**From:** Eric Bogatin (*eric@bogent.com*)

**Date:** Thu Nov 02 2000 - 17:28:58 PST

**Next message:**Michael Nudelman: "Re: [SI-LIST] : Unit failing ESD testing"**Previous message:**Jeff Reeve: "[SI-LIST] : Unit failing ESD testing"**In reply to:**Larry Miller: "RE: [SI-LIST] : differential impedance calculations"**Next in thread:**Jason Xiao: "RE: [SI-LIST] : differential impedance calculations"

RE: [SI-LIST] : differential impedance calculationsLarry-

Thanks for bringing up this issue of how to calculate diff impedance, and

diff impedance calculators. Your question is really related to "what method

can I use, and HAVE CONFIDENCE in, (my emphasis added) to calculate the diff

impedance of a diff pair of transmission lines?"

The very quick answer is, if you want to have confidence in the result, you

need to use a 2D field solver that has been verified. I have verified the

Ansoft 2D extractor and the Hyperlynx tool and their accuracy is better than

1%- for these details see my DesignCon 1999 paper which is available for

download from my web site. There may be other 2D field solvers that are as

accurate, I just haven't looked into this.

Think about the case of approximations for single ended characteristic

impedance, such as the IPC approximations. Too many engineers feel that

since they are equations, and some rather complex ones, and they are so

widely used, they must be right. In some specific cases, they can be more

accurate than 5%, but in most cases their accuracy is in the 10-20% range.

For the case of low impedance lines, the IPC microstrip equations are off by

more than 30%! Do you want to trust them for a design sign off? that might

ultimately cost time and money?

Not everyone likes hearing you have to use a field solver. It sure would be

nice to be able to use a simple closed form formula that you could just put

in a spread sheet. Unfortunately, with the exception of just a few formula,

EVERY SINGLE EQUATION YOU SEE USED IN SIGNAL INTEGRITY APPLICATIONS IS AN

APPROXIMATION. If you don't know the accuracy of the approximation, you do

not want to use it in a situation where 2-5% accuracy is required, such as

in a design sign off, especially when there are alternative tools available

that can provide the required accuracy. Saving one respin by getting the

board stack up right the first time will pay for the tool many times over.

And many of the 2D solvers available off the shelf are as easy to use as

spread sheets.

However, having said these disparaging comments about approximations, they

have some positive virtues. They are very useful when you want to explore

the design space and do initial design trade offs, precisely because you can

run them in a spreadsheet. They identify the first order effects and their

approximate relationship. They are a happy medium between ease of use and

closeness to reality. Approximations are one of the three types of analysis

tools every engineer should have in their tool box, the other two being

rules of thumb and numerical simulation tools. They each have their

appropriate time for use. You can read more about these three levels of

analysis in the paper on my web site, "Rules of thumb I have known and

loved".

I looked at a number of approximations for diff impedance and the National

Semi one is one of the best I've found. In the presentation I gave at the

RMCEMC workshop, I showed a comparison of the predictions of the National

Semi approximation and the results calculated from the Ansoft 2D Extractor.

The National approx results, for the special case of a pair of 50 Ohm single

ended lines, brought close together, are actually pretty good. If I were

doing some quick estimates, I would probably use this approximation.

However, if I were signing off on a design, I would not. I would use a 2D

field solver, because I have confidence the tool would take into account

some of the real world second order effects, such as trace thickness and

presence of soldermask.

The presentation I gave at the RMCEMC was not on how to calculate diff

impedance, nor even how to design diff pairs. It was on what is diff

impedance, and how to get a better intuitive feel for what it means. The TDR

examples I used graphically illustrated how the impedance of one line really

does depend on how the other line is driven, and by the way, you can use

these TDR measurements to extract the complete characteristic impedance

matrix of a diff pair. I hope this clarifies what I presented at the RMCEMC

workshop.

as always, comments are welcome.

--eric

Eric Bogatin

BOGATIN ENTERPRISES

Training for Signal Integrity and Interconnect Design

v: 913-393-1305

f: 913-393-1306

e: eric@bogent.com

web: <http://www.bogatinenterprises.com/>

ftp: ftp://ftp.BogatinEnterprises.com

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

From: Larry Miller [mailto:ldmiller@nortelnetworks.com]

Sent: Thursday, November 02, 2000 9:42 AM

To: chasgra; Charles Grasso; Gary Peterson; si-list

Cc: eric

Subject: RE: [SI-LIST] : differential impedance calculations

Hello, all,

Well, Mr. Grasso, you could be right inasmuch as I did not have the

opportunity to attend the presentation in person.

However,

1) The preceding part of the paper presents equations that deal with the

measurements (principally TDR) that show how differential lines work, and

these look very OK.

2) It appears to require a field solver to get the impedances required for

the formulae if you do not want to do TDR measurements. This greatly limits

usefulness for a "paper design" where you do not have a test board available

to measure (for example, I do have the TDR instrument(!) )

3) The only closed-form calculations I see in the paper are the National

ones, and National (in AN-905) points out that these formulae, used on

Slides 45 and 46 are from empirical measurements (i.e., curve-fitting to

measured data) and your mileage may vary.

