Dear romano088 ,

Thank you for your question. The short answer is the two dielectric constants need to be combined. But they do not simply add together. A crude ballpark approximation is 3.85 when they are averaged together. A better approximation is explained here.

For a microstrip geometry, without soldermask, Dkeff is the mixture of air Dk above the trace and laminate Dk below the trace. This is what you called Ereff and it is what you eventually use to calculate propagation delay of microstrip.

Recalling from first principles that a capacitor is simply a dielectric between two conductive plates. By definition, Dkeff is the ratio of the actual structure’s capacitance to the capacitance when the dielectric is replaced by air.

Cactual/Cair =Dkeff/Dkair ………. (1)

From eq. (1) we see Cactual is directly proportional to Dkeff.

When there are two prepregs, with different Dks between two copper plates, the effective total capacitance of the dielectric is the capacitance due to each prepreg in series. If we call this Cmix, then total capacitance in series is:

Cmix = 1/(1/C1 + 1/C2) ………. (2)

If C1 = Dk1*er0*A/h1 and C2 = Dk2*er0*A/h2; where: er0 is permittivity of free space (~8.85pf/m) A is the area of copper plates and h1, h2 are the thicknesses of each prepreg, then the total capacitance is:

Cmix = 1/(1/Dk1*er0*A/h1 + 1/Dk2*er0*A/h2) ………. (3)

Example:

Assume h1 = 152.4um; h2 = 127um; and A =1 sq.m; Dk1 = 3.12; Dk2 = 4.58;

Then from Eq. (3):

Cmix = 1/(1/3.12*8.85E-12*1/152.4E-6+ 1/4.58*8.85E-12*1/127E-6) = 1.156E-7F

Now if we replace the two prepreg thickness with air (Dk of 1) in eq. (3), then the capacitance between plates, Cair is:

Cair = 1/(1/1*8.85E-12*1/152.4E-6+ 1/1*8.85E-12*1/127E-6) = 3.168E-8F

Then from eq (1):

Dkmix = Dkair * Cmix/Cair = 1*(1.156E-7/3.168E-8) = 3.65

So this is the Dk to use for the mixed prepregs. Once you have the Dk of mixed prepregs, a good field solver, is best to calculate Dkeff for microstrip. Once you have Dkeff of microstrip geometry, then you can calculate the propagation delay.

But the best option is to use an accurate electromagnetic 2D field solver that allows for mixed dielectric to calculate the impedance and propagation delay of the transmission line geometry.

I hope this helps.

-Bert

]]>e.g.: suppose we have the following stackup: copper-foil, prepreg1, prepreg2, core’s foil, dielectric-core, core’s foil, prepreg2, prepreg1, copper-foil; Where DK_prepreg1 = 3.12 and DK_prepreg2 = 4.58, on this case in order to calculate the propagation delay in a microstrip, the resultant Dk should be = (Dk_prepreg1 + Dk_prepreg2) or how should I calculate the Dk in order to be used with the propagation delay formula?. And one last thing, should we use Ereff instead of just the given Dk?(I’m asking because I have no Idea if this’s correct or not given the microstrip structure I will use with this stackup). Thanks Bert. ]]>