Webinar: From Noise to Knowledge

This blog post accompanies our webinar From Noise to Knowledge.

A big thank you to Nadine Nabben and Marvin A. Weiss from the University of Konstanz who presented their recent experimental results, showing how to extract meaningful information about noise. The recording is available here.

Thank you to everyone who joined the webinar and participated in the lively Q&A session. The answers to all the questions, along with a summary of the content, can be found below.

Summary

The webinar was divided into three parts:

• Tutorial: What is noise and how to measure it.
• Measuring magnetization fluctuations using the anomalous Hall effect (Nadine Nabben).
• Measuring ultrafast spontaneous spin switching using femtosecond noise correlation spectroscopy (Marvin A. Weiss).

Part 1: What is noise and how to measure it

When measuring noise, it is important to be able to distinguish noise components at different frequencies, because this allows us to identify the source of the noise and the underlying processes. Therefore, one typically measures the noise spectral density which shows the noise amplitude (or noise power) as a function of frequency. A schematic illustration of typical noise sources is shown in Figure 1.

For a detailed explanation of the mathematical background, please refer to the blogs by my colleague Mehdi about how to measure noise and the noise analysis of signal components including amplitude, phase and quadrature components.

In the webinar, we discussed three techniques to measure noise and their respective advantages and disadvantages. We also gave a live demo of the techniques using the MFLI Lock-in Amplifier (see recording).

1. Using Lock-in Detection

To measure the noise spectral density with a lock-in amplifier, you can follow these six steps:

• Demodulate at a reference frequency f_ref
• Record the result as the X or Y component
• Repeat the measurement many times to record a time trace
• Calculate the standard deviation using this equation: \(\sigma = \sqrt{\frac{\sum (x_i - \mu)^2}{N}}\)
• Normalize by the measurement bandwidth
• Repeat for different frequencies to get the full frequency spectrum

If you use a Zurich Instruments lock-in amplifier, these steps are implemented automatically using the built-in analysis tools.

Sweeper: You can do a noise amplitude sweep to perform all the steps above and get the noise spectral density in a custom-defined frequency range with a selectable resolution and precision.

Spectrum: If you are interested in noise with a high frequency resolution around a specific frequency, you can use the Spectrum tool to look at the FFT of the demodulation result. Spectral density calculation, power correction and filter compensation are done automatically, if activated.

2. Using an oscilloscope

Noise spectral density can also be measured with an oscilloscope, such as the Scope tool in LabOne, available in all our lock-in amplifiers. Here you can either use the built-in FFT calculation, or record a time-trace and calculate the noise spectral density from the Wiener-Khinchin theorem by post-processing. This method gives you a full frequency spectrum and is especially useful when interested in noise at very low frequencies (below 1 Hz), where the noise amplitude sweep is very time-consuming since it is based on individual measurements.

However, beware of artifacts due to the FFT operation:

• You need to choose window functions to avoid spectral leakage (more information in this blog)
• The effect of the window function needs to be compensated (amplitude or power correction).

With the LabOne Scope tool, these corrections can be done automatically.

When analyzing the data, it is important to note that the FFT also contains information about coherent signals, if there are coherent signals at certain frequencies.

3. Probing noise optically

In order to measure ultrafast noise, that is on timescales where electronics reaches the limits, it is possible to probe noise optically by imprinting the signal onto optical pulses. In this case, the frequency limit is given by the time delay between two pulses – which can be on picosecond timescales.

For more details, please have a look at our application note, together with Marvin A. Weiss.

Part 2: Measuring magnetization fluctuations using the anomalous Hall effect 

By Nadine Nabben, University of Konstanz

In this part, we discussed how magnetic noise measurements can yield valuable insights into magnetic domain wall dynamics in a ferromagnetic thin film. The anomalous Hall effect, with its linear dependence on magnetization, serves as an effective tool for detecting these magnetic fluctuations. Information encoded in the noise spectrum – particularly in its amplitude and frequency dependence – allows to distinguish between different underlying magnetic processes [1]. Two primary types of magnetic noise are: Barkhausen noise, resulting from abrupt changes in the magnetic domain configuration (exhibiting a 1/f² spectral dependence) and domain wall jittering (characterized by 1/f noise).

