Skip to main content
Log in

Analysis and investigation of CDBA based fractional-order filters

  • Published:
Analog Integrated Circuits and Signal Processing Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  1. Ortigueira, M. D. (2011). Fractional calculus for scientists and engineers. New York: Springer.

    MATH  Google Scholar 

  2. Podlubny, I. (1999). Fractional differential equations. Mathematics in science and engineering (Vol. 198). San Diego: Academic Press.

    MATH  Google Scholar 

  3. Miller, K. S., & Ross, R. (1993). An introduction to the fractional calculus and fractional differential equations. New York: Wiley.

    MATH  Google Scholar 

  4. Kulish, V., & Lage, J. L. (2002). Application of fractional calculus to fluid mechanics. Journal of Fluids Engineering, 124(3), 803.

    Google Scholar 

  5. Magin, R. (2004). Fractional calculus in bioengineering, part 1. Critical Reviews in Biomedical Engineering, 32(1), 1–104.

    Google Scholar 

  6. 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.

    Google Scholar 

  7. Lazo, M. J. (2011). Gauge invariant fractional electromagnetic fields. Physics Letters A, 375(41), 3541–3546.

    MathSciNet  MATH  Google Scholar 

  8. Engheta, N. (1997). On the role of fractional calculus in electromagnetic theory. Departmental Papers (ESE), 4, 2.

    Google Scholar 

  9. 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.

  10. Bia, P., Mescia, L., & Caratelli, D. (2016). Fractional calculus-based modeling of electromagnetic field propagation in arbitrary biological tissue. Mathematical Problems in Engineeringhttps://doi.org/10.1155/2016/5676903.

  11. 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.

  12. Maundy, B., Elwakil, A., & Gift, S. (2010). On a multivibrator that employs a fractional capacitor. Analog Integrated Circuits and Signal Processing, 62(1), 99.

    Google Scholar 

  13. 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.

    MathSciNet  MATH  Google Scholar 

  14. 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.

    MATH  Google Scholar 

  15. 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.

    Google Scholar 

  16. 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.

    Google Scholar 

  17. 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.

  18. Freeborn, T., Maundy, B., & Elwakil, A. S. (2015). Approximated fractional order Chebyshev lowpass filters. Mathematical Problems in Engineeringhttps://doi.org/10.1155/2015/832468.

  19. 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.

    MathSciNet  MATH  Google Scholar 

  20. 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.

    Article  Google Scholar 

  21. 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.

    Google Scholar 

  22. Khateb, F., Kubánek, D., Tsirimokou, G., & Psychalinos, C. (2016). Fractional-order filters based on low-voltage DDCCs. Microelectronics Journal, 50, 50–59.

    Google Scholar 

  23. 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.

  24. 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.

  25. 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.

    Google Scholar 

  26. Oldham, K. B., & Zoski, C. G. (1983). Analogue instrumentation for processing polarographic data. Journal of Electroanalytical Chemistry and Interfacial Electrochemistry, 157(1), 27–51.

    Google Scholar 

  27. Mondal, D., & Biswas, K. (2013). Packaging of single-component fractional order element. IEEE Transactions on Device and Materials Reliability, 13(1), 73–80.

    Google Scholar 

  28. 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.

  29. 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.

    Google Scholar 

  30. Steiglitz, K. (1964). An RC impedance approximation to s−1/2. IEEE Transactions on Circuit Theory, 11, 160–161.

    Google Scholar 

  31. 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.

    Google Scholar 

  32. Krishna, B. T., & Reddy, K. V. V. S. (2008). Active and passive realization of fractance device of order 1/2. Active and Passive Electronic Componentshttps://doi.org/10.1155/2008/369421.

  33. 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.

    Google Scholar 

  34. 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.

    Google Scholar 

  35. 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.

    Google Scholar 

  36. 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.

    Google Scholar 

  37. 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.

    Google Scholar 

  38. 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.

    Google Scholar 

  39. 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.

    Google Scholar 

  40. Radwan, A. G. (2012). Stability analysis of the fractional-order RLC circuit. Journal of Fractional Calculus & Application, 3, 1–15.

    Google Scholar 

  41. Özoğuz, S., Toker, A., & Acar, C. (1999). Current-mode continuous-time fully-integrated universal filter using CDBAs. Electronics Letters, 35(2), 97–98.

    Google Scholar 

  42. 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.

    Google Scholar 

  43. 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.

    Google Scholar 

  44. 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.

    MathSciNet  Google Scholar 

  45. 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.

    Google Scholar 

  46. El-Khazali, R. (2015). On the biquadratic approximation of fractional-order Laplacian operators. Analog Integrated Circuits and Signal Processing, 82(3), 503–517.

    Google Scholar 

  47. Ahmad, W., El-Khazali, R., & Elwakil, A. S. (2001). Fractional-order Wien-bridge oscillator. Electronics Letters, 37(18), 1110–1112.

    Google Scholar 

  48. 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.

  49. 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.

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Gagandeep Kaur.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

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

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10470-020-01683-0

Keywords

Navigation