Design formula for a printed disc capacitor

Abstract

An established formula for capacitance C of a thin metal disc printed on a dielectric substrate with height h and relative permittivity ${\epsilon }_r\ge 2.2$, backed by a conducting ground plane, is inverted into a closed formula. The latter yields disc's radius r for a given C and a given substrate, with an accuracy of 5 % of C or better if $r\ge h/2$. It will save the design engineer time, whose alternative is to resort to a numerical field solver and go by trial and error.

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