Radiation Efficiency Issues in Planar (Patch) Antennas on Electrically Thick Substrates and Solutions

I found a really interesting study on radiation efficiency of patch antennas. They analyzed the trade-off between radiation efficiency and other antenna properties and have proposed solutions for this problem.


Abstract:
The paper addresses the problem of the radiation efficiency of planar antennas on electrically thick substrates. First, the non-monotonic dependency of the radiation efficiency of an infinitesimal horizontal electric dipole on grounded and ungrounded substrates versus the substrate electrical thickness is analyzed. Next, the phenomenology of the observed radiation efficiency is explained with the help of a novel substrate dipole approach, which reduces the actual structure to an equivalent source dipole composed of the original dipole and the substrate dipole radiating into free space. Finally, two solutions for enhancing the efficiency at electrical thicknesses where the efficiency is minimal are studied.

Link to article http://ieeexplore.ieee.org/document/6507325/