# Modulation Index

1. Apr 9, 2013

### davenn

hi gang,

just a quick clarification please :)

was looking at the Wiki articke on Frequency modulation
http://en.wikipedia.org/wiki/Frequency_modulation

This comment is in the Modulation Index section.....
The signal frequency is referring to the applied audio signal doing the modulating isnt it ?
Thats the way I read it when it goes on to say .....

Cheers
Dave

2. Apr 9, 2013

### sophiecentaur

Afaik, "Modulation Index" is usually a term applied to Amplitude Modulation and it is the constant B in the expression for an amplitude modulated signal:
A(t) = A0 (1+BCos(ωmodt))Cos(ωcarriert)
B lies between -1 and +1 (More than that will produce overmodulation which sounds highly distorted).

FM is much more difficult to describe and analyse. For FM, there is no limit to the deviation index that can be used and it is specified in terms of deviation frequency per volt of modulating signal. For starters, the deviation figure would refer to 'peak deviation'. However, FM is further complicated because it is common to use pre-emphasis of the modulating signal, in order to optimise the noise performance (demodulated FM noise has a 'triangular' spectrum) - which actually can turn it into Phase Modulation rather than actual Frequency Modulation. So the basic modulating signal would not look like the audio signal into the transmitter but very much HF boosted.
If wiki had used the term 'modulation frequency' then there might have been less confusion.
Yes, there is a very broad way of classifying FM systems into high deviation (wideband) and low deviation (narrow band). The noise performance for high deviation FM can be many times better than the equivalent AM signal but, for a deviation of 1, the noise performance is pretty much the same as for AM. This is not surprising because the first pair of FM sidebands are about the same level for narrow band FM and AM.

Analogue TV is / was transmitted as FM for satellite and terrestrial links - in which a very 'lop-sided' modulating signal (the TV waveform) produces a really weird looking FM spectrum - partly symmetrical and partly asymmetrical.

Another complication is that the FM sidebands extend to infinity (although you can truncate without too much distortion).

3. Apr 9, 2013

### davenn

Yes I agree,

In my AM transceiver repair days, modulation index was a well "bandied about" term. But wasnt one I was familiar with when it came to FM transmission

I get the impression from that Wiki article that the FM modulation index is basically a ratio of the difference of the carrier freq to the maximum modulated signal freq ie. + - 3.5kHz low index, + - 75kHz high index

it seems almost a pointless bit of info, as it's already described by saying what the FM deviation level is

Maybe I'm missing something ?

Dave

4. Apr 9, 2013

### the_emi_guy

Adding on to sophiecentaur's good input:

Your interpretation seems correct, and you are right, if you know both the FM deviation and the modulating signal bandwidth, then you also know the modulation index.
However, it may be a useful metric since it indicates the spectral efficiency vs. SNR tradeoff (High modulation index = high SNR but poor spectral efficiency).
It's also important to note that the occupied bandwidth is not necessarily the FM deviation, but depends on the modulation index.

FWIW, here is how I mentally get my arms around this...
1GHz RF carrier with a 10KHz deviation and the *extremely* low frequency modulating signal of one cycle per day (10^-5 Hz).
Once a day the RF carrier will sweep across the 10KHz deviation:
(1GHz - 10KHz) at noon on Monday
(1GHz + 10KHz) at midnight
(1GHz - 10KHz) at noon Tuesday.

Its intuitive that the occupied bandwidth will be simply 20KHz.

The modulation index is enormous (millions), and the Bessel function table that shows that actual spectral lines of the resulting signal would have millions of significant terms. It would be fair to consider that the signal is essentially "visiting" every frequency between (1GHz-10KHz) and (1GHz+10KHz).

If I increase the modulating signal frequency to once cycle per hour, the same reasoning can apply.

However, if I increase the modulating signal to 10KHz I can no longer use the above analogy. With 10KHz deviation, a 10KHz modulating signal
is modulating it "too fast" for it to visit every frequency. Bessel function tables show that, in this case, only 4 sidebands have significant energy in them.

More significantly, the overall signal bandwidth is *larger* than 20KHz (see "Carson's rule").

This may seem counterintuitive, since the carrier is only deviating by +/-10KHz, but remember that modulated AM has a non-zero bandwidth even though
its carrier frequency deviation is zero.

5. Apr 10, 2013

### sophiecentaur

AM is a linear form of modulation and, as such, the AM signal occupies a limited bandwidth, defined by the bandwidth of the modulating signal. FM is basically non-linear and has an infinite bandwidth. 'Carson' (hadn't given him a thought for twenty years or so - a blast from the past) is a good practical indication of effective spectral occupancy. But, from the start, the Pre and De- emphasis that is used in FM is very relevant to the whole thing and shouldn't be ignored when discussing deviation.
The difference between high and low deviation systems is well demonstrated if you google "FM spectrum" and press the Images button. You see a whole range of spectral shapes for different deviations which do not resemble each other at all. For low deviation, you see a set of a few sidebands, which get smaller as you go out. For high deviation, the spectrum analyser picture is like 'angel's wings', with a vast array of fence posts (sidebands), spaced by the frequency of the modulation, but at the extremes, there are two humps, due to the longer time that the carrier spends at the max and min of the modulating sinewave - giving more mean power at the upper and lower limits.
I googled to find typical spectra of FM TV signals but could only find one suitable link. It may hurt your brain to make sense of the plot but it is a good illustration of how FM can be very confusing to relate to - compared with dear old AM.

6. Apr 10, 2013

### davenn

Thanks Sophi and emi guy

good to know I was heading down the right path :)

Dave

7. Apr 10, 2013

### skeptic2

8. Apr 10, 2013

### sophiecentaur

9. Apr 10, 2013

### skeptic2

I think different countries may define deviation index differently. In the U.S. the deviation index is the peak deviation divided by the highest audio frequency transmitted which is a dimensionless number.

10. Apr 11, 2013

### sophiecentaur

OK, that makes better sense. I wonder what it signifies, though. In AM, the mod index tells you how 'loud' it gets and SNR would then relate to Carrier to Noise ratio. The FM index would, I suppose, tell you the general 'shape' of the spectrum of the FM signal when carrying the maximum programme frequency at maximum level, Could it tell you something useful about the SNR with a non pre-emphasised baseband signal, perhaps?

11. Apr 11, 2013

### skeptic2

Many years ago I worked with a phase modulated transmitter with a deviation index of 0.15. The sidebands as I recall were about 20 dB below the carrier. The receiver used a SNR activated squelch. I believe the principle effect of a larger deviation index is to reduce the capture ratio.