFig. 2(b))i ( 3 )j P ~ ~ o=e j P ~ ~ oCO S (4-4)

where 4 is the observation angle, and 4 is the angle of thesource point on the ring. Using (2) and ( 3 ) , he surface-wavefield of the ring may be obtained as$= - H i 2 ( P T M o P ) B ( Z )

cos 4cos ( 4 - ) e j D T M o a cos (+-+)U d, (4)where

r h

is another amplitude function which is unimportant at present.Using a =4 - 4, the integration may be written as+= H ! ~ ) ( P T M ~ P ) B ( ~ )

. ~ n [ ~ o s ~ ~ o s 2- i n ~ c o s a s i n ~ r ] e ~ ~ ~ ~ ~ ~ ~ ~ ~6)To evaluate the a integral in (6), the Jacobi-Anger expansionis used:

COe ~ P ~ ~ oC O S a - O(PTM~U) +2Cj,~n(PTMou)COS(7La).

n=l (7)


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h I

MAGNETIC CURRENT RING(b )

Fig. 2.used in the far-field surface-wa ve calculation .(a ) A ring of magnetic current within a substrate. (b) The geometry

After invoking the orthogonality of the Fourier series termscos(na) and using the identity

Equation (9) is a fundamental design equation, which statesthat a ring of magnetic current will not excite the TMo surfacewave, provided the radius is chosen to satisfy

which yields

To have the smallest possible ring, the value xi1 = 1.841 ischosen. This corresponds to a circular patch with the smallestpossible radius.An interesting feature of a magnetic current ring with radiuschosen according to (10) is that such a ring will have areduced space-wave radiation along the air-dielectric interface,in addition to having no surface-wave field, at least for thinsubstrates. This is because the space-wave field along aninterface is dominated by the so-called lateral wave, whichis a component of the continuous spectrum space-wave fieldthat propagates radially with a wave number IC0 [4]. Since

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a20.30

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RING RADIUS : PTMo a = j

b

I I I I I I I I I0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10

-tFig. 3.to elim inate surface-wave excitation.Patch radius versus substrate thickness, for a patch radius necessary

PTM,E IC0 for thin substrates, (10) is also a condition forreducing the TM lateral wave component.Fig. 3 shows a plot of normalized ring radius versusnormalized substrate thickness, for several different substratepermittivities, obtained from (11) with n = 1. For thinsubstrates the solution is nearly independent of permittivity,since PTM,E ko.

111. PATCHDESIGNSFor any specified substrate thickness and frequency, acircular patch with radius chosen according to (11) will notexcite the TMo surface wave, according to the approximateassumptions of the cavity model. However, a patch of thisradius will not in general be of resonant size. According tothe cavity model, a resonant patch operating in the TMllomode will have a radius determined from

h a =&, (12)where IC1 is the substrate wave number. Dividing (1 1) (usingn = 1) by (12) yields

PTMu =1. (13)klEquation (13) will never be satisfied, since

P T M ~ ki. (14)Equation (14), together with (1 1) and (12), implies that a patchwhich eliminates the TMo excitation will be larger than a


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c < ~ < a :

Substrate CoreSIDE VIEW

TOPVIEW

Fig. 4. Cored patch design, which has a central core of radius c removedand replaced by a material with a different permittivity (the feed probe isnot shown).

resonant patch (and thus have a lower resonant frequency).This increase in patch size is a disadvantage, and couldimpose design restrictions for an array of such patches. Inorder to make the patch resonant, without changing the outerradius a, the resonant frequency needs to be raised (equivalentto lowering the effective permittivity of the substrate). Twopossible methods for doing this are discussed next.A . Cored Patch Design

