Complimentary Split Ring Resonator

We are doing a project on patch antenna miniaturization using metamaterials. We are using complimentary split resonator on ground plane of the patch antenna. The frequency of operation was reduced from 10 GHz to 3.28 GHz. Can anybody explain how that happened. I mean what is the scientific reason behind the reduction? Please help!

Your patch antenna is made on a dielectric substrate. The square root of its permittivity is the "shortening" constant. In your case, your dielectric apparently has k ~ 9.3 approx.