Solution of Reduced Equations of Injection-Locked Oscillator

Abstract

Oscillators with the primary tone synchronization and based on the frequency-divider mode have been considered in this study. The paper proposes a generalized model of injection-locked oscillator using the linear polynomial approximation of nonlinear characteristic of its amplifying element, and a new analysis technique based on peculiarities of the oscillator operation in injection-locked mode. These peculiarities imply that the oscillation amplitude can be considered as steady-state at an arbitrary instantaneous value of phase shift and that the curvature of phase characteristic of the oscillator decreases with the rise of synchronization signal amplitude within certain limits. The development of the new technique involved the use of the linear approximation method of reduced equations of injection-locked oscillator and the small parameter method. The new technique is insensitive to the form of nonlinear terms, and it allows us to obtain analytical solutions of reduced equations having different nonlinear terms that depend on the oscillator operation mode. This technique features small errors and essentially simplifies the investigation of injection-locked oscillators and their systems. The experimental test confirmed its high efficiency.