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.

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

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.

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.



---
This email has been checked for viruses by Avast antivirus software.
https://www.avast.com/antivirus

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

In article , says...

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


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.


I should have been clearer. I was thinking of the comercial two way
radios like the public service of police and taxi cabss. Not the
FM broadcast stations.

The FM broadcast stations are deviating much wider than the 5 and 15
kHz we were talking about.

---
This email has been checked for viruses by Avast antivirus software.
https://www.avast.com/antivirus

In article ,
Ralph Mowery wrote:

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.

Yup. Here in NoCal, some parts of the 2-meter spectrum use 20 kHz
spacing, and others use 15 kHz. There was a proposal to move things
down to even narrower 12.5 kHz spacings a few years ago, but some
experiments (which I helped perform) demonstrated that a lot of the
then-available mobile and hand-held radios would suffer some pretty
severe adjacent-channel bleed-through - their IF filters aren't
sharp/narrow enough to avoid it. Getting people to cut their peak
deviation down to 2.5 kHz would also have been difficult (older radios
often don't have this available as an option, and those that do are
often easy to mis-adjust).

The 440 band is still on 20 kHz spacings. Keeping peoples' transmit
oscillators accurately centered within 1 kHz or so is harder, up at
those higher frequencies, and it pays to make allowance for some
amount of drift when doing the frequency planning.

In article ,
says...



Yup. Here in NoCal, some parts of the 2-meter spectrum use 20 kHz
spacing, and others use 15 kHz. There was a proposal to move things
down to even narrower 12.5 kHz spacings a few years ago, but some
experiments (which I helped perform) demonstrated that a lot of the
then-available mobile and hand-held radios would suffer some pretty
severe adjacent-channel bleed-through - their IF filters aren't
sharp/narrow enough to avoid it. Getting people to cut their peak
deviation down to 2.5 kHz would also have been difficult (older radios
often don't have this available as an option, and those that do are
often easy to mis-adjust).

The 440 band is still on 20 kHz spacings. Keeping peoples' transmit
oscillators accurately centered within 1 kHz or so is harder, up at
those higher frequencies, and it pays to make allowance for some
amount of drift when doing the frequency planning.

In NC, actually many of the southern states as the South Eastern
Repeater Association is the co-ordinating body, usually below 146 MHz
is 20 kHz and above 146 is 15 kHz spacing. As always there is some
oddball or non standard pairs being used.

At the state of the art and money wise it is difficult to go to the 12.5
kHz spacing. Even if the deviation is cut back to 2.5 kHz on the older
rigs it is my understanding they may produce enough 'trash' to cause
problems. The rigs will need to be designed to produce less phase
noise. As hams hold onto rigs for many years, going to much less than
15 kHz spacing and about 5 hZ deviation will take a long time if ever in
our lifetime.

I was licensed in 1972 and I think most everything around here was on
the 30 and 5 standards then. That was back when the ham rigs still
seemed to have IF filters of about 30 Khz or more. I remember the
Regency rigs did not even have a trimmer for the receive crystals.
As there were very few frequency counters many rigs were just tuned by
ear. Sometimes someone would have a rig with a discriminator meter and
the locals would just net to whatever he was on.




---
This email has been checked for viruses by Avast antivirus software.
https://www.avast.com/antivirus

Jeff wrote:

Yup. Here in NoCal, some parts of the 2-meter spectrum use 20 kHz
spacing, and others use 15 kHz. There was a proposal to move things
down to even narrower 12.5 kHz spacings a few years ago, but some
experiments (which I helped perform) demonstrated that a lot of the
then-available mobile and hand-held radios would suffer some pretty
severe adjacent-channel bleed-through - their IF filters aren't
sharp/narrow enough to avoid it. Getting people to cut their peak
deviation down to 2.5 kHz would also have been difficult (older radios
often don't have this available as an option, and those that do are
often easy to mis-adjust).

Hi

Just to point out that on 2m the Region 1 & 3 band plans used to use
25kHz spacing and moved to 12.5kHz about 20 years ago!!

The commercial world in Europe have used 12.5kHz spacing for even longer
on VHF.

Jeff

Adjacent channel interference is sometimes a problem, depending on the
width of your filters, the deviation of the adjacent station, and the
accuracy of the frequencies.
(FM stations often are accurate only to about 1.5 kHz and of course
when the station above you is 1.5 down it makes the interference worse)

While a 12.5 kHz spacing is used for repeaters here, generally the
frequency coordination is done in such a way that adjacent repeaters
are not 12.5 kHz apart.

In general, 12.5 kHz works well. Note that on 10m (and CB), the channel
spacing is only 10 kHz. That is more problematic, it requires a tiny
deviation and low audio cut-off frequency to do it well.