Generalization of the mode-matching technique or a new theory of this commonly used method

A generalization of the conventional mode-matching technique, which corresponds to a new formulation of the problem of mode diffraction on the waveguide discontinuity, is proposed. To represent the sought-for solution of the problem the Fresnel formulae for scattering operators are introduced. It is shown that the correctness of this matrix model is completely determined by the found properties of the scattering operators. The universality of the obtained operator model is established for a whole class of the considered problems of mode diffraction on the abrupt and resonant discontinuities in a waveguide. The unconditional convergence of the projection approximation to the true solution is proved analytically. The analytical estimations for condition number of exact and approximate matrix models are obtained. To state the results the matrix-operator formalism of the modal analysis is used. The proposed approach was developed for efficient and rigorous analysis of microwave devices.