A Numerical Solution for the Round Disk Capacitor by Using Annular Patch Subdomains

Abstract

Abstract-A numerical method is presented for determining the static charge distribution and capacitance of a round disk capacitor. Based on equivalent surface charge distributions, an integral equation subject to the boundary conditions is transformed into an algebraic equation by using the method of moments. In the proposed scheme to eliminate the discretizing errors often encountered in other techniques, annular patch subdomains are introduced, not only to improve the accuracy of solutions, but also to reduce the matrix size of the resultant equation. By solving the transformed algebraic equation, the charges per unit area on the interfaces are numerically determined. With use of the free charge on plates obtained by using annular patches, the capacitance is more accurately calculated. The equipotential lines around a round disk capacitor are also calculated.In order to show the usefulness of this method, the employed scheme is applied to a single circular disk with an exact solution, and to the dielectric filled capacitor partially covered by plates. Those results are examined and discussions are also made to support the validity of the presented scheme.

Moment method analysis for capacitance and charge distribution of dielectric coated metallic disk and closed truncated cone isolated in free space

“…Close agreement of the data on the capacitance per unit radius of the disk for these parameters, C/r = 70.768 pF/m, to that computed by analytical method (8e 0 r), 70.832 pF/m justifies the validity of the analysis. The result of the proposed method 70.768 pF/m is matching with the result available in [21], 70.55 pF/m with good accuracy. The result available in [12], 68.36 pF/m resulted into lesser accurate capacitance value compare with the result presented in this paper, 70.768 pF/m, because of the consideration of rectangular subsections in [12].…”

“…Capacitance is a very important circuit parameter needed for the analysis of electrostatic discharge (ESD), which causes EMI as mentioned earlier. The electrostatic modeling for the evaluation of capacitance and charge distribution of finite metallic bodies of different geometrical shapes like rectangular plate, cylinder, truncated cone, paraboloid, hemisphere, cube, and the like, which are widely used in the orbiting spacecraft, is discussed in . Metallic bodies of spacecraft are covered with dielectric material for thermal control.…”

Analysis of Charge Distribution on Rectangular Microstrip Structures

“…1 are widely used in various microwave devices, such as microstrip meander delay lines [1,2], slow-wave deflecting systems [3], metamaterials forming [4,5] etc. RMS are also successfully used for the analysis of physical models, for example, complex planar structures [6][7][8], microstrip discontinuities [9][10][11], etc. Main characteristics of an RMS are charge distribution on the microstrip section or total capacitance of this sec- * corresponding author; e-mail: edvardas.metlevskis@el.vgtu.lt tion.…”

Evaluation of Amount of Blood in Dry Blood Spots: Ring-Disk Electrode Conductometry

“…Conversely, K will decrease with increasing D and also asymptotically approach a limiting value K ∞ as D approaches infinity. Solutions to similar problems have previously been advanced by finite element , or similar “annular patch subdomain” methods for capacitance probes. The only extant analytical equation for conductometry with interdigitated planar electrodes is applicable solely to a solution of semi-infinite boundaries …”