[1] Nabben, N. et al., Phys. Rev. Research 6, 043283 (2024) 

Part 3: Measuring ultrafast spontaneous spin switching using femtosecond noise correlation spectroscopy

By Marvin A. Weiss, University of Konstanz

In this part, we presented Femtosecond Noise Correlation Spectroscopy (FemNoC) - an optical technique for probing incoherent magnetic fluctuations on ultrafast timescales, beyond the bandwidth limits of conventional electronics. FemNoC extracts polarization fluctuations induced by transient magnetization noise on two femtosecond optical probes via the magneto-optic Faraday effect. These fluctuations are detected by separate polarimetric detectors, subharmonically demodulated with a lock-in amplifier to extract the pulse-to-pulse fluctuations, and then correlated to retrieve the spin noise autocorrelation (see Fig. 1) [2-4].

FemNoC was applied to the canted antiferromagnet Sm_0.7Er_0.3FeO₃ near its spin-reorientation transition, thereby resolving temperature-induced softening of the quasiferromagnetic magnon mode and furthermore uncovering a new form of ultrafast stochastic behavior: picosecond random telegraph noise [2].

2. Weiss, M. A. et al. Discovery of ultrafast spontaneous spin switching in an antiferromagnet by femtosecond noise correlation spectroscopy. Nature Communications 14, 7651 (2023).

3. Weiss, M. A. et al. Subharmonic lock-in detection and its optimization for femtosecond noise correlation spectroscopy. Review of Scientific Instruments 95, 083005 (2024).

4. Weiss, M. A. et al. Quantifying the amplitudes of ultrafast magnetization fluctuations in Sm_0.7Er_0.3FeO₃ using femtosecond noise correlation spectroscopy. Preprint at https://doi.org/10.48550/arXiv.2501.17531 (2025).

Q & A

Q1: For magnetic materials four-probe method, is there any effect of probe materials?

A1 (Nadine): For my samples, it was not necessary to optimize the electrical contacts. My microstructured Hall bars are entirely fabricated from the magnetic material and I connect them to the gold pads of the chip carrier with aluminum bond wires.

Q2: To measure noise in magnetic materials, what is the optimized data acquisition rate?

A2 (Nadine): As I mentioned during the webinar, there is the scope rate and scope length that define the resolution of your noise spectrum. So, to measure low-frequency magnetic noise, a small scope rate is enough and by then setting the scope length, you can define the minimum frequency of the noise spectrum. Thus, there is no "optimized" data acquisition rate, it just defines the frequency range of the noise spectrum. For my case, it is often sufficient to have a scope rate of about 7 kHz and a scope length of 2^15.

Q3: What does the amplitude of 1/f noise tell you in the case of magnetic domain fluctuation measurement?

A3 (Nadine): A higher amplitude in 1/f noise indicates larger fluctuations in the magnetization, often due to more active or less stable domain walls. Thinking in the picture of anisotropies: A domain wall must overcome a local energy barrier to fluctuate. If it has enough energy, it can easily cross this barrier, leading to stronger fluctuations - and thus higher 1/f noise.

Q4: How do you efficiently record/store time-dependent noise as plotted in the lower graph?

A4 (Nadine): For each magnetic field value I approach, I measure around 10 to 50 time traces, each with approximately 2¹⁵ to 2¹⁸ data points. After each time trace, the voltages measured by the MFLI are read out, and after all the time traces for one magnetic field value, the values are stored in an .hdf5 file. This process is repeated for all (between 50 and 200) magnetic field values, and in the end, the file size reaches about 0.5 GB (sometimes up to 30 GB). So it's somewhat inconvenient but not too much to evaluate it 'normally.' HDF5 is convenient as a file format because you can easily read individual slices without loading the entire file. The waterfall plot is rasterized, plotted only up to 30 Hz, and the plot itself is saved as a PNG to reduce file size.

Q5: Does the magnetisation fluctuation happen due to the fluctuation in the external magnetic field?

