Pseudo-Differential (2 + α)-Order Butterworth Frequency Filter

Abstract

This paper describes the design of analog pseudo-differential fractional frequency filter with the order of $(2+\alpha)$ , where $0 < \alpha < 1$ . The filter operates in a mixed-transadmittance mode (voltage input, current output) and provides a low-pass frequency response according to Butterworth approximation. General formulas to determine the required transfer function coefficients for desired value of fractional order $\alpha $ are also introduced. The designed filter provides the beneficial features of fully-differential solutions but with a less complex circuit topology. It is canonical, i.e. it employs a minimum number of passive elements, whereas all are grounded, and current conveyors as active elements. The proposed structure offers high input impedance, high output impedance, and high common-mode rejection ratio. By simple modification, voltage response can also be obtained. The performance of the proposed frequency filter is verified both by simulations and experimental measurements proving the validity of theory and the advantageous features of the filter.

Keywords

• Current conveyor
• fractional Butterworth transfer function
• fractional-order filter
• pseudo-differential filter