Sinusoidal Currents in Linearly Tapered Loaded Transmission Lines

Working formulas for the calculation of input impedances and attenuation are obtained for a transmission line in which the resistance and inductance per unit length are linear functions of distance, and in which the capacitance and leakance are constant. Generalized functions depending on the initial constants and the rate of taper are introduced, in such a way that the formulas and the functions are analogous to the usual formulas and hyperbolic functions. The latter are secured as special cases of the former. The theory is applicable to the tapered loaded submarine cable. Propagation in such a transmission line, as distinguished from that in the smooth uniform line, is characterized by the fact that the current attenuation is, in general, different from the voltage attenuation.