Contents I. Introduction
To increase the achievable data rate, mm-wave frequencies offer larger bandwidth to cope with the increasing demands for data. Unfortunately, to support higher data rates, complex modulation schemes are utilized. This puts stringent requirements for low phase noise (PN) of the oscillators while consuming low power consumption. To avoid degradation of the quality factor of the LC tank at mm-wave frequency, a sub-harmonic injection technique can be used, which allows the possibility of using an oscillator running at a relatively lower frequency, e.g. 20GHz as a source to inject to the oscillator at higher frequency, e.g. 60GHz [1], [2]. Unfortunately, a sub-harmonic injection-locked oscillator (ILO) usually exhibits an extremely small locking range. [3] explains different injection methods for a sub-harmonic ILO for various multiplied ratios (M), which is defined as the output frequency divided by the injection frequency. However, the analysis and theoretical explanations are missing. Therefore, the designer has to rely on the tedious transient simulation to verify the locking range of the ILO. This usually takes thousands of oscillator cycles to settle and lock. In addition, precise input frequency steps and careful verification of locked waveforms are required to identify accurate locking range at various injection levels.
