Perturbation theory for inhomogeneous transmission lines

Abstract

We present a novel technique to calculate the transmission and reflection properties of inhomogeneous lossy transmission lines. It is based on a perturbation expansion of the relevant telegrapher's equation around the homogeneous solution. The method reveals that the transmission properties are unaffected to first order in the impedance and admittance, while reflection properties are modified by first-order terms. Extending the analysis to second order, we find correction terms for both transmission and reflection. These allow us to understand the statistical properties of the information bearing capacity and the echo of the inhomogeneous transmission line. The correction to the transmission properties is fully reciprocal, despite the absence of any symmetry properties. We compute scaling laws for echo and capacity.