Improved formulas for the resonant frequencies of dual frequency arrow shaped compact microstrip antenna

In this article, simple expressions for calculating the resonant frequencies at TM10 and TM01 modes of dual frequency arrow-shaped compact microstrip antennas are presented. These empirical expressions are derived with the use of differential evolution algorithm by using the simulation data reported in the literature. The resonant frequency results achieved in this study are compared with the simulation results and theoretical results of the design formulas proposed elsewhere. It is shown that our formulas provide more accurate results with respect to the theoretical analyses previously published in the literature. The new formulas also give a simpler way to calculate the resonant frequencies of arrow-shaped compact patch antenna with dual frequency. (C) 2007 Wiley Periodicals, Inc.