[SI-LIST] Re: How to do termination in differential signal with series termination ?

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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