RE: [SI-LIST] : Transmission Lines Formulae

Eric Bogatin ([email protected])
Wed, 13 Jan 1999 14:02:06 -0600

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Lum Wee-

I see versions of your question on the SI list every few months or so. It is
a very important issue when you are designing the stack up geometry for a
board, and want to get the design right the first time. For those new to the
field (no pun intended) it must be very confusing to see so many equations
to use for calculating characteristic impedance for microstrip and
stripline, and not know which one is the "right" one to use.

10 years ago, I looked into this question and wrote a paper in IEEE Trans of
CHMT Vol 11 (3), Sept 1988, "Design Rules for Microstrip Capacitance" (The
same equation for the capacitance can get you the characteristic impedance).
I compared about 8 different equations that had been reported in the
literature, all looking very different, and of different levels of
complexity. What surprised me was that most of them agreed with each other
and matched the measured data I used as my reference, pretty well. So, even
though there are a lot of models out there, many of them might be ok for

These days, the IPC has made things easier for us. There are a number of
design guides published with Z0 approximations. For example, look at the
IPC-2141 "Controlled Impedance Circuit Boards and High Speed Logic Design"
document. I think Dana Korf, now at Hadco, was instrumental in putting this
fine document together. You should still ask the question, how good are the
approximations offered by the IPC.

I am giving a talk at Design Con 99, in San Jose in early Feb that addresses
this question. I looked at the IPC approximations and compared their results
with the results from a 2D field solver from Ansoft. I had previously
verified this field solver to less than 1% absolute error. What I found with
the IPC approximations for microstrip and stripline was that as long as your
geometry was about 50 Ohms or greater, and you used FR4, the approximations
were within 5% accurate. However, if you use low impedance designs, mixed
dielectrics, asymmetric stripline, offset broadside coupled, then these
approximations do not apply.

The only reliable method to calculate the characteristic impedance for an
arbitrary stack up is using a 2D field solver. I personally believe a good,
easy to use 2D field solver is as useful to the engineer doing stack up
design, as a calculator or spreadsheet tool is. It should be a critical tool
in your tool kit. The only one I have direct experience with is the Ansoft
2D tool, which is relatively easy to use. However, I have appended a brief
list of web sites of other vendors of 2D field solvers that you might want
to check out. I personally believe that any engineer who needs to worry
about the stack up design should have ready access to a 2D field solver they
are comfortable using.

I am giving a half day workshop at the PCB West show in Santa Clara, in
March, on using 2D field solvers to do stack up design. The only tools I
will be using in this workshop will be ones that are as easy to use as a
calculator. All are welcome to sign up.

Also, I will extend the offer (again), if anyone would like a reprint of the
paper I am giving at Design Con, I will send you a hardcopy when it is
available (probably late Feb), if you send me your snail mail address off

brief list of 2D field solver vendors:

Ansoft ( )
ApSim ( )
OptEM Eng ( )
Pacific Numerix ( )
Polar Instruments ( )
Quantic Labs ( )

Does anyone have other vendors that I should add to my list?


Eric Bogatin
Signal Integrity/EMI Technology Analysis and Training
26235 W. 110th Terr.
Olathe, KS 66061
v: 913-393-1305
f: 913-393-1306
e: [email protected]
pager: 888-775-1138

-----Original Message-----
From: [email protected]
[mailto:[email protected]]On Behalf Of Lum Wee Mei
Sent: Tuesday, January 12, 1999 8:01 PM
To: '[email protected]'
Subject: [SI-LIST] : Transmission Lines Formulae

While working on my Z calculation for transmission line, I noticed that
different reference books provide different variations of the
transmission line formulae be it microstrip or stipline.

As a designer, I am expected to be proffesional in my work and able to
explain the rationale why I use the formulae from this reference book
and not the other. Can someone enlighten me on which formula to use and
the reason, if any?

BTW, an engineer in another dept of mine mentioned that I need not have
to bother with manual Z calculation because the PNC SI tool is able to
extract the information. I have attended the PNC workshop and do not
find it friendly to use. Moreover, the accuracy of the output depend
heavily on the accuracy of the input. That is just my feeling ;)p, I do
not know about the rest of you who have use this PNC SI tool?

Hope to hear from anyone of you.
Thanks and regards.

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