Compact Expressions for Efficiency and Bandwidth of Patch Antennas Over Lossy Magneto-Dielectric Materials

Closed-form formulas for calculating the radiation efficiency and bandwidth of patch antennas over lossy magneto-dielectric materials are proposed by using the cavity model. These expressions agree well with simulations. It is well known that the bandwidth of microstrip antennas is enhanced when the dielectric substrate is replaced by a magnetic one. Here, we confirm more generally that not only the bandwidth, but also the radiation efficiency, can be improved when the permeability (μ
_r
) is greater than the permittivity (ε
_r
).