Synthesis of Three-Terminal Networks with Two Kinds of Elements

Abstract

The present paper is concerned with the synthesis of LC, PC, and RL-three-terminal networks without mutual inductance. It shows that the immittance matrices which satisfy the following sufficient conditions may be realized as networks of these kinds: (sufficient condition for RC case) 1) Admittance (or impedance) matrix satisfies the realizability conditions as a four-terminal RC network. 2) Numerator of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">y_{12} (z_{12})</tex> is a polynomial with nonnegative coefficients whose zeros are restricted to the left half of the complex frequency plane including boundary, where the denominator is assumed to be a polynomial with nonnegative coefficients. 3) <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(y_{11} - y_{12}): (y_{22} - y_{12}) = 1 :n [(z_{22} - z_{12}): (z_{11} - z_{12}) = 1 :n)]</tex> . The theory may be applicable to the two important problems in network synthesis; that is, to the synthesis of filter circuits as three-terminal reactance networks and to the realization of RC transfer functions as three-terminal RC networks without mutual inductance. Furthermore, for the case of a symmetrical circuit, the theory offers the theoretical method of transforming from a symmetrical lattice to an unbalanced form.