[SI-LIST] Re: rational function approximation
- From: Ray Anderson <Raymond.Anderson@xxxxxxx>
- To: si-list@xxxxxxxxxxxxx
- Date: Mon, 19 Apr 2004 16:03:11 -0700
Joel R. Phillips wrote:
>>Date: Fri, 16 Apr 2004 13:38:56 -0700
>>From: Ray Anderson <Raymond.Anderson@xxxxxxx>
>>Subject: [SI-LIST] Re: rational function approximation
>>
>>
>>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.
>
>
> Ray,
>
> Let me try to address some items and comment on some others that appeared
> earlier in the thread.
>
> 1. Checking passivity by examining eigenvalues of Y/Z, or I-S*S'.
>
> Two warnings here.
>
> While this approach is quite widely used, it has a problem in that checking
> positive realness at points does not actually insure the positive realness
> of a rational function. First, the PR condition must be established over
> the entire frequency axis, up to "infinite" frequency, and this is hard to
> do. Second, there is the problem of what happens between the points at
> which the check is performed. In practice, using very dense samplings over
> a wide frequency range often works, but I have seen some squirelly
> counter-examples. In particular, putting such a check inside an
> optimization loop can result in the optimizer driving its approximation to
> non-passivity in strange places you are unlikely to ever look. There is a
> paper by Anderson, Manrous, Kraus, "A new test for strict positive
> realness", IEEE Trans CAS-I, p. 226, 1995, that discusses grid-based tests
> that can be guaranteed to work.
>
remainder of reply deleted......
Joel-
Thank you and the several others who replied to my questions regarding
rational function approximations. It is truly amazing what one can
learn regarding esoteric topics by posing a question to this list.
I have downloaded a copy of your paper "A Convex Programming Approach
for Generating Guaranteed Passive Approximations to Tabulated
Frequency-Data" from the IEEE Explore site. It looks like it will
require some time and a lot of thinking to fully appreciate/understand
all that is contained in that paper. Thanks for pointing the way to
that resource.
You have pointed out many non-obvious pitfalls related to passivity
checking that I had not really considered. After digesting your paper
and comments I may have further questions. Thanks to all for your
insightful discussion.
-Ray Anderson
Sun Microsystems Inc.
------------------------------------------------------------------
To unsubscribe from si-list:
si-list-request@xxxxxxxxxxxxx with 'unsubscribe' in the Subject field
or to administer your membership from a web page, go to:
//www.freelists.org/webpage/si-list
For help:
si-list-request@xxxxxxxxxxxxx with 'help' in the Subject field
List FAQ wiki page is located at:
http://si-list.org/wiki/wiki.pl?Si-List_FAQ
List technical documents are available at:
http://www.si-list.org
List archives are viewable at:
//www.freelists.org/archives/si-list
or at our remote archives:
http://groups.yahoo.com/group/si-list/messages
Old (prior to June 6, 2001) list archives are viewable at:
http://www.qsl.net/wb6tpu
Other related posts:
