The Nonuniform Transmission Line

The problem of transmission of periodic waves along a transmission line, whose series impedance and shunt admittance per unit length very as any powers of the distance from some point, is solved. The solution is given in terms of Bessel functions. A length of such a line is considered as a four-terminal network, and the more important parameters of the network are given. From these parameters one derives immediately the attenuation of current and voltage along the line. The solution is given for a line consisting of a number of parts, each of which is of the form described above. The line constants (so-called) need not vary continuously from one part to the next. The results can be applied to the cases of a tapered submarine cable, an overhead line with a pronounced sag, and end effects in a high tension line.