Bounding of thermal Σ-Δ modulators output for sensors

Analytical bounds for the output of electrothermal Σ-Δ converters are derived considering a generic M-pole thermal filter. Derivation is based on a Fourier analysis of the open loop circuit and the results have been compared with simulation of the circuit using a C program and parallel computing. Parameters such as uncertainty, operation frequency and sensitivity can be calculated for a given application. As an example, the values of a two-pole thermal circuit derived from experimental measurements of a water flow meter based on an electrothermal Σ-Δ converter have been used to analyse the effects of the value of the flow and of the operating frequency on the analytical bounds and how they compare with detailed simulations