A spectral convolutional net for co-optimization of integrated voltage regulators and embedded inductors

Integrated voltage regulators (IVR) with embedded inductors is an emerging technology that provides point-of-load voltage regulation to high-performance systems. Conventional two-step approaches to the design of IVRs can suffer from suboptimal design as the optimal inductor depends on the characteristics of the buck converter (BC). Furthermore, inductor-level trade-offs such as AC and DC resistance, inductance and area can not be determined independently from the BC. This co-dependency of the BC and the inductor creates a highly non-linear response surface, which raises the necessity of co-optimization, involving multiple time-consuming electromagnetics (EM) simulations. In this paper, we propose a machine learning based optimization methodology that eliminates EM simulations from the optimization loop to significantly reduce the optimization complexity. A novel technique named as Spectral Transposed Convolutional Neural Network (S-TCNN) is presented to derive an accurate predictive model of the inductor frequency response using a small amount of training data. The derived S-TCNN is then used along with a time-domain model of the BC to perform multi-objective optimization that approximates the Pareto front for 5 objectives, namely inductor area, BC settling time, voltage conversion efficiency, droop and ripple. The resulting methodology provides multiple Pareto optimal inductors in an efficient and fully automated fashion, thereby allows to rapidly determine the optimal trade-offs for possibly contradicting design objectives. We demonstrate the proposed framework on co-optimization of solenoidal inductor with magnetic core and BC that are integrated on silicon interposer.