Carl, you have pointed up both an error and an omission in my overly long
First, you are entirely correct: I said 90 degrees when I meant 180
degrees, or more correctly the appropriate half of the keying pulse
duration for the rise or fall time interval. And you concisely stated the
key point: "For clickless operation we must start and stop at zero slope."
The waveform which Martinez and others call a "cosine" waveform is more
correctly termed a "cosine-like" waveform. In actual keying practice, the
waveform might be the output of a cosine-squared filter or a raised-cosine
filter. I think that Peter used the more generic term in the interests of
Such filters and waveforms readily can be constructed with the aid of DSP
processing and are to be preferred for modern digitally based transmitters.
Older, more conventional transmitters using on/off keying have relied upon
RCL filter circuits to shape the keyed waveform.
Although Terman in his classic texts shows what he terms "lag circuits" to
*minimize* clicks, he clearly states that the keyed waveform must be smooth
and continuous at *all* points if clicks are to be avoided. But his
waveform drawings clearly show discontinuities at the end of the rise time
and the start of the fall time. These are, of course, consequences of using
exponential keying waveforms.
Historically, designers have relied upon exponential filter outputs for
keying largely due to the ease with which they can be obtained from
inexpensive circuit components. As a result, the exponential keyed waveform
has become the classic example of click-reduction filtering even though its
performance falls far short of the results to be obtained with more
appropriate and effective waveforms.
Because of this canonical aspect of exponentially keyed waveform filtering,
most hams and many engineers have come to accept such waveforms as the norm
and seek only to vary the rise and fall time intervals in an effort to
control click generation and occupied bandwidth.
Although this approach of controlling transition time intervals can affect
bandwidth, only the avoidance of keying function discontinuities can
Thank you for pointing out my numerical error.
72/73/oo, George W5YR - the Yellow Rose of Texas
Fairview, TX 30 mi NE of Dallas in Collin county EM13qe
Amateur Radio W5YR, in the 56th year and it just keeps getting better!
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> I'm a little confused over the cosine shape as you have descibed it.
> The zero slope points on a cosine curve (or sine curve) are 180 degrees
> apart and not 90 degrees apart. A sine wave starts out at 0 degree point at
> 0 amplitude but with a slope of 1. It reaches full amplitude at 90 degrees
> phase and here it has zero slope. 90 degrees later, the amplitude is back
> to zero, but the slope
> is -1. So, I don't follow the argument. For clickless operation, we must
> start and stop at zero slope. A sine or cosine wave does not do this.
> Carl Moreschi N4PY