## 1. Introduction

[2] Modern microwave and millimeter-wave equipment, present in mobile, wireless and space communication systems, employ a wide variety of waveguide components [*Uher et al.*, 1993]. Most of these components are based on the cascade connection of waveguides with different cross-section, as recognized by *Conciauro et al.* [2000]. Therefore, the full-wave modal analysis of such structures has received a considerable attention from the microwave community [*Sorrentino*, 1989; *Itoh*, 1989; *Boria and Gimeno*, 2007]. The numerical efficiency of these methods has been substantially improved by *Mansour and MacPhie* [1986] and *Alessandri et al.* [1988, 1992] by means of the segmentation technique, which consists of decomposing the analysis of a complete waveguide structure into the characterization of its elementary key building blocks, i.e. planar junctions and uniform waveguides.

[3] The modeling of planar junctions between waveguides of different cross-section has been widely studied in the past through modal analysis methods, where higher-order mode interactions were already considered by *Wexler* [1967]. For instance, in order to represent such junctions, the well-known mode-matching technique has been typically formulated in terms of the generalized scattering matrix [*Safavi-Naini and MacPhie*, 1981, 1982; *Eleftheriades et al.*, 1994]. Alternatively, the planar waveguide junction can be characterized using a generalized admittance matrix or a generalized impedance matrix, obtained either by applying the general network theory of *Alvarez-Melcón et al.* [1996] or by solving integral equations of *Gerini et al.* [1998] A common drawback to all the previous techniques is that any related generalized matrix must be recomputed at each frequency point.

[4] In the last two decades, several works have been focused on avoiding the repeated computations of the cited generalized matrices within the frequency loop. For instance, frequency-independent integral equations have been set up when dealing, respectively, with inductive (or H plane) and capacitive (or E plane) discontinuities in the works of *Guglielmi and Newport* [1990] and *Guglielmi and Alvarez-Melcón* [1993], steps in the works of *Guglielmi et al.* [1994] and *Guglielmi and Gheri* [1994], and posts in the work of *Guglielmi and Gheri* [1995]. On the other hand, following the Boundary Integral-Resonant Mode Expansion (BI-RME) technique developed at University of Pavia (Italy), a generalized admittance matrix in the form of pole expansions has been derived for arbitrarily shaped H plane [*Conciauro et al.*, 1996] and E plane components [*Arcioni et al.*, 1996], as well as for 3-D resonant waveguide cavities in the work of *Arcioni et al.* [2002].

[5] More recently, the BI-RME method has been combined by *Mira et al.* [2006] with an integral equation technique in order to provide a generalized impedance matrix, in the form of quasi-static terms and a pole expansion, for planar waveguide junctions. However, in order to get convergent results, such method requires a bigger number of accessible modes than the original formulation of the integral equation technique [*Gerini et al.*, 1998]. Furthermore, the cascade connection of planar waveguide junctions was solved by *Mira et al.* [2006] within the frequency loop. Therefore, the implementation of the wideband solution proposed by *Mira et al.* [2006] was not very computationally efficient.

[6] In this paper, we present two novel contributions in order to increase the numerical efficiency related to the pole expansion technique proposed by *Mira et al.* [2006]. First of all, by considering additional static (frequency independent) terms in the integral equation formulation, we are able to reduce the number of accessible modes required in the convergent characterization of planar waveguide junctions. Secondly, a very efficient iterative algorithm is proposed for combining the generalized impedance matrices of planar junctions and interconnecting waveguide sections, thus providing a wideband representation of any passive device based on the cascaded connection of such basic elements. For validation purposes, this wideband modeling technique has been successfully applied to the full-wave analysis of two waveguide filter examples.