A5 (Nadine): I had the same question myself, so I already looked into it further. I measured magnetic noise in a sample where the magnetisation is not saturated at 0 T. So I could compare the magnetic noise spectrum with the electromagnet power supply turned OFF vs ON. It was clearly visible that the electromagnet did not introduce any significant additional noise.

I also repeated the measurement using a Halbach magnet array, which provides a stable field and eliminates external magnetic field fluctuations. The same magnetic noise was observed, confirming that the noise originates from the sample itself and not from the magnetic field source.

Q6: How is the internal stress of the sample changing the spectral response?

A6 (Marvin): While we have not investigated this in detail, I suspect that the stress of the sample may severely change the fluctuation properties/spectral response via modification of the internal magnetic anisotropies (e.g., magnetocrystalline anisotropy). In the paper I presented during the webinar, we see that the fluctuation magnitude increases with decreasing magnetic anisotropy, as is the case at the critical points of the spin-reorientation transition of the measured SmErFeO₃ orthoferrite. At the same time, the frequency of the corresponding magnon mode is significantly lowered/softened. So it can be expected that strong magnetic anisotropy decreases the signal strength, but at the same time increases the fluctuation frequency.

However, how exactly such a stress-induced anisotropy change would manifest is entirely nontrivial in my opinion and may depend, for example, on the lattice structure of the sample or the crystallographic axes where the stress is dominant.

If the question is targeted towards the more “macroscopic” fluctuations like Domain walls or Barkhausen jumps, then I believe the physical mechanisms are similar: Stress → Change in magnetic anisotropies → stabilising/destabilising of magnetic configuration → decreased/increased fluctuations.

Q7: What is the physical significance of the coefficient of 1/f noise ? Why is 1.8 ...it depends on dimension, right? 

A7 (Nadine): The coefficient 1.8 is the result of the averaging of noise spectra with shape 1/f and 1/f². When measuring the Hall voltage in the steep part of the hysteresis several times, many steps occur in most of the time traces (yielding a spectral shape of 1/f²), but there are also some time traces where no fast/irreversible change in the domain wall configuration happens (1/f noise). That is why one averaged noise spectrum in the steep part of the hysteresis may show a 1/f^1.8 dependency. And in the less steep part of the hysteresis, Barkhausen steps may only happen in a few number of time traces, leading to an averaged noise spectrum with a spectral shape of 1/f^1.2, near 1/f.

Q8: Without having strong magnetic Anisotropy, how effective is it to measure noise using optical mode? What is the best resolution we can achieve in this method? 

A8 (Marvin): This question requires a bit of further explanation, which is why I did not want to answer it during the live webinar.

In the paper that I presented during the webinar, we see that the fluctuation magnitude increases with decreasing magnetic anisotropy, as is the case at the critical points of the spin-reorientation transition of the measured SmErFeO3 orthoferrite. At the same time, the frequency of the corresponding magnon mode is significantly lowered/softened. So it can be expected that strong magnetic anisotropy decreases the signal strength, but at the same time increases the fluctuation frequency. It is actually advantageous in terms of signal strength to probe systems with small magnetic anisotropies. But then the major advantage of our technique, which of course is the very large bandwidth, is meaningless. So, in summary, it is a trade-off of signal strength and frequency bandwidth.

Regarding the resolution, I would like to refer you to our most recent manuscript:
M. A. Weiss et al., Quantifying the amplitudes of ultrafast magnetization fluctuations in SmErFeO using femtosecond noise correlation spectroscopy, arXiv:2501.17531 (2025)

Here, we quantify the resolution of magnetisation-induced Faraday rotation to be approximately 0.52 µrad²/(mW*√n), where n is the number of averaged correlation time traces. So this gives the resolution of our setup as a function of probing power and measurement time, abstracted in terms of measurement repetitions. nV/Hz

Q9: For long-time noise measurements, how do you avoid the Joule effect (could give heating deviation in nsd)? What is the Barkhausen noise value in that case and how could you differentiate it from flicker noise in ambient environment?

