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 and the characterisation of their noise response are presented. A simple calibration setup developed at INRIM is used to calibrate the magnitude and phase of digital lock-in amplifiers. These quantities are typically loosely or not specified, respectively, by the manufacturers. Furthermore, since the low-pass filter of a lock-in amplifier can introduce correlations, which may affect the correct estimation of the measurement type A uncertainty, the noise response of this instrument has been analysed in terms of the Allan deviation for an autoregressive 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 lock-in amplifiers 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).