> > Therefore, I am wondering if anyone has taken frequency measurements > such
as s-parameters and found a reliable method to approximate the > poles and
zeros? If so, do you use the Laplace approach mentioned by > Dmitri to
incorporate the model into a transient circuit simulation? > > Mike
I've used a program by Applied Simulation Technology (was Contec) called SPAR.
This program accepts s-parameters (either measured or derived by some other
means such as a field solver) and extracts poles and zeros of the responses over
some specified frequency range. It then performs a Pade' approximation (ratio
of polynomials) and creates a "black-box" spice model that consists of
polynomial defined voltage and current sources.
I've utilized these models a few times and found them to work fairly well. You
can specify the order of the polynomial to use thereby giving you some control
over the effective bandwidth of the model.
A couple of caveats:
The model produced contains no delay information. Therefore the model is
pretty accurate for electrically small structures, however as the electrical
size grows, the delay (or lack of it) through the model becomes more
critical. I think you might be able to specify a delay externally to the
derived subcircuit but I haven't really investigated that angle.
Second, you need to be watchful when you extract the poles and zeroes. I've
seen cases where a pole showed up in the RHP and caused a passive device to be
modeled as an unstable circuit. There are things you can do to eliminate
the problem, but you need to be aware of it.
Thirdly, The program will interpolate between input data points. As long
as the structure that was characterized by the s-parameters is fairly
well behaved (whatever that means :) it is usually pretty safe to do
interpolation, however you need to be careful if you extrapolate beyond the
frequency range of your input data on the high side. Usually I've found
the extrapolating on the low side is relatively safe, but, extrapolating
on the high frequency side can sometimes lead to suprising results. Also,
if there resonances between your data points that you miss because your
data points are too sparse you are in trouble too.
Anyone else have any experience/comments on the method, tool, or similar
tools?
Ray Anderson
Sun Microsystems Inc.