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.

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