Generic Model for Multi-Phase Ring Oscillators

We present a generic model for Multiple Phase Ring Oscillators (MPRO) with 2n phases, and derive equations for frequency, phase and phase error under the simplifying approach of injecting the error in a single element. Extensive Monte Carlo simulations, at transistor level, for the four and eight phase circuits, are in accordance with these assumptions. These results are validated by two prototype integrated circuits, implemented in a 130 nm CMOS technology: The first prototype, which is a standalone four phases Ring Oscillator (RO), validates the theoretical analysis concerning the non-linear model main conclusions and, the second prototype, which is an eight phase RO, incorporated as a block of an ISM receiver, validates the generic model for CRO concept.