Nonuniform Transmission Line Model

Spherical harmonic expansion provides an effective analytical tool for evaluating the radiation property of radiators in free space. Because the spherical harmonic modes are orthogonal, we can analyze the radiation fields mode by mode and obtain the total radiation fields by summing up the contribution from those modes of significance. In this chapter, by comparing the governing equations for the transverse electric field and the transverse magnetic field of a spherical harmonic mode with the standard Telegraphers’ equations, we create an equivalent nonuniform transmission line (NTL) model for the spherical harmonic modes in both time domain and frequency domain. Similar to conventional waveguides, the equivalent NTL model consists of a propagating zone and an evanescent zone, separated by a cut-off interface with the cutoff radius. Local lumped element circuit model of the NTL is developed with nonuniform distributed inductances or capacitances. The electromagnetic radiation process in free space and in media with radially varying parameters can be illustrated more intuitively with the NTL model.