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REVIEW 3 major objections 6 minor 23 references

Software-defined lock-in demodulator for low-frequency resistance noise measurements

T0 review · 3 major / 6 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read A software-defined lock-in amplifier replaces commercial lock-in hardware and lowers the 1 Hz background voltage-noise power spectral density by about two orders of magnitude.

desk verdict A genuinely useful streaming software lock-in with clean code and a solid SR830 cross-check, but the headline two-order noise improvement is measured on the bare ADC and may not survive the SR560 preamp in the real measurement chain. read the letter →

arxiv 2412.00093 v2 pith:4DCD2ZT6 submitted 2024-11-27 physics.ins-det cond-mat.other

Tim Thyzel This is my paper · ORCID
classification physics.ins-detcond-mat.other
keywords software-definedlock-inamplifier1/fnoiseresistancelow-frequencymeasurementsdigitaldemodulationdataacquisitionreal-timesignalprocessingspectroscopy
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper claims that a software-defined lock-in amplifier can replace commercial lock-in hardware in low-frequency resistance noise measurements and outperform it. The key result is a background relative voltage-noise power spectral density at 1 Hz of about $2\times10^{-13}\,\mathrm{Hz}^{-1}$, roughly two orders of magnitude below the $\sim2\times10^{-11}\,\mathrm{Hz}^{-1}$ of the SR830 instrument, because the digital demodulator does not add amplitude-dependent $1/f$ noise. If correct, this would let researchers measure very low-noise devices without bridge circuits, using only an off-the-shelf data acquisition system and open-source code. The claim is supported by a comparison on a real device showing the two spectra agree within about 5%.

What carries the argument

The central mechanism is the streaming digital demodulation chain: a 24-bit $\Delta$-Sigma ADC samples the amplified DUT voltage and a simultaneous reference channel; the DUT stream is mixed element-wise with the reference, amplitude-corrected using an RMS detector that tracks the reference amplitude, low-pass filtered, and decimated. Filter state is carried across time-series blocks so the output is continuous, and a block-wise Observer pattern permits quasi-real-time display and low data rates. This replaces the analog mixer and filter of a hardware lock-in, and because the demodulation is numeric, the instrument's own semiconductor and algorithm noise does not scale with input amplitude.

What would settle it

Measure the background voltage-noise power spectral density at 1 Hz for the full chain — signal generator, SR560 preamplifier, and the software-defined lock-in — at $\langle V\rangle = 1\,\mathrm{V}$; if $S_V(1\,\mathrm{Hz})/\langle V\rangle^2$ rises from about $2\times10^{-13}$ toward $2\times10^{-11}\,\mathrm{Hz}^{-1}$, the claimed two-order advantage disappears in the configuration users would actually run.

Watch

Extended reading notes

Core claim

The paper establishes that performing the lock-in demodulation entirely in software yields a cleaner low-frequency background than the commercial instrument it replaces. With a pure sine input and identical source and load conditions, the software-defined system shows no amplitude-dependent $1/f$ noise up to $\langle V\rangle = 1\,\mathrm{V}$, whereas the SR830 background scales as $S_V(1\,\mathrm{Hz})/\langle V\rangle^2 \approx 2\times10^{-11}\,\mathrm{Hz}^{-1}$. At 1 Hz the software background is $S_V(1\,\mathrm{Hz})/\langle V\rangle^2 \approx 2\times10^{-13}\,\mathrm{Hz}^{-1}$, about two orders of magnitude lower. On a real DUT with strong $1/f$ resistance noise, the software and hardware spectra match to within about 5% over the measured range, confirming the digital processing preserves the signal.

Load-bearing premise

The two-order improvement was measured with the signal generator connected directly to the ADC, bypassing the SR560 preamplifier used in the real measurement chain; if that preamplifier contributes amplitude-dependent 1/f noise comparable to the SR830's, the claimed improvement would not hold for actual DUT measurements.

Editorial extensions

If this is right

  • Devices whose relative resistance noise is below roughly $10^{-11}\,\mathrm{Hz}^{-1}$ at 1 Hz become measurable without bridge circuits or cross-correlation setups.
  • The demodulator runs quasi-real-time on a general-purpose computer with off-the-shelf DAQ hardware, so it can replace lock-in hardware without custom electronics.
  • Decimation during acquisition keeps the output data rate low, making multi-hour or multi-day noise runs practical to store and process.
  • The author suggests that adding cross-correlation with multiple channels and preamplifiers, or using multiple reference channels, could suppress the residual correlated $1/f$ contribution further.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the residual correlated $1/f$ floor originates in the signal source, as the paper speculates, swapping in a lower-phase-noise generator should push the floor below $2\times10^{-13}\,\mathrm{Hz}^{-1}$; this direct test is not performed in the paper.
  • The two-order advantage was demonstrated without the SR560 in the signal path; repeating the background test with the preamplifier would show whether the full measurement chain keeps the advantage.
  • Because demodulation is software-only, the same acquired data stream can be demodulated at multiple carrier frequencies or with a software phase-locked loop, enabling multi-frequency noise spectroscopy or low-frequency impedance measurements without hardware changes; the paper notes the PLL extension but not multi-frequency demodulation.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 6 minor

