Mathematical Modeling, Equivalent Circuit Analysis and Genetic Algorithm Optimization of an N-sided Regular Polygon Split Ring Resonator (NRPSRR)

In this paper, a mathematical model is proposed to estimate the resonant frequency of a N-sided Regular Polygon Split Ring Resonator (NRPSRR), which is extended to the Circular Split Ring Resonator (CSRR) for N tending to infinity. The model also predicts the variation in the resonant frequency with the angle of rotation (skew) between the inner and the outer polygon. It is mathematically shown that the minimum resonant frequency is obtained at zero skew. Genetic Algorithm Optimization is used over the independent parameters deciding the geometry of the NRPSRR to optimize them for a particular desired resonant frequency by minimizing the relative error between the calculated and desired frequency. NRPSRR metamaterial loaded microstrip antenna could be used to obtain highly directional beam pattern and increased gain for miniaturized (electrically small) antenna systems in the microwave regime.