Example
Let's go through an example. Let's say we want to pick up signals from 0 to 30 MHz. We'll divide this into 30 1 MHz bands, and translate them to a band at 44-45 MHz. To convert 0-1 MHz, the first oscillator must be 45 MHz, to convert 1-2 MHz it must be 46 MHz, and so on. Meanwhile, we also mix the first oscillator with harmonics from a 1 MHz crystal and put the result through a 42 MHz filter. Only one harmonic gets through. When the first oscillator is 45 MHz, it is the third harmonic, because 45 - 3 = 42. At 46 MHz, it's the fourth harmonic, and so on. The oscillator does not have to be exactly 45, 46, and so on, only close enough to get through the 42 MHz bandpass filter. Let's say it is 45.1 . Then we get 42.1 from the filter, and 45.1 - 42.1 is still 3. When we mix the high IF with the 42 MHz, we get a band of signals from 3 MHz to 2 MHz, from which we select the desired signal, perhaps with a conventional superheterodyne back-end converting 3-2 MHz to 455 kHz and finally demodulating the signal back to audio. The overall receiver drift consists of the crystal's drift plus the 3 MHz back-end, so when we're listening to a 30 MHz signal, this receiver is about ten times as stable as one using a high-frequency tunable VFO.
To a new user, the feel of the first oscillator tuning control is counterintuitive. Although the knob moves in a continuous, analog fashion, its effect on receiver operation is discrete, that is, the tuning advances in 1 MHz jumps.
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“Our intellect is not the most subtle, the most powerful, the most appropriate, instrument for revealing the truth. It is life that, little by little, example by example, permits us to see that what is most important to our heart, or to our mind, is learned not by reasoning but through other agencies. Then it is that the intellect, observing their superiority, abdicates its control to them upon reasoned grounds and agrees to become their collaborator and lackey.”
—Marcel Proust (18711922)