Optimal design and implementation of compact fractional order microwave integrator

Abstract

The implementation of novel, stable, accurate, and wideband infinite impulse response fractional order microwave integrators (FOMIs) is presented. The formulation of FOMIs is employed with equal length line elements in cascading. The optimum values of characteristic impedances of the line elements are determined by approximation to the ideal fractional order integrator (FOI). The hybrid algorithm (HPSO-GSA) combining particle swarm optimization (PSO) and gravitational search algorithm (GSA) which integrates PSO's exploitation and GSA's exploration ability is used. The comparison of HPSO-GSA with PSO and GSA is carried out for the proposed FOMIs. The performance criteria used are magnitude response, absolute magnitude error, phase response, pole-zero response, percentage improvement graph, and convergence rate. The simulation analysis affirms the superiority of proposed FOMI using HPSO-GSA. The absolute magnitude error of proposed 0.5 order HPSO-GSA-based FOMI is as low as 0.9436. The structure of the designed FOI is implemented with microstrip configuration on RT/Duroid substrate with permittivity 2.2 and thickness 0.762 mm that is eligible for wideband microwave integrator. The designed FOMI is compact in size and suitable to cover microwave applications. The measured results are established in fine agreement with simulation results in the frequency range of 2-9 GHz in MATLAB and Advanced Design Software environment.