Determination of circular microstrip disc by Noble's variational method

In the paper, Noble's variational method is applied to the calculation of the static capacitance of a circular microstrip disc by using a linear combination of two types of charge distributions, namely, a uniform charge distribution, or gate function, and the classical form of the charge distribution for the infinitely thick slab, or Maxwell's function. The variational method reduces the dual equations describing the microstrip problem to the evaluation of three similar integrals, which can then be evaluated efficiently and accurately by the Gauss-Laguerre quadrature. It is found, as a rule, that the method gives a more accurate representation of the charge distributions on the disc, yields values of capacitance which are within better than 0.4% of the values obtained from a numerically accurate method and is capable of being implemented on a programmable calculator, e.g. the HP -41C.