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Re: Modeling and simulation



Original poster: "Jim Lux" <jimlux-at-earthlink-dot-net> 

 > SPICE deals with nonlinear systems in the following way, essentially:
 > 1)The circuit is linearized around the last available solution, and a
 > new solution for the linear circuit so formed is calculated.
 > 2)If the new solution is almost identical to the previous, the solution
 > was found. If not, return to 1), using the calculated solution.
 > This is actually Newton's method for finding a solution of a nonlinear
 > system of equations. It really finds the correct solution, or one of
 > them if there are more than one.

I was under the impression that it's actually even a bit fancier than a
straight Newton's method (or perhaps, that's what differentiates vendor A's
spice from vendor B's?)... better/faster convergence and all that...

 >

 >
 > Most of the convergence problems in SPICE-like programs are due to the
 > nonlinear circuits, specially ones that change quickly between
 > different states. The numerical integration methods can also get
 > lost in some situations, but this is more difficult.
Precisely the problem I was alluding to.. nice smooth behaviors work fine,
discontinuous less so...

 >
 >  > If you have a nonlinear device in the system (like a mixer, or a
diode),
 >  > programs like spice don't work so well... The diode can be modeled as a
 >  > "switch" and a resistor for the DC and transient case. It can be
modeled as
 >  > appropriate parasitic C and L and R for the AC case. It can even be
modeled
 >  > as a (relatively smooth) nonlinear function of inputs in the transient
case
 >  > (and the AC/DC cases, where the solver goes through multiple iterations
of
 >  > the network equations until everything settles down to a steadystate
 >  > equilibrium)..
 >
 > Ok. The model can be as complex as you want if you use subcircuits.

But, still no matter how complex, you're still approximating the actual
behavior, just at a finer and finer scale (as with a piece wise linear),
and, of course, the performance starts to get pretty wretched as the model
complexity grows.  I also suspect, without being analytically sure, that
overly complex models tend to be very sensitive to small changes

 >
 >  > If you had infinite computational resources, you could conceivably do
SPICE
 >  > like transient simulations with sufficiently fancy solvers in the time
 >  > domain to model almost anything, IF and ONLY IF, you had sufficiently
 >  > accurate models, which, in practice, do NOT exist for most RF
components (or
 >  > for components of great interest to TC'ers, like spark gaps and
 >  > leaders/streamers/sparks).  We're talking about models that adequately
 >  > represent the behavior on a sub nanosecond time scale. (FDTD is
starting to
 >  > get there, but is computationally intensive)
 >
 > A question of making models. If the physical models are too complicated,
 > behavioral models can be built, that simulate just what is observed.

But, to take spark growth, for example, there's not a heck of a lot of
suitable observations to build that behavioral model on.  The physics isn't
even all that well understood, although there are some physics based FEM
dynamic models being used.  Then there's the problem of model validation...
how do you validate the "fine scale" structure of the model.. The gross
behavior is adequately well predicted by fairly simple models (e.g. the 200K
+ 3pF/meter model for a streamer)

 >  > (Imagine what trying to
 >  > create a simple SPICE model for an original Pentium would be like.. a
 >  > million transistors, several million transmission lines, several
million
 >  > capacitors and resistors, and you'd have to simulate at a time step of
 >  > something like 1-10 picoseconds)
 >
 > But these systems are simulated. Not necessarily complete at the lowest
 > level, but using informations from low-level analysis for simulations
 > at higher levels.

Simulated, yes, but poorly... ASIC design is sort of a combination of
moderately ok behavioral models and a set of design rules that provides
reasonable assurance that the model is accurate.  However, the classic
problem is that it doesn't work at all temperatures or clock rates,
necessitating a respin (if you can even figure out what to change)...
Testability is also sort of a dicey problem... It's not practical to
generate exhaustive test vectors for a million gate design, so you test in
chunks, and pray there's no interactions (helped by those design rules..)

The problem is particularly tough with mixed mode circuits.. One thing to
simulate gate propagation delays, where the signal gets "regenerated" at
every stage.. totally another when you've got nominally linear circuits in
there too.
 >
 >  > Ultimately, though, those models need to be validated, and that's why
this
 >  > mailing list is full of folks who actually build the coils, rather than
just
 >  > talk about it....
 >
 > And in all examples, the models are being validated. Even the problems
 > predicted by the theory are appearing too, as the low rms output of
 > too fast magnifiers.

Yep.. although, I think where the ragged edge is, is where there's poor
understanding of the behavior (spark growth in the fine scale)... For
instance, at a qualitative level, the physical configuration of the topload
should have an effect on spark growth (other than from radius of curvature),
because the energy to have the leader grow the next step has to come from
the topload, but there isn't a good behavioral model or sufficient empirical
data to make a definitive statement whether, for instance, a 30 pF topload
with overall diameter A and tube diameter B is better or worse than overall
diameter C and tube diameter D...  From the behavioral models, and even the
FEM models, they would be the same... the quasi static field looks the same,
the resonances look the same, etc.

 >
 > Antonio Carlos M. de Queiroz
 >
 >