On the design and generation of the double exponential function

For the double exponential function f(t)=K(e/sup -at/-e/sup -bt/), which is used for impulse testing of electrical components and systems, we derive an approximate relation between the ratio y/sub m/=T/sub m//T/sub max/, where T/sub max/ and T/sub m/ are, respectively, the times to reach the peak value F/sub max/ and the value F/sub 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/sub 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 /spl delta/(t), as well as from the step function u(t).