On 8/30/2016 3:30 PM, Dave Platt wrote:
In article , rickman wrote:

What is the total bandwidth of an FM phone transmission having 5 kHz
deviation and 3 kHz modulating frequency?

The correct answer is 16 kHz, (3 kHz + 8 kHz) * 2. But I don't get why.
The only page I've found so far that tries to explain refers to
"heterodyning" the carrier, the audio bandwidth and the maximum
deviation, Df. Df is not really a signal, it is just a parameter
describing the RF signal. Further, there is no hetreodyning.

Am I just getting hung up on terminology?

A bit, but your concern is reasonable - for FM you aren't
heterodyning, and the rules are a bit different.

FM modulation is mathematically more complex than AM/SSB. AM and SSB
involve multiplication of two sines (the carrier and the content) and
you end up with precisely two sidebands per content-tone (at
carrier+tone and carrier-tone). So, the bandwidth is easy to
determine... it's twice that of the highest frequency in the content
signal (for AM) and half that for SSB.

FM is trickier. If you work out the formula for the instantaneous
value of the RF carrier (given an information signal of a given
frequency and maximum carrier deviation) you end up with a "sine of a
sine" equation, and this is *not* as "well behaved".

In principle, the actual occupied bandwidth of an FM-modulated carrier
is *infinite*. If you FM a carrier with a 1 kHz tone, the resulting
RF spectrum contains discrete sidebands at 1 kHz offsets from the
carrier frequency, in both directions, going out "forever".

Fortunately for us all, the amplitudes of these sidebands drop off
very sharply once you get out beyond the maximum instantaneous
deviation of the carrier. The actual amplitudes of the sidebands are
the results of the Bessel functions.

So, we don't have to treat the occupied bandwidth as literally
infinite... we just treat it as the portion of the spectrum that has
enough energy in it that would interact with other transmissions.

What we tend to use (for most audio-modulated FM) is what's known as
Carson's rule (or rule-of-thumb). Add together the peak deviation,
and the bandwidth of the modulating signal, and that's the amount of
spectrum you need on each side of the carrier. So, you double this
number to get "occupied bandwidth".

So - a voice-audio signal of DC - 3 kHz, modulating an FM carrier by
up to +/-5 kHz, requires 2*(3+5) KHz of bandwidth, or 16k. Running FM
voice channels on 20 kHz separations is thus practical. In areas
where hams use 15 kHz channelization, it's best practice to keep peak
deviation down to 3.5 kHz or so.

Thanks, I've never derived the equation for an FM signal, so I wasn't
aware it was that complex. Now that you have explained the basis of it,
I don't need to actually go through the math, I'll believe Carson.

While I've got your attention, what is the basis for the 150 Hz
bandwidth for CW signals? What data rate (or symbol rate) is assumed?
I'm working on a WWVB decoder and would like to figure out the bandwidth
needed to detect the signal edges reasonably well (for various values of
"reasonable"). I expect these are similar since they are both pulse
width encoded.

--

Rick C