Frequency Synchronization Analysis in Digital lock-in Methods for Bio-impedance Determination

The lock-in method is one of the most frequently used methods for reconstruction of measured signals and as such frequently applied in the (bio)impedance method to determine the modulus and phase of the (bio)impedance. In implementation of the method in a (bio)impedance measurement device one has to consider possible non synchronized frequencies of the reference and the analyzed signals as well as potential sources of noise. In this work we analyzed these errors theoretically and experimentally. We show that both amplitude and phase errors depend on the relative difference of the frequencies of the reference and investigated signal as well as the number of integration periods. Theoretically, these errors vanish during the determination of the (bio)impedance modulus and phase. In practical implementation the inaccuracies appear at points of very low determined signal amplitudes due to the limited accuracy of analog to digital converters and are distributed around these points due to other sources of noise inherent in implementation of the measurement device.