[SI-LIST] Re: Mixed-mode impedance matrix

Yuriy and others,

Thanks for your excellent inputs. I will check the details later.

Have a great weekend.

Mick

-----Original Message-----
From: Yuriy Shlepnev [mailto:shlepnev@xxxxxxxxxxxxx]=20
Sent: Friday, June 30, 2006 12:05 PM
To: Zhou, Xingling (Mick); si-list@xxxxxxxxxxxxx
Subject: RE: [SI-LIST] Re: Mixed-mode impedance matrix

One correction to the de-normalization equation below. The
de-normalization matrix for impedance parameters is D=3Ddiag{either =
0.5*Zo
for common-mode port or 2*Zo for differential-mode port} . Normalization
matrix is inversed of D.
It provides simple Zo multipliers for de-normalization of the
common-differential impedance matrix elements.

Yuriy

-----Original Message-----
From: si-list-bounce@xxxxxxxxxxxxx [mailto:si-list-bounce@xxxxxxxxxxxxx]
On Behalf Of Yuriy Shlepnev
Sent: Friday, June 30, 2006 7:24 AM
To: xlzhou@xxxxxxxxx; si-list@xxxxxxxxxxxxx
Subject: [SI-LIST] Re: Mixed-mode impedance matrix

Mick,

All matrix transformations to get Zmm are isomorphic as long as Z is
non-singular (that is always true for non-ideal lossy structures).
Thus, it does not matter how you get it. S->Z->Zmm is fine if you start
with S. Smm->Zmm is even better if you have to start with Smm. Zmm
obtained from Smm with the Cayley transform has to be denormalized to
relate regular voltages and currents in the differential-common mode
basis. It can be done multiplying it with two diagonal matrices D from
left and right D*Zmm*D, D is the denormalization matrix with
1/sqrt(0.5*Zo) on diagonal for the common-mode ports, and 1/sqrt(2*Zo)
on diagonal for the differential-mode ports. Your common-differential
impedance is going to be multiplied simply by 1/sqrt(Zo). It is assumed
that all original ports are normalized to the same impedance Zo.

What are the benefits of Zmm? Comparing to S-parameters, It does not
contain numerical normalization error caused by the Cayley transform.
This is obviously applicable only if you compute Zmm directly and not
through Smm.
Poles and zeros are more visible with Z. In addition, some tools do not
use S-parameters internally and convert them into Y or Z - it is better
to use Y or Z directly in that case. Something else?

Yuriy=20

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: Friday, June 30, 2006 6:30 AM
To: shlepnev@xxxxxxxxxxxxx; si-list@xxxxxxxxxxxxx
Subject: [SI-LIST] Re: Mixed-mode impedance matrix

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,=3D20

Mick



-----Original Message-----
From: Yuriy Shlepnev [mailto:shlepnev@xxxxxxxxxxxxx]=3D20
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:=3D20 Zm=3D3DTv*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=3D3DTv*V;  =3D
Im=3D3DTi*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=3D3D(Ti^-1)".=3D20
Backward transformation from Zm to Z is Z=3D3D(Ti")*Zm*Ti

Simple example. For a two-port structure elements of 2 by 2 matrix Tv
can be defined as Tv11=3D3D1.0; Tv12=3D3D-1.0; Tv21=3D3DTv22=3D3D0.5 =3D
Corresponding elements of the matrix Ti are Ti11=3D3D0.5; Ti12=3D3D-0.5;
Ti21=3D3DTi22=3D3D1.0 =3D 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 =3D Vd=3D3DV1-V2;
Id=3D3D0.5*(I1-I2) Vc=3D3D0.5*(V1+V2); Ic=3D3DI1+I2 Elements of the =
mixed mode
matrix of two-port are
Zm11=3D3DZ11-Z21-Z12+Z22
Zm22=3D3D0.25*(Z11+Z21+Z12+Z22)
Zm12=3D3D0.5*(Z11-Z21+Z12-Z22)
Zm21=3D3D0.5*(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:=3D20 Zm=3D3D(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=3D20

Yuriy Shlepnev
Simberian Inc
shlepnev@xxxxxxxxxxxxx=3D20

-----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.=3D3D20

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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