An Analysis of $1/f$ Noise to Phase Noise Conversion in CMOS Harmonic Oscillators

We present a study of tail-bias-current 1/f noise upconversion into 1/f³ phase noise for both CMOS Colpitts and differential-pair LC oscillators. We focus on the incremental Groszkowski effect, i.e., the modulation of the shift in oscillation frequency induced by the higher current harmonics flowing into the LC tank of a harmonic oscillator induced by bias instabilities, as we show that there is no upconversion of 1/f noise into phase noise from the core MOS transistors in either topologies. Quantitative results match very well numerical simulations run with spectreRF, and show that the Groszkowski effect may indeed be a dominant cause of 1/f³ phase noise generation.