A Multiplication Theorem for Positive Real Functions

Abstract

Modern network synthesis relies heavily on the use of Positive Real Functions. A function Z(s) of the complex frequency s is said to be a P.R.F. (short for Positive Real Function) when it satisfies the following three conditions. (a) Z(s) is analytic and single valued for Re s^O except possibly for poles on the imaginary axis, (b) Z(s) is real for real s, (c) Re Z(s) ^ 0 for Re 5 ^ 0. When in addition Re Z(iy)=0, the function Z(s) will be called an