I would like to make four points in response to your request and
comments:
1. Semi-empirical formulas were introduced a long time ago and were
initially published with limitations (limits for dimensions for which
they were tested). They are frequently reprinted without these limits
and if used for dimensions outside their original domain they can
produce ridiculous results (like the negative characteristic impedance
that you mention),
2. Characteristic impedance that you measure includes all RLCG
parameters of the transmission line and for some frequencies cannot be
simply replaced with sqrt(L/C),
3. Parameters that influence the characteristic impedance are
frequency dependent, and therefore characteristic impedance is
frequency dependent (please see below) - how many frequency dependent
formulae did you find so far?
4. With the rise time 28ps you are using very high frequencies. It
is very likely that the harmonics up to 100 GHz influence your
results. The dielectric constant that you specified (4.7) suggest
that you are using FR-4 as a dielectric. The problem is that this
value is good for FR-4 for lower frequencies, and it is very likely
that at 100 GHz this value is 3.5 or even lower and that there is
substantial dielectric loss (however, since this is only my guess, the
frequency dependence of permittivity was not included in the
simulation below).
Now the results calculated by our EM solver for a microstrip:
Trace width = 10 mils
Trace and gnd plane thickness = 1.37 mils (Cu)
Ground plane/Trace separation (dielectric height) = 8 mils
Relative permittivity = 4.7
Please let me know if we can help you and if you are interested in
using our solver in the future.
Sincerely yours
Juliusz Poltz
# Parametric plot data from OptEM Interconnect Designer.
#
# x=frequency (log scale)
# y=Z
#
1 MHz, Z=75.3185 Ohm,
2.15443 MHz, Z=66.1253 Ohm,
4.64159 MHz, Z=63.0613 Ohm,
10 MHz, Z=61.8454 Ohm,
21.5443 MHz, Z=61.2823 Ohm,
46.4159 MHz, Z=60.9349 Ohm,
100 MHz, Z=60.63 Ohm,
215.443 MHz, Z=60.39 Ohm,
464.159 MHz, Z=60.18 Ohm,
1 GHz, Z=60.02 Ohm,
2.15443 GHz, Z=59.91 Ohm,
4.64159 GHz, Z=59.83 Ohm,
10 GHz, Z=59.77 Ohm,
21.5443 GHz, Z=59.73 Ohm,
46.4159 GHz, Z=59.71 Ohm,
100 GHz, Z=59.69 Ohm,
> Date: Thu, 20 Aug 1998 11:14:51 +0200
> From: casperdd <Dominic.Casperson@cern.ch>
> Organization: CERN
> To: "si-list@silab.eng.sun.com"
> <si-list@silab.Eng.Sun.COM> Subject: [SI-LIST] : Trace
> impedance
>
> Hi
>
> 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.
>
> I would appreciate it if anyone could show me where I have been
> going wrong, or point me in the direction of an accurate formula.
>
> Many Thanks
>
> Dominic Casperson
"Juliusz Poltz" <jpoltz@optem.com>
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