Re: CPW impedance

John Larkin <jjlarkin@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx> wrote:
: But if I go to coplanar waveguide, 16 mil trace with 60 mil gaps,
: again 20 mils above ground, the trace impedance goes *UP*, to 82 or 78
: ohms for the two programs. I have to crank the gap down to about 20
: mils to get back down to 74 ohms.

Like others have suggested, such a wide gap is probably outside the
valid approximation range of the equations used. The analytic formula
from Waddell's book (involving elliptic integrals) gives about 81 ohms
for your geometry and er=4.9, and Zo does not approach the microstrip
value when the gap gets infinitely wide. Perhaps this is the formula
used by your programs as well.

When fiddling with the formula in Excel I got a feeling that
the formula would ignore the microstrip stray capacitance and only the
plate capacitance to the lower groundplane is accounted for. Then the formula
would work reasonably well in the case that the main capacitance contribution
near the trace edges is due to the top side groundplanes.

Anyway, I'm getting from the Waddell's eq. for your trace width, er=1 and
infinitely wide gap Zo = 192 ohms, which would correspond to 17.4 pF/m.
The microstrip approximation gives Zo = 139 ohms for er=1 (indeed 75 ohms
for er = 4.9) corresponding to 24 pF/m. Both are much more than the
parallel plate contribution of 7.1 pF/m. So the formula must fail in a more
subtle way.

It's curious that Waddel does not comment on the limits of the validity
of the formula, especially because it looks like it might be an exact
analytical result. The original paper by Ghione and Naldi however says that
they used approximate conformal mapping and assumed a perfect magnetic
boundary at the gap, which fails for wide gaps.

Regards,
Mikko
.

Relevant Pages

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