Gyratorless realization of a class of three-variable positive real functions†

The necessary and sufficient conditions for realizing a class of three-variable positive real functions of degree one in two variables as the driving-point impedance at port 1 of a reciprocal three-port network in the domain of the higher degree variable, and with a unit inductor or a unit capacitor termination at port 2 in the domain of the second variable, and a unit inductor or a unit capacitor termination at port 3 in the domain of the last variable, are given in this paper An example is given to illustrate the synthesis procedure. Extension of the synthesis technique to a class of multivariate positive real functions is possible.