Hello Everyone,
As a response to my AR in last week’s meeting minutes:
“Arpad will ask Vladimir if it is possible to reduce ports in the pole-zero
format [AR].”
I thought I should post a summary of my conversation with Vladimir on the
question
on port reduction when the interconnect is described in the Pole/Zero format.
Q: If we had a .pls file for a huge S-parameter file, say 100 ports, can that
.pls file be
reduced to just a few ports without having access to the original S-parameter
file?
A: Port reduction is very simple if we assume that eliminated ports are loaded
with impedance that is equal to the corresponding ports’ normalizing impedance.
In such case eliminating the ports means removing rows and columns from the
S-parameter matrix that correspond to these ports. This could be certainly
done for the fitted data as well. However, in more general case, when we assume
that eliminated ports are terminated by a different impedance, possibly
complex, or left open or connected to ground, the task becomes non-trivial even
for the sampled data. In general, if the termination of a port being
eliminated is different from its normalization impedance, all remaining
components will be affected. Zero elements in the original S-parameter matrix
may become fully populated (non-zero) after such “reduction”. In this case,
yes, we need to rebuild fitted model accordingly.
Q: Does this mean that in general it is not possible to reduce the number of
ports
of the fitted model without the original S-parameter data?
A: It is possible, but will require re-fitting and re-enforcing passivity.
The steps would
be this: Convert fitted model back into the sampled (S-parameter) format (this
is
always possible), then reduce ports, then fit the resulted reduced model to
pole/zero
format.
Q: Is the reduction of the fitted model possible when the termination is the
same as
in the S-parameter data?
A: Yes, it is possible, without re-fitting and most likely without passivity
enforcement.
Q: Does this going back and forth result in loss of accuracy?
A: Not much, compared to the fitting errors. Regarding the sample points, one
can
use resampling with step adaptation (like adaptive sampling). It doesn’t
compromise
accuracy because of resampling, especially with smaller resolution factor.
However,
smaller resolution factor increases the number of data points in the Touchstone
file.
I hope this answers our question about port reduction with the pole/zero format.
Thanks,
Arpad
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