Realizability of a Resistively Terminated Cascade of Lumped Two-Port Networks Separated by Noncommensurate Transmission Lines

The necessary and sufficient conditions are presented under which a multivariable impedance function may be realized by means of a cascade of passive, lumped, lossless, two-port networks connected by means of noncommensurate transmission lines and terminated in a positive resistor. Reference is also made to the particular case of a cascade of noncommensurate transmission lines with lumped, shunt capacitors at the junctions of adjacent lines.