Transformer-based S-parameter Extraction for Coupled Transmission Lines with Vias

S-parameters are a crucial tool for simulating and analyzing high-speed, high-frequency signal transmission, particularly in advanced packaging and PCB designs such as chiplets and 3DICs. However, traditional 2.5D/3D electromagnetic (EM) field solvers are computationally expensive and time-intensive, making them impractical for agile and automated design iterations. Existing neural network-based methods for S-parameter prediction are often limited to predefined 2D planar structures, restricting their applicability. In this work, we propose SFormer, a transformer-based deep learning framework that predicts the S-parameters of coupled transmission line pairs directly from their layout while supporting highly flexible configurations. Our method accounts for variations in multiple layout parameters, including line length, segmentation, bending direction, line spacing, line width, and line-to-ground distance. The layout is represented as a graph, processed by a graph convolutional network (GCN) to extract geometric and topological features, which are then refined by a transformer encoder. Finally, a multi-layer per-ceptron (MLP) predicts the corresponding S-parameter matrix elements. Additionally, we introduce a specialized scheme for efficiently generating S-parameters of multi-layer transmission lines connected by vias, enabling rapid extraction for truly 3D structures. Compared to commercial EM solvers, SFormer achieves over 500× speed improvement while maintaining a mean absolute error (MAE) below 1e − 2 for 4-port network extraction up to 15 GHz in commercial design cases.