RE: [SI-LIST] : differential impedance calculations

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From: Eric Bogatin ([email protected])
Date: Thu Nov 02 2000 - 17:28:58 PST

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,
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

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

as always, comments are welcome.


Eric Bogatin
Training for Signal Integrity and Interconnect Design
v: 913-393-1305
f: 913-393-1306
e: [email protected]
web: <>

  -----Original Message-----
  From: Larry Miller [mailto:[email protected]]
  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.


  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

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

  Larry Miller

    -----Original Message-----
    From: chasgra [SMTP:[email protected]]
    Sent: Wednesday, November 01, 2000 9:04 PM
    To: Miller, Larry [SC7:322:EXCH]; Charles Grasso; Gary Peterson;
    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

    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:[email protected]>
      To: Charles Grasso <mailto:[email protected]> ; Gary Peterson
<mailto:[email protected]> ; si-list
<mailto:[email protected]>

      Cc: eric <mailto:[email protected]>
      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:[email protected]]
      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
      should help answer this question.

              Please goto <> Click on Last
Meeting and
      follow the instructions for the presentation download.


              Charles Grasso
      Ansoft Corporartion
      p: 303-666-1400
      f: 303-666-1499
      ----- Original Message -----
      From: "Gary Peterson" <[email protected]>
      To: <[email protected]>
      Sent: Wednesday, November 01, 2000 12:50 PM
      Subject: [SI-LIST] : differential impedance calculations

> I seem to recall Dr. Howard Johnson mentioning that impedance
> formulas made assumptions (since closed-form solutions aren't
> Can someone comment on assumptions made for the equation for
> impedance shown below? Seems to me that as traces get closer
> single ended impedance would be affected. When I calculate
> values for differential impedance using Hyperlynx LineSim, I do see
> single-ended impedance change when the spacing between the pair gets
> Thanks,
> Gary Peterson
> (Embedded image moved to file: pic27894.pcx)

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