1990The RCS of a Rectangular Micro Strip Patch in A

8/2/2019 1990The RCS of a Rectangular Micro Strip Patch in A

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2 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 8, NO . 1 , JANUARY 1990

The RCS of a Rectangular Microstrip Patch in aSubstrate-Superstrate GeometryAbstmct-A general scattering formula is derived for an arbitrary res-onant conductive body within a layered medium, which shows that thebody radar cross section (RCS) is directly related to the radiation effi-ciency of the body. The radar cross section of a rectangular microstrippatch antenna in a lossy substrate-superstrate configuration is then in-vestigated a s a specific case. Results are presented to show the effectsof loss in the substrate, a lossless superstrate, and a lossy superstrate.

E nc'iI. INTRODUCTION

ICROSTRIP PATCH ANTENNAS are attractive ele-M ments at microwave frequencies due to their inherentadvantages, such as conformability and simplicity of design[l]. One of the main disadvantages of the patch, however, isits small bandwidth, since the patch antenna is fundamentallya resonant structure, typically with high Q. This resonant na-ture introduces another characteristic of the patch which maybe undesirable for certain applications: a large radar crosssection (RCS) at the resonant frequencies. In fact, the RCSat resonance is usually very large compared with the physicalarea of the patch, resulting in a large scattered signal at thesefrequencies [ 2 ] , 3].

One way to reduce the RCS is by reactively loading thepatch [3]. As shown in [3], the proper load impedance maysignificantly reduce the patch RCS, especially at the resonantfrequencies. Another method for reducing RCS, investigatedin this article, is through the use of material effects.

A general scattering formula for the RCS of a resonantconductive body within a layered medium is first derived.This formula shows that the body RCS is directly related tothe radiation efficiency of the body. The specific case of arectangular patch antenna within a lossy substrate-superstrategeometry is then considered. Results showing RCS reductionare presented for the following three cases: a lossy substrate,a lossless substrate with a lossless superstrate, and a losslesssubstrate with a lossy superstrate. In each case, the RCS re-sults are consistent with the general scattering formula.

II. GENERALCATTERING~ R M U L ABefore the specific case of scattering from a patch antenna is

analyzed, the more general case of scattering from an arbitrarybody in a layered dielectric region is considered, shown inFig. 1. An arbitrarily shaped conductive body S is embeddedwith the layered structure, illustrated in the figure as a singlelayer. (The following discussion is general, however.)

Manuscript received March 18, 1988; revised November 18, 1988.The author is with the Electrical Engineering Department, University ofIEEE Log Number 8929466.Houston, Houston, TX 77204-4793.

LAYEREDe TRUCTURE/ / / / I / /

Fig. 1. Arbitrary cond uctive body S embedded within a layered structureover a ground plane (shown for a single layer).If the body exhibits any appreciable resonance at the inci-

dence signal frequency, it may be assumed that the scatteringcurrent J, induced on the body is relatively form-independentof the signal polarization and arrival angle. That is,

I , ( P ) = I , J b ( r ) (1)where J b P ) is a mode function independent of the signal, andthe amplitudeI, depends on the signal amplitude and polariza-tion. If the incoming wave is polarized in the &direction, anequivalent dipole source at (r l , 81, $1) producing the incidentsignal may be written as

Because the body is conductive, E S x A = -Ei, x A on thesurface, which leads to

( I s , , ) = - Einc J, d S (3)bwhere the brackets denote reaction [4],

DefiningV = Einc J b d ~J,z, = - ( J b , J b )

allows (3 ) to be written asI, = v / z , . ( 4 )

Denoting EL as the field radiated into space (excludingsurface-wave fields) by J b , it follows from reciprocity that

0018-926X/90/0100-02$01.00 0 990IEEE

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JACKSON: RCS OF RECTANGU LAR MICROSTRIP PATCH

The total power radiated into space by J b is3

z( 6 )12Prb = -Rs e r

where R , = Re { Z , } and e, is the radiation efficiency of thebody, defined as the ratio of radiated power to total (radiated+dissipated) power:with Pdb denoting the power dissipated by J b in the layeredstructure. For lossless layers, this corresponds to surface-wavepower. It is also convenient to introduce the power per solidangle in the 2-polarization radiated by J b at angles 81 , $ 1 ,which is

From this the partial gain at angles (81, $1) in the 2-polarization may be defined as

Gu( 8 i , $ 1 ) = 47&(81, $ l ) / P r b - (9)The radar cross-sectional area for a scattered field in the

polarization direction fi at (e2,$2 ) due to the incident signalpolarized in the &direction arriving at angles (81, $ 1 ) is thengiven as

