Greetings and salutations Cliff.
Congratulations on another amazing "job well done"!
"Inquiring minds would like to know."
Could you please explain in more detail the specific adjustments that need to be made to accomplish emulating the 'symmetrical/asymmetrical switch' of the Timmy for those of us who are presently somewhat 'technically challenged'?
It's natural to think of an amplifier as making a signal get bigger, and you can imagine the electricity coming from your guitar travelling through the amp, getting bigger and coming out the other end to the speakers. But it doesn't really work like that. Generally the electricity from your guitar is treated as a control signal which creates a wave from electricity that comes from some sort of power source.
In a stompbox, the power is generally something like a 9V battery and the amplification is provided by a transistor or an IC (which is just a bunch of transistors). Generally, these can only make the signal vary between 0V and +9V, and you can't generate a -ve voltage (you can with two batteries, but it's not generally done). So assuming a single 9V power supply:
The guitar signal is going to come in with values that range from (let's say) -150 mV to +150 mV, and as an examples lets assume the amplification part of the circuit is going to multiply that by a factor of 30 which should result in an output from -4.5V to +4.5V. Except we can't do negative outputs from the transistor. So the original signal is bumped up by adding a DC voltage of 150 mV, so that now it varies from 0 mV to 300 mV, which when amplified will generate an output wave that varies from 0V to +9V (then a filter is applied which removes the now amplified DC voltage and you get a signal that varies from -4.5V to +4.5V).
This bumping up is called biasing.
But what if the biasing isn't set up to set the centre of the variance right at the centre of the voltage range of the power source? What if we apply a 100 mV biasing voltage? Then the input signal will vary from -50 mV to 250 mV. Now, when the biased input signal goes negative, the transistor still isn't going to generate an negative output voltage, but just 0V. This is going to flatten out the bottom of the waveform, resulting in distortion.
By the same token, if you bias by 50 mV too much, then the signal will vary from 50 mV to 350 mV which will have the positive peaks of the amplified signal at 10.5V, which is more than the battery can supply. So the tops of the waveforms will be flattened out, causing distortion.
Both of these are examples of asymmetrical distortion. A neutrally biased transistor can still clip if the gain is sufficient to produce an output signal that varies by more than plus or minus 4.5V, but that would be symmetrical clipping.
It's important to note that the way that a transistor stops at 0V and the way that the battery fails to give more at 9V are going to be slightly different, and result in a different distortion tone. You should also note that, although the voltages are way bigger, and the mechanics are different, pretty much all of this applies (to some degree) to tubes. Tubes amps generally distort asymmetrically, so some distortion pedals want to do this too in order to sound more "tube-like".
The Timmy pedal doesn't use the amplification itself to cause distortion, it simulates it with diodes (which I'm not going to explain). It has three diodes to clip the tops of the waveforms, and three diodes to clip the bottoms of the waveforms. More diodes means more clipping (and more distortion). There is a three way switch which allows you to use all three diodes in both sets, just one diode in each set, or one diode in one set with all three in the other. This last setting is the asymmetrical setting.
That's the theory. The modelling is weird because the stompbox simulates the asymmetrical clipping of biasing with different numbers of diodes, but the model simulates the asymmetrical clipping by simulating the biasing. Does the actual Timmy pedal more accurately simulate under-biasing or over-biasing? Only your ears can tell, I guess. How much biasing? Same thing.
OK, it was still long and I'm sure lots of people will pick technical holes in it, but that's the simplest I can explain it.