Radiation from patches on grounded cylindrical substrates with arbitrary cross-section

One of the advantages of microstrip antennas is the possibility to make the microstrip patches conformal to the mounting structure. However, bending the patch and the mounting structure usually complicates the analysis because it requires complicated numerical techniques. Some simple conformal microstrip antennas mounted on simple surfaces may be readily analyzed, such as circular cylinders, spherical surfaces, and conical surfaces. These mounting surfaces were chosen because it was possible to derive the Green's functions that may simplify the analysis. We present a simple solution to compute the radiation patterns of microstrip antenna patches that are mounted on an infinitely long cylinder with arbitrary composite cross-section. The cylindrical cross-section can be shaped to control the radiation pattern of the patch. The patch could also be embedded in a multilayer dielectric substrate. The dielectric substrates need not necessarily be of uniform thickness in the cross-section, however they must be uniform in the direction of the cylinder. In our analysis we assume a known current distribution on the patch. For the time being we assume that the main radiation is contributed by one mode. We consider each of the first two modes of the rectangular patch, namely, the TM01 and TM10 modes. In using these modes we assume the current distribution to be sinusoidally varying in one direction and constant in the other direction.