In applications where low signal-to-noise ratios are encountered, the use of phase-sensitive detection (PSD) is highly advantageous and is applied widely. However, the characteristics of lock-in amplifiers that utilize the PSD technique, such as the linearity of the output and the gain of these instruments, have not been extensively evaluated. The author proposes a method for measuring the linearity characteristics of lock-in amplifiers and describes how this method was used to measure the linearity factor of three nominally identical commercially available digital lock-in amplifiers. The results of this study show that the linearity factor of these lock-in amplifiers can deviate from unity by more than 0.1% over a factor of 2 change in output. Moreover, the linearity characteristics of these lock-in amplifiers vary from one instrument to the next. The linearity characteristics were shown to be independent of the reference frequency, the time constant, and the temporal profile of the signal being analyzed. However, they were found to be dependent on the sensitivity settings of these instruments. The linearity characteristics of these instruments were observed not to change with time. This implies that, where the uncertainty contribution due to the nonlinearity of a lock-in amplifier is significant, the nonlinearity can be evaluated by using the method described in this article and can be used to apply corrections.
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