I was referring to the diode idea.
With a single-ended multiplier you will get even and odd harmonics. The transistor multiplier mentioned previously is essentially a class-C stage, and squarewave drive works as well (or better) than sinewave. As you know, the beauty of a balanced multiplier is the minimization of the odd harmonics.
Well yeah that works great, for a sine input. For a square (not rectangular, I mean 50% square), if you prefer the Fourier picture, the harmonics mix, superimpose and cancel out. You don't get even harmonics, you just get more odd harmonics. In short, as I said at the start of this thread, you can't square (the math function) a square (the waveform), you just get DC. The class C amp is just a unipolar class D amp, reproducing the signal with actually unusually good fidelity. There is no instantaneous (stateless time domain) function, even or odd, which can break the squareness of a square wave. At best you get skewing of rise/fall times; in which case I suppose we should really be discussing a trapezoidal wave, which is the more practical case after all.
Anyway, the point about a diode was, given various assumptions about the signal path, one could introduce even harmonics by unbalancing the edges. An ordinary amp with no additional assumptions, won't do that, but given similar assumptions, can do the same thing (i.e., a capacitive load driven by asymmetrical on/off source resistances, to unbalance the edge rates).
I once redesigned a clock tripler in a piece of telecom gear: 51.84 MHz to 155.52 MHz. We had a nice square wave clock input, and the original design had a single-transistor Class-C style multiplier with fancy filtering and amplification to get rid of all the undesired harmonics (especially the 2nd). I replaced all that with a simple circuit that sent the squarewave clock into a 155 MHz SAW filter, followed by an ECL buffer to square up the 3X output. Worked great. Wouldn't have worked at all as a doubler. Fourier is your friend.
Indeed, triplers work very nicely from whatever input, and you can basically use a comparator (ECL input stages are basically diff pairs) to not just generate rich 3rd harmonic (as in ~1/3 the fundamental amplitude), but by overdriving the input, the rise/fall time and amplitude becomes much less significant, i.e. it acts as a limiter too.
Consider a square wave into a filter. The filter will essentially produce repeated step responses, overlapping (superimposed) as they do. The effect is that, though the 3rd harmonic has been selected as dominant, the 1st and 5th combine as sidebands, producing apparent amplitude modulation at the 2nd harmonic (being (3-1) and (5-3)). Feed this into another stage, and the amplitude modulation can be overdriven to give a flatter output, even without a follow-up filter; in Fourier terms, the sidebands have been mixed together and canceled out. Which of course works fantastic for FM radio, where insensitivity to AM (environmental fading, tuning error) is a virtue.
I don't know that Fourier analysis is all that useful of a way to reason about nonlinear systems (outside of a harmonic balance analysis, and anyway, have fun doing that by hand?), i.e. as thinking about harmonics and how they mix. The toy, the cartoon picture really, of multiplying sines, is only valid for what it is -- a translinear multiplier applied to pure tones. It's more complicated when multiple tones are present, and much, much more complicated when highly nonlinear mixers are added on top of that. Higher order mixing products will completely destroy your image rejection, in the context of radio design. (For multipliers, who cares, at least all the products are synchronous!)
Tim