Which part of amp is the most difficult thing to model ?

I would imagine all of it.

You could take the sum total of human knowledge of electricity/physics and create the most accurate simulation of an amp known to man. Finding a piece of hardware that could run that in real time is a non-starter, much less finding one on the average musician's budget.

So, compromises have to be made. All this talk about "it's all about the code" is a direct reflection of that.
 
Preamp ? Power amp section ? Someting else ?

The part between the input jack and your ears...

More seriously, all of the bits are interconnected. The glory of the AxeFX is how it does cover so many of the interactions between components, keeping in mind that the interactions can change depending on input drive, how hard the virtual amp is working, frequency dependent things like resonance, etc., etc., etc.

TT
 
- Cliff: The Axe-Fx II is unique in that it is the only modeling device that accurately replicates a tone stack along with the interaction of the controls and influence of surrounding circuitry. I had to solve the mesh equations for each of the major tone stack types which wasn't easy. A tone stack is a 3rd-order network and coding that was a real challenge.

- Cliff: Heck it took months just to figure out how to model an output transformer.

- Cliff: I've spent months researching and perfecting note decay. / I spent months and months researching what caused a tube amp to do that and how to recreate it.

- -

What I admire most is like mentioned before: that the interaction between dozens or hundreds of parameters works as well.
I suspect both a great deal of precision and a great deal of good taste is involved. Easy to overdo some internal setting cos you like it at that moment.
 
All of it. And this is not a trite answer.

Consider this: You have a dynamic system (meaning it is changing with the complexities of the sounds, i.e. guitar) feeding a signal into another dynamic system (the vacuum tube amplifier).

Either you look INTO the amp from the preamp-side and you'll see that the poweramp affects it, or you can look INTO the amp from the poweramp-side and you'll see that the preamp and phase inverter affects it. All the while, you have a gaggle of vacuum tubes, each with a set of characteristic curves that are changing with the 'sound' of the signal being fed to it, and yet this is still an insufficient model because the non-linear and dynamic response of the speakers and the Output Transformer (hysteresis for one, saturation for another) also alter this ideal. Now, assume you sufficiently understand these aforementioned interactions in total: you now have to effectively code these for DSP. Which seems hardest to you?
 
I imagine anything regarding the "non-linearity of tubes" is extremely difficult to produce mathematically. "Fractal..."
 
I imagine anything regarding the "non-linearity of tubes" is extremely difficult to produce mathematically. "Fractal..."

I would imagine this too. Non-linearity... Hard to figure out randomness and then actually plot it with 0 and 1...
 
Yeah. We are specifically exploiting the shortcomings of how a vacuum tube amplifies a signal. When the level is low and the tubes are in their linear range, everything is pretty simple and predicable. But we purposely push them beyond that neat and tidy range into a sort of odd controlled failure range. From an engineering perspective, distortion is usually a bad thing yet it is what we are specifically seeking out for our "tones". That's a tough thing to recreate.
 
The hardest part is modeling the fragile harmonics that don't survive in crystal lettuce.

Ok, so how do the fragile harmonics do in iceberg lettuce? I was thinking that crystal lettuce was found only in solid state amps….we're not talking about crystal radios, are we?….I'm confused.
 
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