Idea about octaving: done before?

[Steben]

...Listen very carefully I will say this only once.... 

The thing is I was experimenting with some Excell sheets an graphs. calculating (co)sinusoides, doubling the frequency etc...
It seems to me there could be way to create really nice offset-free (no knee voltages) analog octaving.
I made sheet of base sine and 2nd order cosine. I added them relatively according to percentage.
When I added 25% pure 2nd order wave to a base wave, I achieved this almost clipped at the top waveform. Which mean one can see 20% octave content in the combined wave.

Now I turn the math around.
Think of a very bad biased class A stage (bipolar or jfet). You will see a asymmetrical distorted output wave: squeezed at the top, spike at the bottom. We all knew this produces a lot of 2nd order harmonic. Now I'm guessing It should be around that 20%. The more you raise the input, the more distortion. If you mix this together with the original signal into a differential opamp circuit, you will get a very close to unclipped octave signal, yet somewhat weaker in amplitude than the input.
The key to this all is balance of amplitudes into the differential amp. It may take some gain tweaking.

here some graphs:
magenta is base wave (freq1)
yellow is octave wave (freq1*2)
blue spotted is the sum 80% + 20% octave = somewhat resemblant to assymetric gain (class A)
dark red is differential result of magenta and blue.


It is my guess that, since this a sine + cosine thing, the bottom spike of the blue line is far more steep in the assymetric class A amp. Which means the differential result might be in reality closer to double freq.

[John Lyons]

I don't know anything about the fundamentals (no pun )  here but  I'm interested in what you are working on.
I'll be watching this...

john

[brett]

Hi

If you mix this together with the original signal into a differential opamp circuit, you will get a very close to unclipped octave signal

Am I right in thinking that the low base-emitter voltage drop of Q1 a fuzzface results in a lot of assymetric clipping, which is fed via the emitter of Q2 back to the base of Q1 (and therefore mixed with the input signal).  That's one reason why the distortion and tone of the fuzzface, especially Ge fuzzfaces, is so affected by the volume of the input signal, and why there are such complex dynamics in the attack and decay of each note.  (Of course, the loading of the pickups is very important, too).

cheers

[GFR]

Feed a sine wave to a distorting class A transistor stage, and get lots of 2nd harmonics. If you feed an inverted version of this sine wave to an identical distorting class A transistor stage, you get lots of 2nd harmonics. Now sum the two distorted signals and you cancel the fundamental, while reinforcing the harmonics - you get octave up. That's been done, look at RG's (mos)fet-doubler.

[brett]

Hi
RE:

The key to this all is balance of amplitudes into the differential amp. It may take some gain tweaking.

Also, the amount of 2nd harmonic is relatively small in many Class A single stages.  I discovered this by building my first version of RG's FET doubler with  low gain (Gm) FETs (probably MPF102s of similar).  I didn't get much octave until I changed them to J201s and reset their bias for lots of gain.
Have a good day!