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Signal Mixing & Heterodynes

posted Feb 26, 2012, 8:02 PM by Charles Boling   [ updated Feb 26, 2012, 8:07 PM ]
When you mix two signals together by simply combining them, the effect they have on each other is called multiplication, and the result, when looked at in the frequency domain, can be considered to have 4 outputs: the two original signals, their sum, and their difference.  In other words:
    {a, b} --> {a, b, a+b, a-b)
This is used a lot in radio and elsewhere; for example, Amplitude modulation mixes an audio signal with an RF carrier in this fashion.  When two relatively high frequency signals are mixed together with the intent of using the lower frequency produced by their difference, this is known as heterodyning.   You can hear this on a piano or other musical instrument if you hold two adjacent notes down; aside from the unpleasant dissonance, you can hear a low-frequencing pulsing -- a tremolo-like effect. When done with the lowest notes on the keyboard, where the notes differ by only a couple of Hertz, the pulsing is only a couple of times per second, and very plain to hear.

If you're geeky enough -- or old enough -- you're familiar with the terms Heterodyne Receiver or Super-heterodyne Receiver.  The radio receiver actually generates an RF signal that tracks with the frequency you're trying to receive, to convert the incoming signal to one particular lower frequency that the subsequent amplifier and other stages are designed to deal with more effectively than they could handle the original signals.

This same concept is used to receive CW signals, which are just a plain fixed-frequency RF wave (an unmodulated carrier, so to speak), which if received on a plain receiver would produce no sound.  The principle is to mix the incoming wave with one that is just a few hundred Hertz away from it, so that the difference produces an audible tone of a constant frequency.  Any signals of nearby frequencies will be heard as different tones.

This same phenomenon can also produce undesirable effects.  For example, when a strong signal (such as the radio broadcast tower you're standing 1/4 mile from with your HT) combines with the local oscillator in your receiver, it might produce an image in the Amateur band, and you'd swear that the radio station is putting out illegal spurious radiation on the ham band, but it's really being produced within your own radio!
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