Electronic – PCB Layer Stack Dielectric Constant Math

dielectricpcbpcb-layers

I have a question reference PCB layer stack and the adding multiple dielectric constants together.

The image and description below should help clarify the question:
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  • The differential pair will be configured in an Edge Coupled External on the top layer, with the signal ground / screen on layer 3.
  • So the Prepreg (between layer 1 and 2) and the Core (between layer 2 and 3) will form a combined dielectric constant.
  • I have not included any differential speed as this will be a factor but not important for the question below, more interested in how best to approach the problem which can then be applied to any differential pair in future. Running the ground on layer 2 is not an option in this case, although it would simplify the problem.

Question: What is the best practice in this scenario for calculating the expected dielectric constant; (1) can we treat this like a series capacitor adding the reciprocals of each, (2) do we simple add them together, (3) do we add them and then divide to produce a mean value, (4) or?

Best Answer

Assuming the frequency is so low that the capacitance as whole board size component is meaningful you can well calculate the capasitance per unit area between the two remaining metal layers with the following formula:

$$\frac{C}{A} = \frac{1}{\frac{s_1}{e_1} + \frac{s_2}{e_2}}$$

Where e1 and e2 are absolute permittivities of the dielectric layers, s1 and s2 are their thicknesses. This applies the idea to have 2 capacitors in series.