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.

本研究提出了第一个基于深度生成模型的方法，使用一维深度图像先验（DIP）适应来自EM求解器的S参数。相对于VF的公共实现，我们的方法表现更好，只使用5-15％的频率样本。我们的方法也具有竞争力，通常在挑战性输入实例中胜过其私有VF工具。

基于深度学习的 S 参数曲线拟合技术及其在电磁求解器中的应用