On the Benefits of the Common-Mode Resonance on the 1/f ² Phase Noise Sideband

Introducing a common-mode resonance in the tank of a class-B differential harmonic oscillator is known to reduce the upconversion of the
$1/f$
noise into phase noise. Additionaly, it also improves the
$1/f^{2}$
phase noise sideband, dominated by thermal noise. This brief analytically shows that the benefit in the thermal noise region can be in the 2-5 dB range, which is significant. The common-mode resonance is shown to improve the
$1/f^{2}$
phase noise sideband in multiple ways: by leading to an increase of the amplitude of oscillation, a decrease of the noise contribution of the tank losses and the cross-coupled pair transistors, and a decrease of the noise contribution from the tail current generator.