The Correlation between Decay Time and Amplitude Response

The object of the present work is to investigate the correlation existing between the decay time and the delay time of the indicial response on the one hand, and the bandwidth and peak values of the steady-state amplitude response and the slope of the phase response on the other. The analysis is applied to five types of electrical networks and to some general classes of circuits, distinguished by the location of their poles in the p-plane. From these investigations the following results are obtained: (a) By interpolation of all numerical results obtained for the five types of networks, the statistical formulae embracing all of them are found, (b) Formulae giving the functional relationship between the decay time and the ratio f3/f6 are derived for each class of circuit considered, (c) The formula for the delay time, tl = [d¿/d¿]¿ = 0, is checked for all five networks considered and is found to be valid for multi-stage, but not for single-stage, circuits.