how to design ring elements in antenna array

hi,

I want to design an antenna array using ring elements. Now I have center frequency and substrate information, how can i calculate the outer radius and inner radius of the ring element?
I read Kai Chang's book <ring resonator>, but i can not find the equation for the design.

Regards,
panou

For closed rings, the circumference has to be equal to lambda (one full wavelength in substrate). Calculate the effective dielectric constant using the height of the substrate, width of the ring and dielectric constant and determine the lambda in substrate at your design frequency.

You can find the formulas for calculating effective dielectric constant and calculating lambda in substrate in any standard textbook

-sv