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[aprssig] APRS Bandwidth - Carson's Rule Recalculated

Stephen H. Smith wa8lmf2 at aol.com
Tue Jun 23 22:14:31 UTC 2009


Keith VE7GDH wrote:
>
> Regarding 500 Hz bandwidth... aren't 300 baud tones just 200 Hz apart?
> I viewed the reply from Chris G4HYG about Carson's rule...
> http://en.wikipedia.org/wiki/Carson_bandwidth_rule. Doesn't that apply
> to FM? See

You are partly correct.  Carson's rule applies to modulating audio or 
data frequencies applied to an FM transmitter. 

> For SSB, I would have thought the 200 Hz difference between
> the two tones would set the bandwidth.
>

Sending FSK data with an SSB transceiver is more like FM than SSB. 

Applying a single audio tone to the mic jack of an SSB rig creates a 
single RF frequency offset from the (suppressed) carrier frequency by 
the frequency of the audio tone.   

Applying an audio tone 200 Hz higher to to the SSB rig will create a 
single RF frequency 200 Hz farther away from the (suppressed) carrier 
frequency.   

The net effect is exactly the same as if you have a single key-down CW 
carrier and shift it 200 Hz periodically (i.e. direct FSK with a 200 Hz 
shift)  
      [Some, mostly higher end, HF transceivers actually offer this 
direct FSK mode.  Rather than having feed alternating audio tones into 
the mic jack, you feed a TTL-logic-level 300 baud (for packet) or 45 
baud (for RTTY)  data stream directly into a special FSK input on the 
radio.]  

The bottom line is that you essentially have a FM (i.e. constant 
envelope power) transmitter modulated by 150 bps square waves rather 
than rather than higher-frequency audio sine waves. 
    

[Note that "300 baud" (300 bits / second) corresponds to only 150 Hz 
square waves.  Assuming the worst case of alternating "1"s and "0"s, 
each square wave cycle will require TWO bits to complete -- not one 
since one bit has to be the high half of the square and next bit the low 
half. Any bit pattern that  has adjacent "1"s or adjacent "0"s will have 
a lower effective "squarewave frequency".  ]

In either case, the occupied bandwidth is greater than just the the 
spacing between the two tones (a.k.a. "mark" and "space" frequencies).  
This is due to the transients created during the instantaneous shift 
from one frequency to the other.    [Even CW transmission has a 
bandwidth greater than a single frequency when you start keying at a 
rate higher than zero!]

The original poster that applied Carson's rule for approximating 
occupied FM bandwidth forgot that the base band modulating "frequency" 
would be 150, not 300 Hz.  Recalculating the occupied bandwidth,

2 (100 Hz deviation + 150 bps) =  500 Hz.     

Considering that  the actual data "frequency" is actually lower than 150 
Hz since runs of 2 or 3  ones or zeros DO frequently occur, the actual 
average occupied bandwidth is actually lower.  [Note that the occupied 
bandwidth created by true square-wave modulation would be greater than 
for sine waves. However, the finite bandwidth of the SSB modulator and 
IF filters "rounds off" the corners of the square waves and increases 
the rise/fall time to be more trapezoidal than square, resulting in a 
bandwidth nearly the same as with sine waves.]

I can attest to the fact that this is "REAL" since I have no difficulty 
receiving 200 Hz HF packet through an 500 Hz bandwidth CW filter on HF 
transceivers.


------------------------------------------------------------------------

--

Stephen H. Smith    wa8lmf (at) aol.com
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