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Fast-Convergent Expression for the Barrel-Plate Capacitance in the Physics-Based Via Circuit Model

The widely used analytical formula for the barrel-plate capacitance in the physics-based via circuit model involves an infinite summation, which requires a truncation during practical computations. Such a truncation is problem-dependent and prone to either underestimate the capacitance value or ruin the computation when truncating too late. This letter proposes a fast-convergent expression of the barrel-plate capacitance based on a convergence study of the original formula. The proposed expression comprises a well truncated and a closed-form part, whose computation is more efficient and free of truncation error. It is validated against quasi-static solutions and measurement.