[sdiy] Modeling circuits

[Scott Nordlund]

> Modeling frequency response is no big deal. Modeling the nonlinearities 
> accurately is _really_hard_, and that's a big part of the tube sound. 
> The problem is that the best models these days are based on the Volterra 
> series which results in huge equations of higher order products and 
> delay terms. Then, tweak a volume or tone control knob and all your 
> model coefficients change radically. Tough stuff...
> 
> Eric (works on RF linearizers & predistortion for the day-job)

David Yeh's doctoral dissertation at Stanford centered around modeling a 
Boss DS-1.  Of course it was used more as an example, and he went beyond
what would typically be done to get a product finished (and the model 
still wasn't perfect...), but it gives some idea of the complexity of the 
problem.

Circuit simulation software finds iterative solutions, so it's not really
practical for real time use.

It can be more or less approximated by breaking it into linear and
nonlinear blocks (and I think many amp models do this), but this doesn't 
really reflect what's actually happening.  I think in many cases they're 
hoping it doesn't make a big enough difference and that something like 
dynamic convolution will do the job well enough. 

The models we have now of transistors are very sophisticated and accurate,
thanks to decades of boundary-pushing microelectronics.  Tube models 
are much more primitive, so anyone trying to "really" model tube amps is
going to have a very difficult time.

Anyway in general I think modeling amps are a lot better now than when 
they just came out, but there's probably a lot of lingering stigma from
10 or so years ago.  Funny to think that the analysis and simulation of
a desirable "vintage" circuit takes far, far more effort than was spent 
designing it in the first place.