Basis functions were studied and identified that provide efficient and accurate solutions for the induced patch currents and the reflection phase in microstrip reflectarrays. The integral equation of an infinite array of microstrip elements in the form of patches or crossed dipoles excited by a uniform plane wave is solved by the method-of-moments. Efficient choices of entire domain basis functions that yield accurate results have been described.
The results showed that an optimum choice would be a sinusoidal basis function with a built-in edge condition along the current flow direction, and uniform current across the current flow direction for a rectangular or square patch. For a dipole, the optimum choice is a sinusoidal basis function without the edge condition along the dipole, and uniform with the edge condition across. The code employing these basis functions was substantially faster than the commercial code HFSS, and it was significantly more accurate than previously developed method-of-moments code.
It was determined that the optimum choice is one basis function for each of the two induced currents in a square or rectangular patch, and one basis function for each dipole. For very thin substrates, there was a need to have 32 basis functions to produce accurate solutions.