# Verifying nonlinear analog and mixed-signal circuits with inputs

## TL;DR

This paper introduces a novel verification method for nonlinear and hybrid analog/mixed-signal circuits with inputs, leveraging input fixing to improve sensitivity analysis and enable more precise simulation-based verification.

## Contribution

It proposes a new input-aware verification algorithm that enhances sensitivity analysis and is demonstrated on complex CMOS circuit models with nonlinear ODEs.

## Key findings

- Improved sensitivity analysis for fixed-input models.
- Verification of nonlinear CMOS circuits with hundreds of exponential terms.
- Analysis of metastability and sensitivity in bistable circuits.

## Abstract

We present a new technique for verifying nonlinear and hybrid models with inputs. We observe that once an input signal is fixed, the sensitivity analysis of the model can be computed much more precisely. Based on this result, we propose a new simulation-driven verification algorithm and apply it to a suite of nonlinear and hybrid models of CMOS digital circuits under different input signals. The models are low-dimensional but with highly nonlinear ODEs, with nearly hundreds of logarithmic and exponential terms. Some of our experiments analyze the metastability of bistable circuits with very sensitive ODEs and rigorously establish the connection between metastability recovery time and sensitivity.