Summary. The paper describes a software-defined lock-in demodulator implemented in Python, using an NI 9239 data acquisition system and streaming signal processing with real-time preview. The authors validate the frequency response against an SR830 lock-in on a real DUT showing 1/f resistance noise, and they measure the background noise of the software chain versus the SR830. The central claim is that the software lock-in achieves a relative voltage noise power spectral density SV(1 Hz)/<V>^2 of about 2e-13 Hz^-1, roughly two orders of magnitude below the SR830's 2e-11 Hz^-1, and that this improvement enables low-frequency resistance noise measurements without bridge circuits.

Significance. If the claimed improvement holds, this work is practically significant for low-frequency resistance noise spectroscopy: it offers an open-source, off-the-shelf alternative to commercial lock-in amplifiers with a much lower 1/f background. The paper's strengths include a reproducible open-source implementation, a streaming architecture with downsampling and real-time preview (a useful advance over earlier packages), and a direct, same-source comparison with a widely used commercial instrument. The frequency-response match to within 5% on a real DUT is a convincing transfer-function check, and the use of cross-correlation in Fig. 5 is a reasonable diagnostic. The main limitation is that the headline two-order improvement is demonstrated only for the ADC/demodulator chain without the SR560 preamplifier that is present in the actual noise-measurement setup.

major comments (3)
  1. [Section III, Figs. 2b and 4c] The two-order background-noise improvement is measured with the DS360 function generator connected directly to the NI 9239 ADC, whereas the full measurement chain in Fig. 2b and the real-DUT comparison in Fig. 4a insert an SR560 preamplifier before the ADC. The text explicitly states the direct connection, but the abstract and conclusion claim a system-level improvement ('our system offers superior low-frequency noise performance'). Because the SR560's noise, particularly any amplitude-dependent or 1/f component at the carrier frequency, could dominate the demodulated spectrum, the as-stated improvement is not yet supported for the configuration actually used in resistance-noise measurements. Please either repeat the background test with the SR560 in the signal path or clearly qualify the claim as applying only to the demodulator/ADC chain.
  2. [Section III, Fig. 5] The residual 1/f-like upturn in Fig. 5 is attributed to either the common reference channel or the sine source, based on the observation that it is fully correlated across channels. However, because all three demodulators share the same reference channel, the cross-correlation cannot distinguish between a source artifact and a reference-path artifact, nor can it exclude a contribution from the ADC's common-mode or clock path. This attribution is therefore speculative. The relative comparison with the SR830 is unaffected, but the absolute value SV(1 Hz)/<V>^2 ≈ 2e-13 Hz^-1 should be presented as an upper bound for the demodulator's own noise floor, not as a demonstrated property of the demodulator alone.
  3. [Section III, Figs. 4 and 5] The headline quantitative claim rests on single smoothed spectra with no repeated measurements, error bars, or confidence intervals. While the two-order margin is large enough that modest run-to-run variations would not change the conclusion, the absence of any uncertainty estimate makes the claimed value (and the implied universality of the 2e-13 Hz^-1 floor) less robust. Please provide at least one repeat measurement or an uncertainty estimate for the background spectra, or explicitly state that the values are representative single traces.
minor comments (6)
  1. [Section III, Fig. 4c] The legend 'Software (0.1 V, 0.3 V, 1 V)' is ambiguous because it is not clear which line corresponds to which amplitude, especially if the curves overlap. Please use distinct markers or a table to identify each amplitude.
  2. [Section III, Fig. 4c and Fig. 5] The paper says the software background 'does not exhibit any such dependence on the input amplitude', but the plotted curves appear to have a small spread at low frequencies. Please clarify whether this spread is within the expected smoothing/statistical scatter, or quantify any residual amplitude dependence.
  3. [Section III, text near Fig. 5] The phrase 'the 1/f noise magnitude is only approximately SV(f = 1 Hz)/<V>^2 ≈ 2e-13 Hz^-1' conflates the measured total background with the demodulator's own noise. Consider rewording to 'the measured background' or 'the system background'.
  4. [Section III, Fig. 4a] The relative difference of about 5% is quoted without specifying how the comparison was made after the SR830 spectrum was corrected for its filter response. Please state the correction method or reference.
  5. [Throughout] There are minor typographical errors, e.g., 'behavoiur' in Section III and 'futhermore' in the Fig. 1 caption. Please proofread.
  6. [Abstract and Introduction] The abstract says 'compared to high-end commercial lock-in instruments' (plural), but the comparison is with a single SR830 unit. Please temper the wording to 'compared to a high-end commercial lock-in amplifier' unless more instruments are tested.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the paper's performance claims are direct experimental comparisons, not derived predictions, and no fitted parameters are renamed as results.

