Load to capacitance transfer using different spring elements in capacitive transducers

Many physical sensors in which a displacement is the result of a change in the variable to be measured rely on the principle of capacitive transduction to transfer this displacement into a suitable electric signal. Commonly, the linearity of this transduction is one of the design criteria. The total transduction of physical load to capacitance change can be subdivided into the transfer from load to displacement and from displacement to capacitance change. The latter is non-linear due to its well-known hyperbolic behaviour. The first one — that of load to displacement — depends on the nature of the spring elements between the two plates of the capacitor. When, e.g., a rubber elastic spring is applied, the load to displacement transfer is also not linear. It is the aim of this paper to show that the two non-linear transfer functions of the mentioned subsystems result into a remarkably increased linearity for the transfer of the total capacitive transducer. The thus obtained theoretical relation is experimentally verified for the most favourable situation, using rubber elastic springs. The results are in good agreement with the theory.