Constraints on Planar and Planar Interdigital Capacitors used in Sensors

Based on geometric considerations, we derive an approximate relation between the capacitance of a planar capacitor and the maximal frequency operation according to the basic formula of planar capacitors in electrostatics. The reciprocal formula results for maximal capacitance of a planar capacitor at a given frequency, for operation under the same electrostatic hypothesis. The formulae involve the square root of the ratio of the dielectric thickness to the relative dielectric constant, and a shape factor. Similar conditions are derived from geometric and EMI considerations. The results are extended to interdigital capacitors. Design considerations and limitations of the use of comb capacitive sensors in flexible circuits and in wearable devices are exposed. The main concern is the driving signal frequency and the electromagnetic interference (EMI). The discussion avoids the use of Smith charts, where the value of the inductance is required. The aim of the article is primarily educational.