# Re: [SI-LIST] : Upper limit of interplane capacitance

From: Ray Anderson ([email protected])
Date: Fri Jun 09 2000 - 10:08:50 PDT

You can calculate the interplane capacitance
(ignoring fringing effects) as

C = (ErEo)/t

Works out to about 225 pF/sq inch for 4 mil FR4

Inductance can be derived from the following
relation:

vel = Co/sqrt(Er) = 1 /sqrt(LC)

Solving for L yields about .13 nH/square for
planes separated by 4 mils.

so Zo = sqrt(L/C) therefore you get .75 ohm-inch
Zo for 4 mil FR4 planes.

We've been able to get very good prediction to measurement correlation
in the lab.

We've created a plane model in spice based on the above relationships.
Simulation of the model provides results with very good correlation
to VNA measurements of actual planes. (i.e. same capacitance,
same inductance, same resonance)

-Ray

>
> What would people expect the characteristic impedance
> to be of a 4" x 6" x 4mil FR-4 structure?
>
> Parallel plates are just two dimensional transmission
> lines with L and C being in units of H/area and F/area.
> The equations pop out pretty much the same as a one
> dimensional transmission line, i.e.
>
> vprop = 1/sqrt(LC)
> Z0 = sqrt(L/C)
>
> In fact, there's some pretty neat derivations
> for parallel plates such as
>
> Z0 = sqrt(mu/epsilon)*d/w
>
> d = distance of separation
> w = width
>
> ignoring fringing effects.
>
> Just was wondering if anyone has done any
> research into correlating pure theory
> versus reality.
>
> - Doug McKean
>

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