[SI-LIST] Re: Mixed-mode impedance matrix
- From: "Yuriy Shlepnev" <shlepnev@xxxxxxxxxxxxx>
- To: <xlzhou@xxxxxxxxx>, <si-list@xxxxxxxxxxxxx>
- Date: Thu, 29 Jun 2006 19:45:14 -0700
Hi Mick,
Conversion of terminal Z-parameters to the generalized mixed-mode form is
quite straightforward. It looks like that:
Zm=Tv*Z*Tv", where Z is the impedance matrix, Tv is the voltage
transformation matrix and " is transposition sign.
Here mixed-mode voltage Vm and current Im vectors are defined trough the
terminal voltage V and current I vectors as follows
Vm=Tv*V; Im=Ti*I; where Tv and Ti are voltage and current transformation
matrices. Every row of matrix Tv contains either 1 and -1 for the
differential mode or 0.5 and 0.5 for the common mode. Every row of matrix Ti
contains either 0.5 and -0.5 for the differential mode or 1 and 1 for the
common. All other elements are zero. Matrices Tv and Ti related as
Tv=(Ti^-1)".
Backward transformation from Zm to Z is Z=(Ti")*Zm*Ti
Simple example. For a two-port structure elements of 2 by 2 matrix Tv can be
defined as Tv11=1.0; Tv12=-1.0; Tv21=Tv22=0.5
Corresponding elements of the matrix Ti are Ti11=0.5; Ti12=-0.5;
Ti21=Ti22=1.0
This is just simple statement of the fact that differential voltage Vd and
current Id and common voltage Vc and current Ic are defined as
Vd=V1-V2; Id=0.5*(I1-I2)
Vc=0.5*(V1+V2); Ic=I1+I2
Elements of the mixed mode matrix of two-port are
Zm11=Z11-Z21-Z12+Z22
Zm22=0.25*(Z11+Z21+Z12+Z22)
Zm12=0.5*(Z11-Z21+Z12-Z22)
Zm21=0.5*(Z11+Z21-Z12-Z22)
Mixed mode matrix defined in that way is exactly what you get transforming
mixed-mode S-parameters directly to Z with the Cayley transform:
Zm=(I+Sm)*(I-Sm)^-1, where Sm is the mixed-mode S-matrix, I is the identity
matrix. The impedance matrix Zm derived from Sm is normalized. Assuming
identical normalization impedance for all ports Zo, common mode ports are
going to be normalized to 0.5*Zo and differential to 2*Zo. It is easy to
derive a generalized expression for the case with non-identical
normalization.
I hope it helps in this scriptic form,
Yuriy
Yuriy Shlepnev
Simberian Inc
shlepnev@xxxxxxxxxxxxx
-----Original Message-----
From: si-list-bounce@xxxxxxxxxxxxx [mailto:si-list-bounce@xxxxxxxxxxxxx] On
Behalf Of Zhou, Xingling (Mick)
Sent: Thursday, June 29, 2006 9:09 AM
To: si-list@xxxxxxxxxxxxx
Subject: [SI-LIST] Mixed-mode impedance matrix
Hi,gurus,
I was asked to simulate differential Z. It was obviously motivated by mixed
mode S parameter theory. So strictly speaking, I need to convert mixed-mode
S to Z. I remember somebody asked the same question last year.
As we know, the mixed-mode S parameter theory is well-establised
(generalized by Andrea Ferrero in 2005). However, I don't know any mixed
mode Z.=20
1. Some engineers do the so-called pure mode conversion, either diff or
common modes. If so, what do we know about the c-d/d-c mode conversion?
Something is missing here? Of course, mathematically you can do it.
2. Is it possible or meaningful to define the mixed-mode Z? We need a
reference impedance to do any S-Z converison, what is it for the d-c part?
What is the latest development in theory other than some personal practices?
I mean we need a solid foundation to do it. Any literature? I think if the
conversion can be defined, we must convert the whole S into Z, not piece by
piece (so-called pure mode conversion). Otherwise the information is
incomplete?
Thanks,
Mick
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