If an antenna resonates at 5.2ghz for e.g of size 28*24*1.6. If we use metamaterial and make them resonate at 2.4 Ghz. How much miniaturization is attained in percentage in this case. Any formula or explanation ?
You may be asking about what is called scalability. If your 5.2 GHz antenna now operates at 2.4 GHz, but being the same approximate size as your origional 5.2 GHz antenna, you have effectively shrunk it by almost 2x (2.4/5.2 = 0.46). That is, you could make your antenna 14x12x0.8 using the metamaterials and will operate at 5.2 GHz again.
but by following that formula, if we make an 8 ghz antenna work at 2 ghz ( 2/8 = 0.25) which comes out to be 25% reduction. Which shouldn't be the case.