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What is a sine wave?Waves index.Frequency multiplication.



For the following examples an RF carrier will be modulated with an audio frequency of ¼ of the carrier. This could be 20MHz modulated with 5MHz or 200MHz modulated with 50MHz or 20Hz modulated with 5Hz. It really doesn't matter, the geometry is the same. Suppose the following is a plot of an RF and audio frequency.

Main 20kHz RF carrierModulating 5kHz audio signal.
Figure 1 The reference frequencies.

For ease of reference, the frequencies will be refered to as kHz. This means, for each diagram showing a waveform, the time period is 1/1000 of a second. These two frequencies have only been used so you can see the plots resulting from signal processing. 5kHz is above a normal audio tone and 20kHz is below the radio frequencies usually used for voice (although they can be).


To AMPLITUDE MODULATE the RF carrier with the Audio Frequency, we do NOT just add the signals. It is actually a multiplication process but, even then NOT a simple OUTPUT = RF x AF relationship. If both signals have the same amplitude and are referenced to 1, the multiplication for 100% modulation is given by RF x ½ (AF+1).

If this multiplication of the two signals is applied, the wave form shown on the LEFT below results. The wave form shown at RIGHT has the original Audio superimposed.

Resulting AM signalResulting AM signal with Audio superimposed.
Figure 2 Amplitude modulated signal.


Sometimes people think, "if a little bit is good, a lot must be better." As a result many turn their microphone gain up and overmodulate to get more power on SSB. True, there may be more average power but STOP AND THINK ABOUT IT. Which is better, a 5x5 copy or a 2x9 copy?

Overmodulating is the cause of spurious emissions and some people just not taking the contact because they can't stand the sound of the other stations voice. SO WHAT IS OVER MODULATION.

If a higher amount of audio is fed into the multilying circuit (often just a single biased transistor) the following signal results.

Overmodulated AM signal.Overmodulated AM signal with modulating Audio superimposed.
Figure 3 Over modulated signal.

Not only does this result in a horrible, unreadable audio but adds a 10kHz component as well as the original modulating 5kHz. Normally, the audio is restricted to 3kHz but if a 2kHz signal is overmodulated in the same way, a 4kHz component is added. THIS MAKES YOUR TRANSMISSIONS ILLEGAL!!!


RULE:- Any repeating wave form can be expressed as a combination of sin waves.

This means the repetative signal shown in Figure 2 above can be expressed as a sum of sin waves. As it turns out, if we add (simply mix) ¼ of (RF-AF) to ½ Carrier to ¼ (RF+AF) ... OR ... ¼ of the 15kHz signal to ½ of the 20kHz signal to ¼ of the 25kHz signal we get the same signal. (Note: The fractions refer to amplitude not frequency)


1/4 Lower sideband signal (15kHz)+1/2 Main Carrier signal (15kHz)+1/4 Upper sideband signal (15kHz)=Resulting signal the same as Amplitude modulating 20kHz with 5kHz.
Figure 4 ¼ Lower Sideband + ½ Carrier + ¼ Upper Sideband = same as AM signal.

Note that this signal is NOT achieved in this manner. It is simply an equivalent. The carrier can now be removed. This is usually done by mixing a reverse copy of the carrier with the AM signal. When the carrier is removed we get a signal like this:-

Double sideband signal.
Figure 5 Double Side Band signal.

This is called a double sideband signal and is the same as if we just added (mixed) a 15kHz signal with a 25kHz signal.

The final step in producing a Single Side Band signal is to filter out one of the Sidebands. In older radios it was done with LC lowpass or highpass filters (LC = Inductor Capacitor). In more modern radios, a crystal filter is used.

Once one of the sideband signals is filtered out and only one remains, the signal will be identical to, in this case, a constant amplitude 15kHz tone for the lower sideband or a constant amplitude 25kHz tone for the upper sideband ie. Figure 4 diagrams 1 (LSB) and 3 (USB).


A good example of a simple demodulator for an AM signal is a single doide detector. This is best demonstrated with a simple, old fashioned crystal radio.

Simple AM radio
Figue 6 Crystal Radio

The coil and capacitor is the tuning circuit. This is a parallel resonant circuit. Above resonance, the capacitor conducts (bypasses) any RF to ground. Below resonance, the coil (inductor) conducts RF to ground. At resonance, the impendance of the LC circuit goes very high meaning, at the resonant frequency, the signal must be conducted through the diode (Converting it to DC) and headphones.

Much the same thing happens in other radios except not usually at the resonant RF frequency. Instead, because RF must be amplified, a superhetrodyne receiver does all the amplifying and detecting at a much lower IF frequency (often 455kHz) but that's another subject.

In any case, to demodulate an SSB signal, the same technique is used. Before this can be done though, the original amplitude modulated signal must be restored. To do this, a local oscillator (producing the same frequency as the transmitter) must be mixed with the incoming SSB signal.

Suppose we want to receive the Upper SideBand signal. If we amplify the incoming RF, somewhere in there will be the Upper Side Band. If we then mix this with an oscillator running at the receive frequency, it will me modified by the presence of the received Upper Side Band signal. The resulting signal will be as follows:-

Upper Side Band (25kHz signal.+Local osciallator.=Resulting signal similar to Amplitude modulating 20kHz with 5kHz.
Figure 7 Upper Side Band signal mixed with local oscillator.

You will notice this is not the same as the original Amplitude Modulated signal but it is close enough. If this is passed through the same detector, the same audio frequency will result."

The same situation exists with the Lower Side Band only in this case the signals are as follows.

Upper Side Band (25kHz signal.+Local osciallator.=Resulting signal similar to Amplitude modulating 20kHz with 5kHz.
Figure 8 Lower Side Band signal mixed with local oscillator.

The resulting Upper Side Band + Carrier AND Lower Side Band + Carrier signals are not the same nor are either the same as the original AM signal but there are the same number of peaks ie. both will produce a 5kHz output signal.


The function of the local receive oscillator can best illustrated by considering what happens if it is not the same as the transmit oscillator. In the above examples, both Upper and Lower Side Band signals are produced and received by semi-duplication of the original Amplitude Modulated signal. The following demonstrate what happens if the receive oscillator is different.

Suppose, in the above examples, the receive oscillator is running 1kHz high ie. 21kHz instead of 20kHz. Mixing 21kHz with the 25kHz Upper Side band signal produces:-

Upper Side Band (25kHz signal.+Local osciallator running high (21kHz).=Resulting signal similar to Amplitude modulating 21kHz with 4kHz.
Figure 9 Upper Side band mixed with receive oscillator 1kHz High (21kHz).

You should notice now there are only 4 peaks indicating a 4kHz received audio tone instead of the correct 5kHz sent by the transmitter. Running the receive oscillator at 21kHz but receiving the Lower Side Band this time produces.

Upper Side Band (25kHz signal.+Local osciallator running high (21kHz).=Resulting signal similar to Amplitude modulating 21kHz with 4kHz.
Figure 10 Lower Side band mixed with receive oscillator 1kHz High (21kHz).

Although it isn't quite as obvious with these diagrams, it should be seen there are 6 peaks instead of 5 showing a received audio tone of 6kHz instead of the 5 sent by the transmitter.

It is a little easier if the LSB and USB signals are viewed with the demodulated Audio superimposed.

Lower Side BandUpper Side Band.
Figure 11 Received LSB and USB signals with resulting audio Superimposed.

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