This is a quick look at how the Bobtavia works.
The Bobtavia is uses the LM386 to amplify the input signal. In the default setup the LM386 has a gain of 20.
The output of the LM386 runs through a 220µ C4 cap into a small audio transformer. The input appears at one output of the transformer and an inverted signal appears at the other. See the image below.
The input (A) drives the transformer. The signal appears at one output and an inverted signal appears at the other (B). The diodes only allow the positive portion of the signal to pass (C). The combined output (C) is twice the frequency, with some imperfections (distortion).
The Bobtavia uses two diodes in series but the effect is the same with the difference that the output from the transformer needs to reach a higher voltage to get past the higher combined forward voltage. This circuit might work better using only a single diode!
In my experiments the LM386 with a gain of 20 was too low. I got a better more pronounced octave with a goan of 200. You can boost the gain of the LM386 to 200 by connecting pins 1 and 8.
The gain control on the original Bobtavia didn’t do anything for me. It also has a low input impedance of 50K. A better set up might to follow the Smash Drive. Something like this:
Here the input has a 1M impedance. The gain control is moved to pins 1 and 8 and has a range of 20 to 200.