Effect of substrate thickness on input impedance of coaxially-fed rectangular patch antennas

An attempt is made to answer the following questions: (1) How does the input impedance of a probe-fed rectangular microstrip antenna change as the substrate thickness increases, other parameters remaining the same? (2) How do the results depend on whether the axial and azimuthal variations of the probe surface current are taken into account? (3) For a fixed feed position, how does the impedance bandwidth change as the substrate thickness increases? (4) Can the feed location be optimized for maximum impedance bandwidth? (5) How does the maximum input resistance depend on the substrate loss tangent? Numerical results are presented.<>