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Background

I've calculated the characteristic impedance of a CoPlanar Wave Guide (CPWG) type transmission line on my 8-layer stack-up between L1 - top layer and L2 - GND1 directly underneath it. The calculations are pretty standard and supported by many freely available calculators. The calculator by Spok consulting, for example, gave the following result:

Spok calculator

Problem

I would like to increase the width of my traces whilst maintaining the same ~50 Ohm nominal characteristic impedance of my line. An obvious solution would be to have my reference plane further away from the top layer. Let's say I want to use L7 - GND. Naturally, I'd clear out all copper from between these two layers.

Question

How do I calculate the effective permittivity of all the different layers of dielectric combined? I couldn't find any calculators that support this.

Stackup Layer Stack

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1 Answer 1

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You're very unlikely to find any simple calculator that will solve these problems.

The way the simple calculator works is that at some point someone did some EM simulations (for example finite element method [FEM] simulations) of a trace geometry, with some variations in the dimensions. Then they found an interpolating formula that fit the simulation results and the calculator uses this fitting formula to produce its results.

With 7 dielectric layers, each with a dielectric constant and height that can be varied, there are simply too many free parameters to make it practical to generate a fitting formula for this geometry.

If you had just a couple of materials with fairly close dielectric constant (say an FR-4 core and FR-4 prepreg, with \$\varepsilon_R\$ of 4.5 and 4.7), you might get adequate results by just averaging the dielectric constant.

But with your widely varying materials (\$\varepsilon_R\$ ranging from 3.5 to 5.1), you will probably have to do the full simulation yourself to get an answer. General EM simulation tools like HFSS from Ansys and Microwave Office from AWR can do this simulation. It looks like Polar (a field solver specialized for finding transmission line impedance) now supports some geometries similar to what you need, but it's unclear if they support as many layers as you have in your problem.

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