## 1 Introduction

[2] The fast-growing microwave and millimeter-wave equipment market creates a constant demand for faster and more efficient computer-aided design (CAD) tools that must be able to meet the requirements of a computationally inexpensive design process. Moreover, modern high-capacity telecommunication equipment is based on a wide variety of waveguide components, which are usually fed using a coaxial excitation [*Uher et al*., 1993]. For instance, standard coaxial cavity filters (either with in-line or folded configurations) and recently proposed orthogonal coaxial filters, all of them typically operating at low-frequency bands (i.e., L-, S- and C-bands), are commonly excited using a collinear end-launcher transition from a coaxial to a rectangular waveguide [*Morini et al*., 2006, 2007; *Höft and Yousif*, 2011]. Evanescent-mode filters, in-line filters, and thick-iris waveguide filters [*Liang et al*., 1992] are also classically fed using a standard (vertical) coaxial excitation. Besides, as it will be discussed afterward, the integration of the coaxial excitation in the input and output waveguides of the structure can be used to raise the order of the designed filter (and then to enhance the response selectivity) without increasing its length. As a consequence, the coaxial-line to rectangular waveguide transition can be considered as a basic building block of a wide variety of microwave and millimeter-wave components, and its integration in general CAD tools becomes crucial to ensure a rigorous and efficient design of all these passive components.

[3] In addition, most of the aforementioned types of filters usually include rectangular waveguide sections with partial-height metallic posts, and this key building block is also found in many other waveguide devices, such as adapters, mode-launchers, comb-line, and interdigital filters [*Ihmels and Arndt*, 1993; *Levy et al*., 1997]. Furthermore, this basic building block also allows to model real tuning screws, which are widely employed in practical implementations of dual-mode and direct-coupled rectangular waveguide filters [*Chang and Zaki*, 1991; *Boria et al*., 1998]. The usual presence of these practical filters in most of present communication systems (e.g., mobile and satellite ones) demands the availability of fast CAD tools, while preserving a high degree of accuracy.

[4] Several attempts to achieve the required efficient and accurate CAD tools have been already performed. For instance, strictly numerical or mode-matching methods, as well as the combination of both approaches in hybrid solutions, have been tried [*Yao et al*., 1995; *Gentili*, 2001]. Although these techniques provide enough accurate results, they cannot be optimal for CAD purposes because of their required computing time. A very fast S-domain method for the accurate modeling of rectangular cavities with several conducting posts (arbitrarily placed and oriented) was proposed by *Mira et al*. [2005a]. Then, a very preliminary contribution for the analysis of standard (vertical) coaxial to rectangular waveguide transitions was presented in reference *San Blas et al*. [2006]. These works, based on the well-known 3D boundary integral-resonant mode expansion (BI-RME) method [*Arcioni et al*., 2002], provide a *Y*-matrix given in the form of pole expansions in the frequency domain for the accurate characterization of such two basic blocks.

[5] The numerical efficiency of these full-wave modal analysis techniques has been greatly improved by means of the so-called segmentation technique [*Mansour and MacPhie*, 1986; *Alessandri et al*., 1988, 1992; *Guglielmi*, 1994], which consists on decomposing the analysis of a complete waveguide structure into the characterization of its elementary key building blocks. The work proposed in reference *Mira et al*., 2005b makes use of this segmentation technique by combining the analysis of resonant cavities using the BI-RME method [*Mira et al*., 2005a] with the integral equation technique for characterizing planar waveguide junctions [*Gerini et al*., 1998]. However, in the above-mentioned work (i.e., *Mira et al*. [2005b]), the analysis of the planar junctions and the cascade connection of the different wideband matrices must be performed at each frequency point, thus dramatically increasing the computational cost of the design process.

[6] In this paper, the main objective consists of developing a very efficient CAD tool, which must be able to avoid the repetition of the cumbersome computations performed in the frequency domain, for the analysis and design of complex waveguide devices composed of rectangular cavities loaded with partial-height metallic cylindrical posts, planar waveguide junctions, uniform waveguide sections, and boxed resonators including a coaxial excitation (either vertical or collinear). To this aim, the 3D BI-RME method is first applied to derive a wideband *Y*-matrix used to characterize boxed resonators with inserted metallic posts that can be fed by a generalized coaxial probe. Next, the new formulation proposed in reference *Mira et al*. [2008] is used to characterize the planar waveguide junctions of the structure, thus obtaining a *Y*-matrix with the same form as the one provided by the BI-RME formulation. Finally, the algorithm proposed in reference *Arcioni and Conciauro* [1999], which has been extended to cope with folded structures including cross-couplings, allows the wideband cascade connection of the previous key building blocks preserving the same form of the pole expansions for the *Y*-matrices. As a result, all the main computations are performed out of the frequency loop, thus reducing the computational effort of the new developed CAD tool. In addition, the *Y*-matrix in the form of pole expansions is preserved for the whole structure, allowing for a circuital representation of the device [*Bozzi et al*., 2009], that can be very useful for synthesis and design purposes. This CAD tool has been successfully used to design four different waveguide filters, all of them including integrated coaxial excitations and partial-height conducting posts: a compact four-pole in-line filter with tuning screws, an evanescent-mode filter with cylindrical posts, and two C-band comb-line filters, one of them with a cross-coupling configuration.