Inductance, capacitance networks terminated in resistance

This paper investigates the properties of the driving point impedance of general, passive, lossless two-ports without transformers which are terminated in resistance (LC-R networks). The culmination of the work consists of synthesis procedures in two areas. 1) A wide class of impedances
Z(p) = [A (p) + B(p)]/[C(p) + D(p)]
is characterized in terms of the locations of the zeros of
(AC- BD)
, where
A,C
and
B,D
are even and odd polynomials, respectively. Then a method of realization as an
LC-R
ladder network is given for members of this class. 2) The even part synthesis problem for an arbitrary, general impedance is solved. The realization takes the forms of a series connection as well as a parallel connection of at most four
LC-R
ladder networks. A number of examples give concrete form to the theoretical developments.