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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 NS cascaded elementary uniform line sections, for large NS. 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.