Fig. 4 shows the cored patch design, in which a circularcore region of substrate material has been removed, andreplaced with a different material having a wave numberk2 < kl, which may be air (k2 = I C o ) . The outer radiusa is chosen according to (11). The core region raises theresonant frequency of the patch, and by suitably choosingthe core radius c, the patch may be made resonant at thespecified operating frequency. It is important to note that eventhough the material below the patch is now inhomogeneous,the equivalence principle may still be applied to model thepatch as the ring source shown in Fig. l(b) (with t, =,I),assuming a perfect magnetic boundary condition (PMC) atp = a . This is because zero fields are assumed within thecavity region when applying the equivalence principle, andtherefore any material may be placed there [5 ,ch. 31, includinga homogeneous material with wave number kl (the mostconvenient choice).To predict the resonant frequency of the cored patch, asimple cavity model is used. The fields within the two regionsare expressed as follows:

p 0) . A second solution of (17)will exist, in general, for arbitrary kl, but this solution willbe nonphysical ( c < 0) unless IC1 is sufficiently large. Fora critical value of IC1 = IC ; the second solution will yieldc = 0, and for kl > ICE the second solution becomes aphysical solution. When c = 0, the second solution becomesthe conventional TM120 circular patch mode. Hence

k;.a =xi2. (18)Dividing (18) by (11) (with n = 1) gives

Assuming a thin nonmagnetic substrate, with P T M ~ ko , thisbecomest:l A 8.3846. (20)

For t,l > tFl, a second physical solution to (17) willexist. This second solution will still correspond to the samemagnetic current ring, since the outer radius a and the angularvariation of the modal fields remain the same. Hence, theradiation pattern should be approximately the same, under theassumptions of the cavity model. The main advantage of usingthe second solution is that the core radius c is smaller, resultingin less fringing fields at the patch edge than when using thefirst solution, which has a core radius nearly equal to the patchradius (as seen in Fig. 5 below). One of the disadvantages ofusing the second solution is that the resonant mode of interest(TM120) is no longer the dominant TMllo mode, so care mustbe used to avoid exciting the dominant mode if the TMlloresonant frequency is sufficiently close to the TM120 resonantfrequency (relative to the patch bandwidth).

Fig. 5 shows a plot of the core radius versus the normalizedsubstrate thickness for several different permittivities, obtainedfrom (17). All of the curves approach the same limiting value,c = a , for thin substrates, since ,L?TM~ E IC0 in the limit.The curves for the higher permittivities are only plotted upto the value of substrate thickness corresponding to the cutoffof the TE1 mode, since the TE1 mode will be excited by the


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IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION,VOL. 41, NO. 8, AUGUST 1993~ ~

CORED SUBSTRATEE r p = 1.0

I I I I I I I I 10 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10

-;bFig. 5 .Fig. 4, fo r a patch which is resonant according to the cavity model.Core radius versus substrate thickness for the cored patch design of

magnetic current ring for thicker substrates. Fig. 6 shows aplot of core radius for the second solution to (17), for severalvalues of high permittivities, including one (eT1=8.5) closeto the critical value of (20). For each value of eT1 there is acritical substrate thickness, beyond which the second solutionis nonphysical. It is interesting to note that for larger t, ~ valuesthis critical substrate thickness is approximately independentof c T1 (h/Xo M 0.053 in Fig. 6).It is important to realize that the results of Figs. 3, 5, and6 neglect the fringing fields at the edge of the patch, since aPMC boundary condition has been used. The accuracy couldbe improved by accounting for this fringing. However, Fig.5 shows that in most practical cases the core will be veryclose to the patch edge for the first solution, so that essentiallythe entire region below the patch is hollow. In this case itis not clear how to best approximate the fringing length,except experimentally. One possible advantage of using thesecond solution, for high-permittivity substrates, is that thesmaller core region will allow for a more accurate design,since the core boundary is not extremely close to the patchedge, as it usually is for the first solution. In this case standardexpressions for the fringing length should be accurate [6].Thesmaller core is also easier to manufacture as well, since thepatch has more supporting substrate below. Accounting for thefringing length, the physical patch radius up is given by

C-a0.6

0.5

0.4

0.3

0.2

0.1

0

h L ,Fig. 6.(the first solution is given in Fig. 5) .Second solution for core radius for the cored patch design of Fig. 4

Equation (21) will account for the effect of fringing fields onthe resonant frequency of the patch. However, the presenceof fringing fields will invalidate the model of a magnetic ringsource existing at a fixed radius, shown in Fig. l(b). Hence,there will always be some surface-wave excitation, even whenfringing fields are accounted for.B. Shorted Annular Ring Patch

Another design which decreases the effective radius of thecircular patch is the shorted annular ring antenna shown in Fig.7. A short-circuit boundary is established at p =c , by usingshorting pins for example. The radius a is chosen from (ll),and the radius c is chosen to adjust the resonant frequency.Because of the short circuit, the region p


