At 06:12 AM 5/11/03, Tom Rauch wrote:
>The spectrum of a OOK (CW) signal at 3 wpm is different from the spectrum at
> > 30 wpm, so what does the last phrase in your response mean? The signals
>will
> > have energy content at (carrier rate +/- symbol rate), so the 30 wpm
>signal
> > would qualify as "more bandwidth" in my book.
>
>Bandwidth is set entirely by the rise and fall time and shape of the rise
>and fall of the signal. My keyclicks web page explains this, and has a link
>to another analysis by W9CF.
There are bandwidths and then there are bandwidths...
The bandwidth of a CW signal at -6 dB wrt peak or average power is set by
the element rate (pulse width) not the envelope shape. The same goes for
the -3 dB BW and the -10 dB BW. Such points lie within the first zeroes of
the signal's spectrum and the frequency at which they are located is
sensitive to the keying rate. This remains true for any reasonable keying
envelope and can be seen in W9CF's analysis.
On the other hand, for bandwidths measured at amplitudes lower than -15 or
-20 dB, the bandwidth will depend on the shape of the keying envelope but
not the keying rate.
> > The ARRL gives a "rule of thumb" in one of their handbooks that goes
> > something like this:
> >
> > "The bandwidth of clean CW signal in Hertz is approximately twice the WPM
> > rate."
>
>The **required** bandwidth is given by that formula, but that is not the
>same as the occupied bandwidth. The occupied bandwidth is set by shape and
>slope of the rise and fall and is absolutely independent of speed.
Well, the twice the WPM "rule of thumb" is a pretty good approximation for
the spacing between the first zeros of the sinc**2 term that results from
OOK. The spacing between the first zeros is the bandwidth containing
approximately 97% of the energy for a "clean" CW signal (4 ms exponential
rise/fall) and approximately 96% of the energy for a "dirty" CW signal (0
ms rise/fall).
At these levels the occupied bandwidth does depend on the keying speed.
The bandwidth occupied by 99.999%+ of the signal power may be the spec
that's appropriate for limiting co-channel interference with a large
dynamic range of signal levels. Then it's the keying envelope and not the
keying speed that determines the occupied bandwidth.
73,
Mike K1MK
Michael Keane K1MK
k1mk@alum.mit.edu
|