Poles and zeroes in two port parameters (passive structures)

[Joel Kolstad]

Would anyone have a pointer to where I might found information about the
'allowable' S-plane locations for poles and zeroes in two port networks
parameters for passive structures, specifically Y, Z, and S parameters?

These are my thoughts:

-- Whatever applies to Y probably applies as Z as well.
-- Since Z11, Z22, Y11, and Y22 can all be seen as simple input
impedances/admittances, none of them should have right half-plane (RHP)
poles OR ZEROES.
-- Z12, Z21, Y12, and Y21 probably can't have RHP poles but probably can
have RHP zeroes.
-- S parameters are a complex enough transformation that it's unclear to me
whether or not there are any particular restrictions.

The reason I ask... I generate equivalent circuit models from measurement
data using curve fitting; the results are in the form of a rational
polynomial that can be readily factored to its pole/zero formulation. It'd
be nice to have an 'eyeball' method of ensuring the resultant ECM is stable.

Pointers to network theory books discussing this would also be appreciated.

Thanks,
---Joel Kolstad

 

[The Phantom]

Would anyone have a pointer to where I might found information about the
'allowable' S-plane locations for poles and zeroes in two port networks
parameters for passive structures, specifically Y, Z, and S parameters?

These are my thoughts:

-- Whatever applies to Y probably applies as Z as well.
-- Since Z11, Z22, Y11, and Y22 can all be seen as simple input
impedances/admittances, none of them should have right half-plane (RHP)
poles OR ZEROES.
-- Z12, Z21, Y12, and Y21 probably can't have RHP poles but probably can
have RHP zeroes.
-- S parameters are a complex enough transformation that it's unclear to me
whether or not there are any particular restrictions.

The reason I ask... I generate equivalent circuit models from measurement
data using curve fitting; the results are in the form of a rational
polynomial that can be readily factored to its pole/zero formulation. It'd
be nice to have an 'eyeball' method of ensuring the resultant ECM is stable.

Pointers to network theory books discussing this would also be appreciated.

Thanks,
---Joel Kolstad

This topic seems a little advanced for this group, but no matter.

You will find what you are looking for in most any textbook on
network synthesis, such as Guillemin or Van Valkenburg for example.

For passive networks, the facts are these:

The zeroes and poles of a driving point immittance must be in the LHP
or on the jw-axis (in the latter case, they must be simple).

The poles of the transfer immittance must be in the LHP or on the
jw-axis (and simple if on the axis). The zeroes may be anywhere in
the complex plane (for a ladder they may not be in the RHP) and for
grounded networks (which would be most typical networks), they may not
be on the positive real axis. Poles may not be at the origin or at
infinity. The degree of the numerator may equal but not exceed the
degree of the denominator.

This is straight out of Van Valkenburg.

 

[Joel Kolstad]

Thanks for the pointer, Mr. Phantom; I'll look up the references.

This topic seems a little advanced for this group, but no matter.

I'm all for suggestions for other groups. Unlike, say, the Physics
newsgroups, most of the electronics newsgroups are design related and none
are really theory related... but I figured 'basic' was as close as I could
get.

You will find what you are looking for in most any textbook on
network synthesis, such as Guillemin or Van Valkenburg for example.

Even with regards to S parameters?

Thanks again,
---Joel

 

[The Phantom]

Thanks for the pointer, Mr. Phantom; I'll look up the references.


I'm all for suggestions for other groups. Unlike, say, the Physics
newsgroups, most of the electronics newsgroups are design related and none
are really theory related... but I figured 'basic' was as close as I could
get.


Even with regards to S parameters?

Not in the older texts such as Guillemin and Van Valkenburg. The
newer texts probably, but I don't have any in my personal library, so
I can't be sure.