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Linear Charge Density Approximation for Calculation of Capacitance for Parallel Rectangular Sheet Conductors in Three Dimensions

IP.com Disclosure Number: IPCOM000043421D
Original Publication Date: 1984-Aug-01
Included in the Prior Art Database: 2005-Feb-04
Document File: 2 page(s) / 40K

Publishing Venue

IBM

Related People

Weeks, WT: AUTHOR

Abstract

Ruehli and Brennan* have described an approximation for calculating capacitance between rectangular conductors in three dimensions. In their method, conductor surfaces are divided into rectangular cells. The surface charge density is assumed constant over each cell, the constant differing from cell to cell. In the case of plane conductors of finite length and width, but of negligible thickness, such that each conductor is the union of rectangles whose edges are parallel to the x and y axes of a rectangular coordinate system, the accuracy of the approximation can be improved by replacing the constant cell surface charge density by one that is linear in the x and y coordinates. Such an approximating function is given by equation [1].

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Linear Charge Density Approximation for Calculation of Capacitance for Parallel Rectangular Sheet Conductors in Three Dimensions

Ruehli and Brennan* have described an approximation for calculating capacitance between rectangular conductors in three dimensions. In their method, conductor surfaces are divided into rectangular cells. The surface charge density is assumed constant over each cell, the constant differing from cell to cell. In the case of plane conductors of finite length and width, but of negligible thickness, such that each conductor is the union of rectangles whose edges are parallel to the x and y axes of a rectangular coordinate system, the accuracy of the approximation can be improved by replacing the constant cell surface charge density by one that is linear in the x and y coordinates. Such an approximating function is given by equation [1].

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where the quantities lij, li+1,j, li,j+1, li+1,j+1 are the values of the charge density at the four vertices of the cell. To generalize the method of Ruehli and Brennan from constant cell surface charge densities to linear charge densities, such as in equation [1], it is necessary to evaluate integrals of the form shown in equation
[2],

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where a, b, c, and d are constants. The integral can be evaluated by finding a function f(x,y,x',y') such that,

(Image Omitted)

Substitution of [3] into [2] reduces the evaluation of the integral to 16 evaluations of the function f. To find f, y...