# RE: [SI-LIST] : connector model for differential signal

From: Daniel, Erik S. ([email protected])
Date: Thu Oct 26 2000 - 08:59:08 PDT

Bob-

If I understand your question correctly, you are asking how even mode
impedance can increase as two traces are brought together, given that in the
limit that the traces touch and become a single trace, twice the width of
the original two traces, this trace must necessarily have lower impedance
than each of the original two thinner traces. Is this a correct
re-statement of your question?

If so, then here is my answer. I think part of the confusion is this pesky
factor of two again. Zeven is the impedance associated with *each line
separately*, given that the signals on each of the two lines are identical
(i.e., even mode). One could consider shorting the two traces together and
measuring the impedance of both lines simultaneously. This impedance would
be Zeven/2 (sometimes defined as Zcommon as I mentioned in my previous
note). So in your question, when you refer to the impedance of the combined
trace (two traces touching), "Zcommon" defined this way would be the
impedance of this combined structure, while Zeven (=2*Zcommon) would be the
impedance allocated to each of the two composite traces. Comparing Zeven to
the combined trace impedance is not really comparing apples to apples.

Given this explanation, a logical next question might be this: If I
consider doubling the width of a single trace, the impedance will roughly be
cut in half, so if I started with a trace of width w and impedance 50 ohms,
a trace of width 2w should have an impedance of roughly 25 ohms. Then,
Zeven for "each half of the trace" should be roughly 25*2 = 50 ohms. Does
this conflict with the statement that Zeven will increase above 50 ohms as
two 50 ohm traces are brought together?

The answer is that there is no conflict. The explanation has to do with all
instances of the word "roughly" above. A line of width 2w will actually
have somewhat larger impedance than 1/2 the impedance of the line of width w
because the edge fringing fields are a smaller fraction of the whole for a
trace of double the width.

- Erik

==================================================================
Erik Daniel, Ph.D. Mayo Foundation
Voice: (507) 284-1634 Guggenheim 1011B
Fax: (507) 284-9171 200 First Street SW
E-mail: [email protected] Rochester, MN 55905
==================================================================

-----Original Message-----
From: Bob Weber [mailto:[email protected]]
Sent: Thursday, October 26, 2000 9:23 AM
To: Daniel, Erik S.
Cc: [email protected]
Subject: RE: [SI-LIST] : connector model for differential signal

Erik,

Regarding: "The terminology I prefer defines the odd mode impedance Zodd and
the even mode impedance Zeven of two completely uncoupled 50 ohm lines as
Zodd=50 ohms, Zeven=50 ohms. Then, if these two lines are brought closer
together (without other changes in geometry), Zodd will drop below 50 with
Zeven rising above 50."

Is the part about with "Zeven rising above 50" really true? Intuitively
(don't laugh too hard <g>), this does not seem likely. In the limiting case
of bringing the two traces together to the point of touching, the impedance
would drop. What am I missing?

Bob Weber
Robert Weber
Principal Engineer
TranSwitch Corporation
3 Enterprise Drive
Shelton, CT 06484
203.929.8810 x2507

-----Original Message-----
From: [email protected]
[mailto:[email protected]]On Behalf Of Daniel, Erik S.
Sent: Thursday, October 26, 2000 8:30 AM
To: [email protected]
Cc: [email protected]
Subject: RE: [SI-LIST] : connector model for differential signal

John-

I agree that the terminology is confusing for impedances of two coupled
lines. The answer is that both sets of equations are "right" -- it is a
matter of semantics and definitions.

The terminology I prefer defines the odd mode impedance Zodd and the even
mode impedance Zeven of two completely uncoupled 50 ohm lines as Zodd=50
ohms, Zeven=50 ohms. Then, if these two lines are brought closer together
(without other changes in geometry), Zodd will drop below 50 with Zeven
rising above 50.

Some people define Zdifferential=2*Zodd because a resistor of this value
places between the two traces provides reflectionless termination of odd
mode signals, but this is equivalent to placing termination resistors of
Zodd from each trace to a "virtual" ground node between the traces, so the
termination resistance allocated to each trace is really Zodd. In fact, in
practice, one sometimes wants to terminate a differential line with
resistors of value Zodd to "true" ground to provide some termination of even
mode signals as well as the odd mode signals.

Similarly, some define Zcommon=Zeven/2 because resistor of this value
connected from ground to both traces (shorted together) will provide
reflectionless termination of even mode signals, but again, I view this as
equivalent to placing resistors of value Zeven from each trace to ground
separately -- there is a virtual "short" between the two traces for true
even mode signals.

To further confuse things, some define Zodd or Zeven not as I did above, but
with these extra factors of 2.

I prefer the terminology without the additional factors of 2 for a number of
reasons, but primarily because it then can be generalized to systems of more
than 2 coupled conductors, or to two conductor systems that are not exactly
symmetric (in which case "Zeven" and "Zodd" are ill-defined quantities, and
the system has to be described by two "eigenmodes" that are neither quite
even or quite odd).

In the end, you can use whatever system of definitions you like as long as
you, your simulation tools, and your board vendor use the same terminology
(or at least know how to convert from one to another) so that embarrassing
factor of 2 discrepancies in impedances can be avoided.

Regarding your question of whether one cares about anything besides Zodd (or
Zdiff), I personally think it is useful to be aware of both Zodd and Zeven
when designing differential line structures as many systems issues (EMC,
noise immunity, common mode rejection, propagation across split planes, ...)
involve considerations of both quantities.

- Erik

==================================================================
Erik Daniel, Ph.D. Mayo Foundation
Voice: (507) 284-1634 Guggenheim 1011B
Fax: (507) 284-9171 200 First Street SW
E-mail: [email protected] Rochester, MN 55905
==================================================================

-----Original Message-----
From: [email protected] [mailto:[email protected]]
Sent: Wednesday, October 25, 2000 8:43 PM
To: Dima Smolyansky
Cc: [email protected]; [email protected]
Subject: RE: [SI-LIST] : connector model for differential signal

Dear Dima,

web site, I find
it is exactly what I am looking for.

However, I got a little confusion about common mode impedance in the paper
"Characterization of Differential Interconnects from TDR Measurement"
,DIFF-1199.pdf.

On the page two, equation 3, the common mode impedance is Z_common=Zeven /
2.

Checking the article "Differential impedance ... finally made simple"
(CAPGLTIF.pdf) by Eric Bogatin, from www.BogatinEnterprises.com,
<http://www.BogatinEnterprises.com> Slide 26, I find the
Z_common=Zeven=Z11+Z12.

Checking the HP54754A TDR user's manual, I find a description with
measurment waveform shown
"The common mode impedance of two 50 ohm uncoupled lines is 25 ohms". It
match what you described Zcommon.

Shall the Z_common be Zeven/2 or Zeven?

To meet Zdiff is always mentioned when doing PCB impedance control. Usually,
I totally forget Zcommon
when try to meet Zdiff. What circumstance shall I maintain Zcomm , instead
of Zdiff , or both?

Thank you for your inputs.

Best Regards,

John Lin
SI Engineer, ARD4
Quanta Computer Inc.,Taiwan, R.O.C.
Email: [email protected] <mailto:[email protected]>
Tel: 886+3+3979000 ext. 5183

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