TY - JOUR
T1 - Resonance Frequency of a Rectangular Microstrip Patch
AU - Chew, Weng Cho
AU - Liu, Qinghuo
N1 - Funding Information:
Manuscript received August 26, 1987; revised December 23, 1987. This work was supported in part by the National Science Foundation under Grant NSF ECS 85-52891, by TRW, and by Northrop. The authors are with the Electromagnetics Laboratory, Department of Electrical and Computer Engineering, University of Illinois, 1406 West Green Street, Urbana, IL 61801. IEEE Log Number 8821 191.
PY - 1988/8
Y1 - 1988/8
N2 - The microstrip patch resonant frequency problem is formulated in terms of an integral equation using vector Fourier transforms. In the spectral space represented by the vector Fourier transforms, the Green's function is diagonal. Using Galerkin's method in solving the integral equation, the resonant frequency of the microstrip patch is studied with both Chebyshev polynomials and sinusoidal functions as basis functions. In the case of the Chebyshev polynomials, the edge singularity is included, but it is not important for convergence. Furthermore, the resonant frequency of the microstrip patch is ascertained with a perturbation calculation. The results for Galerkin's method and experiments are in good agreement. The perturbation calculation agrees asymptotically with Galerkin's method. With the aim of developing a computer-aided design formula, the solutions obtained via Galerkin's method are interpolated with a three-variable polynomial. The polynomial formula can reproduce the solution of the integral equation using Galerkin's method rapidly.
AB - The microstrip patch resonant frequency problem is formulated in terms of an integral equation using vector Fourier transforms. In the spectral space represented by the vector Fourier transforms, the Green's function is diagonal. Using Galerkin's method in solving the integral equation, the resonant frequency of the microstrip patch is studied with both Chebyshev polynomials and sinusoidal functions as basis functions. In the case of the Chebyshev polynomials, the edge singularity is included, but it is not important for convergence. Furthermore, the resonant frequency of the microstrip patch is ascertained with a perturbation calculation. The results for Galerkin's method and experiments are in good agreement. The perturbation calculation agrees asymptotically with Galerkin's method. With the aim of developing a computer-aided design formula, the solutions obtained via Galerkin's method are interpolated with a three-variable polynomial. The polynomial formula can reproduce the solution of the integral equation using Galerkin's method rapidly.
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U2 - 10.1109/8.7216
DO - 10.1109/8.7216
M3 - Article
AN - SCOPUS:0024055624
SN - 0018-926X
VL - 36
SP - 1045
EP - 1056
JO - IEEE Transactions on Antennas and Propagation
JF - IEEE Transactions on Antennas and Propagation
IS - 8
ER -