full rationale

The paper makes no derivation from fitted inputs. Its central claims are empirical: the software-defined lock-in's output spectrum matches an SR830 on a real DUT to within about 5%, and its background voltage noise power spectral density at 1 Hz is measured directly by feeding the same sine source into both instruments. No parameter is fitted to the SR830 data and then used to 'predict' the software spectrum; the two spectra are independently measured. The cross-correlation analysis in Fig. 5 is a further measurement, not a consequence of the claim. The comparison in Fig. 4c is made with the function generator connected directly to the ADC, bypassing the SR560 preamplifier used in real DUT measurements; this is a limitation on the generalizability of the absolute improvement, but it is not circularity because the stated result is transparently about the configuration that was measured. Self-citations (Refs. 11 and 20) appear only in contextual remarks about DC checks and DUT noise properties, and they are not load-bearing for the software's noise-floor claim. The demodulator algorithm is standard lock-in DSP, and its correctness is checked against an external commercial instrument. Therefore, no step reduces to its own inputs, and no 'prediction' is forced by construction.

Assumptions & free parameters 0 free parameters · 4 assumptions · 0 invented entities

No fitting parameters were introduced; the central performance numbers come from direct spectral measurements. The main assumptions are standard DSP preprocessing, the validity of lock-in mixing, and the transfer of the measured direct-input background to the preamplified measurement chain.

assumptions (4)
  • standard math Standard lock-in demodulation: multiplying the DUT signal by the reference and low-pass filtering recovers the amplitude without adding baseband 1/f noise.
    Invoked in Section II and in the circuit descriptions (Fig. 2, Fig. 3); this is the foundational DSP operation the software implements.
  • domain assumption The DUT resistance noise is not bias-dependent for the AC-measurement scheme to be valid.
    The authors explicitly note in Section II that this needs to be verified with suitable DC methods, citing their own prior work (Ref. 11).
  • domain assumption The residual low-frequency 1/f noise seen in cross-channel correlation is caused by the common reference channel or the signal source, not by the software demodulator.
    Section III, Fig. 5: the cross power spectral density matches the single-channel spectrum, but the exact source is not identified; the authors speculate about oscillator frequency noise.
  • domain assumption The background measured with direct signal input, without the SR560 preamplifier, is representative of the full preamplified measurement chain.
    Section III, Fig. 4c: the performance comparison bypasses the SR560 that appears in the practical setup (Fig. 2b); this transfer is assumed but not tested.

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Cite this review

Pith. "Pith review of Software-defined lock-in demodulator for low-frequency resistance noise measurements." pith.science (2026). https://pith.science/paper/4DCD2ZT6

@misc{pith2026241200093,
  author       = {Pith},
  title        = {Pith review of: Software-defined lock-in demodulator for low-frequency resistance noise measurements},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/4DCD2ZT6}},
  note         = {Machine review of arXiv:2412.00093}
}
read the original abstract

The resolution of low-frequency resistance noise measurements can be increased by amplitude modulation, shifting the spectrum of the resistance fluctuations away from the 1/f noise contributed by measurement instruments. However, commercial lock-in amplifiers used for de-modulating the fluctuations exhibit a problematic 1/f noise contribution, which imposes a hard lower limit on the relative resistance noise that can be detected. We replace the lock-in amplifier hardware by equivalent digital signal processing performed using open-source software and off-the-shelf data acquisition systems. Compared to previous implementations of the lock-in principle, our solution offers real-time preview capabilities and is resource-efficient for long acquisition times at high sampling rates. Importantly, compared to high-end commercial lock-in instruments, our system offers superior low-frequency noise performance with a reduction of the voltage power spectral density by about two orders of magnitude.

Figures

Figures reproduced from arXiv: 2412.00093 by the authors.

Figure 1
Figure 1. FIG. 1. Comparison of the output signal of our software pack [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Data flow diagram of the software package. Each rectangle (except for the ADCs on the far left) represents a signal [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 4
Figure 4. a shows that the power density spectra ob￾tained by both methods match almost perfectly. Indeed, the relative difference is less than about 5 % over the whole frequency range, except at high frequencies, where the demodulator’s low-pass filter depresses the spectrum of the software method. Note that SR830 normally also exhibits this downturn, and in an even broader fre￾quency range, because it employs cascaded R-C-t… view at source ↗
Figures from the paper (1 more)
Figure 5
Figure 5. Figure 5: FIG. 5. Lower-frequency measurement of the noise back [PITH_FULL_IMAGE:figures/full_fig_p005_5.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

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