(10)~[1z , ~ p ~ ( 8 ~ ,2)1A,, = IE inc 2 .Using (4) for I,, and substituting (8) and (9) into ( 5 ) for Vthen results in

This equation indicates the basic effect of the material pa-rameters and geometry on the RCS of the body. Clearly, if thegain in either the incident or observation directions is reduced,the RCS will be reduced. However, this may not be practicalin most situations, since the arrival angle may be unknown.Because of the e, term in the equation, the RCS in generalwill be lowered when the radiation efficiency is reduced. Areduction in the efficiency of a patch radiator can easily beaccomplished by introducing loss in the layer, or by using asuperstrate layer, with or without loss. It may not be desirableto reduce the efficiency too low, however, since the antennabecomes a poor radiator.

The final term in (11) is ( R s / l Z s l ) 2 ,which involves theimpedance properties of the body. The RCS is minimizedwhen the body resistance is minimized relative to the totalbody impedance. A qualitative interpretation for this condi-tion is that the current J b is concentrated at the reactiveparts of the structure, away from the radiative parts. For ageneral body, it is difficult to give much discussion for therealization of such a condition. However, for the special caseof a microstrip patch terminated with a load impedance, thiscondition implies choosing the proper load impedance to min-

t

rL-DX _I

Fig. 2. Rectangular patch in a substrate-superstrate geo metry.

imize the radiative currents on the patch surface [3]. The res-onant patch surface is resistive at resonance, while the probeconnected to the terminating load is mainly reactive.

111. RCS OF A RECTANGULAR PATCHThe geometry of a rectangular microstrip patch is shown in

Fig. 2, with the patch assumed to be at the interface betweenthe substrate and the superstrate. The substrate has relativepermittivity and permeability 1 , p1, as well as arbitrary di-electric and magnetic loss tangents l l , ml . The superstratesimilarly has 2 , p 2 , 12 , m2. The complex relative permittiv-ities and permeabilities are then

= i(1 - r i )p; = pj(1 - jm i ) . (12)

A basis function representation for the surface current onthe patch may be written as

NJs(x, Y ) = C I n B n ( x , U) (13)

where a convenient choice of basis functions are the cavity-mode functions [3]

n = l

i s i n p ( x + D , / ~ ) c o s ~ o , ~ ~ / 2 )J s in CO ) + D y / 2 ) c o s ~ ( ~Dx/2)

(14)DY{ 1 D XBn(x, Y ) =where n denotes indices p , q . The basis functions may benumbered according to increasing resonant frequency.

Reactions and excitation coefficients are then defined asZmn = - ( B m , Bn ) (15)

(16)

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4 IEEE TRANSACTIONSON ANTENNAS AND PROPAGATION, VOL. 38 , NO . 1, JANUARY 1990

-30

-40

Aee(dB)

-50

-60

-70

Galerkin's method may be applied to enforce the condition of

-

-

-

-

I

zero tangential electric field onof equations is obtained:

N

n = l

which may be written in matrix

the patch. The following set

m = 1, 2 , . . . , N (17)

form as

The matrix coefficients Zmnare determined by a plane-wavespectrum approach based on the Sommerfeld solution [5]. Theexcitation coefficients V, may be found in a straightforwardmanner by using plane-wave reflection theory to find the E-field inside the layered structure in the absence of the antenna161, and analytically integrating over the required basis func-tion.

After (18) is solved for the current amplitudes, the radia-tion field from each basis function of current may be founddirectly using reciprocity, by first finding the far field of ahorizontal infinitesimal dipole within the structure [6], andthen multiplying by the free-space array factor of the partic-ular patch current mode. Summing over all modes gives thetotal scattered field. If the incident field is polarized in theU direction and the 6 component of the scattered field E' isconsidered, the RCS is given as

4nr2 E: 2A,, = - [ E i n c 2IV. RESULTS

In order to verify the calculations, monostatic RCS resultswere first obtained for the patch geometry used by Newman[2]. The "exact" solution shown in Fig. 3 uses the first 18lowest frequency modes. The RCS values are normalized to1 m2 and expressed in dB (dB = lOlog,,, [A,"[) .he resultsagree almost exactly with the calculated and measured resultsof [2]. Also shown in Fig. 3 are the results obtained whenonly one particular @, q ) cavity mode basis function is used.Each resonant peak in Fig. 1 is labeled with the mode re-sponsible for the RCS peak, which is also the mode used inthe corresponding one-mode result. The only exception is the(1, 1) mode, where both2 nd9 currents are assumed, in orderto accurately describe this mode. In each case, the one-modesolution gives accurate results near the corresponding resonantfrequency.

