# A question about measuring white noise in practice

I have some confusion about practical aspects of dealing with white noise.

Let's say you want to quantify or view the white noise component of a power supply output or a constant transducer output. How is the white noise component be extracted from a measured signal in practice? Such a measurement can be done by a scope or data acquisition sampling.

But white noise power spectral is constant over infinite frequency. But how can such a signal as white noise be sampled then? If it has infinite bandwidth what should be the minimum sampling frequency when sampling white noise? Or it doesn't matter?

I know the sampling theorem but this white noise is hard to grasp when it comes to practice. Again an example would help. Let's start we have a 9V power supply and we have access to its terminals. One can see the switching noise from the FFT of the logged output signal as long as sampled at least twice the switching noise or more ect. But suppose one wants to verify the white noise component, what could be done in practice?

## 3 Answers

When you come to measure the wideband noise of a system, you start with a definition of the bandwidth you're interested in.

How do you define that bandwidth?

It may be a bandwidth that's relevant to your use (say 20Hz to 20kHz if it's an audio application), or it may be that it's limited by your test gear (my 'scope only goes up to 50MHz), but somehow, somewhere, you have to choose a bandwidth. If you're building your own test gear, or you don't know enough yet about your system or application, then it may be an educated guess.

Once you've chosen your bandwidth, you put an anti-alias filter in front of your digitiser (or maybe it's there already, defining your bandwidth). The AA filter passes the whole band of interest, and protects the digitiser from aliasing.

If you don't realise that the measuring instrument has chosen a bandwidth for you, then you may run into calculation or interpretation problems later.

What do you do next?

If your measurements of noise correlate with the behaviour of your system, so it allows you to predict behaviour, design improvements, reject and investigate faults, then it's job done. If you find it doesn't, or suspect there's noise at a higher frequency than you're measuring, then you have to revise your guess. Build, buy or rent better test gear, and measure it to a higher frequency. Rinse and repeat.

This iterative method of seeing what bandwidth is relevant is useful, as it means you don't have to measure to infinite frequency for every job. Start with the simplest measurement that you hope will do the job, then increase cost and complexity if you find it's necessary.

• In practice if we use an antialising filter as you say and we have the sampled data(of a DC output of a transducer or a supply) for one minute logged data, how can we quantify how much of this signal has wide band noise? We have the logged data samples we have the sampling freq. we can use a tool like MATLAB. Should we subtract the mean value of the sampled data from the sampled data? And what to do later to say anything about the nature of the noise component? Especially the wide-band. – GNZ Feb 13 '19 at 9:33
• @Genzo if you think that you've captured the entire band of interest, then take the spectrum. If the energy drops with increasing frequency and is insignificant at the top of your AA filter passband, then you may well have got all the noise that's there. If its shape follows that of the AA filter, then you probably haven't, and need to do a wider band measurement. This can be done with a fast 'scope, or a wideband power meter. Do the power meter measurement with and without the AA filter. If the with measurement is unexpectedly less than without, then your digitiser isn't seeing some power. – Neil_UK Feb 13 '19 at 12:22

To begin, there is no white noise in practice. The noise is always gets screwed/filtered by load network (wire inductance/pad capacitance etc.) and measurement network (probe / scope / ADC bandwidth).

I suspect you mean how to characterize "wide-band" noise that can emanate from power sources, from Zener diodes, etc. with possibly interposed with regular ripples, or something like that.

To get a sense (get confident estimates) of "noise floor" component of a signal people use so-called "anti-aliasing filters" in front of data samplers, and then sample the signal in accord with Nyquist-Shannon-Kotelnikov-Whittaker sampling theorem. This gives you an idea of the amplitude and shape of the noise floor within the bandwidth of your filter. If in doubt that the noise is much wider than your anti-aliasing filter passes through, you double the filter bandwidth and double the sampling rate, and compare the noise amplitudes where they overlap. And so on, until doubling the bandwidth of your data acquisition system doesn't change the shape of power spectrum, or/and when the result fits the shape of thermal noise floor.

• I would like to vary the antialising filter curt off as you mentioned. Do you in practice use active or passive first order RC filter for antialisaing in general? Or is there a filter type used for such purpose that one can vary by a pot ect? – GNZ Feb 13 '19 at 9:38

All electronic components have non-zero size, or they do not exist. With non-zero size, there is a computable energy stored in the electric fields.

Given an energy in the electric fields, we can compute the capacitance required.

Given the capacitance, we can use Vrms = sqrt(K * T / C) to provide the

TOTAL INTEGRATED THERMAL NOISE.

For 10 picoFarads, at 290 degrees Kelvin, the Vrms is exactly 20.0 microVolts RMS.

Again, that is the TOTAL INTEGRATED THERMAL NOISE.

Thus independent of the bandwidth, we know the total noise (RMS).

Switched_capacitor_filter design uses this math.

You can walk thru any circuit where you know the capacitance at a node, and be able to predict the Total Integrated Thermal Noise.

And if you have NO other capacitors except that one node, and no dependent sources, you will be correct.

• I don't understand anything. Imagine I give you a power supply a scope and a sampling data acquisition system also a data analysing tool like MATLAB; and want you to quantify the white noise component. What do you do in practice to measure the white noise and quantify it. A practical method if exists. – GNZ Feb 13 '19 at 2:27
• Your scope (and the 10MegOhm probe) will be much noiser (random electron noise) than most circuits, unless you amplify the noise before feeding the scope probe. ---------- and one of my points with the anwer using sqrt(k * T / ) was to hint at your need to estimate the BANDWIDTH, so you know if the scope is adequate. What is the bandwidth of 1.6K Ohm resistor into 10pF capacitor? and what is the total integrated noise? – analogsystemsrf Feb 13 '19 at 2:32
• Why do you write very implicit? Do you want to say it is impossible to measure the white noise component? – GNZ Feb 13 '19 at 2:40
• Can you use a 7A22 Tek plugin? The noise floor is approximately 20 microVolts RMS, when the plugin has both (+) and (-) inputs tied to ground. Thus the plugin is displaying its own random electron noise, in its highest bandwidth condition. Does this make any sense? Assume the input overvoltage protection resistor is 1Kohm, which produces 4 nanoVolts RMS per rootHertz of bandwidth. At 1MHz bandwidth (the plugin has variable bandwidth), the 4nanoVolts is scaled up by sqrt(1,000,000) or 4nV * 1000 == 4 microVolts RMS. I recall seeing about 10microVolts RMS, thus 1Kohm is too low an estimate. – analogsystemsrf Feb 13 '19 at 4:12