Propagation of Periodic Currents Over a System Of Parallel Wires

The first section of this paper is devoted to the formal mathematical theory of the propagation of periodic currents over a system of parallel wires energized at its physical terminals only. The theory developed is essentially a generalization of the classical theory of transmission over a single wire (with ground return) or over a balanced metallic circuit. The solution here given furnishes the fundamental formulas and a good deal of information regarding what takes place in a system of parallel wires; for actual calculations, however, the method of treatment is not so well adapted as that developed in the remaining sections of the paper. The second section deals analytically with the problem of propagation over a line or a circuit exposed throughout its length to an arbitrary impressed field of force. The resulting solution is immediately applicable to problems of crosstalk and interference, and to the theory of the wave antenna. The last two sections are devoted to the development and application of a more physical or synthetic method of treatment, based on the substitution of 'equivalent electromotive forces' for the arbitrary impressed field. This synthetic treatment, which permits of an intuitive or physical grasp of the various problems, has been found quite useful in dealing with crosstalk and interference, and also with the wave antenna. The method is illustrated (in the last section) by application to two representative problems of a diverse nature.