Accurate 3D Capacitance of Parallel Plates from 2D 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. Such lines with assumed zero thickness conductors have been used as a standard for calculation validations, comparisons and for many other uses. Unfortunately, the exact determination of the 3D electromagnetic E and H field of even this basic case is analytically intractable for all but the most simple cases, and hence is either approximated with 2D solutions by assuming infinite length, or by large scale numerical computations which are rather complex and time consuming. The 2D solutions assume the fields are uniform in the direction of the line length and hence neglect any fringe fields in this orthogonal direction. Simple methods to achieve the full 3D solution with high accuracy are thus highly desirable and the subject of this work. It will be shown that accurate values of the total 3D capacitance of a parallel plate capacitor having thin plates of any length, width, and separation can be determined from the superposition of the exact 2 dimensional capacitance obtained from an analytic solution using elliptic integrals, in a very simple manner. The accuracy is determined for a range of cases by comparison of the analytic values with those obtained from a 3D numerical calculation using a 64-bit 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 3D model and the elliptical integral evaluations. This superposition method is far more accurate than would normally be expected.