# How to find the modulation index of an amplitude modulated signal from the spectrum analyser?

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.

(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


• you need to know your message signal's spectrum, otherwise: no chance. Commented May 19, 2021 at 8:15
• 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? Commented May 19, 2021 at 8:17
• 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. Commented May 19, 2021 at 8:18
• Isn't the modulated signal the same as message? Commented May 19, 2021 at 8:19
• 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! Commented May 19, 2021 at 8:20