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Electronically Tunable Multifunction Transadmittance-Mode Fractional-Order Filter

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Abstract

In this paper a multifunction transadmittance-mode fractional-order filter is proposed for the very first time. The proposed structure provides fractional-order low-pass filter, fractional-order high-pass filter and fractional-order all-pass filter. It uses two operational transconductance amplifier and one fractional capacitor (FC). The FC is realized using the twelfth-order continued fraction expansion-based RC ladder. Functional verification of proposed fractional-order filter is verified through PSPICE using 180-nm CMOS technology model parameters. The transfer functions sensitivities’ with respect to various circuit parameters are examined through simulations. The effect of parameter variation on filter responses is studied using Monte Carlo analysis. Furthermore, the proposed filter possess electronic tunability through bias currents. Moreover, the circuit is tested experimentally using discrete components to realize the fractional-order capacitor showing great matching with the theoretical data.

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References

  1. Debnath, L.: Recent applications of fractional calculus to science and engineering. Int. J. Math. Math. Sci. 54, 3413–3442 (2003)

    MathSciNet  MATH  Google Scholar 

  2. Elwakil, A.S.: Fractional-order circuits and systems: an emerging Interdisciplinary research area. IEEE Circuit Syst. Mag. 10(4), 40–50 (2010)

    Google Scholar 

  3. Chen, Y.Q.; Petras, I.; Xue, D.: Fractional order control—a tutorial. In: Proceeding American Control Conference (ACC), pp. 1397–1411 (2009).

  4. Das, S.; Pan, I.: Fractional order signal processing—introductory concepts and applications. In: Springer Briefs in Applied Sciences and Technology (2012).

  5. Dorcak, L.; Valsa, J.; Gonzalez, E.; Terpak, J.; Petras, I.; Pivka, L.: Analogue realization of fractional-order dynamical systems. Entropy 15(10), 4199–4214 (2013)

    MATH  Google Scholar 

  6. Podlubny, I.; Petras, I.; Vinagre, B.M.; Leary, P.O.; Dorcak, L.: Analogue realizations of fractional-order controllers. Nonlinear Dyn. 29(4), 281–296 (2012)

    MathSciNet  MATH  Google Scholar 

  7. Suksang, T.; Loedhammacakra, W.; Pirajnanchai, V.: Implement the fractional-order, half integrator and differentiator on the OTA based PI\(\lambda \)D\(\mu \) controller circuit. In: IEEE Conference on ECTICON (2012). https://doi.org/10.1109/ECTICON.2012.6254136

  8. Geddes, L.A.; Baker, L.E.: Principles of Applied Biomedical Instrumentation, 3rd edn. Wiley, New York (1989)

    Google Scholar 

  9. Faria, A.C.; Veiga, J.; Lopes, A.J.; Melo, P.L.: Forced oscillation, integer and fractional-order modeling in asthma. Comput. Methods Programs Biomed. 128, 12–26 (2016)

    Google Scholar 

  10. Bertsias, P.; Mohsen, M.; Said, L.A.; Elwakil, A.S.; Psychalinos, C.; Radwan, A.G.: Design and implementation of an optimized artificial human eardrum model. Circuits Syst. Signal Process. 39, 3219–3233 (2020)

    Google Scholar 

  11. Tsirimokou, G.; Psychalinos, C.; Elwakil, A.: Design of CMOS Analog Integrated Fractional-Order Circuits: Applications in Medicine and Biology. Springer, Berlin (2017)

    Google Scholar 

  12. Sheng, H.; Chen, Y.Q.; Qiu, T.S.: Fractional Processes and Fractional-Order Signal Processing: Techniques and Applications. Springer, New York (2011)

    MATH  Google Scholar 

  13. Hamed, E.M.; Said, L.A.; Madian, A.H.; Radwan, A.G.: On the approximations of CFOA-based fractional-order inverse filters. Circuits Syst. Signal Process. 39, 2–29 (2020)

    Google Scholar 

  14. Tlelo-Cuautle, E.; Pano-Azucena, A.D.; Guillén Fernández, O.; Silva-Juárez, A.: Analog/Digital Implementation of Fractional Order Chaotic Circuits and Applications. Springer, Berlin (2020)

    Google Scholar 

  15. Muñiz-Montero, C.; Sánchez-Gaspariano, L. A.; Sánchez-López, C.; González-Díaz, V. R.; Tlelo Cuautle, E.: On the electronic realizations of fractional-order phase-lead-lag compensators with OpAmps and FPAAs. In: Fractional Order Control and Synchronization of Chaotic Systems, vol. 688, pp. 131–164 (2017). ISBN: 978-3-319-50248-9

  16. Sayed, W.S.; Radwan, A.G.: Generalized switched synchronization and dependent image encryption using dynamically rotating fractional-order chaotic systems. AEU Int. J. Electron. Commun. (2020). https://doi.org/10.1016/j.aeue.2020.153268

    Article  Google Scholar 

  17. Toker, A.; Cicekoglu, O.; Ozcan, S.; Kuntman, H.: High output-impedance transadmittance type continuous-time multifunction filter with minimum active elements. Int. J. Electron. 88, 1085–1091 (2001)

    Google Scholar 

  18. Nand, D.; Pandey, N.: Transadmittance mode first order LP/HP/AP filter and its application as an oscillator. IOP Conf. Ser. Mater. Sci. Eng. 225, 012150 (2017)

