[aprssig] APRS Bandwidth

Stephen H. Smith wa8lmf2 at aol.com
Thu Jun 25 04:43:47 CDT 2009

G0JXN Jim wrote:
> It has been suggested that the 300bd APRS signals can be considered 
> both as FM or AM signals. Dealing with the FM approach first using 
> Carson’s Rule we have that 98% of the power will lie within the bandwidth:
> Bt=2(pF+Fm)
> Where Bt = bandwidth, pF = deviation & Fm = modulating frequency
> pF = 100Hz (being half the tone spacing) & Fm = 150Hz (being half the 
> baud rate)
> Bt = 2(100+150) = 500Hz
> This would sit neatly in the requirement of the 500Hz bandwidth 
> requirement but FM signals have sidebands that go on ad infinitum, 
> albeit declining rapidly.
> While the first sideband at + & -150Hz would be within the 500Hz 
> bandwidth the second at + & - 300Hz would not and it would be only 
> some 20% of the carrier. This would not fit in with the UK license 
> requirement ‘that not more than 1% of the mean power of the 
> transmission falls outside the nominal modulated carrier bandwidth’.
That's the whole point of Carson's Rule -- it takes into account the 
total energy in ALL of the sidebands. If it defines the effective 
bandwidth as being where 98% of the energy is located, then only 2% of 
the energy would remain in ALL of the higher order sidebands combined.

> In any event the argument is flawed in that an FM signal only has one 
> carrier that moves between the deviation limits not two as suggested.

Nothing was said about "two carriers". With FSK, there is only ONE RF 
signal moving +/- 100 Hz from a center frequency (i.e. "carrier 
frequency") midway between the mark and space frequencies. Since you 
never have "no modulation" (i.e. you are always sending either a "1" or 
a "0"), the "unmodulated" center resting frequency of the carrier never 
appears.You are always at either "peak deviation high" or "peak 
deviation low".

[Telecomm regulations and commercial/military users typically DO specify 
the "frequency" of an FSK signal by referring to the phantom center 
frequency +/- so many Hz shift; i.e our standard North American 30M APRS 
channel would be quoted as: "10,149.30 Khz +/- 100 Hz", rather than the 
ham convention of saying something like "use mark/space frequencies of 
10,149.20 and 10.149.40 KHz" or "mark frequency of 10,149.40 with shift 
of 200 Hz". ]

If the modulation is truely square wave (i.e. like data), the effect is 
that the single RF signal is always either on the mark or space freqs 
(but not both at the same time), and never at the midpoint "carrier" 

The only way to visualize FSK as "two carriers" is to consider it as a 
pair of CW transmissions with key-up on one frequency always 
corresponding to key-down on the other freq.

Now the occupied bandwidth becomes whatever the bandwidth of two 
separate CW signals 200 Hz apart, each keyed at the rate of 150 
dits/second, consume. [At that keying rate and spacing, the keying 
sidebands of the two signals would overlap substantially.]

With both CW and FSK, a major factor in determining the effective 
occupied bandwidth is the rise/fall time of the keying waveform. A pure 
square wave or infinitely-fast on/off CW keying will occupy an 
excessively wide bandwidth. Normally, the rise/fall time of CW keying is 
intentionally "shaped" (i.e. increased) to minimize "key clicks" on 
adjacent channels.

In a similar manner, the square wave FSK keying waveform with 
essentially zero rise/fall time is modified into more of a rounded 
trapezoid, either by shaping the the audio tones used in AFSK, or by 
limiting the slew rate (i.e. intentionally increasing the rise & fall 
times) of direct FSK keying circuits.



Stephen H. Smith wa8lmf (at) aol.com
EchoLink Node: WA8LMF or 14400 [Think bottom of the 2M band]
Skype: WA8LMF
Home Page: http://wa8lmf.net

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