Impedance Transformation Using Lossless Networks

Two impedances are said to be compatible if one of them can be realized as the input impedance to a two-terminal-pair lossless network terminated in the other impedance. A uniqueness property of the Darlington realization procedure and the methods of cascade synthesis are used to determine a simple, concise set of necessary and sufficient conditions under which two given realizable impedances can be compatible. Applications are discussed.