Galerkin solution for the thin circular iris in a TE11-mode circular waveguide

An integral equation for the transverse electric (TE) field in the aperture of a concentric circular iris in a transverse plane of a circular waveguide is approximately solved using Galerkin´s method. The aperture field is represented by a finite sum of normal TE and TM (transverse magnetic) circular waveguide modes that fit the circular aperture. The numerical convergence of the Galerkin solution is demonstrated using the resultant aperture field distributions and equivalent shunt susceptance for the case of dominant TE₁₁-mode excitation. The resultant aperture electric field distribution closely resembles that of the TE₁₁ aperture mode alone, except for edge contribution behavior at the edge of the iris. A resonant or capacitive iris is possible over a restricted range of frequencies