[SI-LIST] : Re: Trace impedance

rbmccammon@mmm.com
Fri, 21 Aug 1998 12:43:48 -0500

Dominic Casperson wrote:

> I was hoping that someone might be able to shed a little light on a
> problem that I have encountered regarding the impedance of stripline,
> and microstrip PCB tracks.
> I require a formula that is capable of predicting the impedance's of
> stripline, and microstrip tracks. I have already found several from
> different source, but none of them seem to agree with each other, my TDR
> results, or the TDR results from "MECL system design handbook" by
> Motorola. All the formulas that I have come across claim to have an
> accuracy to within about 5%, but as far as I can tell the discrepancy
> can reach up to 20%, depending on the dimensions involved.
> The region of interest to me is:
>
> >Track width = 10 mils
> Track thickness = 1.37 mils
> Ground plane/Track separation (dielectric height) = 8 mils
> Relative permittivity = 4.7
> TDR edge rise time = 28ps
>
> >The most alarming problem that I have encountered is the natural
> logarithm that most formula seem to have, this then returns a negative
> number when its argument is smaller than one, even though most formula
> claim to still be accurate at this limit.

Yes, that formula has a restricted domain of accurate application.
This used to appear explicity in the application notes for ECL,
but it got lost along the way. For very wide traces, Z is
proportional to H/W.

The Motorola 1995 "High Performance ECL Data book" says the formula

Z = (87/sqrt(Er + 1.41)) ln (5.98H/(0.8W + T)) is accurate to 5%

for 0.1 < W/H < 3.0 and 1 < Er < 15

which gives 57.4

Using formulas from 'High Speed Digital Design' by Howard
and Graham, appendix C gives

Z = 57.76

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