On Voltage and Current Continuity in the Youla-Weissfloch Circuit (Correspondence)

Any lossless 2n-port can be represented as a cascade of three 2n-ports: an all-pass network, a set of n uncoupled ideal transformers, and another all-pass network. The 2n-port may be either a physical 2n-port [i.e., a device with an even number of ports considered as a device mapping the scattering (impedance) matrix of a device connected to one half of the ports into the input scattering (impedance) matrix ], or it may be a multimode transmission line. In the latter case the network may be a set of uniform lines with a discontinuity, and there may be a condition that the mode voltages or currents are continuous across the discontinuity. If a₁, a₂, b₁, and b₂ are the incident and reflected wave vectors, the voltage continuity requires a₁+b₁ = a₂ +b₂, while current continuity requires a₁-b₁ = a₂ -b₂.