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 ------------------------------------------------------------------ To unsubscribe from si-list: si-list-request@xxxxxxxxxxxxx with 'unsubscribe' in the Subject field or to administer your membership from a web page, go to: //www.freelists.org/webpage/si-list For help: si-list-request@xxxxxxxxxxxxx with 'help' in the Subject field List FAQ wiki page is located at: http://si-list.org/wiki/wiki.pl?Si-List_FAQ List technical documents are available at: http://www.si-list.org List archives are viewable at: =20 //www.freelists.org/archives/si-list or at our remote archives: http://groups.yahoo.com/group/si-list/messages Old (prior to June 6, 2001) list archives are viewable at: http://www.qsl.net/wb6tpu =20 ------------------------------------------------------------------ To unsubscribe from si-list: si-list-request@xxxxxxxxxxxxx with 'unsubscribe' in the Subject field or to administer your membership from a web page, go to: //www.freelists.org/webpage/si-list For help: si-list-request@xxxxxxxxxxxxx with 'help' in the Subject field List FAQ wiki page is located at: http://si-list.org/wiki/wiki.pl?Si-List_FAQ List technical documents are available at: http://www.si-list.org List archives are viewable at: //www.freelists.org/archives/si-list or at our remote archives: http://groups.yahoo.com/group/si-list/messages Old (prior to June 6, 2001) list archives are viewable at: http://www.qsl.net/wb6tpu