Linearly Tapered Loaded Transmission Lines
Working formulas for the calculation of input impedances and attenuation are obtained for a transmission line in which the inductance and resistance per unit length are linear functions of distance, and in which the capacitance and leakance are constant. Generalized functions used in the formulas, which were developed in an earlier paper, are here expressed in terms of Bessel's functions of the initial constants and the rate of taper, a form more readily applied in some cases. For the tapered loaded submarine cable the formulas are further simplified through the use of the hyperbolic functions applicable to the smooth uniform line, with appropriate correction factors.