Unit Real Functions in Transmission Line Circuit Theory

A new class of functions is introduced which has a direct physical significance in transmission line theory. These are called "unit real" (u. r.) and are derivable by bilinear transformations from positive real (p. r.) functions. The complex reflection coefficient is a unit real function of the "line vector"exp(-2jθ), where the electrical length of a section of line in a resistor-transmission line circuit. Just as in lumped constant circuit theory the impedance is a p.r. function of the complex frequency. U.r. and p.r. functions are compared. A new proof and a discussion of Richards' theorem are also presented.