Abstract

This paper presents a phasor-domain study of injection-locking of harmonic oscillators under multiple injections with the consideration of the effect of the nonlinear characteristics of the oscillators. The relation between lock range, oscillation condition, and the nonlinear characteristics of oscillators is obtained. The lock range of oscillators under multiple injections and that under a single injection are also obtained. We show that harmonic oscillators with harsh nonlinearities exhibit a larger lock range. We further show that harmonic oscillators with multiple injections exhibit a larger lock range as compared with those with single injection. The maximum lock range of oscillators with dual injections is twice that with a single injection. The theoretical findings are verified using the simulation results of LC oscillators designed in IBM 130 nm 1.2 V CMOS technology.

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