Microscopic Origin of Regeneration Noise in Relaxation Oscillator and its Macroscopic Circuit Manifestation

This paper augments the existing macroscopic circuit noise model for phase noise in relaxation oscillators by showing the microscopic origins of the noise and explains temperature dependency. The noise arises from fluctuation of the energy accompanying the excess carriers on device (transistors) capacitors in the oscillator. Such fluctuation has its physical origin from the noise of such carriers, which, microscopically, are distributed across the energy levels (Fermi-Dirac). Furthermore this energy can be interpreted, circuit-wise, such that its gradient, with respect to circuit state variables, correspond to time evolution of current and voltage i.e. the oscillator dynamics. Three methods: potential energy based (macroscopic), free energy based (microscopic), Langevin equation based, are used to develop the noise model. The model temperature variation over range of 77K-300K was compared to measured results on oscillators fabricated in 0.13 {\mu}m CMOS technology. The trend agree reasonably well, where above a crossover temperature, the phase noise is a monotonic increasing function of temperature, while below the crossover temperature, the phase noise stays relatively constant and an explanation based on Langevin equation, extended to quantum regime, is offered.