    Resonant Frequency Calculation for Circular Microstrip Antennas Using Artificial Neural Networks S ¸eref Sagiroglu, 1 Kerim Guney, 2 Mehmet Erler 2 ˘ ˘ ¨ 1 Intelligent Antenna Design and Research Group, Department of Control and Computer Engineering, Erciyes University, 38039, Kayseri, Turkey; e-mail: ss@zirve.erciyes.edu.tr 2 Intelligent Antenna Design and Research Group, Department of Electronic Engineering, Erciyes University, 38039, Kayseri, Turkey Recei  ed 25 February 1997; re ised 10 December 1997 ABSTRACT: A new method based on artificial neural networks for calculating the resonant frequency of circular microstrip patch antennas is presented. This neural method is simple ( ) and is useful for the computer-aided design CAD of microstrip antennas. The theoretical resonant frequency results obtained by using the method are in very good agreement with the experimental results reported elsewhere.  1998 John Wiley & Sons, Inc. Int J RF and Microwave CAE 8: 270277, 1998. Keywords: microstrip antenna; circular antenna; resonant frequency; artificial neural net- works INTRODUCTION Microstrip antennas are attractive due to their low profile and conformality, potential low cost, and the ease with which they can be integrated with printed feed networks and active circuits   1  5 . These attractive features have increased the applications of microstrip antennas recently and stimulated greater effort to investigate their performance. Microstrip antennas have been used in various configurations: square, rectangular, cir- cular, triangular, trapezoidal, elliptical, etc. In circular microstrip antenna designs, it is impor- tant to determine the resonant frequencies of the antenna accurately because microstrip antennas have narrow bandwidths and can only operate effectively in the vicinity of the resonant fre- quency. So, a model to determine the resonant frequency is helpful in antenna designs. The reso- nant frequency of such antennas is a function of the radius of the patch, the permittivity of the Correspondence to: S ¸eref Sagiroglu ˘ ˘ substrate, and its thickness. A number of methods   1  29 are available to determine the resonant frequency of circular patch antennas, as this is one of the most popular and convenient shapes.  For a circular disc antenna, it has been shown 6 that there exists a series of modes that are identi- cal to those of a cylindrical cavity except for the boundary conditions at the edge of the disc. The resonant frequencies of these modes were given in ref. 6. In ref. 7, the resonant frequency of the circular microstrip patch antenna was obtained numerically by employing Galerkin’s method and using a basis function which corresponds to a constant charge distribution. The effective radius and dynamic dielectric constant concepts used in calculating the resonant frequency were devel-  oped by Wolff and Knoppik 9 . The resonant  frequency formula proposed by Watkins 6 was   also used by Howell 10 . The resonant frequency   was obtained by Borkar and Yang 11 by solving a dual integral equation. Numerical integration was then used to carry out certain integrals. For   practical usage, Shen et al. 12 devised an ap-  1998 John Wiley & Sons, Inc. CCC 1096-429098030270-08 270