A frequency-domain study of lock range of harmonic oscillators with multiple injections

This paper presents a frequency-domain study of the lock range of harmonic oscillators with multiple injections. The intrinsic relation between the lock range of harmonic oscillators with multiple injections and that with a single injection is obtained. We show that harmonic oscillators with multiple injections exhibit a larger lock range as compared with those with single injection if the phases of the injection signals is properly chosen. The findings are validated using LC oscillators with single injection and dual injections designed in IBM 130 nm 1.2 V CMOS technology.