Transmission zeros and the two-port parameters

This paper presents relationships between the transmission zeros of an impedance and the two-port impedance parameters zij(s) (i, j = 1, 2) or the chain parameters of its Darlington equivalent. The odd and even properties of the two-port parameters are investigated. It is shown that z12(s) and z21(s) of a lossless two-port network need not be odd functions. A general relationship between the complex-normalized scattering matrix of a two-port network with complex load impedances and the unit-normalized scattering matrix of its augmented two-port network, when the complex load impedances are represented by their Darlington equivalents, is given.