Accurate 3-D Capacitance of Parallel Plates From 2-D Analytical Superposition

The two conductor strip line is a classic transmission line structure which has been extensively studied and used in endless applications for decades. Unfortunately, the exact determination of the 3-D capacitance of this basic case is analytically intractable. It will be shown that accurate values of the total 3-D capacitance of a parallel plate capacitor with thin plates of any length, width, and separation can be determined from the superposition of the exact 2-D capacitance obtained from an analytic solution using elliptic integrals in a very simple manner. The accuracy is determined for a range of cases through a comparison of the analytic values with those obtained from a 3-D numerical calculation, using a work station with very large memory and processing capability. For most cases, the accuracy of the capacitance obtained by this superposition method falls nearly within the bounds of the numerical accuracy of the 3-D model and the elliptical integral evaluations. This superposition method is far more accurate than expected.