Driving-point synthesis of a resistor-terminated cascade composed of lumped lossless two-ports and commensurate stubs

The necessary and sufficient conditions are derived, for the realization of a two-variable impedance function as a resistor-terminated cascade of arbitrary lossless lumped two-ports and commensurate, series short-circuited and shunt open-circuited, stubs. It is shown that in addition to the two-variable positive real condition and the appropriate location of the zeros of the even part, the given impedance function must satisfy certain algebraic constraints.