Modulation index problem

[crazyjim30]

I stumbled across this problem. If a 2 kHz audio tone is tone causes a frequency deviation of 4 Hz, what is the modulation index? Since my iPad doesn't do Greek letters very well, I'm including what I THINK are the right formulas. Any help would be appreciated. I can do the math. I just need to know the formulas and maybe a little help in using them would be a good thing too.
Formula 1- modulation index = delta / modulating frequency
Formula 2- delta = modulator sensitivity * peak value of the modulating signal (in Volts)
Formula 3- modulator sensitivity = change in frequency / instantaneous modulating signal amplitude
Question 1- Peak value in volts? No volts in the problem. Makes me think I might not be using the right formula.

[rf+tech]

Hi crazyjim,

Your conclusions are correct on both counts - that there are no volt units given in the problem and formula 3 is not applicable. 

With this in mind, what does this tell you about formula 2?
Hint: In what units is amplitude expressed in?

The rest I'll leave as an exercise for the student...

RF+ Tech

[crazyjim30]

Amplitude is expressed in volts. As far as what it tells me about formula 2, I don't know. I'm missing the math required to understand this class. No problem, they say. It's a conceptual class, they say. Until exam time, then we're trying to do blankety-blank advanced coursework w/o the background.😡

[rf+tech]

Okay, formula 3 may need a bit more explanation. Modulation sensitivity (for FM) is expressed in kHz or MHz per volt - how far a carrier can be moved from its nominal center frequency per one Volt of modulating audio signal amplitude.

If we have 100 mV peak-to-peak of 2 kHz audio applied to a modulator with a sensitivity of 100 kHz/Volt, we can expect the modulator to produce 10 kHz total carrier deviation.

Now, applying formula 2 where delta = modulator sensitivity * peak value of the modulating signal, and using our example above, the peak signal amplitude is one half of the peak-to-peak, or 50 mV. So 100 kHz * 0.05 Volts = 5 kHz delta. We express this as +/- 5 kHz deviation.

Back to your original problem, we have now ruled out formula 2 and you have previously ruled out formula 3, leaving only formula 1.

In the original problem, we are given a carrier deviation (delta) of 4 Hz, produced by a 2 kHz signal, and asked to find the modulation index. Stated differently, modulation index is the ratio of how far a carrier is deviated to the frequency of the modulating signal (not the signal amplitude).

Hopefully you'll now have a clearer understanding and can post back with your solution.

RF+ Tech

[crazyjim30]

Just checking back in. My instructor wound up eliminating that problem on  that particular quiz. I encountered it again, word for word, during the final and was able to solve it. @RF+ Tech, thanks for the help.

Sent from my SM-G900V using Tapatalk