Optimal design of compact microwave fractional order differentiator

This paper presents a stable, accurate and wideband microwave fractional order differentiator (MFOD) based on infinite impulse response filter. The fractional order differentiator (FOD) design problem is formulated in the z-domain. This formulation alliances with the transmission line elements in cascading. Real coded genetic algorithm (RCGA), particle swarm optimization (PSO) and cuckoo search algorithm (CSA) are applied to determine the optimum values of the characteristic impedances of the transmission line elements. The performance measure criterion of CSA algorithm as compared with other nature inspired algorithms-based differentiator are carried by the magnitude response, absolute magnitude error, phase response, pole-zero response, percentage improvement graph and convergence rate. The simulation and statistical analysis clearly affirm that the proposed MFOD using CSA outperforms RCGA and PSO in all state-of-the-art. The absolute magnitude error for the designed fifth order is as low as 2.9022. The designed fractional order differentiator is implemented in the form of microstrip on RT/Duroid substrate with dielectric constant 2.2 and thickness 0.762 mm. that is eligible for wideband microwave differentiator. The proposed design is compact in size and has low absolute magnitude error over the entire bandwidth. The measured result agrees well with the simulated result in the frequency range 1-12.5 GHz in MATLAB and advanced design software (ADS) environment.