On the Upconversion of the Cross-Coupled Pair 1/ <i>f</i> Noise Into Phase Noise in Current-Biased Class-B CMOS Oscillators

Despite extensive research, the upconversion of 1/f noise into phase noise in harmonic oscillators is still an open topic of investigation. A few upconversion mechanisms are not fully understood yet. In particular, in class-B CMOS oscillators, the reason why a large tail capacitance combined with transistors entering the triode region for a portion of the oscillation cycle dramatically amplifies the 1/f noise upconversion has not been clearly pinpointed. This work introduces a simple yet powerful model to fully capture the 1/f noise upconversion mechanism. It shows that when the transistors enter the triode region, charge sharing between the tail capacitance and the tank capacitance injects a noise charge into the tank, generating phase noise perturbations quantified by the impulse sensitivity function. The analytical description results in closed-form equations that predict the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$1/f^{3}$</tex-math> </inline-formula> phase noise sideband accurately, without relying on complex harmonic analysis or specific device nonlinearities. The excellent agreement with simulations performed both using idealized and real 55nm CMOS transistor models confirms the validity and robustness of the proposed framework, offering new insights and practical design guidelines for low phase noise CMOS oscillators.