Realizability Theorem for Mid-series of Mid-shunt Low-pass Ladders Without Mutual Induction

This paper treats the synthesis of nondissipative low-pass ladders without mutual induction. Necessary and sufficient conditions for physical realizability of mid-series or mid-shunt nondissipative low-pass ladders without mutual induction are presented here and the complete proof is given. The essence of the conditions imposed upon the input impedance of the network terminated in a pure resistance is a relation between the finite frequencies at which the loss is infinite and the roots of a polynomial which appears in the rational fractional representation of the input impedance. The method used is the ladder development of a two-terminal impedance which is elementary in network synthesis. Furthermore, a sufficient condition for physical realizability of general low-pass ladders without mutual induction, which is wider than the above conditions, is also given. This paper is concerned with the realization problem of a dissipative two-terminal impedance by means of a nondissipative two-terminal-pair network without mutual induction terminated in a pure resistance. The above-mentioned conditions are also necessary and sufficient in order that a dissipative two-terminal impedance can be realized by means of a mid-series or mid-shunt nondissipative low-pass ladder without mutual induction terminated in a pure resistance.