Abstract
In this work, a new design of continuous time current differencing buffered amplifier based low-pass, high-pass, band-pass, all-pass and notch fractional-order filters is reported. The design of proposed filters is based on the approximation of fractional-order filters by using an appropriate integer order transfer function. Signal flow graph approach is used for the realization of fractional-order filters of order (1 + α). The frequency responses of the proposed circuits are verified using MATLAB in conjunction with SPICE. The evaluation of the realized fractional-order filters are also performed through the AC analysis and corner analysis. Furthermore, stability and sensitivity investigations are also investigated. It is observed from the simulation results that the fractional-order filters are appropriate for IC implementation.
Similar content being viewed by others
References
Ortigueira, M. D. (2011). Fractional calculus for scientists and engineers. New York: Springer.
Podlubny, I. (1999). Fractional differential equations. Mathematics in science and engineering (Vol. 198). San Diego: Academic Press.
Miller, K. S., & Ross, R. (1993). An introduction to the fractional calculus and fractional differential equations. New York: Wiley.
Kulish, V., & Lage, J. L. (2002). Application of fractional calculus to fluid mechanics. Journal of Fluids Engineering, 124(3), 803.
Magin, R. (2004). Fractional calculus in bioengineering, part 1. Critical Reviews in Biomedical Engineering, 32(1), 1–104.
Vosika, Z. B., Lazovic, G. M., Misevic, G. N., & Simic-Krstic, J. B. (2013). Fractional calculus model of electrical impedance applied to human skin. PLoS ONE, 8(4), e59483.
Lazo, M. J. (2011). Gauge invariant fractional electromagnetic fields. Physics Letters A, 375(41), 3541–3546.
Engheta, N. (1997). On the role of fractional calculus in electromagnetic theory. Departmental Papers (ESE), 4, 2.
Yang, X.-J., Lopes, A. M., Hristov, J. Y., Cattani, C., Baleanu, D., & Mohyud-Din, S. T. (2016). Special issue on advances in fractional dynamics in mechanical engineering. Advances in Mechanical Engineering. https://doi.org/10.1177/1687814016654094.
Bia, P., Mescia, L., & Caratelli, D. (2016). Fractional calculus-based modeling of electromagnetic field propagation in arbitrary biological tissue. Mathematical Problems in Engineering. https://doi.org/10.1155/2016/5676903.
Vinagre, B. M., & Chen, Y. Q. (2002). Fractional calculus applications in automatic control and robotics. In 41st IEEE conference on decision and control tutoral workshop 2, Las Vegas.
Maundy, B., Elwakil, A., & Gift, S. (2010). On a multivibrator that employs a fractional capacitor. Analog Integrated Circuits and Signal Processing, 62(1), 99.
Radwan, A. G., Elwakil, A. S., & Soliman, A. M. (2008). Fractional-order sinusoidal oscillators: design procedure and practical examples. IEEE Transactions on Circuits and Systems I: Regular Papers, 55(7), 2051–2063.
Maundy, B., Elwakil, A. S., & Freeborn, T. J. (2011). On the practical realization of higher-order filters with fractional stepping. Signal Processing, 91(3), 484–491.
Tsirimokou, G., Koumousi, S., & Psychalinos, C. (2016). Design of fractional-order filters using current feedback operational amplifiers. Journal of Engineering Science and Technology Review, 9(4), 71–81.
Kubanek, D., & Freeborn, T. (2018). (1 + α) fractional-order transfer functions to approximate low-pass magnitude responses with arbitrary quality factor. AEU-International Journal of Electronics and Communications, 83, 570–578.
Langhammer, L., Sotner, R., Dvorak, J., Domansky, O., Jerabek, J., & Uher, J. (2017). A 1 + α low-pass fractional-order frequency filter with adjustable parameters. In 40th International conference on telecommunications and signal processing (TSP) (pp. 724–729). IEEE.
Freeborn, T., Maundy, B., & Elwakil, A. S. (2015). Approximated fractional order Chebyshev lowpass filters. Mathematical Problems in Engineering. https://doi.org/10.1155/2015/832468.
Freeborn, T. J., Elwakil, A. S., & Maundy, B. (2016). Approximated fractional-order inverse Chebyshev lowpass filters. Circuits, Systems, and Signal Processing, 35(6), 1973–1982.
Langhammer, L., Dvorak, J., Jerabek, J., Koton, J., & Sotner, R. (2018). Fractional-order low-pass filter with electronic tunability of its order and pole frequency. Journal of Electrical Engineering, 69(1), 3–13. https://doi.org/10.1515/jee-2018-0001.
Koton, J., Kubanek, D., Sladok, O., Vrba, K., Shadrin, A., & Ushakov, P. (2017). Fractional-order low-and high-pass filters using UVCs. Journal of Circuits, Systems and Computers, 26(12), 1750192.
Khateb, F., Kubánek, D., Tsirimokou, G., & Psychalinos, C. (2016). Fractional-order filters based on low-voltage DDCCs. Microelectronics Journal, 50, 50–59.
Jerabek, J., Sotner, R., Dvorak, J., Langhammer, L., & Koton, J. (2016) September. Fractional-order high-pass filter with electronically adjustable parameters. In International conference on applied electronics (AE) (pp. 111–116). IEEE.