A9 (Nadine): The current through the sample is low enough that heating effects aren’t a problem. Even after a long measurement time, I do not see any drifts (one measurement routine sweeps the magnetic field in one direction and then back in the opposite direction, so I would see a drift if the last Hall voltage deviates from the first ones).

Barkhausen noise has a spectral shape of 1/f^2.

In order to identify flicker noise from the environment, I measure the Hall voltage noise with the sample’s magnetization fully saturated. Here, it is clearly visible that the background noise consists only of the intrinsic noise of the MFLI (at low frequencies) and Johnson-Nyquist noise from the sample resistance. Any additional 1/f noise (e.g., from the current through the sample) would be visible here and could be prevented with better shielding. 

Q10: I have an application with a few-microsec pulse that produces a phase shift in a few-MHz continuous wave. I can see the phase shift in the Plotter if I open up the LPF bandwidth to a few hundred Hz. I'd like to be able to measure phase shifts within the few-microsecond duration of the pulse. Obviously, that would increase noise, but I wonder what consequences opening up the LPF bandwidth would have for the phase measurement.

A10: There is always a trade-off between measurement speed and signal-to-noise ratio. One way is to just try it out with the MFLI. Alternatively, you can look at Table 1 in our whitepaper about lock-in detection. Here you will find the settling times of the filter as a function of the time constant. Let’s say you want to have 90% settling of the filter, then you have to wait 6.68 time constants (using a 4th-order filter). To detect a 10 µs pulse, you would then need a time-constant of below 1.5 µs (or a 3dB bandwidth above 46 kHz) – if I did the math correctly. This is possible.

The other challenge is that the continuous data transfer rate is limited to 100 kSa/s, corresponding to a time-resolution of 10 µs. If you want to detect smaller changes, you can use gated data transfer as described in this blog, which allows to increase the data transfer to 857 kSa/s during a limited measurement window.

Whether or not you will be able to see the phase shift in your final experiment will, of course, also depend on the noise level of the experiment.

Q11: Is it possible to measure accurately the signal around -120dB, below the noise floor (when the dynamic range of the VNA = 100 dB)?

A11: The definition of the dynamic range is typically the ratio between the largest and smallest measurable value. From this perspective, it is not possible to accurately measure at -120dB when the dynamic range is 100 dB. However, two things should be noted: 1) Often, dynamic range is specified with a single value, but it can depend on the input range and the frequency. There are configurations where the device's performance is better than the specification. 2) For lock-in amplifiers, instead of the dynamic range, often the dynamic reserve is defined. For example, for the MFLI, we specify a dynamic reserve of 120 dB, which means, for example, that a 10 nV signal can be measured down to 1% accuracy in the presence of a 10 mV signal. However, different manufacturers unfortunately have different definitions of dynamic reserve, and we at Zurich Instruments use a very demanding definition.

Q12: How can machine learning be used in such noisy measurement data, and what kinds of insights can be gained?

A12: Machine learning certainly holds a lot of potential for the analysis of noise data. It could be used for prediction: by analyzing different noise measurement datasets, it might be possible to predict the base choice for the modulation frequency in an experiment, for example. Additionally, it could be used for data mining, finding correlations or unknown properties in a set of noise measurements.

Q13: Is it possible to post-process (FFT) a plotter series of time-dependent demodulated data? If using a carrier freq. where amp noise is low (eg few kHz), then can we measure with a lower noise floor than standard FFT in scope mode?

A13: Yes, it is possible to post-process a plotter series of time-dependent demodulator data. However, please note that you need to normalize by the measurement bandwidth, and you need to be careful with artifacts due to the FFT operation. More information in this blog post. The safe solution would be to use the LabOne spectrum tool, which does exactly an FFT of the time trace – and in the Spectrum tool, there are built-in functions for the spectral density calculation, filter compensation and power correction (as you saw during the live demo).

Using the demodulated data for the noise analysis is faster compared to the Scope FFT, in the case when you are only interested in the noise around a certain carrier frequency. However, the noise floor is the same because the noise floor is a physical quantity related to your setup; it does not depend on the measurement tool. (At least not on the software tools, the noise floor does depend on hardware configuration, such as the input range).

