Partial derivative properties of multivariable cascaded networks

Abstract

Some partial derivative properties of the impedance function of a resistively-terminated network which is a cascade of m lossless two-ports of variables p 1 to p m dre established. Those cases where some of the lossless two-ports are lowpass or highpass ladder networks with all of their transmission zeros at the origin or at infinity are also examined. Necessary and sufficient conditions involving partial derivatives and under which an m-variable reactance or positive real function can be realized as the impedance function of a p i-variable lowpass or highpass ladder network, with all of its transmission zeros at p i = 0 or p i = ∞, and terminated in a reactance or positive real impedance function in the other variables are derived.