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a___)C

Shoning pinsSIDE VIEW

TOP VIEWShorted annular ring design, which has shorting pins placed at radiusig. 7.

c (the feed probe is not shown).with

(24)= -.Equation (23) is a transcendental equation for determining c.One solution exists for all values of ICl, and a second solutionwill exist for sufficiently large values of k1 such that kl > CY ,with ICE being the same critical value found for the solutionof the cored-patch transcendental equation, given by (19).Hence, for a nonmagnetic substrate, a second solution existsfor E,I > given by (20). Fig. 8 shows a plot ofthe radius c versus normalized substrate thickness for severaldifferent permittivities, up to the TE1 cutoff thickness (thesolution corresponding to the largest c value is used for thehigher permittivity cases).Because the material below the patch is homogeneous in thisdesign, the usual formulas [6] for the patch edge extensionA a may be used to predict the physical radius u p to makethe patch resonant. As mentioned previously, however, thefringing fields will result in some surface-wave excitation.

kl X i 1P T M ~

with

Iv. RADIATION FROM A RINGSOURCEIn order to numerically demonstrate how the radiationefficiency and fields from a magnetic current ring are affectedby the choice of ring radius, the space-wave and the surface-wave power radiated by the ring source of height h in Fig.

l(b) have been calculated. A closed-form expression for thesurface-wave power P,, radiated into the TMo mode by themagnetic current ring of Fig. l(b) has been derived in 121, andthis derivation will not be repeated here. For completeness,the final result is

1P,, =- IC h)J ; " (pTMoa)F2(h)2qoT ( O

60.25

SHORTED ANNULAR RING

0.05 I I I I 1 I I I I

tFig. 8.substrate thickness, for the shorted annular ring design of Fig. 7.The radius of the circle on which the shorting pins are placed, versus

where

and(27)tan (x)tanc (z) = -,

X

with kz0 and kZ l being the wave numbers in the air anddielectric regions, respectively, for the TMo surface wave.The power Psp adiated into space may be calculated fromthe far-field components of the ring source, by integratingthe Poynting vector over a large hemisphere at infinity. Theradiation pattern of the ring source is found by first calculatingthe far-field pattern of a Hertzian magnetic dipole at heightz' within the substrate. This pattern may be found from areciprocity calculation, similar to the method described in171 for a Hertzian electric dipole. The dipole pattern can beintegrated analytically in z' from 0 to h. Next, an integrationin 4' is performed from 0 to 27r around the boundary ofthe ring, using an appropriate factor to account for the phasedelay out to the observation point, along with geometry factorswhich account for the changing current direction. The resultingintegration may be done in closed form, in a similar manner asfor the derivation of (9), resulting in a closed-form expressionfor the radiated fields. The far-field power density may then be


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analytically ntegrated in 4 over the hemisphere at infinity. Theresulting expression for radiated power involves a numericalintegration in 6 from 0 to 7r/2, and is given as

wheref ( ~ )tanc2( k , l h ) sinB

with

and

with n1 =m. he radiation efficiency of the ring isdefined asn

Fig. 9shows a plot of radiation efficiency versus normalizedring radius for a magnetic current ring in a substrate witht, =2.2, having different substrate thicknesses. Regardless ofsubstrate thickness, the efficiency is 1.0 for a radius equal tothe value predicted by (1 1) (this radius is different for eachsubstrate thickness). For larger radii the efficiency reaches 1 Oa second time, corresponding to the second solution of (1 1)( n = 2 ) . it is also seen from this figure that the efficiencyenhancement is more narrow-band (sensitive to a / A o ) forthicker substrates.In order to demonstrate the faster decay of the fields froma ring source which does not excite surface waves, a spectral-domain formulation for the field E, of a ring source was used.For simplicity in the formulation, the ring source of Fig. l(b)was replaced by a collapsed ring current at z' =h/2, shownin Fig. 2(a). The field E, was calculated at the ground plane( z =0) for convenience. Omitting the details, the final result isE z - 3 7 o ( ~ o a ) ~ 0os 4

where the numerical integration is along a Sommerfeld contourin the complex p = k , / ko plane which detours above thesurface-wave pole on the real axis. The function I,'"(P)arises from the transmission ine modeling used in the spectral-domain immitance method [SI, and is defined as the current atz =0 (whereE, is evaluated) in the TM, equivalent circuit ofFig. 10when a 1 V source is placed at z =h/2 (correspondingto the location of the ring source).

