Estimation of the Signal Parameters Measurement Error for the Case of ADC Nonlinearity Approximation by Chebyshev Polynomial

Abstract

The phenomenon of nonlinearity of the ADC conversion function leads to the errors of different signal parameters as complex spectrum, reactive power, apparent power, active power, root mean square. In case of calculating of the signal parameters measurement error, it is necessary to take into account the ADC nonlinearity, since there are no simple procedures for its elimination that can be used in commercial devices. The paper considers a technique of describing of the nonlinearity of ADC transfer function by applying Chebyshev polynomials. This approach allows to effectively approximate the ADC nonlinearity and obtain an estimate of the error of such parameters as root mean square, amplitude spectrum, apparent power, reactive power and active power. Analytical expressions are obtained for each of the measured parameters, that make possible to calculate of the error estimate. The impact of the ADC nonlinearity form to the error estimation is considered. Conditions are obtained under which the measurement errors of the signal parameters take on the maximum values. A technique has been developed for the measurement error estimation of power parameters and spectrum when the case of typical shape of ADC nonlinearity and nonlinear parameters are known (dynamic parameters, differential nonlinearity – DNL, integral nonlinearity – INL). The obtained mathematical dependences are verified by comparing the simulation results and results of mathematical relations at special test points.