Fig. 4 shows the RCS predicted by using the first two cavity-mode basis functions, the (1, 0)k and (0, 1 ) j modes. Thecurve for a lossless substrate (l1 = 0) is very close to the exactsolution of Fig. 1, over the frequency range shown. Curvesfor loss tangents of ZI = 0.1 and 1 1 = 1.0 are also shown.It is noticed that the resonant nature of the RCS is quicklydiminished with the introduction of loss into the substrate.

All of the following results in Figs. 5-7 are for a resonantpatch of dimensions D, = 1.27 cm, D, = 1.91 cm with1 = 2.2. Monostatic RCS is shown for a broadside incidence,

- - - 1 MODE ONLY

-70 2L4 5f (GHz)

Fig. 3. Results for the patch of [ 2 ] (single lossless substrate layer), showingboth an 18 mode solution and one-mode approximate solutions. 1 =2.17,b = 0.158 cm, D, = 3.66 cm, D , = 2.60 cm , 0 = 60 4 = 45'.

-201

with 8 = 0" and 6 = 0". A one-mode solution ((1, 0)x mode)is used in each case.

First, Fig. 5 shows the effects of both loss in the substrateand substrate thickness. Note from Fig. 5(a) that the RCSfor the lossless case is very insensitive to the electrical layerthickness. As the loss tangent increases, however, the RCS israpidly reduced. At first it may seem surprising that a lossysubstrate underneath the patch would have so dramatic an ef-



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JACKSON: RCS OF RECTANGU LAR MICROSTRIP PATCH

-20

-120c0.02 0.04 0.06 0.08

f (GHz)

e,

c, = 2.2

E l = 2.2

0.00 0.02 0.04 0.06 0.08

c, = 2.2loo[0

DY

.IO

D, 14

zI I n i I I I I I I , :" "-0 10 20 30 o 0. 1 0.2 0.3 0.4 0.5 0.6 0. 7 0.8 0.9

Fig. 5 . Results fo r a resonant length patch on a single substrate layer having various loss tangents. Patch dimensions ar e D , = 1.27cm , D, = 1.91 cm. (a) RCS versus normalized substrate thickness. (b)Efficiency versus normalized substrate thickness. (c)Resonant frequency versus loss tangent for two different values of normalized subs trate thickness. (d) Resonant inpu t resistanceversus loss tangent for two different values of normalized substrate thickness.

fect on the RCS. This is predicted from ( l l ) ,however, whichrelates RCS to the radiation efficiency of the patch. The ef-ficiency is reduced for a lossy substrate, since more poweris dissipated within the substrate. The efficiency e, is shownin Fig. 5(b). The efficiency is seen to decrease fairly rapidlywith loss tangent, except for the interesting feature that someof the layers with more loss may have a higher efficiency forthin substrates. This is due to the rapid decrease in resonantfrequency with increasing loss tangent, which tends to coun-terbalance the decrease in efficiency. The resonant frequency

for two choices of substrate electrical thickness is shown inFig. 5(c). Regardless of thickness, the resonant frequency de-creases rapidly with increasing loss tangent. In Fig. 5(d) theresonant input resistance of the patch is shown, when fed asan antenna with a probe feed, using the formula [7]

zi, = -z~,/z,,.The resistance becomes small very rapidly as the loss in-

creases, especially for the thinner substrate.



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6 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 38, NO . 1 , JANUARY 1990

-lo[t l = + = 0, = 2.2b = ,0787 cm

-5010.1 0.2 0.3 0.4 0.5 0.6 0.7n,t/X,(a)

E , = 2.2b E .0787 cm

E p = 2.0

7. 0

I \(GHz)

5.00t.1 0.2 0.3 0.4 0.5 0.6 0.7n2t lXo

(C)

1.0r0.9 b = . 0 7 8 7 c m

0.8

0.7

0.60.5

0.4

0' I I I I I 1 I0 0.1 0.2 0.3 0.4 0.5 0.6 0.7n2t /Xo

(b)

c , = 2.2b = ,0781 m

D,X p = D . 1 4

120Dx

2olI I I I I I0 0.1 0.2 0.3 0.4 0.5 0.6 0.70'

Fig. 6. Results showing the effects of a lossless superstrate for a resonant length patch on a lossless substrate. Patch dimensionsare the same as in Fig. 5 , with b = 0.0787 cm . (a) RCS versus normalized superstrate thickness. (b) Efficiency versus normalizedsuperstrate thickness. Note that efficiency is minim ized near n2t/ho Y 0.5. (c) Resonant frequency versus norm alized superstratethickness. (d) Resonant input resistance versus norm alized superstrate thickness.

