Why so high values of noise température of a spectrum analyser?

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

• A noise figure of 22 dB is pretty standard. It's probably in the specifications of the unit too. What were you expecting? Nov 10 '21 at 15:20
• @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. Nov 10 '21 at 15:39
• @tomnexus, the temperature converted from the NF just looks to big comparing to 300K of room temperature Nov 10 '21 at 16:27

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.