Lock-in amplification based on sigma-delta oversampling

Lock-in amplification based on sigma-delta oversampling

Synchronous detection is used to detect and measure very low-level signals in the presence of significant noise. A defining characteristic of this measurement approach is the use of a periodic probe signal to excite the system under test. This is followed by mixing of the reference signal and its phase-quadrature with the measured signal. Standard analog to digital converters are employed, usually with the mixing and filtering performed digitally. Most practical high-resolution analog to digital converters employ oversampled sigma-delta modulation and are incorporated as a separate functional block. This paper derives a processing algorithm that combines the oversampled analog to digital conversion with signal mixing into one functional block. There are several important advantages of this approach. The computational complexity of the lock-in amplifier is substantially reduced, with no loss of accuracy. Moreover, the requirement for high-resolution analog-to-digital conversion is relaxed; it is replaced with low-resolution high-rate sampling, which is typically much easier to realize in practice. Experimental results are presented to demonstrate the correctness of the technique as determined via theory and simulation.

This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in Review of Scientific Instruments, 94 (5), 054706, 2023 and may be found at https://doi.org/10.1063/5.0144732