This same argument ensued in a design review for a radar that
I attended a few months ago. This radar was a good analogy to
clicky CW as it has a relatively low PRF (e.g. keying speed)
and a very fast rise time for the pulses. For square pulses,
the bandwidth is determined by the width of the pulse. The
repetition rate of the pulses or PRF (pulse repetition frequency)
determines the spacing of the discrete sidebands which make-
up the spectrum, but the overall bandwidth is determined
by the pulse width. This is where people get the idea that
CW speed effects the bandwidth of the resulting signal - higher
speed = narrower pulse width = wider bandwidth. For an
unshaped CW signal with very fast rise and fall times, this is in
fact true (in this case the envelope of the CW waveform looks
like a train of rectangular pulses). As CW speed increases, the
pulse width (in this case the dits) get shorter and the bandwidth
gets wider.
Fortunately, nobody uses square pulses to key their CW
rigs (at least nobody who has a clean signal). The reason
why can be seen in the sin(x)/x or so-called "sinc" function
which is the mathematical representation of the spectrum of a
rectangular pulse train. If you plot the function
Y(f) = sin(pi*f*tau)/(pi*f*tau) where tau is the width of the
rectangular pulse and "f" is frequency, you will see that as
tau gets smaller (shorter pulse width), the nulls in the sin(x)/x
function get further apart and bandwidth is increased. The
problem is that if you look at the -60dB points of this power
spectrum they are hundreds of times wider than the bandwidth
suggested by the symbol rate of the CW characters. For
example, at symbol rate of 10 hertz (I think this is typical for
20 wpm morse dits), the resulting -60dB bandwidth is several
KHz. whereas the 3dB bandwidth is only a few hertz. In fact, if
you plot the power spectrum for rectangular pulses, you will
see that it rolls off very slowly. This is why we don't use
rectangular pulses to modulate our CW signals
To minimize occupied bandwidth and avoid "key clicks", we
use shaped keying to limit the rise and fall time of our pulses.
When we do this, the pulse width or speed is no longer the
dominate factor in determining the bandwidth. In this case, the
bandwidth for shaped keying is no longer predicted by the
simple sin(x)/x function. Unfortunately, slower rise times do place
a limit on how fast we can send CW since the pulse must be
at least as long as the sum of its rise and fall time. For very fast
CW, some have commented that the slower rise and fall times
associated with anti-click modifications make keying too
soft for good copy at these higher speeds. Ostensibly this is why
some manufacturers offer user adjustable rise and fall times. The
30 wpm DX/Contest crowd can use slow rise times to minimize
bandwidth on crowded frequencies in the presence of weak
signal, and the QRQ ragchewers can run faster rise times at the
expense of greater bandwidth.
73 de Mike, W4EF.........................
> Tom:
>
> 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.
>
>
> Chuck
>
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