Application of Scattering Matrices to the Synthesis of n Ports

Scattering matrices are applied to the synthesis of finite passive -ports ( -terminal pair networks) with frequency dependence. A realizability theorem for scattering matrices is shown and an -port is synthesized as a nondissipative network terminated in resistances. By considering the various numbers of resistance terminations and introducing the notion of generalized minimum phase shift, the relation among all the equivalent networks with a prescribed scattering matrix is studied. Reciprocal or nonreciprocal networks containing the minimum number of reactances or the minimum number of reactances and resistances are generally treated.