Nonlinear oscillations in a distributed network

Abstract

The oscillations of small amplitude in a lossless transmission line terminated with a nonlinear circuit are studied by perturbation theory. The equations describing this system are reduced to a difference-differential equation with one delay. A general procedure is given for equations of this type for finding the expansion of the oscillation to any order in terms of the coefficient of the fundamental frequency. The frequency-amplitude relations are obtained to second order and compared with results found on the computer. Both the autonomous and forced cases are studied. It is indicated in the forced case that the frequency-amplitude relation gives approximately the range of “locking in".