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Circuits, Systems, and Signal Processing

, Volume 39, Issue 1, pp 2–29 | Cite as

On the Approximations of CFOA-Based Fractional-Order Inverse Filters

  • Esraa M. Hamed
  • Lobna A. SaidEmail author
  • Ahmed H. Madian
  • Ahmed G. Radwan
Article

Abstract

In this paper, three novel fractional-order CFOA-based inverse filters are introduced. The inverse low-pass, high-pass and band-pass responses are investigated using different approximation techniques. The studied approximations for the fractional-order Laplacian operator are the continued fraction expansion and Matsuda approximations. A comparison is held between the ideal filter characteristic and the realized ones from each approximation. A comparative study is summarized between the proposed circuits with some of the released inverse filters introduced in the literature. Foster-I realization is employed to transform the obtained fractional-order capacitor (FOC) from the investigated approximations into an RC parallel–series circuit topology. Additionally, to discuss the sensitivity of the FOC to component tolerances, Monte Carlo simulations are carried out which shows immunity to the component tolerances. Numerical examples, as well as SPICE circuit simulations, have been introduced to validate the theoretical discussions. Finally, the three CFOA inverse filters are tested experimentally.

Keywords

Fractional order circuits Inverse filters Fractance Approximations Matsuda CFE Foster-I 

Notes

Acknowledgements

Authors would like to thank Science and Technology Development Fund (STDF) for funding the project \(\#\) 25977 and Nile University for facilitating all procedures required to complete this study.

