Linear passive networks: Functional theory

Linear passive time-variable networks are investigated primarily through the use of distributional kernels as applied to the scattering matrix treated in the time domain. Necessary and sufficient conditions for passivity are obtained, and the scattering matrix is shown to be a measure satisfying an energy form constraint. Lossless constraints pertinent to synthesis are developed while networks consisting of a finite number of circuit elements are considered in some detail. Examples illustrating interesting behavior are presented.