A description of properties and errors of simple and stacked sensors

In this paper the physical sensing effect in a generic sensor is described as a transfer function from a measured input magnitude to the desired output magnitude. Parasitic effects such as the influence of non-constant environmental conditions, sensor ageing and, to a certain extent, also the effect of noise, quantization and hysteresis may be described by the use of additional input variables. Applying a second-order Taylor approximation in multiple variables, the generic sensor is approximated and a system of sensor parameters is generated. All steady-state sensor properties, among them sensitivity, parasitic and cross-sensitivity, drift, resolution, non-linearity, accuracy and the detection limit, are defined in one straightforward description. This system is used to mathematically analyse different cases of stacked sensors. In this way, the effects of well-known principles such as modulation or the use of a reference at different stages on the accuracy and the detection limit are analysed for generic sensor structures. As a result, the properties of a stacked sensor can be calculated if just some basic properties of the elementary sensors constituting the stack are known. For all designs, the behaviour of the stack follows a simple pattern.