Q14: Is it possible to use one demodulator to lock on one signal, such as a laser pulse, and a second demodulator to lock on some of the background noise? I.e. is can you remove noise in this manner?

A14: Yes, it is possible to use a second demodulator on a different frequency (provided that you have the Multi-Demodulator / Multi-Frequency Option available on your instrument). However, it is unfortunately not possible to remove the background noise in this way. In fact, you would even increase the noise in the measurement if you subtract the two measurements because the noise at the two frequencies is uncorrelated. The mathematical explanation is the following:

• Let’s say we measure the signal of the laser pulse at frequency f₁. The measurement captures the signal (let’s denote it with S) and the noise (N).
• At a different frequency f₂, we measure only the background noise (M).
• If you subtract the two measurements, you will get S+M-N.
• Then you need to take the variance to determine the noise, which gives: var(S+N-M) = var(S) + var(N) + var(M) = 0 + var(N) + var(M).
• There you see that the noise is increased because the variance is added.

So if you want to reduce the noise, you need to try other approaches. One idea would be to split the signal and use a cross-correlation measurement, as described in this application note. This helps if you are limited by the input noise of the instrument. In many cases, however, you are not limited by the input noise but rather by other noise sources (laser noise, etc). In this case, it is best to analyze the noise environment (using the tools that I presented in the webinar) to choose the best modulation frequency where there is low background noise, and to optimize the noise environment of the setup.

Q15: Wondering if we could measure and analyze electron mobilities in an atom?

A15: Electron mobilities can be characterized with various techniques involving our instruments. For electrical devices, this is possible using transport measurements, as described on our application page. Additionally, it is possible to extract electron mobilities from THz spectroscopy (I have actually had a collaboration on this topic during my PhD, here is a link to the article).

Q16: C an you study stochastic resonance with these techniques?

A16: Our instruments are actually commonly used to study non-linear systems, and an interesting field is the chaotic regime. The built-in analysis tools, such as the frequency sweeper and the time-domain Plotter, are very helpful to characterize the hysteresis of a nonlinear device as a function of excitation voltage, for example. Additionally, we can analyze the non-linearities by measuring multiple higher harmonics simultaneously or doing backbone measurements.

Q17: What considerations should one take to measure temperature-dependent noise?

A17: The techniques that we presented in the webinar can all be used at different temperatures, so from a measurement perspective, there are no differences, but you, of course, need a system to stabilize the temperature. Any additional control system can introduce noise (e.g., due to pumps or vibrations), therefore, you could consider characterizing the background noise at various temperatures without a sample before the real measurements.

Q18: I work with organic thin Film electronics and my device suffers from trap noise due to material defects and other factors that we want to explore. What measurements and methods are to be used for that? Any special tips?

A18: Deep-level transient spectroscopy (DLTS) is a great technique for defect characterization. You can find out more on our application page.

In addition, we also have an application note about the technique, where we show how to perform DLTS MFIA Impedance Analyzer combined with the DynaCool System from Quantum Design for temperature control.

Q19: How would you recommend measuring specifically Johnson-Nyquist noise for a high-precision thermometry application?

A19: I would suggest two approaches:

• Using the noise amplitude sweep using the Sweeper, which I showed in the demo. With this, you can analyze the noise over a large frequency range.
• Alternatively, you can also monitor Demod X and/or DemodY over time using the Plotter tool (or stream the data via the API, of course) and then calculate the standard deviation of the time trace at this particular frequency. This should work because Johnson-Nyquist noise is almost independent of frequency (at room temperature – at low temperature, one would need to check the frequency dependence). This approach gives you a nice time evolution of the noise/temperature. Note that the normalization by the measurement bandwidth needs to be done in post-processing.

A nice explanation can be found in this blog post. At the bottom of the blog, there is also an example of measuring the thermal noise of a 2.2 kΩ resistor. This is an interesting example because the thermal noise at room temperature is only 6 nV/√Hz, which is already close to the input noise of the MFLI (2.5 nV/√Hz). But the blog post also shows that the correct result can be obtained by subtracting the input noise from the measurement (this needs to be done in the noise power).

