Novel Spatial Domain Integral Equation Formulation for the Analysis of Rectangular Waveguide Steps Close to Arbitrarily Shaped Dielectric and/or Conducting Posts

Abstract

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.

On the analysis of capacitive rectangular waveguide discontinuities close to arbitrarily shaped conducting and dielectric posts

“…, the magnetic vector ⃗ A PPW q , electric vector ⃗ F PPW q and electric scalar Φ e PPWq potentials, leading to similar expressions as those presented in Quesada Pereira et al [13] [Equation ( 4)]. In this notation, the sub-index q indicates which waveguide is used as reference for defining the potential or variable (1-input waveguide, 2-output waveguide) being considered.…”

“…The posts can be metallic or composed of homogeneous dielectric material. This formulation is an extension of the numerical techniques reported in previous articles for the analysis of rectangular waveguide structures Quesada Pereira et al [11], Quesada Pereira et al [12], Quesada Pereira et al [13]. We must emphasize that the treatment of metallic and homogeneous posts in the vicinity of a step discontinuity with capacitive symmetry is addressed for the first time in this paper.…”

“…In this notation, the sub-index q indicates which waveguide is used as reference for defining the potential or variable (1-input waveguide, 2-output waveguide) being considered. It is important to note that, contrary to the analysis of inductive steps discussed in Quesada Pereira et al [13], the contribution of the electric scalar potential (Φ e PPWq ) is not zero for capacitive symmetry and must, therefore, be explicitly included in the formulation. The source and observation coordinates z ′ and z are global values for both input and output equivalent problems, since the origin (z = 0) is placed, without loss of generality, on the plane defined at the step discontinuity.…”

“…Finally, the last of the seven IEs is used to couple input and output equivalent problems enforcing the continuity of the tangential magnetic field across the step. These integral equations have the same form as those derived in Quesada Pereira et al [13] Figure 4: Internal equivalent problem corresponding to the homogeneous post inside the rectangular waveguide 1. Negative currents are defined on the contour of the objects, and the whole space is filled with the constitutive parameters of this homogeneous post (ϵ d 1 , µ d 1 ).…”

An inclusive analysis of inductive dielectric and/or metallic discontinuities in a rectangular waveguide

“…The limitations on the homogeneity of dielectric discontinuities are removed by a hybrid technique 13 for an efficient analysis of inductive dielectric discontinuities employing a volumetric MoM procedure but this proposal was not handling metallic discontinuities. Although the analysis of inductively loaded waveguides has enormously advanced in terms of efficiency and capability since 1940s, 4 the recent methods provide the best for the analysis of cylindrical objects dependent on different auxiliary methods 9 for different geometries, or the analysis of metallic and homogeneous dielectric objects 12,14 or only dielectric discontinuities even if providing the inhomogeneity 13 . Most importantly, the analysis methods dealing with dielectric and metallic discontinuities lose their validity if the dielectric and metallic discontinues are aligned horizontally and require the obstacles to be separated longitudinally.…”