Fig. 6studies the effect of a lossless superstrate layer overthe patch. The geometry is the same as in Fig. 5, exceptthat the substrate thickness is fixed at b = 0.0787 cm andthe superstrate thickness is variable. The superstrate mini-mizes the RCS when n z t / X o N 0.5 for larger 2 values, wheren2 =m.he efficiency is likewise reduced. The resonantfrequency is reduced for larger 2 values, but is not affectedas dramatically as for the lossy substrate case. Therefore, theresonant resistance is also less affected, for a given amountof RCS reduction. Results for a lossless magnetic superstrate

(not shown) show a similar RCS reduction for large p2 , whenn 2 t / h 0 cv 0.25.

Fig. 7shows the effect of a lossy superstrate layer having2 = 2.0, with the patch dimensions and substrate the same asin Fig. 6. For large loss tangents, the RCS in dB is almost alinear function of the superstrate thickness. This is because theincident signal is exponentially attenuated before reaching thepatch. As for the previous cases, the efficiency is decreasedalong with the RCS. The efficiency is not affected as much asin the previous two cases, however, for a given RCS reduction.

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7ACKSON: RCS OF RECTANGULAR MICROSTRIP PATCH

8 = + = oE p =2.0E . =2 . 1 e ,=0

-1000 0.2 0.4 0.6t / Xo

(a )

E* = 2.0l.o r

I

1

0.9 b = .0787 c m

0. 8

0.7

0.60.5

0.40.30.20.10.00.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

6.6l I I I I I I 10 0.1 0.2 0.3 0.4 0.5 0.6 0.7t / X o

(C)

xo(b)

2 = 2.0, = 2.2b = ,0787 C m

2 j y , I I I ,5. 000 0.1 0.2 0.3 0.4 0.5 0.6 0.7t / X o

(d)Fig. 7. Results showing the effects of a lossy superstrate for a resonant length patch on a lossless substrate. Patch and substratedimensions are the same as in Fig. 6. (a) RCS versus norm alized superstrate thickness. (b) Efficiency versus normalized super-strate thickness. (c) Resonant frequenc y versus normalized superstrate thickness. (d) Resonant input resistance versus norm alizedsuperstrate thickness.

The resonant frequency and resonant input resistance are alsoless affected.

the localization of current near the more radiative parts ofthe body. A reduction of RC S may thus be accomplished byminimizing the currents in the radiative parts of the body,or by decreasing the radiation efficiency of the body. For aloaded patch antenna, the decrease in body resistance may beachieved by proper selection of the load impedance, a resultwhich has been discussed in [3]. The radiation efficiency ofa patch may be reduced by putting loss into the substrate, by

V. CONCLUSIONA formula showing the RC S behavior of a conductive body

in a layered medium has been derived. This formula showsthat the RCS is related to the radiation efficiency of the body,as well as the body radiation resistance, which measures

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8 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 38, NO. 1 , JANUARY 1990using a lossless superstrate, or by using a lossy superstrate.In each case, the resonant frequency and resonant input resis-tance (when driven as an antenna) decrease as the efficiency isreduced. Using a lossy superstrate usually gives the greatestRCS reduction for a given reduction in efficiency and inputresistance.

REFERENCESI. J. Bahl and P. Bhartia, Microstrip Antennas. Dedham, MA:Artech House, 1980.E. H. Newman and D. Forrai, Scattering from a microstrip patch,ZEEE Trans. Antennas Propagat., vol. AP-35, pp. 245-251, Mar.1987.D. M. Pozar, Radiation and scattering from a m icrostrip patch on a

uniaxial substrate, ZEEE Trans. Antennas Propagat., vol. AP-35,pp. 613-621, June 1987.[4] R. F . Harrington, Time-Harmonic Electromagnetic Fields. Ne wYork: McGraw-Hill, 1961.[5] D. R. Jackson and N. G. Alexopoulos, Analysis of planar strip ge-ometries in a substrate-superstrate configuration, ZEEE Trans. An-tennas Propagat., vol. AP-34, pp. 1430-1438, Dec. 1986.[6] - Gain enhancement methods fo r printed circuit antennas, ZEEETrans. Antennas Propagat ., vol. AP-33, pp. 976-987, Sept. 1985.[7] M. D. Deshpande and M. C. Bailey, Input impedance of mi-crostrip antennas, ZEEE Trans. Antennas Propagat. , vol. AP-30,pp. 645-650, July 1982.

David R. Jackson (S84-M84), for a photograph and biography please seepage 910 of the July 1988 issue of this TRANSACTIONS.

1990The RCS of a Rectangular Micro Strip Patch in A

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