Synthesis of optimal inhomogeneous ladder networks

In homogeneous ladder networks in which each ladder series arm impedance is
f_{i}z(s)
and each shunt arm admittance is
g_i y(s)
are Investigated. The necessary and sufficient conditions for synthesis of a second-order matrix as a chain matrix of a reciprocal inhomogeneous ladder network are given. It is shown that if the network is either symmetrical or antimetrical, only one chain parameter is needed to specify the network. It is also proven that the necessary and sufficient condition for the sum of all
f_i
and
g_i
to be minimum is that the network be either antimetrical or symmetrical with a specified immittance level.