Bw= 2x(D+M)

[KF6GUB]

N3JBH:  Been to both those sites; I still don't get the difference.  thx  Jim

[AC7ZN]

Hi Jim,

It might help to think of it this way:

1.  Your modulating signal is +-1 V maximum and goes from DC to 20 kHz in frequency.  You feed in a DC signal of 1 volt and measure how much the frequency deviated from the carrier.  This is the deviation, D.  The bandwidth occupied by a +-1v signal will be double this, as long as the modulating signal changes slowly.

2.  If you begin changing the modulation frequency quickly, additional sidebands form just like they do with an AM signal, but with FM the sidebands follow a mathematical Bessel function that is not as simple as AM or SSB.  However, the basic rule of thumb...'the higher the modulating bandwidth the wider the sidebands' still applies.  2M, where M is the maximum modulating frequency, is an estimate of the bandwidth occupied by most of the resultant sidebands.

3.  These two effects tend of sum so the formula you gave results.
 

73,
Glenn AC7ZN

[G3RZP]

M is modulation index and is the ratio of the deviation to the modulating frequency.

So if the modulation frequency is 1 kHz and the deviation (D) is 10 kHz, M = 10/1 = 10


The older ARRL handbooks are pretty good on this.

[KF6GUB]

Then the modulating frequency is not the fm carrier but is imposed on the fm carrier.    Correct?  thx  Jim

[N5KNG]

It may be helpful to think of the modulation process in terms of "information" and "carrier".  Thus, the information and the carrier are two different things.  The process of modulation alters (modulates) the carrier so that the resulting signal is a combination of the carrier and the information.  For FM, it is the frequency of the carrier that is changed, according to the information that is used to modulate it.  With demodulation at the receiver, the information can be extracted from the modulated signal that was provided by the transmitter.

The Navy has a document available that discusses these concepts in detail, with some examples.  See http://www.fas.org/man/dod-101/navy/docs/es310/FM.htm

[G3RZP]

Jim,

Yes, the modulating frequency is imposed on the carrier. So if you have a deviation of 10kHz and modulating frequency of 1 kHz, the modulation index is 10, regardless of if you have a carrier at 1 MHz  or 100GHz.