The General Equations of the Electric Circuit-III

Abstract

In the usual theory of transients the assumption is made, that resistance, inductance, capacity and conductance are constant. This however, is not correct, and as the result thereof, it was not possible to theoretically investigate, and numerically calculate the dissipation of high-frequency disturbances, the flatening of the wave fronts of impulses, the rounding off of steep waves, etc., with the time and the distance of travel, and there-from to determine the distance, to which the danger from such disturbances extends, and to investigate the conditions of line construction, which limit the danger zone of such phenomena to the smallest local extent. In the following, two of the foremost causes of change of the line constants with the equivalent frequency are investigated, the unequal current distribution in the conductor, and the electric radiation from the conductor, and shown, that within the range of frequencies which may be met in industrial circuits, the effective resistance of the conductor, and its attenuation constant, may increase more than a million fold. Equations of the line constants as function of the equivalent frequency are derived, and applications thereof made to a few problems: (1) The laws of conduction of high-frequency currents, such as produced by lightning discharges and similar disturbances, and the conclusions resulting therefrom on the nature of the conductor. (2) The decay of high-frequency sine waves in transmission lines. (3) The attenuation of rectangular waves. (4) The flattening of the wave front of steep impulses.