Synthesis of the lossless reciprocal three-port based on a canonic form of its scattering matrix

The canonic form of the three-port scattering matrix is deduced from the relations expressing the constraints of reciprocity and losslessness. One gives a particular construction of the denominator of the entries, which allows to solve the divisibility conditions resulting from the basic equations. The necessary and sufficient conditions are given which allow to synthesize the three-port as three two-ports connected in parallel with a shunt lossless impedance at the common port.