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We know that the displayed average noise level(DANL) and noise figure(NF) of a spectrum analyser is given by the following equation:

\begin{equation} NF_{𝑆𝐴} = 𝐿_{𝐷𝐴𝑁L}[dBm] + 174dBm −10 \cdot log_{10}(R𝐵W/1𝐻𝑧) +2.5 dB \end{equation}

where RBW is a resolution bandwidth 2.5 dB is some constant coming from a detector (anyway it is not clear for me, but it is a detail for now). By the way there is no signal sent to analyzer in the experiment.

So what I see that for some spectrum analyzer the DANL is about -90 dBm for RBW = 2.4 MHz, so I get the value of NF = 22dBm. Then from the NF equation \begin{equation} T = T_0 (10^{NF}-1) = 46500 K \end{equation}

So the question is, where is a catch, is it OK to have such an astronomic values? Could it come from all the electronics of the spectrum analyzer? Another question, what is the origin of the $NF_{SA}$ formula? I can understand that 174 dBm and the term of RBW comes from the noise of a resistor at 300K, but the term of $ L_{DANL}$ is not clear for me, is this just a definition

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  • $\begingroup$ A noise figure of 22 dB is pretty standard. It's probably in the specifications of the unit too. What were you expecting? $\endgroup$
    – tomnexus
    Nov 10 '21 at 15:20
  • $\begingroup$ @tomnexus I have a budget SA and it says DANL is -165 dBm/Hz, I'm not sure if this compares to 22 dB or not. $\endgroup$
    – Jack0220
    Nov 10 '21 at 15:39
  • $\begingroup$ @tomnexus, the temperature converted from the NF just looks to big comparing to 300K of room temperature $\endgroup$ Nov 10 '21 at 16:27
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A noise figure of 22 dB is pretty normal for a spectrum analyser.

Expressed as a noise temperature it looks like a large number, but there are many equations which yield unexpected and large numbers. Try calculating the noise temperature of a transmitter for example! Noise temperatures are convenient when they're below room temperature, and when you have other Kelvin-denominated temperatures like sky temperature. dB would work too but the numbers are small and don't add intuitively.

Noise figure can be improved by putting a high gain, low noise amplifier in front of the more noisy input. These amplifiers bring a big compromise - they are sensitive but easily overloaded by all the strong signals out there - FM broadcast, TV, cellphones. A spectrum analyser doesn't start with a low noise amplifier, it starts with an attenuator, mixer and a filter, hence the higher noise figure. See how every second question about SDRs asks about some unidentified strong signal that can be found every 5 MHz right across the band. A spectrum analyser is mostly immune to this, you can look at quite weak signals near to strong ones. And receive chains that depend on a low noise preamplifier, like GPS, have a narrow filter before the preamplifier, to prevent any of the strong signals from interfering.

On your question about $L_{DANL}$ - this isn't so much a fixed parameter of the instrument, as simply the input-referred (internal) noise of the receiver, displayed as a trace.

If you want to know where the correction factor comes from, and many other useful facts about noise and how to measure it, I recommend reading the whole of the Agilent Application Note AN 1303. It's no longer on their website but there are many copies floating around. Keysight now seems to offer AN 5966 4008 which covers the same subject but more aimed at all-digital instruments. It's not as easy or quick to understand.

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