More on the $1/{\rm f}^{2}$ Phase Noise Performance of CMOS Differential-Pair LC-Tank Oscillators

Abstract

This paper presents a rigorous phase noise analysis in the 1/f <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> region for the differential CMOS LC-tank oscillator with both nMOS and pMOS switch pairs. A compact, closed-form phase noise equation is obtained, accounting for the noise contributions from both tank losses and transistors currents, which allows a robust comparison between LC oscillators built with either one or two switch pairs. The fabricated oscillator prototype is tunable between 2.15 and 2.35 GHz, and shows a phase noise of -144 dBc/Hz at 3 MHz offset from the 2.3 GHz carrier for a 4 mA bias current. The phase noise figure-of-merit is practically constant across the tuning range, with a minimum of 191.5 dBc/Hz. A reference single-switch-pair oscillator has been implemented and tested as well, and the difference between the phase noise levels displayed by the two oscillators is very nearly the one expected from theory