Uncertainty and Worst Case Analysis for a Low-Pass Filter Using Polynomial Chaos Theory

In this paper, the authors propose an analytical method to estimate the worst case in terms of uncertainty propagation in a measurement operation. The theory is exemplified with a specific application: power measurement with a signal conditioning stage including a low-pass filter. In AC power measurement the low pass filtering affects magnitude and phase of each harmonic component. The low pass filter is usually made of discrete components, which inherently contain parameter uncertainty. The effect of this uncertainty must be quantified to determine its effect on the quality of the power measurement. In this paper, the authors describe the use of Polynomial Chaos Theory (PCT) to quantify the effect of parameter uncertainty of a second order low pass filter such as the Sallen-Key filter. Furthermore, the authors demonstrate the use of PCT to obtain the probability density function (PDF) of the Sallen-Key filter given a certain parametric uncertainty. In particular it is shown how to use PCT to obtain the worst-case, expected and best-case output of the Sallen-Key filter without actually reconstructing the whole PDF. This result demonstrates the potential to determine significant boundary on the final measurement uncertainty.