Study of Mutual Crosstalk Between Hemispheres in Roughness Hemispherical Model

Current state-of-the-art roughness models often overlook mutual crosstalk, like between planes and protrusions or among protrusions themselves, resulting in limited generalization or accuracy at high frequencies. Building on this premise, this letter delves into the unexplored realm of mutual crosstalk between hemispheres, a factor previously omitted in the hemispherical models. Through refined calculations of internal inductance, this study effectively enhances the predictive accuracy of the hemispherical model. Regarding the sidewall roughness hemispherical model of through-glass vias (TGVs), the mutual inductance of two hemispheres in parallel and series is derived by arranging the sidewall roughness of TGVs into an equivalent model with a rows and b columns, respectively. Subsequently, it separately derives the parasitic internal inductances originating from planes and hemispheres, comparing internal inductances in cases that consider or disregard mutual crosstalk between hemispheres. The findings underscore underpredicted internal inductance values when mutual inductance is not accounted for. Finally, the proposed model undergoes comparison with measurements up to 40 GHz, demonstrating good agreement and validating the model’s efficacy.