The influence of certain transmission-line associated apparatus on travelling waves

The paper commences by very briefly reviewing the causes and characteristics of travelling waves on transmission lines. It is pointed out that these transients can be represented mathematically by a combination of two or more exponential functions, and four typical wave-shapes are selected and employed throughout the paper for illustrative purposes. A general operational impedance equation, involving the Heaviside operator p is then given. The particular operar tional equations of the circuits dealt with in the paper can be immediately deduced from this general one; and these in turn can be solved directly by means of further general solutions. Various circuits connected to transmission lines are then discussed, their practical applications are pointed out, and (by means of the general solutions) equations are given which show their response to any incident travelling wave. These equations are then plotted and examined for specific values of the circuit constants, and for the cases in which the travelling waves are given by the four typical shapes chosen earlier in the paper. Finally, a series of high-speed cathode-ray oscillograms is reproduced which bear interesting comparison with the mathematical results obtained and check many of the theoretical premises.