Q20: I perform Noise measurements every day with MFLI. I've used Demod X Noise. When should I use Demod Y Noise?

A20: In most experiments, the noise of Demod X and Demod Y is the same. However, as I mentioned during the live Q&A, there are some applications, such as squeezed light, where the state is prepared such that the noise of the quadratures is different. If you use the Sweeper, then you get both results at the same time, so it is easy to check whether there is any difference.

Q21: Could you build 1/f Extrapolation from 100k down to lower Hz into MFLI software? I do overnight measurements, but getting “projected” low frequency is useful BEFORE doing overnight.

A21: Thanks for the suggestion, we will keep this in mind for future product development features. We have a “linear fit” in the math tools, but this is an actual linear fit, not a linear fit on a log-log plot. For now, I can only suggest running the noise amplitude sweep in “reverse” mode, and then exporting the data as csv (before the measurement is finished) and plotting it with Python, etc.

Q22: I need to get agreement between Spectrum Analysis and MFLI in a common band, like 1MHz.

A22: If you compare the noise spectral density in the LabOne Spectrum tool with a noise amplitude sweep in the Sweeper, you will get the same results, as I showed in the demo. It is important that you activate “spectral density”, “filter compensation” and “power correction” (note that power correction is only available in the latest LabOne version, please update to 25.04, for example). The last thing to note is that the data transfer rate (i.e., the Spectrum frequency span) needs to be significantly larger than the demodulator low-pass filter bandwidth. If this is not the case, the demodulated result is undersampled, leading to folding of high-frequency noise, which then wrongly leads to an increase in noise amplitude -> feel free to try this out to see the difference.

Q23: Was the water in the video from Obersee by the Uni?

A23: Finally, no the video from the lake in Marvin’s part was not recorded at Obersee but at Schmugglerbucht😊.

Q24: When using Zurich instruments, the R value is lower than X or Y for a signal. Why?

A24: For a signal, R = √(X²+Y²), showing that the R value is larger or at most equal to X or Y. For the noise of R, X, and Y, it is actually important to note that R has a Rayleigh distribution, while X and Y have a Gaussian distribution, and the corresponding noise is smaller. The mathematical background is nicely explained in this blog post by my colleague Mehdi.

Q25: What are some of the best resources for using ziPython for coding one's own functionality with Zurich instruments?

A25: We have a large repository with examples on Github: https://github.com/zhinst/labone-api-examples

Q26: Zurich instruments use LabOne: What are some of the key differences between how the Plotter, Scope, and Sweeper work?

A26: In short:

• The Plotter shows the time trace of demodulated signals (and other signals are available, such as PID Error, etc). The data stream is continuous with a user-defined rate.
• The Scope shows the raw input signal (before any signal processing). The sampling rate depends on the instrument, e.g., 60 MSa/s for the MFLI. Due to the high data volume, the Scope shows individual shots of the signal.
• The Sweeper allows to measure the response when sweeping a parameter. This can be frequency (for a frequency-response analysis), but also many other parameters, e.g., amplitude, phase, etc.

You can find a nice overview of all LabOne tools here.

Q27: What are the most robust / simplest methods for eliminating noise in photoconductors?

A27: There are two things: measurement setup and the sample itself. For the measurement setup, you need to optimize cabling (use shielded cables, avoid long cables, avoid loops), keep the temperature stable, and avoid vibrations. The good thing is that you can monitor whether there is an improvement by performing noise measurements with the MFLI before and after some changes. About the sample itself, here it really depends on your sample fabrication and I cannot provide an answer. For the analysis part, in addition to doing the noise measurements that I discussed during the webinar, you could perhaps also consider deep-level-transient spectroscopy (DLTS) to analyze defects in your device.

Q28: What ZI products are used to measure spectral density?

A28: The measurement tools and techniques that I presented during the webinar (and were used by Nadine and Marvin) are available in all our 5 Lock-in Amplifiers, and also in our MFIA Impedance Analyzer.

Q29: Why is the noise spectral density higher at lower frequencies?

