Influence of the ADC Errors on the Frequency Measurement Error for the Case of Applying of the Quadrature Demodulation Technique

Frequency measurement is one of the most important tasks in measurement technique today. The method based on quadrature demodulation is widely used to measure frequency of the electric power networks. The frequency measurement error by using this method contains two components: instrumental (associated with the imperfection of the used chips) and methodical (associated with the applied measurement method). The instrumental component associated with used chips imperfection (primarily the analog-to-digital converter – ADC) is discussed in this paper. The additive, multiplicative components error components nonlinearity and quantization error are considered. It is shown that the additive and multiplicative components practically do not affect to the frequency measurement error by the method under consideration. Particular attention is paid to ADC nonlinearity, since for most ADCs it prevails over quantization error and cannot be compensated for by approaches such as zero adjusting and calibration. To represent nonlinearity, the “worst case” method, approximation by polynomial functions, and representation of nonlinearity as random (stochastic) function are considered. Analytical expressions were obtained for estimating the frequency measurement error by the quadrature demodulation technique when it is represented by the discussed approaches. It is shown that the largest error occurs for nonlinearity, which form is close to pseudorandom. A simulation model of frequency measurement by this method was designed by Matlab and Simulink software packages, taking into account the considered ADC imperfections.