[SI-LIST] even/odd/common/differential

Yuri:
Thank you for a cogent explanation.  Insisting that only even and odd
modes exist is like insisting that only standard S parameters are valid,
despite the usefulness and clarity of mixed mode S parameters where they
are applicable.  (For the curious among us, see
http://cp.literature.agilent.com/litweb/pdf/5988-5635EN.pdf )

Regards,
Orin Laney

On Fri, 5 Dec 2008 12:49:53 -0800 "Yuriy Shlepnev"
<shlepnev@xxxxxxxxxxxxx> writes:
> Weston,
> 
> I think that the differential and common modes do exist in the same 
> way as
> the even and odd modes.
> Each of 2 modes in symmetrical 2+reference conductor line can be
> characterized by propagation constant (G), characteristic impedance 
> (Z) and
> modal voltage (V) and current (I) distributions. Knowing those 
> parameters we
> can describe voltage and current distribution along the line with 
> any
> termination conditions. There are multiple possible ways to define 
> the
> parameters, but for practical purpose just two ways are important 
> (see more
> on that at page 10 of the last presentation at
> http://www.simberian.com/TechnicalPresentations.php).
> 
> With the even and odd modes we have:
> Even mode: Ze, Ge and Ve=[1/sqrt(2),1/sqrt(2)], 
> Ie=[1/sqrt(2),1/sqrt(2)]
> Odd mode: Zo, Go, and Vo=[1/sqrt(2),-1/sqrt(2)], 
> Io=[1/sqrt(2),-1/sqrt(2)]
> 
> Or with the common and differential modes we have:
> Common mode: Zc=Ze/2, Gc=Ge and Vc=[0.5,0.5]=sqrt(2)*Ve/2,
> Ic=[1,1]=sqrt(2)*Ie
> Differential mode: Zd=2*Zo, Gd=Go, and Vd=[1,-1]= sqrt(2)*Vo,
> Id=[0.5,-0.5]=sqrt(2)*Io/2
> 
> Those are two sets of parameters that are totally equivalent 
> solutions of
> the Telegrapher's equations for 2-conductor lines with 2 by 2 
> impedance Z
> and admittance Y matrices per unit length that satisfy both the 
> symmetry
> (Z11=Z22, Y11=Y22) and reciprocity (Z12=Z21, Y12=Y21) conditions. 
> The
> equations can even describe non-TEM modes without any sacrifice of 
> accuracy
> (corresponding Y and Z matrices have to be extracted with the 
> full-wave
> analysis). 
> As you see, the difference in the even/odd and common/differential 
> solutions
> is simply in the normalization (scaling) of the modal voltage and 
> current
> vectors that leads to differences in the impedance definition.
> Common/differential normalization coincides with the common and 
> differential
> excitation or termination definitions and thus may be more convenient 
> for
> practical applications.
> 
> Considering the non-symmetric conductor or dielectric case - you are 
> right,
> only common and differential excitation or termination can be 
> defined. No
> common and differential modes exist for that case and no even and 
> odd mode
> exist either. Modes in non-symmetrical lines can be classified as c
> (conductor currents and voltages are opposite but not equal) or pi
> (conductor currents and voltages have the same sign and not equal) 
> according
> to Triathi (see IEEE Trans. on MTT, N2, 1977, p140). The 
> differential
> excitation produces combination of the c (predominantly) and 
> pi-modes. An
> ideal termination can be defined for these modes, but additional 
> signal
> degradation may occur if the propagation constants of the modes are
> different.
> 
> Best regards,
> Yuriy Shlepnev
> www.simberian.com 
> 
> 
> -----Original Message-----
> From: si-list-bounce@xxxxxxxxxxxxx 
> [mailto:si-list-bounce@xxxxxxxxxxxxx] On
> Behalf Of Beal, Weston
> Sent: Friday, December 05, 2008 8:35 AM
> To: Santos Fernandez, Jesus
> Cc: si-list@xxxxxxxxxxxxx
> Subject: [SI-LIST] Re: How to do termination in differential signal 
> with
> series termination ?
> 
> Jesús,
> 
> It actually avoids confusion if we understand and use the proper 
> terminology
> when discussing differential pairs. The modes are an intrisic 
> property of
> the conductor geometry. They are specific states of excitation in 
> the two
> conductors. This says nothing, yet about what signal is actual sent 
> down the
> pair at any one time. The terms differential and common refer to the 
> signals
> that are applied to the structure. There really is no such thing as
> differential mode and common mode. There is differential signal and 
> common
> signal. We can also measure or determine the differential and common
> impedance of the differential transmission line by applying a 
> differential
> or common signal to the structure. The differential impedance is 
> that
> impedance that a purely differential signal sees as it propagates 
> down the
> transmission line pair. Odd-mode impedance is the impedance of one 
> conductor
> when the pair is excited in the odd mode. That's why Zdiff = 2*Zodd. 
> The
> same applies to common signal
>  , common impedance, and even-mode impedance; except that Zcommon =
> 1/2*Zeven.
> 
> Since we send differential signals - and they always contain some 
> amout of
> common signal in our non-ideal world - we want to terminate the 
> differential
> impedance and the common impedance.
> 
> Notice that I did not use the terms common mode (CM) nor 
> differential mode
> (DM) in this explanation. Those are the terms that get us confused 
> when we
> try to figure out common impedance and differential impedance.
> 
> If you would like a more detailed explanation I suggest the book, 
> Signal
> Integrity - Simplified by Eric Bogatin.
> 
> Regards,
> Weston
> 
> 
> -----Original Message-----
> From: si-list-bounce@xxxxxxxxxxxxx 
> [mailto:si-list-bounce@xxxxxxxxxxxxx] On
> Behalf Of Santos Fernandez, Jesus
> Sent: Thursday, December 04, 2008 11:50 PM
> To: steve weir; King Da
> Cc: si-list@xxxxxxxxxxxxx
> Subject: [SI-LIST] Re: [Help] How to do termination in differential 
> signal
> with series termination ?
> 
> Is there any necessity to use the names of ODD and EVEN instead of 
> the more
> descriptive CM and DM?
> 
> Jesús
> 
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