Resonant frequency and bandwidth of a superstrate-loaded rectangular patch on a uniaxial anisotropic substrate

Abstract

In this paper, the effects of both uniaxial anisotropy in the substrate and isotropic superstrate loading on the resonant frequency and bandwidth of a rectangular microstrip patch in a substrate–superstrate configuration are investigated. The problem is rigorously formulated using an integral equation, the kernel of which is the full-wave spectral domain dyadic Green's function for multilayer dielectric substrates. The proposed method for determining the Green's function leads to a concise form of this, diagonalized in the (TM,TE) representation. Using Galerkin's moment method to solve the integral equation, the complex resonance frequencies for the TM01 mode are studied with sinusoidal basis functions. The improper double integrals of the moment method matrix are efficiently calculated by means of a proper choice of the path of integration in the complex wavenumber plane, the upper bound of truncation, and the method of quadrature. For an isotropic substrate, it is demonstrated that the bandwidth decreases with increasing ratio of superstrate-to-substrate thickness for high permittivity and low thickness of superstrate. Also, we show that the resonant frequency and bandwidth are highly dependent on the permittivity variations along the optical axis. Simple approximate formula for the resonant frequency is derived. Other theoretical results obtained show that the resonant frequency decreases monotonically with increasing superstrate thickness, the decrease being greater for high permittivity loading and negative uniaxial anisotropy of the substrate. Thin superstrate with high permittivity together with negative uniaxial anisotropy of the substrate are shown to be the favourable conditions for severe degradation of the half-power bandwidth of the antenna. Copyright © 2000 John Wiley & Sons, Ltd.