Synthesis of a Variable-Parameter One-Port

It is shown that a positive real function containing a parameter in the form of a linear function can be realized as the input impedance of a nonbilateral passive two-port terminated in a loaded ideal transformer. The same impedance can also be synthesized by a pair of bilateral two-ports, each of which is terminated in a loaded or ideal transformer. The method of synthesis for the case where is a complex variable is also given. It is found that any two positive real functions can be realized as the open-circuit and the short-circuit driving-point impedances of a nonbilateral two-port or, under additional conditions, of a bilateral two-port.