Effective permittivity of a stacked substrate

I have a dipole antenna on stacked substrate of different materials with different er.
Is it possible to calculate an effective permittivity for the substrate to use it for the antenna design?

sure...but you would have to do so in a EM simulator to get it right. That is because the "effective" dielectric constant depends on what percentage of the Efields are contained in each substrate, and that is determined by the circuit shapes, frequency, the thickness and dielectric constants closest to the conductor, etc.

Ok thx.
So I have to model the stack in an simulator and then have to determine to the "effective" dielectric constant?
How can I get the "effective" dielectric constant?
My first guess would be to use some real word techniques (like a T-resonator) within the simulation environment. What is the best way to do this?

i would just make a length of what i thought to be 50 ohm transmission line, and see what the return loss was. If it turned out to be non-50 ohm line, it would be easy to deduce the effective dielectric constant you really had.

There are some early papers advocating using lightly coupled λ/2 resonators to more accurately do that (Gopinath)