# I'm missing something when it comes to understanding FM

I understand why FM is preferred for music: noise is mostly amplitude modulated, FM yields much higher fidelity. I also understand why commercial FM signals have a much larger bandwidth than commercial AM signals: the signal spectra of the former are 5-10 times wider than the latter. I also understand the mathematics of FM, Bessel functions 'n all.

What I don't understand is the reason for using a large modulation index >> 1. A modulation index of 1 indicates that the width of the FM modulated spectrum is comparable to the width of the signal spectrum. If the modulation index is >> 1, the width of the FM modulated spectrum is much larger than the width of the signal.

It seems to me that the wider bandwidth doesn't provide any additional information. As a matter of fact, the signal power for a large modulation index is divided up among multiple carriers and sets of sidebands instead of being concentrated in a single carrier and set of sidebands.

Why is a large modulation index used?

• In addition to the sources given in the answers, I recommend the last chapter of Wozencraft, on twisted modulation.
– MBaz
Feb 3 at 13:52

In addition to the perspective offered in @Ash's answer, Claude Shannon touches on FM in his paper "Communications in the Presence of Noise" (Proceedings of the IRE, January 1949). He demonstrates, at least intuitively, how FM with a large modulation index is a form of forward error correcting code, just one that is all analog*.

Like any FEC, wideband FM tends to suppress errors at low signal to noise ratios, at the cost of having errors increase tremendously at high signal to noise ratios. It's just that with FM, the errors aren't bit errors, but rather the output SNR.

* Which, personally, I find mind-bendingly cool.

• Another insightful comment. To call Claude Shannon awesome would be an understatement. Feb 4 at 15:32

Large modulation indexes are preferred because the signal-to-noise ratio has a cubic dependence on modulation index ($$\beta$$).

$$SNR_{FM}=3\beta^2(\beta+1) CNR$$

Where CNR is the carrier-to-noise ratio. Source.

• I honestly did not know this. I googled a bunch of different variants of "FM what at the advantages of a large modulation index" and got nothing. I don't recall this in my signal processing books, either. Thanks. Feb 2 at 21:40
• Since the noise bandwidth goes up (and CNR correspondingly goes down) with (β+1), the "useful" effect on SNR is effectively β^2, right? Granted, that's still pretty good. Feb 3 at 19:01