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(a)

(b)

Fig. 2. Configuration of a cavity-backed microstrip patch antenna. (a) Topview. (b) Side view.

(a)

(b)

Fig. 3. A microstrip patch antenna on a circular cylinder attached to a plate.(a) Three-dimensional view. (b) Cross-sectional view.

For cylinders without coatings, (7) and (8) reduce to the

well-known equations

for in conductor

for everywhere else (9)

(a)

(b)

Fig. 4. Radiation patterns of a microstrip patch antenna on a circular cylinderattached to a plate with the longer side of the patch parallel to the axis of thecylinder. (a) For antenna 1. (b) For antenna 2.

for polarization and

for in conductor

for everywhere else (10)

for polarization. The detailed procedure to solve (7) and

(8) using the method of moments is described in [17].

To summarize the proposed method, we first compute the

equivalent magnetic current over the cavitys aperture by

applying the finite-element method to (2). Then, we compute

the surface magnetic field induced on the region of the cavitys

aperture by applying the method of moments to (7) and (8) or

(9) and (10) when there is no coating. Finally, we calculate

the radiated field using (5) and (6).

III. NUMERICAL RESULTS

In this section, we present some numerical results to demon-

strate the validity and capability of the formulation described

above. Without loss of generality, the same microstrip patch

antenna depicted in Fig. 2 is used in all examples to follow.

This antenna consists of a rectangular conducting patch fed

with a probe and housed in a larger dielectric filled rectangular

cavity. The first resonance mode at GHz radiates a

field whose plane is perpendicular to the shorter side of the

patch and whose plane is perpendicular to the longer side

of the patch.

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JIN et al.: CALCULATION OF RADIATION PATTERNS OF MICROSTRIP ANTENNAS 129

(a)

(b)

Fig. 5. Radiation patterns of a microstrip patch antenna on a circular cylinderattached to a plate, with the shorter side of the patch parallel to the axis ofthe cylinder. (a) For antenna 1. (b) For antenna 2.

The first set of results is computed for the microstrip patch

antenna on a finite circular cylinder sitting on a conductingplate, illustrated in Fig. 3. The radiation patterns are calculated

for two different positions of the antenna whose longer side

is parallel to the axis of the cylinder. These patterns are

shown in Fig. 4 and compared with measured data provided by

Mission Research Corporation, Dayton, OH. As can be seen,

the agreement is surprisingly good within the first 30-dB range,

demonstrating the validity of the method. The disagreement in

the deep-shadow region is due to the field diffracted by the

sides of the plate perpendicular to the cylinder and also by

the ends of the cylinder, which are ignored in our simplified

approximate calculation. The corresponding results when the

antenna is rotated 90 are shown in Fig. 5. Note that in this

case, the predicted sidelobes are significantly higher that thosein Fig. 4 because of stronger surface waves propagating around

the cylinder.

The proposed method can, of course, handle multiple patch

antennas or arrays such as the one sketched in Fig. 6. The

patches and dielectric substrate have the same parameters as

the one in Fig. 2. The edge-to-edge distance between twoadjacent patches is 1.5 cm, and the array is centered at

225 . Fig. 7 shows its radiation patterns with and without the

plate. The cavity size for the case of Fig. 7(a) is 12 cm in

the direction and 6 cm in the direction, and for the case

of Fig. 7(b) is 15 cm in the direction and 5 cm in the

Fig. 6. Three microstrip patch antennas on a circular cylinder attached toa plate.

(a)

(b)

Fig. 7. Radiation patterns of three microstrip patch antennas depicted in

Fig. 6. (a) The longer side of the patches parallel to the axis of the cylinder.(b) The shorter side of the patches parallel to the axis of the cylinder.

direction. The asymmetric pattern in Fig. 7(b) for the case

without the plate is due to the asymmetric placement of the

feed.

