Design and implementation of fractional‐order microwave differentiator

Abstract

The new design of a fractional‐order microwave differentiator is proposed. It is first of its kind and uses short‐circuited stub and transmission line sections to emulate the behaviour of an ideal fractional‐order differentiator. Least mean square error‐based objective function is formulated to obtain the transfer function of the proposed design, using the chain scattering parameters of line elements in the Z‐domain. During the optimisation process, impedance values of equal‐electrical‐length line elements are considered in the range 10–150 Ω, such that they are practically realisable on the microstrip format. The structure is implemented on the FR4 substrate with permittivity of 4.4 having 1.6 mm thickness. The measured result for the magnitude response of the transmission coefficient is found to be in good agreement with ideal one in the operating frequency range from 0.8 to 6.6 GHz.