The use of polynomial partial derivatives in the synthesis of doubly-terminated multivariable networks

Abstract

A multivariable positive real function whose polynomial partial derivative is a sum of a resistance and a multivariable reactance function is discussed. It is shown that the input impedance of certain doubly-terminated multivariable lossless networks satisfy this property. Necessary and sufficient conditions are discussed for a multivariable positive real function with unity degree in each variable to be the input impedance of a doubly-terminated cascade of two lossless two-ports in mutually exclusive variables and separated by a series inductor or a shunt capacitor in another variable. A method is given whereby a multivariable positive real function with unity degree in each variable can be realized as a doubly-terminated lossless ladder network with all of its transmission zeros at infinity.