Feedback mixer. Super harmonics?

[Folding time]

I know some things about electronics but not enough for this, could you help me with choosing a mixer configuration for this task? I want a broad spectrum frequency signal using a mixer feedback loop

I know that mixers are non-linear and give f1 + f2 and |f1- f2|. And other forms such as 2f1 + f2 or 3f1+f2 ect...
I want all these harmonics. So no filtering or balancing mixer. Plus I would like to create a feedback into the mixer to expand the range of harmonics and frequencies..

Using just the basic f1 + f2 and excluding the other frequencies.. I want the feedback to look like this:

f1 + f2 = f3
f2 + f3 = f4
f3 + f4 = f5
f4 + f5 = f6
....

where f3 is the mixed signal and its component harmonics, then a new mix of f3 and f2 is made to get f4 and so on.. where in the end I have a very broad range mix of harmonics starting from the two input frequencies..

I'm just getting started with this question so any refinement you can teach me to bettering my understanding of attaining this would help. Even help better writing my question would help. thanks

Edit:

It's kind of hard to imagine the spectrum analysis of this broad spectrum signal. Do you know of anything that would let me see that this feedback loop circuit would give? Will adding f5 plus f4 give me all the harmonics located in f3 and so on.. So will the spectrum analysis (Fourier transform) shift away from all previous harmonics or mixing of signals as we add more, or will it contain the harmonics inside of all previous frequencies? Giving me one big higher and lower frequency containing range of mixer created harmonics?

 

[Harald Kapp]

Welcoem to EP.
I'm not quite sure what you want to achieve. Looks like you want to increase the harmonic content? This will not work the way you envision. Take your equations:
f1 + f2 = f3
f2 + f3 = f4
f3 + f4 = f5
f4 + f5 = f6
This is equivalent to
f1 + f2 = f3
f2 + f3 = f4 = f2 + (f1 + f2) = f1 + f2 (not f1 + 2*f2 as adding two signals of the same frequency will result in a signal with the same frequency, not twice teh frequency)
f3 + f4 = f5 = (f1 + f2) + (f2 + f3) = (f1 + f2) + (f2 + (f1 + f2)) = f1 + f2
...

If you want a very broad spectrum signal, use noise (white noise for constant power spectral density or pink noise for equal noise energy within each octave). Use filters to shape the energy distribution of the noise to match your requirements.

 

[ramussons]

Not too sure whether I have understood your query, but
fn can be generated from a*f1 + b*f2, where a and b are amplitudes that follow a pattern:
for n > 6, a(n) = a(n-1) + a(n-2)
b(n) = b(n-1) + b(n-2)