One-Dimensional Deep Image Prior for Curve Fitting of S-Parameters from Electromagnetic Solvers

TL;DR

This paper introduces a novel deep learning approach using one-dimensional Deep Image Prior to efficiently fit S-parameters from electromagnetic simulations, significantly reducing sampling requirements while outperforming traditional industry-standard methods.

Contribution

It is the first to apply deep generative models with a custom architecture and smoothing spline-inspired regularization for S-parameter fitting from EM solvers.

Findings

Outperforms publicly available Vector Fitting implementations with only 5-15% of samples.

Competitive with or surpasses proprietary Vector Fitting tools.

Requires fewer samples for accurate broadband S-parameter reconstruction.

Abstract

A key problem when modeling signal integrity for passive filters and interconnects in IC packages is the need for multiple S-parameter measurements within a desired frequency band to obtain adequate resolution. These samples are often computationally expensive to obtain using electromagnetic (EM) field solvers. Therefore, a common approach is to select a small subset of the necessary samples and use an appropriate fitting mechanism to recreate a densely-sampled broadband representation. We present the first deep generative model-based approach to fit S-parameters from EM solvers using one-dimensional Deep Image Prior (DIP). DIP is a technique that optimizes the weights of a randomly-initialized convolutional neural network to fit a signal from noisy or under-determined measurements. We design a custom architecture and propose a novel regularization inspired by smoothing splines that penalizes discontinuous jumps. We experimentally compare DIP to publicly available and proprietary industrial implementations of Vector Fitting (VF), the industry-standard tool for fitting S-parameters. Relative to publicly available implementations of VF, our method shows superior performance on nearly all test examples using only 5-15% of the frequency samples. Our method is also competitive to proprietary VF tools and often outperforms them for challenging input instances.