Prasad, D., Kumar, M., & Akram, M. W. (2019). Current mode fractional order filters using VDTAs with Grounded capacitors. International Journal of Electronics and Telecommunications, 65(1), 11–17.
Verma, R., Pandey, N., & Pandey, R. (2019). CFOA based low pass and high pass fractional step filter realizations. AEU-International Journal of Electronics and Communications, 99, 161–176.
Oldham, K. B., & Zoski, C. G. (1983). Analogue instrumentation for processing polarographic data. Journal of Electroanalytical Chemistry and Interfacial Electrochemistry, 157(1), 27–51.
Mondal, D., & Biswas, K. (2013). Packaging of single-component fractional order element. IEEE Transactions on Device and Materials Reliability, 13(1), 73–80.
Adhikary, A., Khanra, M., Sen, S. & Biswas, K. (2015). Realization of a carbon nanotubes based electrochemical fractor. In IEEE international symposium on circuits and systems (ISCAS). IEEE.
Carlson, G., & Halijak, C. (1964). Approximation of fractional capacitors (1/s)(1/n) by a regular Newton process. IEEE Transactions on Circuit Theory, 11(2), 210–213.
Steiglitz, K. (1964). An RC impedance approximation to s−1/2. IEEE Transactions on Circuit Theory, 11, 160–161.
Biswas, K., Sen, S., & Dutta, P. K. (2006). Realization of a constant phase element and its performance study in a differentiator circuit. IEEE Transactions on Circuits and Systems II: Express Briefs, 53(9), 802–806.
Krishna, B. T., & Reddy, K. V. V. S. (2008). Active and passive realization of fractance device of order 1/2. Active and Passive Electronic Components. https://doi.org/10.1155/2008/369421.
Nakagawa, M., & Sorimachi, K. (1992). Basic characteristics of a fractance device. IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, 75(12), 1814–1819.
Sierociuk, D., Podlubny, I., & Petras, I. (2013). Experimental evidence of variable-order behaviour of ladders and nested ladders. IEEE Transactions on Control Systems Technology, 21(2), 459–466.
Sugi, M., Hirano, Y., Miura, Y. F., & Saito, K. (2002). Frequency behaviour of self-similar ladder circuits. Colloids and Surfaces A: Physicochemical and Engineering Aspects, 198, 683–688.
Radwan, A. G., Soliman, A. M., & Elwakil, A. S. (2008). First-order filters generalized to the fractional domain. Journal of Circuits, Systems, and Computers, 17(01), 55–66.
Radwan, A. G., Elwakil, A. S., & Soliman, A. M. (2009). On the generalization of second-order filters to the fractional-order domain. Journal of Circuits, Systems, and Computers, 18(02), 361–386.
Kaur, G., Ansari, A. Q., & Hashmi, M. S. (2017). Fractional order multifunction filter with 3 degrees of freedom. AEU-International Journal of Electronics and Communications, 82, 127–135.
Kaur, G., Ansari, A. Q., & Hashmi, M. S. (2019). Fractional order high pass filter based on operational transresistance amplifier with three fractional capacitors of different order. Advances in Electrical and Electronic Engineering, 17(2), 155–166.
Radwan, A. G. (2012). Stability analysis of the fractional-order RLC circuit. Journal of Fractional Calculus & Application, 3, 1–15.
Özoğuz, S., Toker, A., & Acar, C. (1999). Current-mode continuous-time fully-integrated universal filter using CDBAs. Electronics Letters, 35(2), 97–98.
Acar, C., & Özoǧuz, S. (2000). Nth-order current transfer function synthesis using current differencing buffered amplifier: signal-flow graph approach. Microelectronics Journal, 31(1), 49–53.
Freeborn, T. J., Maundy, B., & Elwakil, A. S. (2010). Field programmable analogue array implementation of fractional step filters. IET Circuits, Devices and Systems, 4(6), 514–524.
Freeborn, T. J. (2016). Comparison of (1 + α) fractional-order transfer functions to approximate lowpass butterworth magnitude responses. Circuits, Systems, and Signal Processing, 35(6), 1983–2002.
Baranowski, J., Pauluk, M., & Tutaj, A. (2017). Analog realization of fractional filters: Laguerre approximation approach. AEU-International Journal of Electronics and Communications, 81, 1–11.
El-Khazali, R. (2015). On the biquadratic approximation of fractional-order Laplacian operators. Analog Integrated Circuits and Signal Processing, 82(3), 503–517.
Ahmad, W., El-Khazali, R., & Elwakil, A. S. (2001). Fractional-order Wien-bridge oscillator. Electronics Letters, 37(18), 1110–1112.
Ahmad, W., & El-Khazafi, R. (2003). Fractional-order passive low-pass filters. In 10th IEEE international conference on electronics, circuits and systems, 2003. ICECS 2003. Proceedings of the 2003 (Vol. 1, pp. 160–163). IEEE.
El-Khazali, R., & Tawalbeh, N. (2012). Realization of fractional-order capacitors and inductors. In 5th-IFAC symposium on fractional differntial and its applications, Nanjing, China.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Kaur, G., Ansari, A.Q. & Hashmi, M.S. Analysis and investigation of CDBA based fractional-order filters. Analog Integr Circ Sig Process 105, 111–124 (2020). https://doi.org/10.1007/s10470-020-01683-0
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10470-020-01683-0