[SI-LIST] Re: rational function approximation
- From: Ray Anderson <Raymond.Anderson@xxxxxxx>
- To: si-list@xxxxxxxxxxxxx
- Date: Fri, 16 Apr 2004 13:38:56 -0700
After responding to Amitava's question regarding rational function
approximation macromodels I was prompted to think about the problem a
bit more which brought a couple items to mind that I'd like to throw
out to the list for comment.
As has been discussed on the list in the past, a model needs to be
passive in order to be useful for circuit simulation. If a model is
based upon s-parameters, passivity can be proved or disproved by
looking at the real parts of the eigenvalues of (I - (S*S')). If the
resulting answer is positive the network that generated the
s-parameters is positive, if the answer is 0 then it is conditionally
passive and if the answer is negative the network is not passive.
Alternatively, one can convert the S-parameters to Y parameters and
check to see that the eigenvalues of the real part of the Y parameter
matrix is greater than zero. (are the conclusions for the case of 0
and <0 the same as stated above when using this method?)
A question that occurred to me was one of: If these two procedures
provide the same info regarding passivity is one preferred over the
other for any reason? If non-passivity is determined and one desires
to 'manipulate' the data to enforce passivity of the model is one
formulation easier to visualize which offending s-parameter(s) were
responsible for the non passivity? I'm thinking the second approach
involving the eigenvalues of the Y parameters may be marginally easier
to deal with in that respect, but I'm not convinced of it.
A second related question that I hope may elicit some discussion is:
As just discussed we know how to determine if a set of measured or
synthesized s-parameter data indicates that the network from which it
was obtained is passive or not. However if we follow the process
through, i.e., take the s-parameter data and use it to create a
rational function approximation or even perhaps a lumped element
model, then in order to assure passivity of the synthesized model is
it necessary to turn around and extract the s-parameters from the
model and go through the eigenvalue process described above, or is the
process of assuring that both the poles AND zeros of the rational
function are in the left hand plane adequate to ensure passivity? (If
I remember correctly that is the criteria...)
Comments, corrections, alternate means solicited.
Regards,
Ray Anderson
Staff SI Engineer
Sun Microsystems Inc.
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