Bandwidth & NBFM Math

Courtesy of Midwest Spectrum Management Alliance

Why do we see such differences, per state, as to channel spacing? One can only think that simple compromise was the driving factor, along with the fear of upsetting the status-quo. Proper, logical, and technical radio spectrum management has not been apparent because of economic, emotional, and political factors. So, without any further delay, lets show the mathematics of the argument.

Simply stated, narrowband FM is described by the following parameters:

+/- 5.0khz peak deviation and a peak modulating audio frequency of 3.0khz
The total bandwidth of the NBFM signal is calculated as:
Bandwidth (kHz) = (2 x Maximum Deviation) + (2 x Maximum Modulating Frequency)
Bandwidth (kHz) = (2 x 5) + (2 x 3)
But wait... we're not done yet! You MUST add the TX frequency error to the equation for the total assigned channel to be defined. Tolerance has been typically (for 144mhz., as an example) +/- 750hz.

Bandwidth = (2 x MD) + (2 x MMF) + (2 x Frequency error)
Bandwidth = (2 x 5) + (2 x 3) + (2 x .750)
17.5khz total channel bandwidth!

Well, the 20khz spacing argument works well here. With a total, maximum 'width' of 17.5khz, a 2.5khz guardband is the result between channels. Add to this fact that most amateur radio NBFM transmitters probably meet this specification. In Indiana, we have a mixture of 15, 20, and 25khz channel spacing, varying as to the frequency band that we're talking about. Using 25khz spacing, we're really wasting space, but using 15khz spacing on the 144mhz band, aren't we 'jamming' things up a bit? You bet we are! We're relying on geographic separation to make our frequency coordination seem like it works! There is nothing worse for the frequency coordinator to say than, "..the band is full", or "you can't use that adjacent frequency pair because it is too close". That time may come, but not quite yet!

In order for this to work, we must adjust our transmitters to a maximum of +/- 4.0khz deviation, NOT +/- 5.0khz. If you plug the numbers into the equation:

Bandwidth = (2 x 4.0) + (2 x 3)
14.0khz total TX bandwidth...
...then add-in the TX-error
Bandwidth = (2 x 4.0) + (2 x 3) + (2 x .750)
15.5khz total channel bandwidth

Since 15khz channel spacing will be 'with us' for a while, NBFM transmitter-deviation reduction is the first step for all of us to use, as we strive towards more efficient utilization of our radio spectrum, while we continue to use NBFM transmitters.