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My aim to is compute the modulation index(u) of a amplitude modulated waveform but I only have access to its power spectrum from the spectrum analyser.

I attached an image from the spectrum analyser.

Power spectrum analyser

(Note: The spectrum analyser has an input impedance of 50 ohms).

The carrier has a power of -26.6 dBm and the two sidebands have power of -38.5 dBm each.

Quite obviously we know the modulation index must be less than 1 because the carrier has more power - but how do I find the exact modulation index?

My thought process:

  1. First I converted the dBm to watts.
  2. Then I found the voltage using P=(V^2)/R, for carrier and sidebands and we know R would be like 50.
  3. Then I just did modulation index= mp/Ac where mp is the voltage in the message signal and Ac is the voltage in the carrier signal which is computed in step 2.

After doing all this I get a u of 0.25. This sounds kind of correct but what do you guys think?


***clear;clearvars;clc;clearAllMemoizedCaches

m_db= -38.5 ; % message power dBm

mpow= (10^(m_db/10))/1000 % message power in watts

c_db= -26.6;  % carrier power dBm

cpow=(10^(c_db/10))/1000  % carrier power in watts

mv= sqrt(mpow*50) % message voltage

cv= sqrt(cpow*50) % carrier voltage

mu= mv/cv % modulation index= message/carrier

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  • \$\begingroup\$ you need to know your message signal's spectrum, otherwise: no chance. \$\endgroup\$ May 19, 2021 at 8:15
  • \$\begingroup\$ Reply to Marcus, I know the message signal has a frequency of 64kHz but I don't know the voltage of it. Its power is -38.5 dBm in each sideband. Is that enough info? \$\endgroup\$ May 19, 2021 at 8:17
  • \$\begingroup\$ Well, you know the spectrum/power of the message signal, or of the modulated signal? If only the modulated signal: not sufficient, the modulation index tells us exactly how the relationship between message signal PSD and unsuppressed carrier is. \$\endgroup\$ May 19, 2021 at 8:18
  • \$\begingroup\$ Isn't the modulated signal the same as message? \$\endgroup\$ May 19, 2021 at 8:19
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    \$\begingroup\$ no. That's the point of a modulation index: you got the carrier coming through, and the modulation index tells you how much, in the end. Different message signals subject to different modulation indices lead to the same RF spectrum. Back to comment 1! \$\endgroup\$ May 19, 2021 at 8:20

1 Answer 1

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The modulation index is commonly defined as the ratio of peak voltages; the peak voltage of the message signal per the peak voltage of the carrier. Index >1 causes distortion in envelope detectors, but not in synchronous demodulation.

There's comments which try to explain that unfortunately you cannot derive the time domain message signal from your coarse spectrum. You must know or guess it otherwise.

If the message happens to be sinusoidal you have already successfully calculated that the sideband peak voltage divided by the carrier peak voltage is 0.25

But there are 2 sidebands which both have 50% of the peak voltage of the signal sinewave. Thus the modulation index is 0.5

If the message is not a pure sinewave the case is complex. Do the resolution bandwidth even cover the sidebands or not? impossible to decide from the given data. I'm afraid you must make a reference measurement and find the message amplitude which generates the same spectrum with the same analyzer settings. You, of course, must have the message signal available.

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  • \$\begingroup\$ Thanks for this! I think you've help me solve this conundrum. I know the message signal is defo a pure sine wave (not triangle or pulse stream) but its amplitude I don't know. The resolution bandwidth(RBW) is small and it covers the sidebands I'm being told, the RBW is not big so it doesn't obscure the harmonics insides. That part about the side bands having half of the message voltage is key I think because I didn't know that before. \$\endgroup\$ May 19, 2021 at 9:53

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