At 4/28/2004 12:34 AM, you wrote:
>Steve S. Bosshard (NU5D) wrote:
> >
> > CARSON'S RULE
> > BANDWIDTH = 2 X (PEAK DEVIATION + HIGHEST MODULATING FREQUENCY)
>
>Thank you for quoting what I've been saying the past two posts.
Here's a question: just what amount of the transmitter's TPO is "Carson's
Rule bandwidth"? -20 dBc? -26 dBc? -30 dBc? I've seen all 3 in various
definitions.
If you use the Bessel functions to calculate bandwidth for worst-case
single-tone emissions, using 3 kHz tone @ 5 kHz deviation, the 3rd sideband
(J3) @ +/- 9 kHz is only 21.85 dB down from the unmodulated
carrier. Fortunately, voice emission PSDs are spread fairly evenly across
the entire 300 to 3000 Hz modulation band (thanks to pre-emphasis,
otherwise the PSD would be sloped toward the low end, & yes we're talking
FM not PM Bob don't go there!!), & in addition there may be an assumption
in Carson's Rule that the upper modulation limit is down by 3 dB due to
conventional analog low-pass filtering, so a 3 kHz tone would only deviate
the TX 3.54 kHz, not 5 kHz. Using 3.54 kHz deviation & 3 kHz modulating
freq. gives a modulation index of 1.178, & corresponding J3 at -30.1 dB &
J2 (+/- 6 kHz sideband) at -16.2 dB. That's more like it! Using linear
interpolation (don't know if that's legit here, but I'm just ranting at
this point), +/- 7.5 kHz would be at -23.15 dB.
As a (in)sanity check, let's try 2 kHz tone modulation. Let's say the
post-limiter filter doesn't kick in yet, so we have full 5 kHz deviation &
corresponding modulation index of 2.5:
J3 (the sidebands at +/- 6 kHz) are 13.3 dB down from the unmodulated
carrier, & J4 (+/- 8 kHz) are at -22.64 dB.
So my guess is that Carson's Rule specifies the 22 to 23 dB bandwidth of a
conventional NBFM voice TX. Am I close?
Bob NO6B
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