Stability and Operation of Injection-Locked Regenerative Frequency Dividers

Injection-locked regenerative frequency dividers can achieve a fractional division ratio similar to regenerative frequency dividers and can provide quadrature output phases. An analysis of the steady-state operation, stability, and phase noise of injection-locked regenerative frequency dividers is presented. In addition, two-stage ring oscillators (based on negative-resistance delay cells) are studied, and their steady-state free-running operation and injection-locked behavior are investigated. Simulation results based on the equations derived in this paper are compared with circuit simulations to examine the accuracy of our analysis, which is quantified in different parts of this paper.