Explicit solutions of two-variable scattering equations describing lossless low-pass two-ports with mixed lumped and distributed elements

Abstract

One of the methods to describe mixed lumped and distributed element two-port networks is to use two-variable scattering equations. In literature, the solutions of these explicit descriptive equations for some classes of low-order ladder networks are derived under some restrictions. In this paper, the complete and explicit solutions of the equations are derived to describe lossless low-pass two-port networks with mixed lumped and distributed elements, up to four elements, without any restrictions.