Any comments are welcome.

keep going. haven't look closely but i wish something that derives transfer function from actual/empiric device's/circuit's behavior, not from theoretical formula, because that we already have in textbook.

I forgot to reply to this post so just now.

I've been working on a symbolic analysis program since the early 1990's and have gotten pretty far with it and along the way i discovered many things about symbolic analysis vs numerical analysis that simulators use.

To answer your wish, i can tell you that if you need to analyze a behavior that is not strictly theoretical but also need to consider parasitic effects for example, all you would need to do is add those parasitics to the schematic yourself, which in most cases would mean creating a model for whatever it is you need to look at. You could get a lot of info from a spice model to help with this.

The drawback is that the more components you add, parasitic or not, the longer the solution will take because for a symbolic analysis the software has to deal with very very very long expressions. For example for a buck converter with various parasitics i did i ended up with expressions that would span several regular size book pages. That's because symbolic expressions for larger circuits have to contain every component in the whole system for every node unless some components get absorbed into others, but that is fairly rare. Sometimes you can simplify them a little by bulking up some parts of the expressions but it's not that easy to do and it still ends up very long.

The beauty of this though is that you can change any component or time value or whatever and do a calculation, and the calculation once the expression has been obtained completes very fast because computers work well with numbers. The only problem there is that you may have to go to a numerical precision that is not math coprocessor friendly, which means you have to use big numbers.

As i was saying in the previous post, some symbolic solutions are simply not possible because there is no closed form for some circuit calculations. An example is a transistor that uses diodes in the model. The exponential terms can not always be solved symbolically and so we end up back to numerical solutions. This is even typical with circuits with just diodes in them too.

So it seems that for some things we will always be dependent on numerical solutions.

It doesnt mean that the symbolic analysis is not useful though, because we can go so far with it until we have to jump back to using numerical solutions. So in a way we get some usefulness even if not the entire solution in one shot.