Fractional-οrder shadow filters : design and implementation

• Κύριος συγγραφέας: Τζάνη, Νικόλαος
• Άλλοι συγγραφείς: Tzani, Nikolaos
• Γλώσσα: English
• Έκδοση: 2023
• Θέματα: Fractional calculus; Fractional-order filters; Shadow filters; Fractional-order capacitors; RC networks Cauer and Foster; Current feedback operational amplifier; CMOS analog integrated circuits; Κλασματικός λογισμός; Φίλτρα κλασματικής τάξης; Σκιώδη φίλτρα; Πυκνωτές κλασματικής τάξης; RC δικτυώματα Cauer και Foster; Τελεστικός ενισvχυτής ανάδρασης ρεύματος; CMOS αναλογικά ολοκληρωμένα κυκλώματα

This M.Sc. Thesis has focused its interest, on the implementation of fractional-order shadow filters, a new family of filters, which provides the benefits of scaling and electronic control over the filters’ parameters. The design of such filters for control systems, and biological/biomedical applications is the core of this work. The first applications, which were related to filtering, were implemented with integer order filters. The need of improving the characteristics of these circuits introduced fractional-order filters. Initially, the filter’s characteristics are studied, with the ideal and approximate transfer functions being compared in the frequency domain. The approximation of Laplacian operator with rational polynomials is achieved, exploiting approximation techniques and specifically Oustaloup approximation method. Subsequently, using the aforementioned study as background, the concept of shadow filters is presented. The simplicity of the design procedure is important in terms of the cost and time spent to build such a filter. As the exploitation of fractional calculus in the branch of engineering is one of the recently developed research disciplines, there is no commercial production of fundamental elements that could directly build a fractional-order circuit. Towards this purpose, RC networks Cauer and Foster are utilized, which emulate the behavior of a fractional-order capacitor. Finally, the topologies of fractional-order shadow filters are imolemented, using Current Feedback Operational Amplifier, as basic active element. The theoretical analysis, as well as the approximation processes, for each case study are performed using the MATLAB software. The performance evaluation of the proposed circuits is based on simulation results obtained using the Cadence software and the Design Kit provided by the Austria Mikro Systeme (AMS) CMOS 0.35 μm technology process.