Lets look at this another way. Sometimes some analysis can put limits on
what we should measure in the lab. This is a guide line to see if we are
making the measurement correctly or if the equipment may not be giving us
the correct answer.
We are looking at a wave which is switched on and off at a 25 Hz rate.
(This is like 100% amplitude modulation with a square wave.) When we do
this, the resulting spectrum shows a carrier and many sidebands spaced 25 Hz
apart on both sides. Lets assume for a moment that the switching signal is
a perfect square wave with very fast rise and fall times. This will give us
a limit. It represents the very worst case we could encounter. i.e.Keying
with no shaping at all. Now lets look at a specific offset frequency of
about 1kHz and calculate what the sideband level would be. Since the
modulation is a perfect square wave, there will only be odd order harmonics.
i.e. 1,3,5,etc. The harmonic we are interested in is 1000Hz/25Hz or the
40th. But there will be no energy there as it's an even order so lets move
to the 39th harmonic at 975 Hz. The Fourier analysis of this waveform shows
that this sideband will be 35.7 dB down. This is confirmed with a
measurement on my old spectrum analyzer.
This means that with the worst possible keying, the signal will be -35.7 dB
down at plus and minus 975 Hz when a string of dots is being sent..
Now lets add some shaping. Shaping will reduce the sideband levels, so lets
see what 5 mS rise and fall times do to the spectra. The 5 mS rise and fall
time is accomplished by passing the modulating signal through a 70 Hz single
pole low pass filter. This filter is 70 Hz wide at -3 dB. At 1 kHz this
filter will be 23.1 dB down. This attenuation will lower the sideband
levels in the case above by 23.1 dB. So for 5 mS rise/fall times the 39th
sideband at 975 Hz will be -35.7 + (-23.1) = -58.8 dB.
Now we have some limits Radios with keying rise times between 5 mS and 0 mS
will have sideband levels at 1 kHz either side between -58.8 dB and -35.7
dB. Unless I'm mistaken, this is a law of nature.
Maybe some mathematical person out there could check over my numbers.
For those interested, the 2000 ARRL handbook shows the line spectra of the
exact case we are discussing on page 17-50.
Note that this only addresses the amplitude modulation sidebands. If there
is any form of frequency or phase modulation during the keying, then the
sideband levels will be different. Typically, if there is FM and AM at the
same time, the spectra will be asymmetrical as the sidebands add on one side
and subtract on the other.
George, W2VJN
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