**From:** J. Eric Bracken (*bracken@ansoft.com*)

**Date:** Thu Dec 02 1999 - 14:32:45 PST

**Next message:**Syed Huq: "[SI-LIST] : Re: [SRe: [SI-List] : XTK multiboard simulation using amp spice connector models....... .."**Previous message:**Mckinley, Jory: "RE: [SI-LIST] : XTK multiboard simulation using amp spice connect or models....... .."**In reply to:**Mckinley, Jory: "RE: [SI-LIST] : Passivity of a Linear System"**Next in thread:**David Instone: "Re: [SI-LIST] : Differential Pair Theory"

The way to test it is to compute the transfer function from the poles

and zeros:

(s-z1)*(s-z2)*...*(s-zm)

H(s) = ---------------------------

(s-p1)*(s-p2)*...*(s-pn)

Assuming that H(s) represents the input impedance or input admittance

of the linear system, then passivity is equivalent to being "positive

real":

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

goes negative.

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.

--Eric

*>>>>> "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 bracken@ansoft.com Pittsburgh, PA USA 15219-1119 http://www.ansoft.com**** To unsubscribe from si-list: send e-mail to majordomo@silab.eng.sun.com. In the BODY of message put: UNSUBSCRIBE si-list, for more help, put HELP. si-list archives are accessible at http://www.qsl.net/wb6tpu/si-list ****

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