1- what is the relationship b/w the bandwidth and metamaterials patch antenna? why is the bandwidth  extending ?

2- what is the relationship b/w the bandwidth and the capacitance?

3- are there principle equations to design the structure array that mounted on the patch as it is showing in the file below? if they are equations please provide them to me ?

4- explain the different b/w metamaterials and conventional patch antenna physically or theoretically ?

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