E , -2.2e r /1 o

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0.1o'2 1 1 I I I I I I I I

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0fi

Fig. 9.shown in Fig. I(b). E, = 2 .2 .Radiation efficiency versus ring radius for the magnetic current ring

+I V

' i hHORT

Fig. 10.field of a magnetic current ring.Equivale nt circuit used in the spectra l-domain formulation for the

Fig. 11 shows results for a substrate having E, =2.6 andh =0.445 cm at a frequency of 5.0 GHz. In this figure E,is plotted versus normalized distance from the ring sourcefor two cases: a ring radius corresponding to a conventionalresonant patch (eq. (12)) and a ring radius calculated from(11) (with n = 1). Both plots are normalized to 0 dB ata radius of 0.5X0 for comparison. Also shown in the figureare plots of the simple functions l / f i and l / p 2 , which arenormalized by equating with the corresponding ring plot at aradius of 4.0A0. The field from the conventional patch matches


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JACKSON er al.: MICROSTRIP PATCH DESIGNS 1033

0IEz l(W

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Fig. 11.

1.o 2.0 3.0P-4

2alculated magnitude of the electric field at the ground Dlane versusY Ira&al distance for the magnetic ring of Fig. 2(a). Curves are presented fora ring radius corresponding to a conventional circular patch ( k l a = xi1)and a patch which eliminates surface-wave excitation ( p ~ ~ ~ axi,). Forcomparison, plots of the functions 1 J7; nd 1 p 2 are also given, normalizedto the two theoretical curves at p/Xu = 4 . 0 . er = 2 . 6 , h = 0 . 4 4 5 cm ,f = 5 .0 GHz.

the l /@ behavior closely for larger p as expected, since theconventional patch field is dominated by the surface-wave fieldfor larger p . For the ring source chosen to eliminate the TMosurface-wave excitation, the field matches very closely with thel / p2 curve. This again is to be expected, since the field is nowdetermined entirely by the space-wave field. For a microstripantenna, the space-wave field along the layer always decays asl/ p2 (and decays as 1/r for observation points in space, when8


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55.00 convcmtionni patch (exp)

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- / p variationc o r d patch exp)-

Fig. 12. Measured electric field magnitu de (IS21 ) at the ground plane versusradial distance, for the cases of a c onventional circular patch and a cored patchdesign with an air core. For comparison, two plots of the function l / f i arealso given, normalized to the two different measured curves at radii 22 cman d 19 cm, respectively. = 2.6, h = 0.445 cm. For the conventionalpatch, a =0.95 cm, TO =0.45 cm, and f =5.15 GHz. For the cored patchdesign, a =1.19 cm, c =1 . 17 c m , T O =0.61 cm, and f =5.08 GHz.approximately39 R. The measured IEzl for this patch is alsoshown in Fig. 12, along with another 1/fi curve, normalizedto the measured curve at a radius of 22 cm. As with thecored patch, the agreement with the l / f i curve indicatesthat it is mainly a surface-wave field that is being measured.Because the resonant impedances of the two patches in Fig.12are similar, the power from the network analyzer goinginto each patch at the resonant frequency is similar (within1.5 dB). Therefore, the values of in Fig. 12show a faircomparison of the relative field levels away from the patches,for the same input powers. It is noted that the field is about 5dB lower for the cored patch than for the conventional patch,verifying a reduced field excited by the cored patch.Fig. 13 shows the measured E-plane pattern for the cored-substrate design on the square ground plane. It is seen that thepattern has a very large amount of scalloping, essentially thesame as for a conventional circular patch on the same substrate .Clearly, the cored patch design for this low-permittivity sub-strate was not effective in reducing the amount of surface-waveand lateral-wave excitation. This observation is consistent withthe results of Fig. 12, which indicate a significant residualsurface-wave field.Next, a cored patch was designed on a high-permittivitysubstrate having er = 10.8 and h =0.064 cm, using an aircore. For this design the second solution of (17) was used, sothat the core radius is not very close to the edge. In this casethe cored patch had an outer radius a =1.67 cm, a core radiusc =0.74 cm, and was fed by a semirigid 0.034 in. OD coaxial-cable probe at a feed radius TO =1.60 cm. The input resistanceat the resonant frequency of 5.17 GHz was approximately 65R. A conventional circular patch on the same substrate wasalso designed, with a radius a = 0.53 cm and a feed radiusTO =0.13 cm (using the same probe connector), which gave aresonant input resistance of approximately 59 R at 4.70 GHz.Fig. 14 shows measured lSzlJversus radial distance fromthe patch, while Figs. 15 and 16 show the measured E -

