Minimal Realization of Fractional-Order Inverse Filters

Abstract

In this paper, a voltage mode (VM) multifunctional structure of fractional-order inverse filter using a single operational amplifier (op-amp) is proposed. The proposed configuration of inverse filter has been designed using a novel R-C op-amp circuit using minimum number of active and passive components (one op-amp, two resistors and two simulated fractional-order capacitors). The presented structure, by appropriate choice(s) of different passive elements, can realize fractional-order inverse low-pass filter, fractional-order inverse band pass filter and fractional-order inverse high-pass filter. The circuits described are eminently suitable for VM signal processing as they have ideally infinite input impedance. Experimental results using µA741 op-amp, discrete resistors and simulated fractional-order capacitors (α = 0.7) realized using Valsa method, numerical simulations using MATLAB and circuit simulations using PSPICE have been presented to establish the workability of the proposed circuits. The stability and sensitivity analyses have also been presented for the realized fractional-order inverse filters.

KEYWORDS:

• Analog signal processing
• Fractional calculus
• Fractional-order inverse filter
• Operational amplifier

Additional information

Notes on contributors

D. R. Bhaskar

D R Bhaskar received his BSc degree from Agra University, BTech degree from Indian Institute of Technology (IIT) Kanpur, MTech from IIT Delhi and PhD from the University of Delhi. Prof Bhaskar held the positions of lecturer (1984–1990) and senior lecturer (1990–1995) at the Department of Electrical Engineering, of Delhi College of Engineering (now Delhi Technological University). He joined the Electronics and Communication Engineering (ECE) Department of Jamia Millia Islamia in July 1995 as a reader and became a professor in January 2002. He served as the head of the department of ECE from 2002 to 2005. Presently, he is working in the Department of Electrical Engineering, Delhi Technological University, Delhi, India. His teaching and research interests are in the areas of bipolar and CMOS analog integrated circuits and systems, current mode/voltage mode signal processing, communication systems, fractional-order filters, and electronic instrumentation. Prof Bhaskar has authored or co-authored 96 research papers, all in international journals of repute, 15 international conference papers and 4 book chapters. He has co-authored four monographs published by Springer/IET. He is a reviewer for several journals of IEEE, IEE and other international journals of repute.

Manoj Kumar

Manoj Kumar is an assistant professor in the Department of Electronics and Communication Engineering, GB Pant Engineering College, Pauri-Garhwal (Uttarakhand) India, was born in Patna, India. He received his BE (Electronics and Communication) in 1999, MTech (bio- Electronics) from Tezpur Central University, Tezpur, Assam, India, in 2008. Currently, he is pursuing his doctoral studies in the Department of Electrical Engineering at Delhi Technological University, Delhi under MHRD (Government of India) scheme of Quality Improvement Program. His teaching and research interests are in the area of analog circuits, filter design and fractional-order systems. Email: [email protected]

Pragati Kumar

Pragati Kumar, professor in the Department of Electrical Engineering, Delhi Technological University, New Delhi, India, was born in Muzaffarpur, Bihar, India. He received his PhD from the University of Delhi in 2008. His teaching and research interests are in the area of network analysis and synthesis, microelectronics, CMOS analog integrated circuits and fractional- order circuits/systems. He has co-authored 16 research papers in various international journal/conferences/edited book volumes. Email: [email protected]