[SI-LIST] Re: Mixed-mode impedance matrix
- From: "Zhou, Xingling \(Mick\)" <xlzhou@xxxxxxxxx>
- To: <shlepnev@xxxxxxxxxxxxx>, <si-list@xxxxxxxxxxxxx>
- Date: Fri, 30 Jun 2006 09:30:08 -0400
Yuriy,
Thanks for your clear explanation in the first part. I think it is a
smart way to do the math, S->Z->Zmm.
In the second part, Zmm includes non-pure diff/comm Zmmdc etc, what is
the reference impedance I should use? Maybe I just need to do some
homework.
After all this math, the next question is: what is the benefit of Zmm?
As a different representation of the network, or a tool, it is fine.
However, when we look at it, it seems not so easy to judge a design
based on Zmm. Smm is much easier as we know. Or Smm is enough.
Regards,=20
Mick
-----Original Message-----
From: Yuriy Shlepnev [mailto:shlepnev@xxxxxxxxxxxxx]=20
Sent: Thursday, June 29, 2006 10:45 PM
To: Zhou, Xingling (Mick); si-list@xxxxxxxxxxxxx
Subject: RE: [SI-LIST] Mixed-mode impedance matrix
Hi Mick,
Conversion of terminal Z-parameters to the generalized mixed-mode form
is quite straightforward. It looks like that:=20
Zm=3DTv*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=3DTv*V; =
Im=3DTi*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=3D(Ti^-1)".=20
Backward transformation from Zm to Z is Z=3D(Ti")*Zm*Ti
Simple example. For a two-port structure elements of 2 by 2 matrix Tv
can be defined as Tv11=3D1.0; Tv12=3D-1.0; Tv21=3DTv22=3D0.5 =
Corresponding
elements of the matrix Ti are Ti11=3D0.5; Ti12=3D-0.5; Ti21=3DTi22=3D1.0 =
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=3DV1-V2;
Id=3D0.5*(I1-I2) Vc=3D0.5*(V1+V2); Ic=3DI1+I2 Elements of the mixed mode
matrix of two-port are
Zm11=3DZ11-Z21-Z12+Z22
Zm22=3D0.25*(Z11+Z21+Z12+Z22)
Zm12=3D0.5*(Z11-Z21+Z12-Z22)
Zm21=3D0.5*(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:=20
Zm=3D(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=20
Yuriy Shlepnev
Simberian Inc
shlepnev@xxxxxxxxxxxxx=20
-----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.=3D20
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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