References

  1. 1.
    A. AboBakr, L.A. Said, A.H. Madian, A.S. Elwakil, A.G. Radwan, Experimental comparison of integer/fractional-order electrical models of plant. AEU Int. J. Electron. Commun. 80, 1–9 (2017)CrossRefGoogle Scholar
  2. 2.
    M.T. Abuelma’atti, Identification of cascadable current-mode filters and inverse-filters using single FTFN. Frequenz 54(11–12), 284–289 (2000)Google Scholar
  3. 3.
    A.S. Ali, A.G. Radwan, A.M. Soliman, Fractional order butterworth filter: active and passive realizations. IEEE J. Emerg. Sel. Top. Circ. Syst. 3(3), 346–354 (2013)CrossRefGoogle Scholar
  4. 4.
    D.R. Bhaskar, M. Kumar, P. Kumar, Fractional order inverse filters using operational amplifier. Analog Integr. Circ. Signal Process. 97(1), 149–158 (2018)CrossRefGoogle Scholar
  5. 5.
    G. Carlson, C. Halijak, Approximation of fractional capacitors (1/s)\(^{\wedge }\)(1/n) by a regular Newton process. IEEE Trans. Circ. Theory 11(2), 210–213 (1964)CrossRefGoogle Scholar
  6. 6.
    B. Chipipop, W. Surakampontorn, Realisation of current-mode FTFN-based inverse filter. Electron. Lett. 35(9), 690–692 (1999)CrossRefGoogle Scholar
  7. 7.
    P. Duffett-Smith, Synthesis of lumped element, distributed, and planar filters. J. Atmos. Terr. Phys. 52(9), 811–812 (1990)CrossRefGoogle Scholar
  8. 8.
    T.J. Freeborn, A survey of fractional-order circuit models for biology and biomedicine. IEEE J. Emerg. Sel. Top. Circ. Syst. 3(3), 416–424 (2013)CrossRefGoogle Scholar
  9. 9.
    T.J. Freeborn, A.S. Elwakil, B. Maundy, Approximated fractional-order inverse Chebyshev lowpass filters. Circ. Syst. Signal Process. 35(6), 1973–1982 (2015)MathSciNetCrossRefGoogle Scholar
  10. 10.
    T.J. Freeborn, B. Maundy, A. Elwakil, Fractional-step Tow-Thomas biquad filters. Nonlinear Theory Appl. IEICE 3(3), 357–374 (2012)CrossRefGoogle Scholar
  11. 11.
    K. Garg, R. Bhagat, B. Jaint, A novel multifunction modified CFOA based inverse filter, in 2012 IEEE 5th India International Conference on Power Electronics (IICPE) (IEEE, 2012), pp. 1–5Google Scholar
  12. 12.
    S. Gupta, D. Bhaskar, R. Senani, A. Singh, Inverse active filters employing CFOAS. Electr. Eng. 91(1), 23 (2009)CrossRefGoogle Scholar
  13. 13.
    S. Gupta, D. Bhaskar, R. Senani, New analogue inverse filters realised with current feedback OP-AMPS. Int. J. Electron. 98(8), 1103–1113 (2011)CrossRefGoogle Scholar
  14. 14.
    E.M. Hamed, A.M. AbdelAty, L.A. Said, A.G. Radwan, Effect of different approximation techniques on fractional-order KHN filter design. Circ. Syst. Signal Process. 37(12), 5222–5252 (2018)CrossRefGoogle Scholar
  15. 15.
    N. Herencsar, A. Lahiri, J. Koton, K. Vrba, Realizations of second-order inverse active filters using minimum passive components and DDCCS, in Proceedings of 33rd International Conference on Telecommunications and Signal Processing-TSP 2010 (2010), pp. 38–41Google Scholar
  16. 16.
    N. Herencsar, R. Sotner, A. Kartci, K. Vrba, A novel pseudo-differential integer/fractional-order voltage-mode all-pass filter, in 2018 IEEE International Symposium on Circuits and Systems (ISCAS) (IEEE, 2018), pp. 1–5Google Scholar
  17. 17.
    S.M. Ismail, L.A. Said, A.A. Rezk, A.G. Radwan, A.H. Madian, M.F. Abu-ElYazeed, A.M. Soliman, Biomedical image encryption based on double-humped and fractional logistic maps, in 2017 6th International Conference on Modern Circuits and Systems Technologies (MOCAST) (IEEE, 2017), pp. 1–4Google Scholar
  18. 18.
    B. Krishna, Studies on fractional order differentiators and integrators: a survey. Signal Process. 91(3), 386–426 (2011)MathSciNetCrossRefGoogle Scholar
  19. 19.
    A. Leuciuc, Using nullors for realisation of inverse transfer functions and characteristics. Electron. Lett. 33(11), 949–951 (1997)CrossRefGoogle Scholar
  20. 20.
    G. Maione, Thiele’s continued fractions in digital implementation of noninteger differintegrators. Signal Image Video Process. 6(3), 401–410 (2012)CrossRefGoogle Scholar
  21. 21.
