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.