Modelling of metallic inclusions on non-homogeneous dielectric substrates

Abstract

ABSTRACT In this article, modelling is done for Square Split Ring Resonators (SSRR) as a quasi-static equivalent circuit in a non-homogeneous environment. The authors propose a new relationship for the relative permittivity for a metallic inclusion etched on top of a dual substrate in a non-homogeneous medium. The stacking sequence of the substrates plays a vital role in the response of the SSRR. This paper highlights the change brought about by the dielectric materials’ stacking order on resonant frequency and quality factor. The analytical and numerical study of SSRR etched on the dual substrates shows a good correlation of values. A comparative study indicates a better fit of the proposed formula for the effective permittivity over the conventional averaging method. This article highlights the advantages of using a dual substrate material for fabricating metamaterial structures for different applications. The advantage of the proposed permittivity equation is its applicability to all kinds of geometries. Three different substrate materials were used for the performance study of the SSRR (FR4, Rogers RT/Duroid 5880 and Alumina).