Frequency-Domain Study of Lock Range of Non-Harmonic Oscillators With Multiple Multi-Tone Injections

This paper presents a frequency-domain study of the lock range of non-harmonic oscillators with multiple multi-tone injections. By representing non-harmonic oscillators with a set of harmonic oscillators, the intrinsic relation between the lock range of harmonic oscillators and that of non-harmonic oscillators is obtained. We show non-harmonic oscillators with a multi-tone injection exhibit a larger lock range as compared with that with a single-tone injection. We further show non-harmonic oscillators with multiple single-tone injections exhibit a larger lock range as compared with that with a single single-tone injection. The condition upon which non-harmonic oscillators with multiple single-tone injections exhibit a larger lock range as compared with those with a single-tone injection is derived. The condition upon which non-harmonic oscillators with multiple multi-tone injections exhibit a larger lock range as compared with those with a single multi-tone injection is also derived. The theoretical findings are verified using a dual-comparator relaxation oscillator designed in an IBM 130 nm 1.2 V CMOS technology and analyzed using Spectre from Cadence Design Systems with BSIM4 device models.