Finding Deterministic Solution From Underdetermined Equation: Large-Scale Performance Variability Modeling of Analog/RF Circuits

The aggressive scaling of integrated circuit technology results in high-dimensional, strongly-nonlinear performance variability that cannot be efficiently captured by traditional modeling techniques. In this paper, we adapt a novel L₀-norm regularization method to address this modeling challenge. Our goal is to solve a large number of (e.g., 10⁴-10⁶) model coefficients from a small set of (e.g., 10²-10³) sampling points without over-fitting. This is facilitated by exploiting the underlying sparsity of model coefficients. Namely, although numerous basis functions are needed to span the high-dimensional, strongly-nonlinear variation space, only a few of them play an important role for a given performance of interest. An efficient orthogonal matching pursuit (OMP) algorithm is applied to automatically select these important basis functions based on a limited number of simulation samples. Several circuit examples designed in a commercial 65 nm process demonstrate that OMP achieves up to 25× speedup compared to the traditional least-squares fitting method.