**From:** Daniel, Erik S. (*Daniel.Erik@mayo.edu*)

**Date:** Thu Oct 26 2000 - 08:59:08 PDT

**Next message:**Ken Church: "[SI-LIST] : HSTL termination"**Previous message:**Peterson, George W: "RE: [SI-LIST] : Search for ADSP-21160 IBIS model"**Maybe in reply to:**ªL´Â·×: "[SI-LIST] : connector model for differential signal"

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: daniel.erik@mayo.edu Rochester, MN 55905

==================================================================

-----Original Message-----

From: Bob Weber [mailto:rweber@txc.com]

Sent: Thursday, October 26, 2000 9:23 AM

To: Daniel, Erik S.

Cc: si-list@silab.eng.sun.com

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: owner-si-list@silab.eng.sun.com

[mailto:owner-si-list@silab.eng.sun.com]On Behalf Of Daniel, Erik S.

Sent: Thursday, October 26, 2000 8:30 AM

To: John@quantatw.com

Cc: si-list@silab.eng.sun.com

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: daniel.erik@mayo.edu Rochester, MN 55905

==================================================================

-----Original Message-----

From: John@quantatw.com [mailto:John@quantatw.com]

Sent: Wednesday, October 25, 2000 8:43 PM

To: Dima Smolyansky

Cc: eric@bogent.com; si-list@silab.eng.sun.com

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

Dear Dima,

Thank you for your response. After downloading the application note for the

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: John@quantatw.com <mailto:John@quantatw.com>

Tel: 886+3+3979000 ext. 5183

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