nL

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Fig. 13. Measured E-plane pattern for a cored patch with an air core.E , = 2 . 6 , h = 0.445 cm, a = 1 . 19 c m , c = 1 . 17 c m , TO = 0.61 cm,and f = 5.08 GHz.

and H-plane patterns for the cored and conventional patches,respectively. The difference in measured field between thecored and conventional designs is between 10 and 20 dB,considerably larger than the 5 dB difference observed for thelow-permittivity case. This can be explained by the fact thatthe fringing fields are reduced for this design, partly becauseof the higher permittivity substrate, and also because the c / aratio is not close to unity. It is interesting to note that themeasured field from the conventional patch exhibits a fieldvariation that matches very closely to a l / p type of decayin the range plotted, seen by comparing with the l / p curvewhich is normalized to the measured curve at a radius of 7 cmin the figure. This behavior (which has also been confirmedby numerical results similar to those of Fig. 1 ), is due to thethinner substrate used here, which results in a relatively smallsurface-wave excitation, and a resulting l / p field variation inthe near field due to the lateral wave. The measured field ofthe cored patch shows a l / p 2 behavior, seen by comparingwith the 1 / p 2 curve in the figure, which is normalized tothe measured curve at a radius of 7 cm. The reduction inmeasured field amplitude is primarily due to the reduction inthe lateral-wave excitation in this case. The E-plane pattern ofthe cored patch in Fig. 15is very smooth. The E-plane patternof the conventional patch in Fig. 16shows a small but quitenoticeable amount of scalloping, due to the diffraction of thelateral wave from the edge of the ground plane.In addition to the reduced E-plane scalloping, anotherinteresting feature of the cored patch pattern in Fig. 15 is thatthe E-plane pattern is narrower than the H-plane pattern, justthe opposite of the pattern for the conventional patch, shownin Fig. 16.Furthermore, the E- and H-plane patterns are moresimilar for the cored patch than the conventional patch, whichcould have practical significance or circular polarization. Thisfeature is due to the larger radius of the radiating aperture,compared with a conventional circular patch.An annular ring patch was designed next, using a thin, low-permittivity substrate with tr =2.35 and h =0.15 cm. Theouter radius of the patch was 1.65 cm, with an inner radiusof 0.82 cm. This ring was constructed by first coring out the


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1035ACKSON et al.:MICROSTRIP PATCH DESIGNS

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Fig. 14. Measured electric field magnitude (IS21 ) at the ground plane versusradial distance, for the cases of a conve ntional circular patch and a cored patchdesign with an a r core. For comparison , plots of the functions l / p and l / p 2are also given, normalized to the two respective measured curves at a radiusof 7 cm . =10 . 8 a nd h =0.06 4 cm . For the conventional patch a =0.53cm , TO =0.13 cm, and f =4.70 GHz. For the cored patch design a =1 . 67cm , c =0.74 cm, TO =1.60 cm, and f =5.17 GHz.

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(b )Fig. 16. Measured E- and H- plan e pattems for a conventional circular patch.( a ) E p l a n e . ( b ) H p l a n e . e , = 1 0 . 8 , h = 0 . 0 6 4 c m , a = 0 . 5 3 c m , r o = 0 . 1 3cm, and f = 4.70 GHz.

