From: J. Eric Bracken (email@example.com)
Date: Thu Dec 02 1999 - 14:32:45 PST
The way to test it is to compute the transfer function from the poles
H(s) = ---------------------------
Assuming that H(s) represents the input impedance or input admittance
of the linear system, then passivity is equivalent to being "positive
Re[ H(s) ] >= 0 when Re[s] >= 0
There are other conditions (complex poles and zeros must be in conjugate
pairs, duh), but this is usually sufficient.
So, to check passivity you just need to plot Re[ H(j*omega) ] for
omega from 0 to infinity on a very fine grid and make sure it never
As for causality, you can't tell from the poles and zeros. Any given
set of poles and zeros can be interpreted in a multitude of ways, some
of which give you causal, anticausal, or two-sided signals. You have
to know the region of convergence for the Laplace transform. See
Oppenheim, Wilsky and Young's book on Signals and Systems (Prentice
Hall) for more information.
>>>>> "CSchuster" == Schuster, Christian writes:
CSchuster> Dear SI-List-Listeners,
CSchuster> I know that the following question is somewhat beyond
CSchuster> the scope of the usual list topics but nevertheless I
CSchuster> hope to get some feedback from you ...
CSchuster> Question: Given the poles and zeros of a linear system,
CSchuster> how can I decide if its passive?
CSchuster> Or weaker: How can I decide if its causal?
CSchuster> Any input is very much appreciated.
CSchuster> Best regards,
CSchuster> Ch. Schuster
-- J. Eric Bracken, Ph.D. Tel: 1.412.261.3200 x135 Manager, Signal Integrity R&D Fax: 1.412.471.9427 Ansoft Corp., Four Station Square, Suite 200 firstname.lastname@example.org Pittsburgh, PA USA 15219-1119 http://www.ansoft.com
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