Spectral analysis of spectrum analyzer

Question

Using measures from a spectral analyzer, I am a bit confused on how to properly compare the power of each spectral line with the fourier coefficients (Parseval).

Take this signal:

Take its spectrum:

My experience with spectrum analyzers being limited, I attempt to compare what I expect with what I read.

The Fourier series coefficients of the ramp signal are: $$ D_n = \frac{-jA_{pk}(-1)^n}{\pi n} $$

So I expect a single spectral line on the spectrum analyzer to have power: $$ P_n = 2 \cdot |D_n|^2 $$ Where the factor 2 is due to the signal being real (taking into account both contributions at -f and f).

And so, for the first spectral line (at n = 1), I'd expect to have: $$ P_n = 2 \cdot \left( \frac{0.1 \cdot (-1)}{\pi} \right)^2 \approx 2.02642 \cdot 10^{-3} W $$

Now, converting the spectrum analyzer's dBm to watts: $$ P_{experimental} = 10^{(P_{dBm} - 30)/10} = 10^{((-13.85) - 30)/10} = \approx 4.12098 \cdot 10^{-5} W $$

It seems I have a somewhat huge error on this measure. However, it seems the spectrum measures are not entirely uncorrelated with the Fourier series powers, in the sense that the factors between the measures and the actual powers calculated using Fourier series seem constant. It seems to be a simple scaling error.

Maybe I miss something, and I wondered if anybody would maybe see something on the instruments captures I don't see.

Answer 1

So here are a few hints;

If you account for the 20 dB attenuation, you get a number that is much closer to your estimate, but off by a factor of 2.

(The picture of your spectrum analyzer says "Att: 20 dB" on the top.)

To resolve that factor of 2, you could try using the mean amplitude instead of the max amplitude in your estimation of the power at the first peak.