Analog circuit design by nonconvex polynomial optimization: Two design examples

摘要

We present a framework for synthesizing low-power analog circuits through global optimization over generally nonconvex multivariate polynomial objective function and constraints. Specifically, a nonconvex optimization problem is formed, which is then efficiently solved through convex programming techniques based on linear matrix inequality (LMI) relaxation. The framework allows both polynomial inequality and equality constraints, thereby facilitating more accurate device modelings and parameter tuning. Compared to traditional nonlinear programming (NLP), the proposed methodology exhibits superior computational efficiency, and guarantees convergence to a globally optimal solution. As in other physical design tasks, circuit knowledge and insight are critical for initial problem formulation, while the nonconvex optimization machinery provides a versatile tool and systematic way to locate the optimal parameters meeting design specifications. Two circuit design examples are given, namely, a nested transconductance(G_m)-capacitance compensation (NGCC) amplifier and a delta-sigma (AS) analog-to-digital converter (ADC), both of them being the key components in many electronic systems.