M LTIMODE E I ALET CIRCIT MODEL FOR B TRATEITEGRATED WAEG IDE DI CO TI ITIE Maurizio Bozzi 1 , Luca Perregrini 1 , Ke Wu 2 , and Giuseppe Conciauro 1 1 Department of Electronics, University of Pavia, Italy email: maurizio.bozzi@unipv.it, luca.perregrini@unipv.it, giuseppe.conciauro@unipv.it 2 Department of Electrical Engineering, Ecole Polytechnique de Montreal, Canada email: ke.wu@polymtl.ca Abstract This paper presents a novel approach for the direct determination of equivalent circuit models of Substrate Integrated Waveguide SIW components. This approach is based on the fullwave analysis of SIW com ponents by using the oundary Integral esonant Mode Epansion I M E method which provides the admittance matri of the component in the form of a pole epansion in the frequency domain. It permits to directly identify the layout of the equivalent circuit and the value of its components avoiding any initial guess or tting procedure. This approach is applied to the modeling of a postloaded SIW discontinuity and is validated by modeling an SIW lter whose frequency response is compared with eperimental results. I. I NTR DUCTI N The determination of equivalent circuit models of microwave components has a long tradition, and was the most common design approach before the development of digital computers [1]. Subsequently, the availability of numerical codes for electromagnetics has allowed for the full- wave analysis of complicated components and circuits. Nevertheless, the use of circuit models of simple discontinuities still represents a viable design philosophy, which has been implemented in several commercial codes. Moreover, the availability of parametric circuit models permits the design of microwave components by using conventional synthesis techniques [2]. A variety of equivalent circuit models of simple discontinuities have been derived in the case of metallic waveguides and printed circuits. Little attention has been paid to the determination of circuit models of discontinuities in Substrate Integrated Waveguide (SIW) technology, which represents an emerging and promising technology for RF and mm wave applications [3]. SIW technology permits to realize waveguide components in a dielectric substrate, by replacing the side walls of the waveguide by arrays of metallized viaholes. The maor advantage of this tech- nology consists in the possibility of easily interconnecting planar transmission lines with active and nonlinear components, by using a cheap and welldeveloped manufacturing process. Accurate circuit models can be derived either by using analytical methods [1] or by adopting numerical simulation codes [2]. The common approach for deriving equivalent models by using numerical codes requires the identication of a reasonable layout of the lumpedelement circuit and the determination of the component values by tting the simulation results. In this paper, we adopt a different strategy: the fullwave analysis is based on the Boundary IntegralResonant Mode Expansion (BIRME) method [4], which provides a generalized admit- tance matrix of the component in the form of a pole expansion in the frequency domain. This peculiarity permits the direct determination of the equivalent circuit model (both the layout and the component values) with no need of tting procedure. The proposed approach is applied to the modeling of a post-loaded SIW discontinuity and is validated by modeling SIW lters, whose frequency response is compared with experimental results. a b c Fig. 1. Examples of two-port waveguide and SIW components: a) standard metallic waveguide component; b) SIW component; c) model of the SIW component, used in the BI RME analysis. 460