[SI-LIST] Re: S-parameter passivity
- From: "Rohan Mandrekar" <rohanmandrekar@xxxxxxxxxxx>
- To: steven.corey@xxxxxxxxxxxxxx, si-list@xxxxxxxxxxxxx
- Date: Fri, 11 Feb 2005 12:35:52 -0500
Steve,
Your explanation is absolutely correct. However what John was referring to
was a type of quick check that is often done to verify passivity. For
passive data, the real parts of the "diagonal elements" of the Z and Y
matricies are always positive (which in John's example is true because the
data is passive). Obviously it is not a sufficient condition to guarantee
passivity, it is more of a property of passive data.
-Rohan
From: Steve Corey <steven.corey@xxxxxxxxxxxxxx>
Reply-To: steven.corey@xxxxxxxxxxxxxx
To: si-list@xxxxxxxxxxxxx
Subject: [SI-LIST] Re: S-parameter passivity
Date: Fri, 11 Feb 2005 08:35:57 -0800
John -- passivity for an impedance (or admittance) matrix doesn't depend
on whether the real parts are negative or not. It depends on what the
eigenvalues of Z+Z' are. In your example, they're both positive, which
means the system is passive.
Note that Z' is not the transpose of Z, but is the conjugate of the
transpose, commonly called "Z hermitian".
As for your scattering function, I don't know what characteristic
impedance you used to compute it, but I don't seem to compute it from
the Z you gave. However, the scattering function you gave satisfies the
passivity constraint on eig(I-S'S) but again you have to use S hermitian
rather than S transpose.
I will also point out that these constraints on the eigenvalues are not
sufficient to ensure passivity. The others are often overlooked because
they're guaranteed for lumped element circuits:
1. The system is causal
2. H(s) = H'(s') where ' is conjugate transpose.
-- Steve
-------------------------------------------
Steven D. Corey, Ph.D.
Time Domain Analysis Systems, Inc.
"The Interconnect Analysis Company."
http://www.tdasystems.com
email: steven.corey@xxxxxxxxxxxxxx
phone: (503) 246-2272
fax: (503) 246-2282
-------------------------------------------
johndp@xxxxxxxx wrote:
> All,
>
> I'm trying to understand the method for passivity correction based on :-
>
> RE{eigenvalues( I-S*S')} >0 (1)
> where
> I is the identity matrix
> S is the S parameter matrix
> S' is the Transpose of the S parameter matrix
>
> I have an example based on the paper published at designcon 2004
> "Advances in Design, Modeling, Simulation and Measurement Validation of
> High Performance Board-to-Board 5-to-10Gbps Interconnects" , Brian
Vicich,
> Scott McMorrow et al. and also the exchange on the SI-list last year, so
excuse me bring this up again.
>
> This shows and example of a non-passive impedance matrix Z such that :-
>
>
> Z=| 1.1+j -0.1-j |
> | -0.1-j 0.1+j |
>
>
>
> and an equivelent S parameter matrix of :
>
> S= 1/13*| 2.9+1.8j -5.9-3.6j |
> | -5.9-3.6j -1.2+7.3j |
>
> Obviously I can see from the Z matrix that this cicuit is non passive
because
> it has some of the real parts negative.
>
> If I apply (1) to the s-paramter matrix (using mathcad) I get eignevalues
:-
>
> eigenvals(I-S*S') = | 1.12 -0.54i |
> | 0.90 +0.08i |
>
>
> Which has positive real parts implying the network is passive according
to (1)
> so I don't see how (1) can be a valid test for passivity in this case.
> The matrix (I-S*S') is non singular and so appears to meet the
conditionsset out in
> the IEEE paper:-
> "Lumped Network Passivity Criteria", RA Rohrer. IEEE transactions on
circuit theory 1968
>
> I'm sure I'm doing somethin wrong but just can not see it :-)!
>
> Regards
>
> John
>
>
>
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