Estimation of the Effective Medium for Planar Microstrip Antennas on a Dielectric and Magnetic Truncated Substrate

This letter proposes a simple formula to estimate the effective medium of planar microstrip antennas printed on a magneto-dielectric truncated substrate. The proposed empirical formulas shown in this letter yield a good accuracy with a maximum error of less than 7% for a permittivity between 1-10, a permeability between 1-10, and a ratio 0.01 <; h/W <; 0.25. These proposed empirical models are validated by electromagnetic simulations and measurements.