Bayesian Model Fusion: Large-Scale Performance Modeling of Analog and Mixed-Signal Circuits by Reusing Early-Stage Data

Abstract

Efficient high-dimensional performance modeling of today's complex analog and mixed-signal (AMS) circuits with large-scale process variations is an important yet challenging task. In this paper, we propose a novel performance modeling algorithm that is referred to as Bayesian Model Fusion (BMF). Our key idea is to borrow the simulation data generated from an early stage (e.g., schematic level) to facilitate efficient high-dimensional performance modeling at a late stage (e.g., post layout) with low computational cost. Such a goal is achieved by statistically modeling the performance correlation between early and late stages through Bayesian inference. Several circuit examples designed in a commercial 32nm CMOS process demonstrate that BMF achieves up to 9× runtime speedup over the traditional modeling technique without surrendering any accuracy.

Compact Model Parameter Extraction Using Bayesian Inference, Incomplete New Measurements, and Optimal Bias Selection

“…Given experimental I-V measurements of a transistor and simulation results generated from the MVS model, inverse uncertainty quantification estimates the discrepancy between the experiment and the mathematical model, as shown in (7). The standard deviation β −1 lnFn is calculated by the average differences between measurements and MVS model predictions using the LSE extracted parameters:…”

“…Bayesian model fusion (BMF) has been proposed to accurately estimate the parametric yield and/or the statistical distribution of circuit performance for both pre-silicon verification and post-silicon validation [5,6,7]. While the virtual probe described in [8] and in [9] focuses on reducing the number of measured dies needed to characterize spatial variation, our work focuses on reducing testing cost per die.…”

Process-Variation Tolerant Channel-Adaptive Virtually Zero-Margin Low-Power Wireless Receiver Systems

“…If test-cost is not a concern a high frequency modulated signal could be used for receiver testing, simplifying process-variation sensing. Moreover, recently published techniques like Bayesian model fusion [33]- [35], could be used to sense the process information without a test input.…”

Statistical Library Characterization using Belief Propagation across Multiple Technology Nodes

“…The first is a novel ultra-compact, analytical model for gate timing characterisation, and the second is a Bayesian learning algorithm for the parameters of the aforementioned timing model using past library characterizations along with a very small set of additional simulations from the target technology. Bayesian approaches were initially introduced in the area of VLSI design for post-Silicon validation and parameter extraction [10]- [15]. The intrinsic simplicity of the proposed timing model combined with the Bayesian learning [16] framework is capable of building very accurate circuit response representations.…”