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rickman · August 30th 16, 10:53 PM posted to rec.radio.amateur.antenna

On 8/30/2016 4:01 PM, Ralph Mowery wrote:
In article ,
says...

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.

Well put Dave for a short answer.

The FM is infinite just as the light from a flashlight may be distance
wise,but as you get far enough away it is not detectable by most
instruments. As most of the power is in the first 8 kHz each side of
the center of the 5 khz deviated by 3 kHz audio, it was just decided to
call that the bandwidth and is good enough for most receivers with the
correct filters.

The 15 kHz spacing comes from years ago. I may be wrong on the spacing
of comercial FM being 60 kHz, but think it was at one time. I know it
was 30 kHz at one time and the deviation was set at 15 kHz. Then as the
bands got more occupied and the stability of the equipment improved the
comercial stuff just went to 5 kHz deviationa and cut the bandwidth in
half to 15 kHz.

I was not aware that FM broadcast radio was ever spaced at 60 kHz. My
understanding is the bandwidth is most of the 200 kHz channel spacing
which is a bit too close to prevent interference on adjacent channels in
many cases. Typically they don't assign adjacent channels in
overlapping areas.

As hams are not reqired to keep the spacing or deviation some areas did
go to 20 kHz spacing and 5 kHz deviation. Other areas went to 15 kHz
spacing and kept the 5 kHz deviation. If the rigs are not very well up
todate and the frequency and deviation set correctly there can be
problems with the 15 kHz spacing.

--

Rick C

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