Dielectric permittivity relation to the fringing, radiated power, efficiency.

Hello,

What is the relation between the dielectric permittivity and the fringing on the edges of the patch? does this have any relation to the radiated power, the efficiency and the bandwidth? your help is appreciated.

Thank you
Kawther

Only bandwidth is unequivocally related to εr, see Balanis chapter 14.4
This is due to the general law that the bandwidth of electrical small antennas is proportional to it's volume.

All other parameters may be affected by εr in a specific design but also depend on substrate losses and of course impedance matching. A lossless and perfectly matched antenna will transmit all input power (100% efficiency).