A Practical Approach for Acquiring the Hall–Huray Surface Ratio Using HFSS Simulations and VNA Measurements

This paper presents a practical, efficient, and automated approach for determining the Hall–Huray Surface Ratio parameter, which is essential for accurately modeling conductor surface roughness losses in high-frequency PCB transmission lines manufactured with FR4 substrates. The growing complexity of modern digital systems and the demand for precise signal integrity analysis require advanced electromagnetic models to predict interconnect behavior. Among several roughness models, the Huray model is widely recognized for its ability to represent conductive losses associated with copper surface roughness in a physically meaningful way. The proposed methodology combines automated parametric sweeps in ANSYS HFSS with experimental validation using a WavePulser 40iX vector network analyzer (VNA), applying time-domain gating techniques to isolate multiple reflection effects. The 3D simulation setup adopts the Wideband Debye model for the dielectric and the snowball (Huray) model for surface roughness characterization. The Hall–Huray Surface Ratio variable was systematically adjusted from 1 to 9 to achieve close agreement with the experimental data. The results demonstrated a deviation of less than 0.04 dB at 10 GHz in insertion loss and a maximum variation of 1.05 Ω in the impedance profile obtained via TDR. Although minor mismatches in the reflection parameter (S11) were observed, the outcomes validate the accuracy, robustness, and practical applicability of the proposed method. This technique offers an effective balance between cost, complexity, and precision for high-frequency structure characterization up to 20 GHz, with promising potential for future extensions in electromagnetic compatibility (EMC) studies and advanced interconnect modeling.