0

(b )Fig. 15. Measured E- and H-plane patterns for a cored patch with an aircore. (a) E plane. (b) H plane. e p =10.8, h =0.064 cm, a = 1.67 cm,c =0.74 cm, ro = 1.60 cm, and f =5.17 GHz.dielectric and ground plane for p < c, and then solderingbrass foil to the ground plane to cover the hole. The short-circuit condition at the inner radius was obtained by using

soldered copper foil. The patch was fed by a semirigid 0.085in. OD coaxial-cable probe at a radius of 1.10 cm, whichgave a resonant input resistance of approximately 60 0 atthe resonant frequency of 5.00 GHz. Fig. 17 shows the E-and H-plane patterns for this patch. The E-plane pattem inthis case is very smooth, indicating an absence of surface-wave and lateral-wave diffraction from the edges of the groundplane. The bump in the patterns near broadside is due toconstructive interferenceof the diffracted waves from all partsof the circular edge of the ground plane. The smoother E-planepattem for this patch, compared with the cored patch of Fig.13,is attributed to both the thinner substrate and the fact thatthe c / a ratio is not close to unity for the annular ring patch,as it is for the cored patch design.Fig. 18 shows the E- and H-plane pattems for a con-ventional patch designed for the same substrate as in Fig.17, with a = 1.06 cm and TO = 0.22 cm, using the 0.085in. coaxial feed probe. The input resistance for this patchwas approximately 54 0 at the resonant frequency of 5.14GHz. The E-plane pattem of the conventional patch showsa noticeable amount of scalloping near the horizon, due todiffraction of the surface-wave and lateral-wavefrom the edgesof the ground plane.


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(b)Fig. 17 . Measured E- and H-plane patterns for a shorted annular ring patch.(a) E plane. (b ) H plane. er =2 . 3 5 , h =0 . 1 5 c m , a =1 . 6 5 c m , c =0 . 8 2cm , TO = 1.10 cm, and f =5 . 0 0 GHz.

Fig. 19 shows the E- and H-plane patterns for an annularring patch design using the same high-permittivity substrate asin Figs. 15 and 16. In this design a = 1.74 cm and c = 1.32cm, with the 0.034 in. coaxial feed probe at a radius TO =1.53cm. This gave a resonant input resistance of about 49 R atthe resonant frequency of 4.63 GHz. As for the cored patchdesign on the high-permittivity substrate, the E-plane patternis smooth and also narrower than the H-plane pattern.

VI. CONCLUSIONSTwo different designs for microstrip antennas which donot excite surface waves have been proposed, a cored patchdesign and a shorted annular ring design. Both designs aremodifications of a standard circular patch, and are based onthe principle that a ring of magnetic current in a substratewill not excite the T M o surface wave, provided that the radiusof the ring is chosen properly. The proposed designs alter theresonant frequency of the standard circular patch, allowing thepatch to be resonant while also having the prescribed radiusnecessary to eliminate the surface-wave excitation. One of thedisadvantages of the proposed designs is that the patches havea larger radius than does a conventional circular patch, whichcould impose restrictions in an array environment.

(b)Fig. 18. MeasuredE- and H-plane patterns fora conventional circular patch.(a) E plane. (b) H plane. c T =2 . 3 5 , h =0 . 1 5 c m , a =1.06 cm , T O =0 . 2 2cm , and f = 5.14 GHz.

Numerical results for a ring of magnetic current in asubstrate demonstrated that surface-wave excitation will beeliminated when the ring radius is chosen properly, as pre-dicted. Results also show that the fields from such a sourcewill decay much faster along the substrate than for a ringsource of different radius, due to the absence of the surface-wave field and also due to a reduction in the amount ofspace-wave excitation along the interface (reduced lateral-wave field). For a practical patch design, there will alwaysbe some surface wave excitation, due to higher-order modesexcited within the patch cavity, and the effects of the fringingfields of the dominant mode at the patch edge. However,experimental results have demonstrated a reduced field withinthe substrate away from the patch, which could have practicalsignificance in the design of large phased arrays, where mutualcoupling due to surface-wave and lateral-wave excitationresults in undesirable scan blindness. Both the cored patchand the annular ring designs achieved a significant eduction insurface-wave and lateral-wave excitation when using a high-permittivity substrate. For a low-permittivity substrate (suchas Duroid), the annular ring design worked better than thecored patch design. This is partly attributed to the fact that thecored patch design requires a core radius nearly equal to thepatch radius, which enhances the fringing fields and makes thefringing length estimate more difficult.


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(b)Fig. 19. Measured E- and H-pla ne pa ttems for a shorted annular ring patch.(a ) E plane. (b) H plane. e,. =10.8 , h =0.064 cm, a =1.74 cm, c =1.32cm , TO = 1.53 cm, and f =4.63 GHz.

