An empirical expression for the edge extension in calculating resonant frequency of rectangular microstrip antennas with thin and thick substrates

This paper presents a simple empirical model for the edge extension in accurately calculating the resonant frequency of electrically thin and thick rectangular microstrip antennas. Based on the experimental results available in literature, a closed-form formula for edge extension is constructed by utilizing the simplex search method; then the resonant frequency of rectangular microstrip antennas is calculated by using this edge extension expression. A comparison between the calculated and experimental resonant frequency values demonstrates that the edge extension expression provides less than 0.51% errors on average. The resonant frequency results presented in this work also show the better agreement with the experimental results as compared to those predicted by several researchers.