|Ok, now we had an accident in the bench, and made a nice
|discovery, a way to double a frequency.

|You can say;  - yeah, yeah, that's easy!
|and probably you have the answer at the tip of your tongue,
|but before you say something, take a look at the following
|picture, and tell me if the solution you are thinking can
|outputs the doubled frequency as the picture shows.

When fed a sine wave with no DC component, a 4-quadrant multiplier
(with both inputs tied together) will indeed output a sine wave with
twice the frequency, but with DC offset.  Given the sum of two sine
waves on the input, the squarer will output the two waves, doubled in
frequency, as well as a sine wave at the sum of the two frequencies and
another at the difference, all this in addition to the DC offset.

More generally, given a combination of waves the device will output ALL
COMBINATIONS of sums and differences(*); it is somewhat interesting to
consider various input and output waveforms, and what this says about
their harmonic content.

(*) If the two inputs of the multiplier are fed the same signal, in the
    same phase, the results may end up being quite different from if it's
    fed signals that are phase-shifted.  What's happening is that the
    phase relationships of the sum and difference tones are shifting.
    For the most dramatic example of this, consider using as the two in-
    puts:

    (A) A square wave--same phase fed into both inputs
    (B) A square wave--with one input delayed 90 degrees.

    Very different output waveforms, eh?