There were a number of investigations made in time domain scattering and
antenna work to approximate time responses using a pole based expansion
with the poles deduced numerically or otherwise from time series data. The
mathematics used is called "Prony's Method". As the order of the poles
increses, the method appears to become more and more unstable in the sense
that the time response has progrssively larger inaccuracies. This was
generally checked by taking the original time series data and comparing it
to the re-constructed time series as deduced by Prony's Method.
Reference to this area of investigation can be found in the IEEE APS
(Antennas and Propagation Society and its predecessor PGAP) and MTS
(Microwave Techniques Society and its predecessor MTT). Much of the source
or context of the work was satellite or aircraft identification from
wideband radar signatures, but the problem is much the same here.
Excellent area for academic investigation, but very tough numerically.
At 03:47 PM 4/24/98 -0700, you wrote:
>> > Therefore, I am wondering if anyone has taken frequency measurements >
>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
>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
>some specified frequency range. It then performs a Pade' approximation
>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.
>can specify the order of the polynomial to use thereby giving you some
>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
>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
>Sun Microsystems Inc.
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