Matrix Description of Waveguide Discontinuities In the Presence of Evanescent Modes

摘要

The properties of the impedance and scattering matrix describing waveguide discontinuities are examined; both propaga¬ting and evanescent modes are considered.nIt is shown how different normalization conditions for the normal mode solutions in the guide affect the impedance matrix. A suitable choice of normalization always leads to a symmetric imaginary impedance matrix for a lossless structure.nThe scattering matrix is no longer symmetric or unitary. The simple relationship S =(Z - U)(Z + U) -1 is shown to hold only under special normalization conditions.nNext the matrices describing a plane of lossless obstacles arranged in a periodic array are examined. A different type of normalization condition must" be used here, since the normal modes are orthogonal in the conjugate sense (bi-orthogonal).nAlthough the structure is reciprocal, none of the matrices are symmetric. A suitable normalization leads to a skew-hermit an impedance matrix and to a unitary sub matrix of the scattering matrix corresponding to propagating modes.