FOR RADIO AMATEURS - NO INTENTION TO TEACH MATHEMATICS
The modern amateur radio transceiver keyed to produce CW.
The key produces the keying signal, typically a voltage
that is +5V for key up and zero for key down.
The keying voltage is mixed with a tone oscillator at
something like 700Hz in a double balanced mixer or some equivalent
circuit producing an audio CW signal, a 700Hz tone that is present
when the key is down and absent when the key is up.
Fig. 1. The CW "modulator". To generate a morse
coded audio tone or a morse coded radio frequency signal one
uses the same fundamental circuitry, a double balanced
mixer (Or some equivalent circuit)
The audio CW signal is then mixed with a local oscillator at
for example 10.7MHz, the one we traditionally regard as the carrier,
producing a radio frequency signal.
The radio frequency signal contains two frequencies, the sum frequency
and the difference frequency at 10.6993 and 10.7007MHz respectively.
These two signals are the lower and the upper sidebands.
By means of a filter one of the sidebands is removed leaving
a single morse coded radio frequency signal.
The RF telegraphy signal at i.e. 10.6993 is classified as a
J2A signal with carrier frequency 10.700MHz.
That is because it is generated with a SSB transmitter that
would be capable of transmitting a voice signal!
The J2A signal can in no way be differentiated from a signal
that is produced by the schematic of fig.1 using the frequency
10.6993 for the local oscillator.
Produced directly, the signal would be classified as A1A
with a carrier frequency of 10.6993MHz.
It is a good idea to forget "carrier" and "modulation".
Thinking about signals in general terms is more fruitful
and will make it easier to see the equivalence between
digital signal processing and the corresponding analog radio
receiver or transmitter.
Describing the CW signal
The CW signal discussed above really has a carrier in the sense
that its spectrum is symmetric with the strongest component at the
center, at 10.6993MHz.
It is however perfectly valid to describe it as a SSB signal with
a carrier frequency of 10.700MHz or any other arbitrary
frequency that one would like to choose
As it turns out one needs complex numbers to describe the CW signal
in case any other frequency than 10.6993MHz is regarded as the
Rather than carriers one could think about reference signals
and baseband signals.
The baseband signal has two components, I (in phase) and
Q (quadrature, 90 degrees out of phase)
The reference signal is a sine wave and a cosine wave of fixed frequency,
a complex pair.
In case we select 10.6993 as the reference frequency, I is the filtered
keying signal while Q is zero. (or vice versa or some combination)
In case 10.700MHz is selected as the reference frequency, both I and Q
are the morse coded audio signal at 700Hz.
I and Q differ in that the phase of the 700Hz signal differs by exactly
The reference frequency is the frequency "from which we observe the signal".
To change the reference frequency for the oscilloscope display
of a signal, a
complex mixer is needed.
The entire complex pair I and Q of the signal at the old reference
frequency is mixed with the sine and cosine of the new reference
frequency to produce a new complex pair I and Q.
That is all. (no filters)
This is the phasing method for SSB generation.
In the frequency domain (on a spectrum analyser display) changing
the reference frequency is the same as moving the spectrum along
the frequency axis (x-axis).
Changing the reference frequency, transposing the frequency or
converting the frequency are different names for the same thing.
It is a linear process that changes the frequency of a signal.
The reference frequency, our observation point is not some
fictive mathematical concept.
It is a physical reality and understanding receivers and transmitters
this way may aviod some common misunderstandings.
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