On the design and generation of the double exponential function

Abstract

For the double exponential function f(t)=K(e^-at-e^-bt), which is used for impulse testing of electrical components and systems, we derive an approximate relation between the ratio y_m=T_m/T_max, where T_max and T_m are, respectively, the times to reach the peak value F_max and the value F_max/m on the tail of the pulse, and the ratio x=b/a. This relation is useful for finding x for a prescribed y_m, where m is usually equal to 2. Our formula is much simpler than that given by Googe, Ewing and Hess (1992), but gives results of comparable accuracy. We also present a number of RC two-ports for generating the test function f(t) from an impulse function δ(t), as well as from the step function u(t).