An Analysis of $1/f^{2}$ Phase Noise in Bipolar Colpitts Oscillators (With a Digression on Bipolar Differential-Pair <i>LC</i> Oscillators)

Abstract

This work presents an analysis of phase noise 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 displayed by both single-ended and differential bipolar Colpitts oscillators. Very accurate and rigorous symbolic phase noise expressions are derived, enabling a deeper insight into the major mechanisms of phase noise generation, and providing new tools for design optimization. Phase noise expressions for the cross-coupled differential-pair LC-tank oscillator are derived as well. The theoretical analysis is validated on a 3 GHz differential bipolar Colpitts VCO implemented in a 0.35 mum SiGe process. Measurements show a phase noise of -123 dBc/Hz or less at 1MHz offset frequency from the 2.8-3.1 GHz carrier, for a phase noise figure-of-merit of at least 183 dBc/Hz across the tuning range. A very good agreement between theory, numerical simulations, and measurements is observed