Theory of coupled modes in a cylindrical cavity of arbitrary cross-section

A general theory of coupled modes in cylindrical cavities of arbitrary cross-section is developed. The excitation of the cavity by a small magnetic loop and the coupling of the modes caused by the loss of orthogonality due to perturbation in the lossy areas are first examined from the point of view of field theory. The frequency shifts and the variation of the quality factors caused by the perturbation are also taken into account by the theory. An equivalent circuit is deduced through the application of Lagrange equation to the magnetic and electric energy stored in the fields and from the losses. Finally, a practical equivalent circuit is developed for the particular case of two coupled modes.