Theory of subharmonic synchronization of nonlinear oscillators

Abstract

General expressions for the theoretical prediction of the subharmonic injection-locking range of oscillators with a nonlinear input-output relationship are presented. This analysis is extended to describe oscillators realized using real nonlinear input voltage and output current relationships. In particular, analytical results for an oscillator represented by a fifth-order polynomial describing a nonlinear current-voltage relationship for subharmonic factors of 2, 3, and 4 are given. Experiments relating the subharmonic locking range of a field-effect transistor oscillator at 18 GHz to the injected signal level are reported.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>