Evaluation of transient-gain functions for nonlinear elements and their use in step-function analysis

It has been shown that the transients occurring in nonlinear systems may be evaluated by using an equivalent gain for the assumed transient process. The equivalent gain depends on the amplitude, damping, and sometimes the frequency, of the transient process, and has been called the halfperiod transient-gain (h.p.t.g.) characterising function. The present paper shows how the h.p.t.g. of many commonly occurring nonlinearities may be derived simply from the h.p.t.g. functions of certain controlling characteristics which are presented. A more direct method of calculating step-function transients is then presented and illustrated with a second-order system having a saturating amplifier. The accuracy of this method is then examined by presenting the errors in prediction arising when analysing 175 nonlinear transients.