    K. Matsuda, H. Fujii, H(infinity) optimized wave-absorbing control—analytical and experimental results. J. Guid. Control Dyn. 16(6), 1146–1153 (1993)CrossRefGoogle Scholar
  22. 22.
    R. Pandey, N. Pandey, T. Negi, V. Garg, CDBA based universal inverse filter. ISRN Electronics (2013)Google Scholar
  23. 23.
    V. Patil, R. Sharma, Novel inverse active filters employing CFOAS. Int. J. Sci. Res. Dev. 3(7), 359–360 (2015)Google Scholar
  24. 24.
    A. Radwan, A. Soliman, A. Elwakil, A. Sedeek, On the stability of linear systems with fractional-order elements. Chaos Solitons Fractals 40(5), 2317–2328 (2009)CrossRefGoogle Scholar
  25. 25.
    A.G. Radwan, A.M. Soliman, A.S. Elwakil, First-order filters generalized to the fractional domain. J. Circ. Syst. Comput. 17(01), 55–66 (2008)CrossRefGoogle Scholar
  26. 26.
    A.G. Radwan, A.S. Elwakil, A.M. Soliman, On the generalization of second-order filters to the fractional-order domain. J. Circ. Syst. Comput. 18(02), 361–386 (2009)CrossRefGoogle Scholar
  27. 27.
    L.A. Said, S.M. Ismail, A.G. Radwan, A.H. Madian, M.F.A. El-Yazeed, A.M. Soliman, On the optimization of fractional order low-pass filters. Circ. Syst. Signal Process. 35(6), 2017–2039 (2016)MathSciNetCrossRefGoogle Scholar
  28. 28.
    L.A. Said, A.G. Radwan, A.H. Madian, A.M. Soliman, Fractional-order oscillator based on single CCII, in 2016 39th International Conference on Telecommunications and Signal Processing (TSP) (IEEE, 2016), pp. 603–606Google Scholar
  29. 29.
    L.A. Said, A.G. Radwan, A.H. Madian, A.M. Soliman, Fractional order oscillator design based on two-port network. Circ. Syst. Signal Process. 35(9), 3086–3112 (2016)MathSciNetCrossRefGoogle Scholar
  30. 30.
    W.S. Sayed, S.M. Ismail, L.A. Said, A.G. Radwan, On the fractional order generalized discrete maps, in Mathematical Techniques of Fractional Order Systems (Elsevier, 2018), pp. 375–408Google Scholar
  31. 31.
    N.A. Shah, M. Quadri, S.Z. Iqbal, High output impedance current-mode allpass inverse filter using CDTA. Indian J. Pure Appl. Phys. 46, 893–896 (2008)Google Scholar
  32. 32.
    N.A. Shah, M.F. Rather, Realization of voltage-mode CCII-based allpass filter and its inverse version. Indian J. Pure Appl. Phys. 44(3), 269–271 (2006)Google Scholar
  33. 33.
    A. Sharma, A. Kumar, P. Whig, On the performance of CDTA based novel analog inverse low pass filter using 0.35 \(\upmu \)m CMOS parameter. Int. J. Sci. Technol. Manag. 4(1), 594–601 (2015)Google Scholar
  34. 34.
    A.K. Singh, A. Gupta, R. Senani, Otra-based multi-function inverse filter configuration. Adv. Electr. Electron. Eng. 15(5), 846–856 (2018)Google Scholar
  35. 35.
    T. Tsukutani, Y. Sumi, N. Yabuki, Electronically tunable inverse active filters employing otas and grounded capacitors. Int. J. Electron. Lett. 4(2), 166–176 (2016)CrossRefGoogle Scholar
  36. 36.
    H.-Y. Wang, C.-T. Lee, Using nullors for realisation of current-mode FTFN-based inverse filters. Electron. Lett. 35(22), 1889–1890 (1999)CrossRefGoogle Scholar
  37. 37.
    H.-Y. Wang, S.-H. Chang, T.-Y. Yang, P.-Y. Tsai et al., A novel multifunction CFOA-based inverse filter. Circ. Syst. 2, 14–17 (2011)CrossRefGoogle Scholar
  38. 38.
    D. Yousri, A.M. AbdelAty, L.A. Said, A. AboBakr, A.G. Radwan, Biological inspired optimization algorithms for cole-impedance parameters identification. AEU Int. J. Electron. Commun. 78, 79–89 (2017)CrossRefGoogle Scholar
  39. 39.
    E. Yuce, S. Tokat, S. Minaei, O. Cicekoglu, Low-component-count insensitive current-mode and voltage-mode PID, PI and PD controllers. Frequenz 60(3–4), 65–70 (2006)Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Nanoelectronics Integrated Systems Center (NISC)Nile UniversityGizaEgypt
  2. 2.Radiation Engineering Department, NCRRTEgyptian Atomic Energy AuthorityCairoEgypt
  3. 3.Engineering Mathematics and Physics Department, Faculty of EngineeringCairo UniversityGizaEgypt
  4. 4.Faculty of Engineering and Basic SciencesNile UniversitySheikh Zayed CityEgypt

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