To demonstrate the capability of the method as well as to

show the effect of dielectric coating, we consider a single-

patch antenna on a circular cylinder having a diameter of

30.48 cm. The antenna is the same as depicted in Fig. 2

and the cylinder is coated with a layer of material having

a thickness of 0.546 cm, relative permittivity , and

relative permeability for the lossless case, and

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(a)

(b)

Fig. 8. Radiation patterns of a microstrip patch antenna on a dielectric coatedcircular cylinder. (a) The longer side of the patch parallel to the axis of thecylinder. (b) The shorter side of the patch parallel to the axis of the cylinder.

and for the lossy case.

The results are presented in Fig. 8 for the cylinder without

coating, with a lossless coating, and with a lossy coating. As

can be seen when the longer side of the patch is parallel to

the axis of the cylinder, it does not excite a surface wave

propagating around the cylinder. Therefore, the coating does

not have a significant effect on the radiation pattern because

it is not thick enough to support a surface wave. However,

when the shorter side of the patch is parallel to the axis of the

cylinder, it excites a surface wave around the cylinder which is

further enhanced by the presence of a lossless coating, raising

the level of radiation in the shadow region. When the coating

is lossy the surface wave is attenuated, resulting in a lowerlevel of radiation in the shadow region.

To show the effect of a finite ground plane, we consider the

microstrip patch antenna of Fig. 2 placed at the center of a

flat conducting plate whose width is and thickness is 0.5

cm. The radiation pattern in the plane perpendicular to the

plate is shown in Fig. 9(a) when the longer side of the patch

is parallel to the axis of the plate, and in Fig. 9(b) when the

shorter side of the patch is parallel to the axis of the plate. The

proposed technique provides a simple way to study the finite

ground-plane effect on microstrip antenna radiation patterns

[18].

(a)

(b)

Fig. 9. Radiation patterns of a microstrip patch antenna on a flat-conductingplate having width . (a) The longer side of the patch parallel to the axis ofthe plate. (b) The shorter side of the patch parallel to the axis of the plate.

Finally, we consider a waveguide-fed trihedral, depicted in

Fig. 10, to show the applicability of the proposed method

to any cavity-backed conformal antennas. The waveguide is

0.9 wide and 0.4 thick and is at the center of one of

the planes. The radiation patterns at GHz in both

the and planes are given in Fig. 11 along with the

measured data. Good agreement is observed over a wide range

of angles. The disagreement in the shadow region is mainly

due to the third plane which is ignored in our simplified

approximate calculation (this was verified by a general three-

dimensional method developed in [19], see [19, Fig. 5]). Since

the waveguide radiator is not a highly resonant structure,

we note that the external structures close to the waveguidecan have nonnegligible effect on the field distribution at the

waveguide opening. As a result, the proposed method can be

less accurate than in the case of highly resonant microstrip

patch antennas.

IV. CONCLUSION

In this paper, we described a method to calculate the

radiation patterns of cavity-backed microstrip patch antennas

on a cylindrical body of arbitrary cross section that may be

coated with dielectrics. In this method, we first employed the

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[12] J. M. Jin,The Finite Element Method in Electromagnetics. New York:Wiley, 1993.

[13] J. M. Jin and S. W. Lee, Hybrid finite element analysis of scatteringand radiation by a class of waveguide-fed structures, Microwave Opt.Tech. Lett., vol. 7, no. 17, pp. 798803, 1994.

[14] R. F. Harrington, Time-Harmonic Electromagnetic Fields. New York:McGraw-Hill, 1961.

[15] M. I. Sancer, Physically interpretable alternative to Greens dyadics,resulting representation theorems, and integral equations, IEEE Trans.

Antennas Propagat.,vol. 38, pp. 564568, Apr. 1990.

[16] J. M. Jin, V. V. Liepa, and C. T. Tai, A volume-surface integralequation for electromagnetic scattering by inhomogeneous cylinders,J. Electromagn. Waves Applicat., vol. 2, no. 5/6, pp. 573588, 1988.

[17] J. M. Jin and V. V. Liepa, Simple moment method program forcomputing scattering from complex cylindrical obstacles, Proc. Inst.

