Determination of the resonant frequencies in a complex cavity using the scattering matrix formulation

A method for computing the resonant frequency in a complex cavity consisting of a series of waveguide sections is derived. The analysis is restricted to transitions in which one waveguide is wholly contained in the other. An eigenvalue problem is formed by cascading the scattering matrix from a given section outwards to the ends of the complex cavity, with appropriate boundary conditions at the ends. The eigenvalue equation is solved numerically by searching for a complex frequency, the cavity Q being determined by half of the ratio of the real to the imaginary part of the frequency. The technique is easily implemented numerically and shows good agreement with experiment. This method is suitable for modeling both abrupt changes in radius and smoothly varying tapers.>