Abstract
AbstractWe provide a rigorous nonlinear analysis of a large class of radio‐frequency (RF) two‐stage differential ring oscillators. We show that the oscillator's behavior can be recast into the classical Hopf planar dynamical system. Relying on well‐known results for such systems, we give a thorough investigation of the oscillator behavior under noise. We also provide compact analytical expressions for all relevant design measures, offering the designer straightforward guidelines for two‐stage ring oscillators. These expressions predict amplitude, frequency, period jitter, and phase noise very accurately. The formulas are validated for three popular differential delay cells using SPICE simulations.
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