Elect. Eng.,vol. 136, pt. H, pp. 321329, Aug. 1989.[18] J. Huang, The finite ground plane effect on the microstrip antenna

radiation patterns, IEEE Trans. Antennas Propagat., vol. AP-31, pp.649653, July 1983.

[19] A. D. Greenwood, S. S. Ni, J. M. Jin, and S. W. Lee, Hybrid FEM/SBRmethod to compute the radiation pattern from a microstrip patch antennain a complex geometry, Microwave Opt. Tech. Lett.,Vol. 13, pp. 8487,Oct. 1996.

Jian-Ming Jin (S87M89SM94) received the

B.S. and M.S. degrees in applied physics fromNanjing University, Nanjing, China, in 1982 and1984, respectively, and the Ph.D. degree in electricalengineering from the University of Michigan, AnnArbor, in 1989.

He joined the faculty of the Department of Elec-trical and Computer Engineering at the University ofIllinois at Urbana-Champaign (UIUC) in 1993, afterworking as a Senior Scientist at Otsuka Electronics(USA), Inc., Fort Collins, CO. From 1982 to 1985,

he was associated with the Department of Physics of Nanjing University,Nanjing, P. R. China, where he started his research on the finite-elementmethod as applied to electromagnetics problems. He continued this researchat the University of Michigan, Ann Arbor, where he was first a ResearchAssistant, then a Research Fellow. In 1990 he was appointed as an AssistantResearch Scientist at the same university. Currently, he is Associate Directorof the Center for Computational Electromagnetics at UIUC. He is currently an

Associate Editor of the IEEE TRANSACTIONS ON

ANTENNAS AND

PROPAGATION

.He has published over 40 articles in refereed journals, authored the bookTheFinite Element Method in Electromagnetics (New York: Wiley, 1993), andco-authoredComputation of Special Functions(New York: Wiley, 1996). Hiscurrent research interests include computational electromagnetics, scatteringand antenna analysis, electromagnetic compatibility, and magnetic resonanceimaging.

Dr. Jin is a member of Commission B of USNC/URSI and Tau Beta Pi.He is a recipient of the 1994 National Science Foundation Young InvestigatorAward and the 1995 Office of Naval Research Young Investigator Award.

Jeffery A. Berrie (S86M92) received the B.S.,M.S., and Ph.D. degrees in electrical engineering in1986, 1988, and 1992, respectively, all from TheOhio State University, Columbus.

From 1986 to 1992, he was a Graduate ResearchAssociate at The Ohio State University Electro-Science Laboratory, Columbus, where he performedresearch in computational and experimental elec-tromagnetics. He is currently a Senior ResearchScientist in the Electromagnetics Observables Sector

of Mission Research Corporation, Dayton, OH. Hiscurrent interests include computational electromagnetics as applied to varioustypes of radiation, scattering, and material extraction problems, as well asexperimental measurements and data processing at both indoor and outdoorradar ranges.

Robert Kipp (S90M93) received the B.S.E.E. and B.S. (math) degreesfrom Rose-Hulman Institute of Technology, Terre Haute, IN, in 1987, and theM.S.E.E. and Ph.D. degrees from the University of Washington, Seattle, in1990 and 1993, respectively.

From 1988 to 1989, he was employed at the Boeing Company as an electro-magnetics engineer, performing research in frequency selective surfaces. Since1993, he has been a Research Scientist with DEMACO, Inc., Champaign,IL, specializing in electromagnetic scattering simulation and applications

development. His current interests are ray tracing and computer graph-ics techniques for CAD-based electromagnetic simulation, three-dimensionalvisualization for electromagnetic applications, hybridization of high- and low-frequency methods, platform-mounted antenna radiation and scattering, andmacro/microcellular propagation.

Shung-Wu Lee (S63M66SM73F81), for photograph and biography,see p. 1139 of the October 1995 issue of this T RANSACTIONS.