A29: There are different noise components, such as the white noise (the same for all frequencies), 1/f noise, and noise spikes due to pick-up at specific frequencies. Both the spikes and the also the 1/f noise (obvious by the name) are higher at lower frequencies. There are typically more spikes at lower frequencies because there are lots of noise sources in the environment, e.g., from the power grid, acoustic noise, and vibrations. And regarding the 1/f noise, this is typical in electronic devices (also known as flicker noise) and comes from impurities, for example. For a more detailed answer, please refer to the literature on different noise sources and noise colors, such as white noise, pink noise, etc.

Q30: If we take a long time for measurement. How do we isolate the system from the environment, like temperature fluctuation, vibration noise?

A30: This is a science by itself, and it also depends on what type of setup you have (optical, transport,…), but here are some tips:

• The building infrastructure has a big impact, e.g., ideally you want to have a constant temperature, be mechanically isolated (often in the basement), far away from magnetic noise (for example, due to railway tracks).
• Use properly shielded coaxial cables and make sure that cables are shielded all the way to the sample, if possible.
• Avoid long cables (and especially loops of cables), which can, for example,e pick up magnetic noise. Some labs also twist the cables together to avoid loops.
• Avoid mechanical vibrations, by putting pumps or other vibrating parts on a different table.
• Avoid ground loops.

Optimizing the experiment can take a long time, but the good thing is that you can just try different cables/configurations etc., and then always perform another noise measurement. And then you will see whether it has gotten better or worse.

Q31: For electrical noise measurements, could you please elaborate on the DUT connection to the tool, and is it possible to use a probe station? Is there any specification that one should consider while connecting the DUT to the tool? 

A31: There are a lot of things that need to be optimized to make sure that you are measuring the noise from the sample, and not just noise from the environment. Some tips are:

• Use properly shielded coaxial cables and make sure that cables are shielded all the way to the sample, if possible.
• Avoid long cables (and especially loops of cables), which can, for example, pick up magnetic noise. Some labs also twist the cables together to avoid loops.
• Avoid mechanical vibrations by putting pumps or other vibrating parts on a different table.
• Avoid ground loops.

These are just a few things; optimizing the setup is a science by itself. The good thing is that you can just try different cables/configurations etc and then always perform another noise measurement to check whether it has gotten better or worse. You can do this without a sample, e.g. just shorting the probes.

Q32: In the Spectrum module, does the transfer rate have to be much larger than the Filter BW? What happens if it is, let's as,y only twice as large?

A32: This is an important consideration; the data transfer rate should ideally be significantly larger than the filter bandwidth. The reason is that the Spectrum tool samples the demodulation result, and here we can have the same artifacts that can always occur when sampling a signal. If you have (noise) components at frequencies that are higher than the sampling rate, then these components will be undersampled and will be folded down into the frequency spectrum. This will then increase the measured noise, making the noise amplitude measurement incorrect.

Q33: What is the range of frequencies possible for noise measurement using MFLI?

A33: With the MFLI, the frequency range of the MFLI is DC to 500 kHz (or up to 5 MHz with the MF-F5M Frequency Extension Option). Noise measurements are possible in the entire frequency range.

• For low frequencies, it is important to note that the measurement time is increasingly long. For example, to measure a frequency of 100 mHz, you need to measure for 10 s to get just one period. For the noise measurements, you need to analyze how the amplitude at the frequency varies, meaning that you need to measure multiple periods. Therefore, even though it would in principle be possible to measure noise down to µHz frequencies, I am not sure whether anyone has done so in practice. In Nadine’s paper, she is presenting data down to 50 mHz.
• For high frequencies, when using the Noise Amplitude Sweep (Sweeper tool) or the Spectrum tool, the frequency is limited to the maximum demodulation frequency (500 kHz or 5 MHz). If you use the Scope tool, you can get the FFT up to 30 MHz (limited by the Nyquist theorem, the sampling rate is 60 MSa/s). However, note that there is a 10 MHz analog low-pass filter at the input to avoid aliasing effects -> therefore, this attenuation needs to be considered if one wants to interpret data above a few MHz.