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

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