Phase-Noise Analysis in Rotary Traveling-Wave Oscillators Using Simple Physical Model

We show that the rotary traveling wave oscillator (RTWO) is well treated as a superposition of multiple standing-wave oscillators (SWOs). Based on the proposed physical interpretation, we derive a phase-noise formula for the SWO, and extend it to the RTWO, which can predict thermally induced phase noise with no more complexity than the well-understood LC voltage-controlled oscillator. Measurement and simulation validate the analysis. The physically based approach and simple resulting expressions make it possible to design the RTWO for a given phase noise without lengthy simulations.