A generalized formula in calculation of the resonant frequency of notch antenna

Notch antenna is constructed by slotting an edge of rectangular patch placed on a substrate over ground plane. Analysis of the notch antenna is complicated and very difficult due to having non-uniform shape. In this work, a novel formulation is proposed for calculating the resonant frequency of the notch antennas. The formulation regarding the resonant length of the antenna reflecting the impact of the slot is derived using Particle Swarm Optimization (PSO). Data vector of 96 notch antennas consisting of seven geometrical and electrical parameters is acquired by simulations. A resonant length formula enclosing those parameters accompanying with optimization variables is constituted in conformity with simulation data. The variables are then optimally determined by fitting the calculated resonant frequency to the simulated one by PSO algorithm. The proposed formulation is verified with simulated/measured data and validated with a test notch antenna fabricated in this study. The results demonstrate that the resonant frequency of the notch antenna can be simply calculated using the proposed formulation without dealing with sophisticated mathematics and performing simulations or measurement.