Magnitude and Phase Calibration of Lock-In Amplifiers, and Analysis of the Noise Response

In this work, a method for the calibration of the magnitude and phase of lock-in amplifiers (LIAs) and the characterization of their noise response are presented. A simple calibration setup developed at INRIM is used to calibrate the magnitude and phase of digital LIAs. These quantities are typically loosely or not specified, respectively, by the manufacturers. Furthermore, since the low-pass filter of a LIA can introduce correlations, which may affect the correct estimation of the measurement type A uncertainty, the noise response of this instrument has been analyzed in terms of the Allan deviation for an autoregressive (AR) low-pass filter with different orders. The presented approach was tested on three units of the same instrument, proving to be consistent but also showing some unit-to-unit differences. The present results show that for the considered measurement settings a substantial improvement of the accuracy of LIAs up to the 10 kHz range can be obtained with commercial instrumentation. The magnitude error can be determined with about a 50-fold improvement in accuracy compared to the specifications of the tested instruments; the phase error, which is not specified, can be determined at the same time. The proposed method also requires a short time per calibration point (a few minutes).