Unified active Q factor formula for use in noise spectrum estimation from Leeson’s and Hajimiri’s models

Abstract

In this letter, we propose unified active Q factor formula for use in oscillator noise spectrum estimation from Leeson’s and Hajimiri’s models. This formula is derived from its oscillation condition as unified expression which covers the conventional formulas. Since this formula can reduce to conventional formulas, we confirm that the unified formula is valid regardless of topology and type of active device. In addition, we applied this unified formula to a cascode FET amplifier based oscillator as an example. As the result, we found that it has Q factor twice as high as a single FET oscillator using the same passive network. From these issues, we conclude that active Q factor can be estimated only if we know the oscillation condition and its frequency slope. It will contribute to low-phase-noise oscillator design and optimization.