Electrical and Wave Digital Modeling of CMOS-Based Ring Oscillators.

We report on a modeling approach for a CMOSbased ring oscillator mimicking the functionality of the leaky-integrate-and-fire neuron model. The oscillator is useful for neuromorphic applications, as it can be used to implement small and energy-efficient analog neural networks with CMOS technology. However, simulating a large number of such oscillators with typical simulation software can be very time-consuming, as the number of implicit equations is proportional to the number of nonlinear components and thus the number of oscillators. Furthermore, the CMOS circuit can not be directly simulated with standard numerical integrators, e.g. those of MATLAB or Python. Therefore, we propose a simplified electrical model with two key advantages: i) the model can be simulated with any numerical integration method, while capturing the nonlinear dynamics of the CMOS circuit; and ii) it can be used to derive a wave digital model for emulation purposes. Our emulation results show that the model is indeed capable of mimicking the CMOS circuit to a suitable degree without having to consider all the sophisticated components appearing in the original circuit.