Mode Analysis by the Method of Auxiliary Sources With an Excitation Source

Abstract

The method of auxiliary sources (MAS) is one of the numerical methods employed for the determination of the cutoff wavenumbers (eigenvalues) of cylindrical waveguides. According to the general scheme of MAS, the eigenvalues are obtained by requiring the square impedance matrix to be singular and therefore its determinant to be zero (or its condition number to be large). For large matrices, such computations are complicated and time-consuming. Additionally, these schemes are frequently contaminated with spurious eigenvalues. To overcome the difficulties, an efficient method based on MAS along with an excitation source has been proposed. The eigenvalues are obtained by measuring the physical response of the waveguide's domain to this source; thus, an interior problem is always solved. This article is a comprehensive presentation of this method and its variants and aims to emphasize fundamental and often unfamiliar attributes. One of the main objectives is to show analytically and numerically that when an internal source is used, the eigenvalues are accurately computed without employing a regularization procedure. The method is applied to hollow simply and multiply connected waveguides with circular, elliptical, and rounded-triangular cross sections. The results are compared with those obtained from COMSOL Multiphysics. Moreover, the phenomenon of divergent and oscillating MAS currents-which may or may not occur depending on the relative position between the auxiliary curve and the excitation source-is discussed. It is emphasized that, with proper care, the phenomenon does not affect the accurate computation of the eigenvalues.