This is one of my favorites, the subharmonic mixer. It sound complicated, it may be, but, to build it is not.
How, let's have a look on the options of mixing.
Mixing of a signal with a local oscillator (LO) can be done in two ways, either enable the bypass of a signal in the "rhythm" of the LO or shorten the signal in the "rhythm" of the LO. Usually this is done by a single "non linear element", e.g. diode. In the positive 0-180 degrees of phase, the diode is open, letting through the signal, in the negative 180-360 degrees of phase, the diode is closed, blocking the signal. Alternatively, shorting the signal to ground using the diode would provide the same results, a sum and a difference of the two frequencies.
So far so good...
But where's the doubling?!
Well, here it comes. Assume that two anti-parallel diodes are used as a mixer. Given that the LO is adjusted to the correct level, the first of the two diodes is open for one 1/4 of the period (90 degrees) on e.g. 50% of the positive half-period of the LO and the second of the two diodes is open for another 1/4 of the period (90 degrees) on e.g. 50% of the negative half-period of the LO. This would correspond to the mixer's diodes being open during the phase angles 45-135 degrees and 225-315 degrees. Compared to the 0-180 degrees a single diode would be open, the frequency is effectively doubled.
There are some advantages to this approach. In a direct-conversion receiver, the LO is far of the receiver's front-end, the preamp would therefore be unaffected. Also, a lower frequency oscillator is less critical in design. Any variation of the LO will have double impact on the operating frequency... this has pros and cons, e.g. VXO.
I like using sub-harmonic mixers, try 'em out for yourself!