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Noise Spike Model in Relaxation Oscillators Based on Physical Phase Change

A new approach to augment existing noise models in a relaxation oscillator by including noise spikes during state change, an important aspect hitherto not covered in existing noise models, is proposed. Such noise spike is due to regeneration at the jump and this paper attempts to offer an explanation by viewing state change as a physical phase change in a thermodynamic system, which is also due to regeneration. The connection is established by viewing the relaxation oscillator as a combination of bistable circuit (exhibits metastability) and a timing capacitor. Similarly the thermodynamic system exhibits physical phase change (metastability). Formula is derived to predict the “magnitude” of the noise spike, as a function of regeneration parameter, and hence design parameter such as gm, R, I0. Simulations (Eldo) on circuits and simulations (Metropolis) on thermodynamic system as well as measurements on circuits fabricated in 0.13 μm CMOS technology are consistent with theory.