Another important consequence of the reduced surface-waveexcitation from the proposed designs is that surface-wavediffraction from the edges of a finite-size substrate and groundplane is reduced, thereby minimizing the perturbing influenceof the diffraction on the radiation pattern of the antenna. Thishas been verified experimentally for both of the designs.One further interesting feature of the proposed designs isthat the beamwidths of the E- and H-plane patterns are morenearly equal than for a conventional circular patch, whichcould have practical significance for circular polarization ap-plications.

ACKNOWLEDGMENTThe authors would like to thank Prof. R. W. P. King ofHarvard University for his useful comments and informationwhich he provided about the lateral-wave excitation from amicrostrip antenna.

REFERENCESN. G. Alexopoulos and D. R. Jackson, Fundamental superstrate (cover)effects on printed circuit antennas, IEEE Trans. Antennas Propagat.,vol. 32, pp. 807-816, Aug. 1984.A. K. Bhattacharyya, Characteristics of space and surface-waves in amultilayered structure, IEEE Trans. Antennas Propagat., vol. 38, pp.D. M. Pozar, Input impedance and mutual coupling of rectangularmicrostrip antennas, IEEE Trans. Antennas Propagat., vol. 30, pp.R. W. P. King, Electromagnetic field of dipoles and patch antenna s onmicrostrip, Radio Sci., vol. 27, no. 1, pp. 71-78, Jan.-Feb. 1992.R. F. Hanington, Time-Harmonic Electromagnetic Fields. New York:McGraw-Hill, 1961.

1231-1238, Aug. 1990.

1191-1196, NOV. 1982.

[6] L. C. Shen, S. A. Long, M. R. Allerding, and M. D. Walton, theresonant frequency of a circular disc, printed-circuit antenna, IEEETrans. Antennas Pro pagat., vol. AP-25, pp. 595-596, July 1977.[7] D. R. Jackson and N. G. Alexopoulos, Gain enhancement methods forprinted circuit antennas, IEEE Trans. Antennas Propa gat., vol. 33, pp.976-987, Sept. 1985.[8] T. Itoh and W. Menzel, A full-wave analysis method for open mi-crostrip structures, IEEE Trans. Antennas Prop agat., vol. 29, pp. 63 48 ,Jan. 1981.

D. R. Jackson, for a photograph and biography, see p. 23 of the January1992 issue of this TRANSACTIONS.

J. T. Williams for a photograph and biography, see p. 1822 of the November1990 issue of this TRANSACTIONS.

Arun K. Bhattacharyya was bom in India in 1958.He received the B.E. (Electronics and Telecommu-nication) degree from Bengal Engineering College,University of Calcutta, in 1 980 and the M.Tech. andPh.D. degrees from the Indian Institute of Technol-ogy, Kharagpur, in 1982 and 1985, respectively.From November 1985 to April 1987, he was withthe Electrical Engineenng Department, Universityof Manitoba, Canada, as a Postdoctoral ResearchFellow. From M ay 1987 to October 1987, he workedwith Til-Tek Limited, Kemptville, Canada, as aSenior Antenna Engineer. From November 1987 to June 1991, he was afaculty member in the Electrical Engineenng Department, University ofSaskatchewan, Canada. He joined the Hughes Space and Communicationgroup in July 1991. His research interests include printed antennas and circuitsand the modeling of planar and nonplanar microwave antennas and circuits.

Richard L. Smit h was bom in Amarillo, TX , onMarch 3 , 1966. He received the BSEE and MSEEdegrees from the University of Houston in 1989 and1992, respectively. At the University of Houston,he joined Eta Kappa Nu and Tau Beta Pi. Hiscurrent areas of interest include high-temperaturesuperconductor applications, microstrip antennas,and electromagnetic measurements.He is currently with Sanders Associated inNashua, NH.

Stephen J. Buchheit was bom in Columbus, OH,on October 29, 1970. He received the B.S. degreein electrical engineering from the University ofHouston in 1992. He is currently pursuing the M.S.degree in electrical engineering at the University ofColorado at Boulder. His interests include th e mod-eling development of microwave and microwave-optics devices.

S. A. Long for a photograph and biography, see p. 1911 of the December1990 issue of this TRANSACTIONS.

Do Not Excite Surface Waves

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