How does signal analyzer go from Vrms to Vrms^2?

[alltherc]

I remember reading a long time ago that when you have a PSD (such as would be given on a SA) that the units of Vrms^2 imply a load of 1 Ohm.

Suppose I want to measure the noise PSD at 1kHz in a 1Hz bandwidth using an ideal BPF and an oscilloscope.

That is, suppose I have this setup:

My scope will measure:

Vx = Vin*RL2/(Rs + RL2) [RMS]

To convert this to how a SA display it, is it sufficient to simply square Vx? Then I have Vx^2

OR do I need to scale it as well to account for my load impedance?

The reason I am asking is because I have an oscilloscope with an FFT function.

For every point along the FFT it gives a value in Vrms per unit BW.

I want to compare my results from my scope to results obtained from a signal analyzer. But the signal analyzer gives results in Vrms^2 per unit bw. (Suppose I'm only interested in 1Hz bw right now). Basically I'd like to use my scope in place of my signal analyzer. But the units are different...

[w2aew]

PSD = Power Spectral Density.

Since it is indicating Power - there most definitely has to be an assumed impedance.  Most of the time, 50 ohms is assumed for nearly all RF applications.  75 ohms for video/CATV applications.  600 ohms is common for audio.  If you are comparing to a standard RF Signal Analyzer or Spectrum Analyzer, then it is most likely using 50 ohms as the load/reference impedance.

The "Spectral Density" part means that the result is normalized to a 1Hz measurement BW.  Many Signal Analyzers do not offer a real 1Hz resolution BW filter, thus will perform a calculation to get there.  More modern signal analyzers will perform this measurement using a discrete Fourier Transform (like FFT or Chirp Z) in order to arrive at the 1Hz effective resolution BW.

Your scope FFT gives you Vrms^2 so that you can divide by your impedance to arrive at Power.  If you want the Signal Analyzer and the FFT reading to match, then you'll have to make sure that you use the same load impedance in both cases (because the source impedance of the thing you're measuring will determine the power delivered to a given load).

[alltherc]

Does the scope give a voltage density as well? Is there any care that needs to be taken to take that into consideration?