Basic Properties of the Generalized Scattering Matrix of Waveguide Transformers

This paper examines analytically the operator properties of the generalized scattering matrix of the H-(E-) plane waveguide transformer in an arbitrary shape. Four fundamental laws of electromagnetism are used to derive a new form of the generalized energy-conservation statement. The structure of spectrum of the generalized scattering matrix and the spectrum localization are established. A practical significance of the considered basic properties is illustrated by the example of matrix models of the waveguide bends. The obtained analytical results are useful for testing the correctness of numerical solutions, as well as for the mathematical justification of the methods based on modal analysis.

Keywords:

• generalized scattering matrix
• energy-conservation law
• waveguide transformer
• Lorentz lemmas
• Cayley's transform