A Periodically Loaded Transmission Line Excited by an Aperiodic Source—A Green's Function Approach

Abstract

A simple and closed-form expression for the Green's function of a periodically loaded infinite transmission line is derived. The spatial-domain formulation is based on distinguishing three coordinate systems, i.e., the observation, primary source, and secondary source coordinates. The Fourier transform is subsequently employed to transform the primary source spatial domain to a spectral domain, wherein Floquet's theorem is applicable. While applying Floquet's theorem, the observation coordinate is Fourier transformed to another spectral parameter that is a function of the primary source spectral parameter. The spatial-domain expression for the Green's function is obtained upon identifying the poles in the spectral parameter complex plane. The derived expression is verified by comparing the values of the voltage along the line obtained analytically with those obtained using a circuit simulator. The effect of the various parameters on the voltage distribution along the line and the dispersion curves is investigated.