FR4 -- er vs frequency relation

I know that for FR4 the ε_r value decreases with frequency.
I want to measure the ε_r at low frequency by measuring the capacitance of a sheet of FR4 and then estimate ε_r at 1 GHz. -- this would be more precise than using the "standard" value of 4.6 .
Do you know the actual relation for ε_r vs frequency ?

Thank you

fr4 is not dielectric controlled, so every board you get will be different from the last. Also, it is anisotropic due to the large fiberglass threads embedded in the epoxy. So...good luck with that

Thanks for the answer.
I use FR4 below 1 GHz and I wanted to measure the sheet of FR4 I will use. This is not for large scale production.

I found a general answer that applies to all dielectrics -- the capacitance should be measured at two frequencies, and εr and loss tangent can be estimated for any frequency.

[URL="https://www.sigcon.com/Pubs/news/4_5.htm[/URL]

yeah below 1 ghz you can use it.

Nice idea, but it is more complicated than that. FR4 is not homogeneous, and not isotropic. The glass fibre and the resin have different ε_r, and the effective ε_r for vertical E-field (=> resonator length) is different from the effective ε_r for horizontal E-field (=> coupling between closely spaced lines). For practical application, we usually talk about some effective ε_r, but technically that isn't exact.

Unfortunately, there is no simple way to extract the frequency dependent parameters from one DC-measurement and one measurement at 1GHz. You better measure at your frequencies of interest (e.g. ring resonator).

Yes, I think the best is to use a ring resonator method AT desired frequency.

https://www.wpi.edu/Pubs/ETD/Availab...d/waldroni.pdf
http://personal.ee.surrey.ac.uk/Pers...s/Transfer.pdf