4) Now maybe Dr Bogatin was slagging these calculations in the verbal

presentation, but there is nothing in the slides to indicate that or that

these National formulae are NOT pretty good, such as curves showing the

error between the formulae and measured data. If this is the case, I would

surely like to know it!

Like many others on this reflector, I have been trying to cope with

differential pair logic (in particular, souped-up LVDS) to model

interconnects for back- and mid-planes for supra-gigabit serial backplane

design. Between having to deal with very high trace density (1000's of diff

pairs) with long runs, huge skin effect losses, and limits on backplane

thickness, this has been a pretty tough exercise, and the literature seems

pretty darned slim.

Working with chip, connector and backplane vendors has not been

particularly satisfactory for planning a design. This is again because

nobody seems to have rolled all the math into a big ball. Maybe it cannot be

done. In any case, we find ourselves doing very pricey iterations that are

little better than cut-and-try. (An informed cut-and-try, to be sure.)

In particular, I have had a hard time finding closed-form equations that

take all of these factors into account, or even applications that do. Most

of the (expensive) tools touted on this reflector have gotten very mixed

reviews. The one Gary mentioned seems to --partly-- solve the problem, and

that seems to be the state of things. I think that there is a sort of

consensus here that the board-level modelers/analyzers are either not very

accurate or require so much input that they are hardly worth the trouble.

(Pardon me for a moment while I duck!)

Having met Dr Johnson when I was working on the IEEE Gigabit Ethernet

committee a couple of years ago (IEEE 802.3z), I requested him to do a 10 Gb

update on "Digital Black Magic". I don't know if he is working on such a

thing.

Now I will stand back for the onslaught.....

Larry Miller

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

From: chasgra [SMTP:chasgra@email.msn.com]

Sent: Wednesday, November 01, 2000 9:04 PM

To: Miller, Larry [SC7:322:EXCH]; Charles Grasso; Gary Peterson;

si-list

Cc: eric

Subject: Re: [SI-LIST] : differential impedance calculations

Hi Larry - Thanks for your comments.

If you are referring to slides 45 & 46 I think you misunderstand the

intent.

Dr Bogatin was, I believe, trying to show comparisons between Ist order

approximations and a field solver. I do not belive any assumptions were

being made. Indeed as I recall he did nake the statement that one should

not always trust approximation BECAUSE of the assumptions.

Charles Grasso

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

From: Larry Miller <mailto:ldmiller@nortelnetworks.com>

To: Charles Grasso <mailto:chasgra@msn.com> ; Gary Peterson

<mailto:Gary_Peterson@Emcore.com> ; si-list

<mailto:si-list@silab.eng.sun.com>

Cc: eric <mailto:eric@bogent.com>

Sent: Wednesday, November 01, 2000 2:04 PM

Subject: RE: [SI-LIST] : differential impedance calculations

Unfortunately, the piece by Dr Bogatin makes and refers to the very

assumptions that Dr Johnson refers to.

All roads lead to the National App Note AN-905.

(I have been battling this same fight myself.)

Larry Miller

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

From: Charles Grasso [SMTP:chasgra@msn.com]

Sent: Wednesday, November 01, 2000 2:23 PM

To: Gary Peterson; si-list

Cc: eric

Subject: Re: [SI-LIST] : differential impedance calculations

Hello - There is an excellent presentation available for

download called

"Differential Impedance finally made Simple" authored by Dr Bogatin

that

should help answer this question.

Please goto <http://www.ewh.ieee.org/rmcemc> Click on Last

Meeting and

follow the instructions for the presentation download.

Enjoy!!

Charles Grasso

Ansoft Corporartion

p: 303-666-1400

f: 303-666-1499

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

From: "Gary Peterson" <Gary_Peterson@Emcore.com>

To: <si-list@silab.eng.sun.com>

Sent: Wednesday, November 01, 2000 12:50 PM

Subject: [SI-LIST] : differential impedance calculations

* >
*

* >
*

* > I seem to recall Dr. Howard Johnson mentioning that impedance
*

calculation

* > formulas made assumptions (since closed-form solutions aren't
*

possible).

* >
*

* > Can someone comment on assumptions made for the equation for
*

differential

* > impedance shown below? Seems to me that as traces get closer
*

together,

the

* > single ended impedance would be affected. When I calculate
*

single-point

* > values for differential impedance using Hyperlynx LineSim, I do see
*

the

* > single-ended impedance change when the spacing between the pair gets
*

small.

* >
*

* > Thanks,
*

* >
*

* > Gary Peterson
*

* >
*

* >
*

* >
*

* > (Embedded image moved to file: pic27894.pcx)
*

* >
*

* >
*

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**Next message:**Michael Nudelman: "Re: [SI-LIST] : Unit failing ESD testing"**Previous message:**Jeff Reeve: "[SI-LIST] : Unit failing ESD testing"**In reply to:**Larry Miller: "RE: [SI-LIST] : differential impedance calculations"**Next in thread:**Jason Xiao: "RE: [SI-LIST] : differential impedance calculations"

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