# Electrical – Quantifying white noise with a spectrum analyzer

microwavenoise-spectral-densityspectrum analyzerwaveform

The setup of my problem is as follows. I have an experiment in which I want to apply a noisy voltage with a white (flat) spectral density over a large frequency range, say 0 to 7 GHz for example. Not only do I want it to be white, I want to be able to tune its amplitude A. I plan to do so by using an AWG and generating Gaussian noise with zero mean and a variance of square root A; one can derive that for gaussian noise with a vanishing mean

$$S(f) = \sigma^2 = A$$

Moreover, I have access to an AWG with a sample rate of up to 50 GSamples, so the frequency range should be attainable as well.

One problem I now have however, is that I need to quantify how well the amplitude I set on the AWG actually corresponds to what is produced. This is because I do not actually generate a new time trace with different amplitudes, I simply produce 1 trace (I can make it 16 Gpoints long) and I change the peak to peak voltage it places the points into. That makes it a bit unintuitive to see what V_pp corresponds to what A.

So my idea was to use a spectrum analyzer and simply measure the spectral density that is being output for a specific V_pp. It'll allow me to verify that the spectral density is actually flat as well. So this is what I started doing, but I am running into trouble due to my limited understanding of how to operate the spectrum analyzer.

The problem is that I do not know how to choose the resolution bandwidth and the video bandwidth in such a way that the resulting spectrum is as accurate as possible. What I mean by that is that, by changing these bandwidths, the actual amplitude of the spectral density measured by the spectrum analyzer also changes, quite considerably. So how do I decide which values make the most sense?

From what I read about the spectrum analyzer, the resolution bandwidth allows for the discrimination of signals with closely spaced frequency components. So as my noise is supposed to be white, should I make this bandwidth as small as possible, to discriminate as many frequency components as possible?

Similarly, the video bandwidth determines the capability to discriminate between two different power levels, as far as I understand. Should this then also be set as low as possible?

It seems obvious to me that my interpretation of the above cannot be correct, as in that case most scenarios would simply boil down to setting these bandwidths to low values. There has to be something more nuisances that I am missing, and this is what I am asking your help for.

As an aside, I will be applying the voltage to a resistor to produce a current, which will be used to produce a flux, which will be sent through squid loops in a Josephson junction. So I suppose there is also the question of if the noise the spectrum analyzer sees (both in the frequency domain and the amplitude domain) is trivially related, or if there are filters and such which complicate things entirely. However, I think at this stage this is not too important. Knowing exactly what signal I sent in is a good starting point before thinking about what arrives.