The multimode equivalent network (MEN) formulation has been originally developed for the efficient and accurate analysis of waveguide devices. In this article, we extend the use of the MEN to the analysis of zero-thickness, planar printed circuits in a metallic enclosure. The formulation is developed for metallic areas of arbitrary shape and includes both internal and external ports in the transverse plane to model connections to external components, and coaxial input/output ports. The boundary integral resonant mode expansion (BI-RME) method is used for the analysis of the arbitrary shape metallizations. On this basis, shielded multilayered microstrip circuits of complex geometry are analyzed in the common frame of the MEN technique. To validate the theoretical formulation, several boxed microstrip structures are analyzed, including multilayered configurations with several metallization interfaces, showing good agreement with respect to both other commercial tools, and measurements. Index Terms-Integral equations (IEs), method of moments (MoM), microwave filters, monolithic microwave integrated circuits (MMICs), multimode equivalent networks (MENs), numerical methods, planar junctions. I. INTRODUCTIONC URRENTLY, computational electromagnetics (CEM) techniques [1], [2] are widely used to save development time and manufacturing costs in the microwave industry. In this context, therefore, new more efficient numerical methods for the design of microwave components are of Manuscript

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The objective of this paper is to extend the use of the Multimode Equivalent Network formulation, originally developed to analyze waveguide junctions, to the analysis of planar circuits that include arbitrary rectangular printed, zero thickness metallizations together with internal and external ports in the transverse plane. The theoretical derivations lead to an accurate and computationally efficient tool for the analysis of boxed, multilayer microwave printed circuits. In addition to theory, the tool developed is used here to analyze two practical examples: a dual-bandpass and a 4-pole bandpass boxed microstrip filters. Good agreement with respect to commercial software tools and measurements is shown, thereby fully validating the theoretical formulation.

In this paper, a novel integral equation formulation expressed in the spatial domain is proposed for the analysis of rectangular waveguide step discontinuities. The important novelty of the proposed formulation is that which allows to easily take into account the electrical influence of a given number of arbitrarily shaped conducting and dielectric posts placed close to the waveguide discontinuity. For the sake of simplicity, and without loss of generality, the presented integral equation has been particularized and solved for inductive rectangular waveguide geometry. In this case, the integral equation mixed‐potentials kernel is written in terms of parallel plate Green's functions with an additional ground plane located on the waveguide step. Therefore, the unknowns of the problem are reduced to an equivalent magnetic surface current on the step aperture and equivalent magnetic and electric surface currents on the dielectric and conducting posts close to the discontinuity. The numerical solution of the final integral equation is efficiently computed after the application of acceleration techniques for the slowly convergent series representing the Green's functions of the problem. The numerical method has been validated through several simulation examples of practical microwave devices, including compact size band‐pass cavity filters and coupled dielectric resonators filters. The results have been compared to those provided by commercial full‐wave electromagnetic simulation software packages, showing in all cases a very good agreement, and with substantially enhanced numerical efficiencies.

Numerical methods are widely used to analyze and design microwave components for communication applications. In the implementation of any numerical technique, however, there are always a set of parameters that must be properly adjusted in order to obtain, at the same time, computational efficiency and numerical accuracy of the results. In this context, therefore, we focus in this paper on the multimode equivalent network formulation for waveguide devices, and we propose a more intuitive and efficient strategy for choosing these parameters. Following our approach, setting only one global numerical variable is sufficient to adjust automatically the specific convergence parameters of each discontinuity to give a specific level of numerical accuracy of the results. As a consequence, the computational efficiency is significantly increased. In addition, the user experience is significantly improved since our approach eliminates all lengthy convergence tests previously needed to assure good numerical accuracy. In addition to theory, we discuss in this paper a number of numerical results that clearly demonstrate how the new strategy is very effective, thereby fully validating the theoretical formulation.