Transients of Resistance-Terminated Dissipative Low-Pass and High-Pass Electric Wave Filters

Abstract

Formulas are derived for the solution of the transient receiving-end currents of resistance-terminated dissipative T- and π-type low-pass and high-pass electric wave filters. Oscillograms taken with a cathode-ray oscillograph for direct- and alternating-current cases are found to agree with the results calculated from these formulas. From these calculations the following conclusions are derived: (1) When the terminating resistance is gradually increased from zero, the damping constants of the damped sine terms begin to differ greatly from each other, ranging in decreasing amplitudes from the first damped sine term to the last term of (approximately) cutoff frequency. Hence, the transient is ultimately of the cutoff frequency. At the last frequency, this constant is greater than the corresponding constant (approximately equal to R/2L), when the termination is absent. (2) For each increase of one section, there is introduced an additional damped sine term with a smaller damping constant. Therefore transients die out faster in filters of a small number of sections. (3) The last resonant frequency of the filters varies with the number of sections used. It approaches the cutoff frequency as the number of sections is increased. This paper deals with the receiving-end transient currents of resistance-terminated dissipative low-pass and high-pass electric wave filters of T- and π-types. Transients of nondissipative electric wave filters were first treated by John R. Carson and Otto J. Zobel, who considered primarily an infinite succession of similar T sections and obtained formulas for the current at any section. In 1935, E. Weber and M. J.