Active and passive sensitivity analysis for the second-order active RC filter families using operational amplifier: a review

This work is a review article that sheds light on the active and passive sensitivities of the active RC filters based on opamp. This work provides a detailed analysis through different filters realization criteria and sensitivity summary tables and quantitative insight by discussing the most significant. However, some are almost forgotten, filters families in the literature over decades. A detailed mathematical analysis for the passive sensitivity to compare the filters’ realizations is presented. The concept of dealing between filter design theory and filter design circuit realization is highlighted. Some filters families are chosen from the literature for the analysis. Some detailed specifications tables for each filter family are given. Monte Carlo simulation is carried out on some filters to compare their passive sensitivity. Furthermore, the effect of the active sensitivity of some filters is verified through simulation by adjusting the input common-mode voltage to lower the DC gain of the amplifier. The results of the simulation match with the theoretical analysis and the summary provided in the specifications tables. © 2022, The Author(s).

On the Design Flow of the Fractional-Order Analog Filters Between FPAA Implementation and Circuit Realization

This work explicitly states the design flows of the fractional-order analog filters used by researchers throughout the literature. Two main flows are studied: the FPAA implementation and the circuit realization. Partial-fraction expansion representation is used to prepare the approximated fractional-order response for implementation on FPAA. The generalization of the second-order active RC analog filters based on opamp from the integer-order domain to the fractional-order domain is presented. The generalization is studied from both mathematical and circuit realization points of view. It is found that the great benefit of the fractional-order domain is that it adds more degrees of freedom to the filter design process. Simulation and experimental results match the expected theoretical analysis. © 2013 IEEE.

A Study on Fractional Power-Law Applications and Approximations

The frequency response of the fractional-order power-law filter can be approximated by different techniques, which eventually affect the expected performance. Fractional-order control systems introduce many benefits for applications like compensators to achieve robust frequency and additional degrees of freedom in the tuning process. This paper is a comparative study of five of these approximation techniques. The comparison focuses on their magnitude error, phase error, and implementation complexity. The techniques under study are the Carlson, continued fraction expansion (CFE), Padé, Charef, and MATLAB curve-fitting tool approximations. Based on this comparison, the recommended approximation techniques are the curve-fitting MATLAB tool and the continued fraction expansion (CFE). As an application, a low-pass power-law filter is realized on a field-programmable analog array (FPAA) using two techniques, namely the curve-fitting tool and the CFE. The experiment aligns with and validates the numerical results. © 2024 by the authors.