Radiation from transmission lines

The aim of this investigation was to contribute something to our knowledge of traveling electromagnetic waves. Among the transient phenomena that occur along transmission lines, these are still little known, especially as far as their “attenuation” and “distortion,” or change in shape near the “wave front” are concerned. It is first seen that the “classical theory” of the propagation of electrical disturbances along lines, as it has been chiefly developed by Heaviside and Poincare, does not give a correct representation of the facts near the wave front, because it assumes an instantaneous penetration of the current in the wires. It is shown that this theory is an “unidimensional” one, as it considers only one space variable, the coordinate along the line, and, from an electromagnetic point of view, amounts to identifying the traveling waves with plane wave phenomena. Steinmetz´s theory of the radiation from traveling waves (Trans. A. I. E. E. Feb., 1919) is then examined, and, as Carson pointed out (Jour. A. I. E. E., Oct. 1921), found based on a misconception of the propagation of the electromagnetic field near the wires of a line. It is remarked that this theory amounts to propagating longitudinal electric waves, a conception in conflict with the basis of Maxwell´s theory. This latter proves very easily that, along a perfect line, i. e., without ohmic or leakage losses, plane electromagnetic traveling waves are propagated without distortion and without attenuation; hence that there is no radiation. Losses do not change anything from the radiation point of view (Mie. Ann. Phys. 2, 1900). In the theory of Steinmetz, the radiation was the controlling factor at high frequencies. Although the question could be considered as settled, in so far as Steinmetz raised it, it is felt that the conditions under which traveling waves are started must be elucidated, in order to decide whether, duri- g the transient process of establishing a plane electromagnetic traveling wave, any loss of energy can occur by radiation in free space. This would reduce the radiation to a transient phenomenon instead of to a steady one, as assumed by Steinmetz, i. e., to an effect produced when the condition of plane wave is departed from, as at the origin or the end of a line (“end effect”). The problem, considered in its broad aspect, i. e., from the electromagnetic point of view of Maxwell, appears to be of great complexity. It involves a study of what might be called time-three-dimensional space transient, while the most complicated transients considered in electrical engineering are time-one-dimensional space transients, as was already noticed. It was found possible, however, to decide whether the radiation is a factor of enginering importance in attenuating and distorting waves. There, first, the distribution of current along the conductors of a line is shown to be a very close approximation to the actual, unknown, distribution, with regard to the possibly existing radiation. Then, from this assumption, the radiation of the system is calculated at a corresponding approximation, and its amount found to be negligible compared to the heat dissipated in the line during the same time. From this it is concluded that the effect of the radiation upon the attenuation and the distortion of the waves along the line must also be negligible, compared to the effect of the joulian losses, and in this result a proof “a posteriori” of the correctness of the initial assumption is seen. The first idea of that procedure, but limited to stationary waves, is probably to be credited to M. Abraham (Phys. Zeit. 2-p. 329–1901) who applied it to the calculation of the radiation from a single isolated wire (oscillator), and found it in practical agreement with a more elaborate theory, based on Maxwell´s equations. As in this latter application the radiation is