162 QUADERNI DELLA SOCIETÀ ITALIANA DI ELETTROMAGNETISMO, VOL. 1, N. 2 LUGLIO 2005 A network theory for fss-based ebg surfaces M. Nannetti, M. Caiazzo, A. Cucini, S. Maci 1 Abstract – This paper presents a novel method for the efficient derivation of an equivalent network representation of electromagnetic bandgap (EBG) structures composed by lossless frequency selective surfaces (FSS) printed on stratified dielectric media. The formulation presented yields a two-port dominant mode equivalent matrix representation of the FSS, and is applicable in the range of frequencies where a single propagating Floquet mode occurs. Otherwise, it can be generalized to the case of an arbitrary number of ‘accessible’ modes. The elements of the diagonalized FSS matrix respect the conditions of driving point LC impedance functions, thus, they can be approximated in terms of poles and zeros, using a simple analytical expression. The final result is a compact form of the dispersion equation, whose solutions identify the modes of the structure. I. INTRODUCTION In recent years, a great interest has been devoted to the study of the dispersion properties of planar structures realized by frequency selective surfaces (FSS) on grounded dielectric slab. This kind of structures are used to realize artificial magnetic conductors (AMC) [1], electromagnetic band-gap (EBG) surfaces, or surfaces which exhibit “soft” and/or “hard” equivalent boundary conditions [2]. As it is well known, an approximate model of an FSS may be given in terms of a quasi-static LC impedance network placed in a TE or TM transmission line. In absence of losses, the FSS impedance is purely reactive. Patch-type FSS are described by a series LC network. At frequencies below the resonant frequency, the FSS is capacitive. This capacitance may resonate in parallel with the inductance provided by the section of short-circuited transmission line, thus, providing an AMC surface. In a certain frequency band, the same structure can provide an inhibition to the surface wave (SW) propagation, acting as an EBG surface. Similar considerations apply to aperture-type FSS which can be described by a parallel LC circuit. This simple circuital representation contains the essential physics to qualitatively justify the basic aspects of the AMC properties. However, the lack of description of important aspects such as the wavenumber dependence of the 1 Dipartimento di Ingegneria dell’Informazione, Università di Siena, Via Roma 56, 53100 Siena, e-mail: nannetti@unisi.it, caiazzo@ieee.org, cucini@dii.unisi.it, macis@dii.unisi.it ID 0001-02-2005 © 2005 SIEM