The Phase Synchronization of a Parametric Subharmonic Oscillator

摘要

The general problem of phase determination for a parametric subharmonic oscillator is formulated. The analyses of several circuits are reduced to the solution of the canonical Mathieu equation. Solution is effected by the Floquet theorem and the parameters discussed in terms of the range of values encountered in experimental circuits. The transient portion of the solution produces arbitrary constants with two possible signs, yielding the two phase states of a growing oscillation. Conditions of oscillation are discussed, and the influence of signal and noise presented.