# [SI-LIST] S-parameter passivity

• From: johndp@xxxxxxxx
• To: si-list@xxxxxxxxxxxxx
• Date: Fri, 11 Feb 2005 14:39:33 +0000

```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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