I was designing an electronic circuit that requires precise frequency control when I realized how much I don't know about the frequency synthesis itself.
For example, when I take my low-end 2-channel arbitrary waveform generator, I'm able to set one of the channels to a sinewave with a frequency of 6.00000000 MHz and the other one to 5.99999999 MHz. When I multiply those two signals and filter out the higher frequency what I get is a precise sine signal with a frequency of 10 millihertz. So the period difference between the two waveforms should be the astonishing 278 attoseconds. That would require a 3.6 PHz of bandwidth just to distinguish the difference over one period! And yet my AWG is able to generate any frequency from 0 to 6MHz with 10mHz precision and with the thermal and phase drift accuracy of a crystal oscillator. (I've checked with an oscilloscope and the frequency is stable up to a 6-digit precision, can't check any further).
So it happens to be beyond my understanding how this can be accomplished (especially under $60). Using frequency division/multiplication would be unthinkable at that bandwidth and any VCO I know of has far more jitter and will eventually drift too much.
Am I missing something? Does any of you engineers know what's happening inside such cheap digital generators?