A Variational Rayleigh-Ritz Method for Modeling H -Plane Bend Rectangular Waveguides

Abstract

This article introduces a novel variational formula for modeling waveguides with uniformly curved longitudinal axes. Using the Rayleigh-Ritz method, we analyze the electromagnetic fields in H-plane bend rectangular waveguides. In addition, we present a Galerkin method solution (GMS) for discretizing the associated vector Helmholtz equation within a local curved coordinate system. The proposed methodologies are validated through comparison with analytical results and a Galerkin-based solution from the literature across several representative scenarios. The rate of convergence, with respect to the number of expansion terms in the Rayleigh-Ritz method solution (RRMS), is observed to be faster than that in Galerkin-based solutions, while requiring comparable computational times. Furthermore, we explore the impact of both dielectric and conduction losses via the Rayleigh-Ritz method, aspects previously unattainable with analytical methods.