Dissipation and fluctuations of CMOS ring oscillators close to criticality

TL;DR

This paper develops a thermodynamically consistent model of CMOS ring oscillators near criticality, revealing how entropy dissipation decreases with oscillation stability and how finite-size fluctuations induce noise-driven oscillations below the critical point.

Contribution

It derives the normal form of the Hopf bifurcation for CMOS oscillators, linking dissipation, stability, and fluctuations near the critical voltage.

Findings

Entropy dissipation decreases in oscillating states for systems with more than three inverters.

Finite-size fluctuations induce oscillations below the critical voltage.

Noise-induced oscillations have a short decoherence time scaling sub-linearly with system size.

Abstract

We analyze a thermodynamically consistent model of CMOS-based ring oscillators near the onset of coherent voltage oscillations. For driving voltages close to the critical value, we derive the normal form of the Hopf bifurcation that underlies the oscillation transition in the thermodynamic limit. Using this normal form, we determine the phase and amplitude dynamics, and demonstrate that entropy dissipation decreases in the oscillating state for ring oscillators with more than three inverters. These findings culminate in a stability-dissipation relation, which links the observed decrease in dissipation to an increase in the local stability of the oscillating state. Next, we characterize finite-size fluctuations of the amplitude and phase near the critical voltage, using a stochastic version of the normal form. We demonstrate that close to the transition, finite-size fluctuations remain important at arbitrary system size, introducing oscillations even below the critical voltage. We further show that these noise-induced oscillations have an anomalously short decoherence time that scales sub-linearly with the system-size, in contrast to the behavior far from criticality.