We have blogged before about the advanced filtering technology of our M81-SSM synchronous source measure system, showing in a related application brief how the filtering can result in faster lock-in measurements. In particular, while discussing how the M81-SSM’s finite impulse response (FIR) filtering compares to the infinite impulse response (IIR) filtering traditionally used on a lock-in’s output filter, we point out that for suitable rejection of higher-frequency components, IIR filters can require long wait times for settled values in the measurement. In contrast, using the M81-SSM FIR output filter feature often allows for faster measurement times. However, that said, FIR filters often fail to provide adequate noise reduction due to their non-monotonic frequency response.
A recently published article in AIP Review of Scientific Instruments expands on this discussion — focusing on the additional hybrid filtering capabilities of the M81-SSM system. This article, authored by our own Jeff Lindemuth and others at Lake Shore*, discusses how the cascaded hybrid lock-in filter combines a short IIR filter with a longer moving average FIR filter. Two specific filter designs are proposed: one with the same measurement time as an IIR filter, and another with the same equivalent noise bandwidth (ENBW) as an IIR filter, termed the “fast hybrid filter.” The first design ensures that the hybrid filter matches the IIR filter’s measurement time while providing superior noise reduction. The second design focuses on achieving the same ENBW as the IIR filter but with a faster settle time, making it more efficient.
The article also provides analytic results for step response, settling time, frequency response, and ENBW of IIR, FIR, and hybrid filters and then examines the performance of the hybrid filter using noise measurements of low-value resistors. As indicated in the article, the hybrid filter provided an 18% reduction in noise compared to an IIR filter for the same measurement time.
Read more: “Hybrid Filter for Lock-in Amplifiers” (subscription required)
*Jeffrey Lindemuth, Emilio Codecido, Noah Faust, Houston Fortney, and David Daughton