Radiation Pattern of a Microstrip Antenna on a Trapezoidal Substrate

This paper deals with a rectangular microstrip antenna on a trapezoidal substrate. It finds radiation pattern of the antenna using the concept of fractional cross product. Results show that as the fraction goes from 1 to 0.1, the direction of null in the H-plane moves from end fire towards broad side. Also, a back-lobe starts to appear in the H-plane.