Description

Fractional calculus has maintained tremendous vitality in various areas of automatic control
systems, signal processing, image processing, circuit theory and biomedical engineering. It
involves a unique feature of generalization of integral and derivative to a non-integer order.
This synopsis presents the designing of integer order and fractional order microwave
differentiators and integrators. These proposed designs are obtained by using different
combinations of transmission line sections and shunt stubs in cascading. Evolutionary
algorithms like cuckoo search algorithm (CSA), particle search optimization (PSO),
gravitational search algorithm (GSA), hybrid PSO-GSA (HPSO-GSA) and real-coded genetic
algorithm (RCGA) are used to obtain the optimal values of the characteristic impedances of
the transmission line elements to approximate the ideal magnitude response. The proposed
designs using CSA, PSO, GSA, HPSO-GSA and RCGA have been proved to be very robust,
simple and generic. The effectiveness of the proposed designs is evaluated and compared with
the existing methods. This work also focuses on the phase response of the proposed integer
order and fractional order microwave differentiators and integrators. Further, the structure of
the proposed differentiators and integrators are implemented in the form of microstrip line on
RT/Duroid substrate with dielectric constant 2.2 and thickness 0.762 mm.