Published in IET Microwaves, Antennas & Propagation Received on 15th September 2008 Revised on 13th July 2009 doi: 10.1049/iet-map.2008.0439 ISSN 1751-8725 Effect of anisotropic magneto-chirality on the characteristics of a microstrip resonator C. Zebiri 1 M. Lashab 2 F. Benabdelaziz 3 1 Electronics Department, University of Se ´tif, Se ´tif 19000, Algeria 2 Electronics Department, University of Skikda, Skikda 21000, Algeria 3 Electronics Department, University of Constantine, Constantine 25000, Algeria E-mail: zebiri@ymail.com Abstract: The effect of a chiral bi-anisotropic substrate on the complex resonant frequency of a rectangular microstrip resonator has been studied on the basis of the integral equation formulation. The analysis is based on the numerical solution of the integral equation by using the Galerkin procedure for the moment method in the spectral domain. This work aims to study first the effect of the chirality of a bi-anisotropic substrate upon the resonant frequency and the half-power bandwidth, and then the effect of magnetic anisotropy via an asymptotic approach for very weak substrate upon the resonant frequency and the half-power bandwidth. The computed results are found to be in good agreement with the previously published work. 1 Introduction The use of microstrip resonators as microwave components started back in the 1950s [1]. However, they had not been extensively investigated until the 1970s [2]. Advantages of microstrip circuits include: small size, ease of manufacturing and conformity to planar and non-planar surfaces. Microstrip antennas are used in a variety of applications including portable phones, base stations, phased arrays and feed for parabolic reflectors [3–5]. The main disadvantages of microstrip resonators and antennas lie in their weak purity of polarisation and narrow half-power bandwidth (typically few percent). Techniques such as increasing the substrate thickness and reducing the relative permittivity of the substrate are commonly used for increasing the bandwidth up to 35% [6]. The resonant frequency of a microstrip resonator is strongly related to the dielectric constant of the substrate. The use of uniaxial anisotropic substrates in a printed circuit resonator was reported in [7, 8]. However, studies concerning the resonant frequency calculation of the microstrip resonator, implemented on a substrate of uniaxial anisotropy [9], have shown that this kind of substrate does not affect the quality factor, the half- power bandwidth and obviously the resonant frequency. For these reasons, other studies have been investigated in cases of positive and negative anisotropy [9–11], or bi- anisotropic medium [12]. In this paper, the spectral domain approach (SDA) is used for the analysis and design of planar structures. In this approach, the tensorial Green’s spectral function that relates the tangential electric field components and the corresponding currents on different conductors have to be determined. A great amount of techniques have been used to evaluate this function [9–11, 13–17]. In [10], Chew showed that the number of mode refines and improves the solution of the integral equation. In this work, only the mode TM 01 is considered for solving the integral equation. Calculations are carried out by a development of software under the professional FORTRAN F90 on a PC with 1.86 GHz Intel Pentium M and 512 MB RAM. The determinant cancellation of the Green’s tensor is obtained in about 65 s. 2 Theory 2.1 Maxwell equations Composite materials that exhibit the effect of chirality at microwave frequencies have been fabricated and characterised in many studies [18–20]. The chiral medium 446 IET Microw. Antennas Propag., 2010, Vol. 4, Iss. 4, pp. 446–452 & The Institution of Engineering and Technology 2010 doi: 10.1049/iet-map.2008.0439 www.ietdl.org