Field coupling to nonuniform transmission lines with linear characteristic impedance

In this paper, plane wave field-coupling onto a nonuniform, lossless, transmission line running over a ground plane is solved analytically by means of a power series expansion in the longitudinal variable z. A linear variation of the characteristic impedance versus z is assumed. It is shown via examples that the obtained analytical results represent the limit solution of the approach based on the decomposition of the nonuniform transmission line into N_S cascaded elementary uniform line sections, for large N_S. Extension of the proposed method to the case of nonuniform lines with a general characteristic impedance profile is also discussed, by resorting to a model based on the cascade of nonuniform lines with linear characteristic impedance.