On a Theorem Used in Determining a Driving-Point Immittance from Its Phase Specifications

A simple and straightforward proof is given of the following theorem: The slope of the numerator polynomial of the odd part of a positive real function F(s) is negative at a pole, and positive at a zero, of F(s) on the imaginary axis, including the origin. The theorem is used in the tangent function method of deriving a drivingpoint immittance from the specification of its phase.