    Google Scholar 

  19. Minaei, S.: A new high performance CMOS third generation current conveyor (CCIII) and its application. J. Electr. Eng. 85, 147–153 (2003)

    Google Scholar 

  20. Cam, U.: A new transadmittance type first order all pass filter employing single third generation current conveyor. Analog Int. Circuits Signal Process. 43, 97–99 (2005)

    Google Scholar 

  21. Herencsar N.; Lahiri A.; Koton J.; Sagbas M.; Ayten U. E.; Vrba K.: New MOS-C realization of transadmittance type all pass filter using modified CBTA. In: International Conference on Applied Electronics, pp. 1–4. IEEE (2011)

  22. Herencsar N.; Koton J.; Vrba K.: Differential input buffered and transconductance amplifier based new transadmittance and voltage mode first order all pass filters. In: International Conference on Electrical and Electronics Engineering, ELECO-2009, pp. 256-259 (2009)

  23. Herencsar N.; Koton J.; Vrba K.; B. Metin: Fully cascadable dual mode all pass filter based on single DBTA. In: 35th International Conference on Telecommunications and Signal Processing, pp. 374–377 (2012)

  24. Sotner, R.; Herencsar, N.; Jerabek, J.; Vrba, K.; Dostal, T.; Jaikla, W.; Metin, B.: Novel first order all pass filter applications of z-copy voltage differencing current conveyor. Indian J. Pure Appl. Phys. 53, 537–545 (2015)

    Google Scholar 

  25. Radwan, A.G.; Soliman, A.M.; Elwakil, A.S.: First-order filters generalized to the fractional domain. J. Circuits Syst. Comput. 17(1), 55–66 (2008)

    Google Scholar 

  26. Radwan, A.G.; Elwakil, A.S.; Soliman, A.M.: On the generalization of second order filters to the fractional order domain. J. Circuits Syst. Comput. 18(2), 361–386 (2009)

    Google Scholar 

  27. Adhikary, A.; Sen, S.; Biswas, K.: Practical realization of tunable fractional order parallel resonator and fractional order filters. IEEE Trans. Circuits Syst. I 63(8), 1142–1151 (2016)

    MathSciNet  Google Scholar 

  28. Mishra, S.K.; Gupta, M.; Upadhyay, D.K.: Active realization of fractional order Butterworth low pass filter using DVCC. J. King Saud Univ. Eng. Sci. 32(2), 158–165 (2020)

    Google Scholar 

  29. Kubanek, D.; Freeborn, T.; Koton, J.: Fractional-order band-pass filter design using fractional-characteristic specimen functions. Microelectron. J. 86, 77–86 (2019)

    Google Scholar 

  30. Hamed, E.M.; AbdelAty, A.M.; Said, L.A.; Radwan, A.G.: Effect of different approximation techniques on fractional-order KHN filter design. Circuits Syst. Signal Process. 37, 5222–5252 (2018). https://doi.org/10.1007/s00034-018-0833-5

    Article  Google Scholar 

  31. Ali, A.S.; Radwan, A.G.; Soliman, A.M.: Fractional order butterworth filter: active and passive realization. IEEE J. Emerg. Sel. Top. Circuits Syst. 3(3), 346–354 (2013)

    Google Scholar 

  32. AbdelAty, A.M.; Soltan, A.; Waleed, A.; Radwan, A.G.: Fractional order Chebyshev-like low-pass filters based on integer order poles. Microelectron. J. 90, 72–81 (2019)

    Google Scholar 

  33. Soltan, A.; Radwan, A.G.; Soliman, A.M.: Fractional order filter with two fractional elements of dependant orders. Microelectron. J. 43(11), 818–827 (2012)

    Google Scholar 

  34. Said, L.A.; Ismail, S.M.; Radwan, A.G.; Median, A.H.; El Yazeed, M.F.A.; Soliman, A.M.: On the optimization of fractional order low pass filter. Circuits Syst. Signal Process. 35(6), 2017–2039 (2016)

    MathSciNet  Google Scholar 

  35. Bhaskar, D.R.; Kumar, M.; Kumar, P.: Fractional order inverse filters using operational amplifier. Analog Integr. Circuits Signal Process. 97(1), 149–158 (2018)

    Google Scholar 

  36. Kamath, D.V.; Navya, S.; Soubhagyaseetha, N.: Fractional order OTA-C current-mode all-pass filter. In: Second International Conference on Inventive Communication and Computational Technologies (ICICCT), Coimbatore, pp. 383–387 (2018)

  37. Khalil, N.A.; Said, L.A.; Radwan, A.G.; Soliman, A.M.: Generalized two port network based fractional order filters. AEU Int. J. Electron. Commun. 104, 128–146 (2019)

    Google Scholar 

  38. Soltan, A.; Radwan, A.G.; Soliman, A.M.: CCII based fractional lters of different orders. J. Adv. Res. 5, 157–64 (2014)

    Google Scholar 

  39. Tripathy, M.C.; Biswas, K.; Sen, S.: A design example of a fractional order Kerwin–Huelsman–Newcomb biquad lter with two fractional capacitors of different order. Circuits Syst. Signal Process. 32, 1523–36 (2013)

    Google Scholar 

  40. Ahmadi, P.; Maundy, B.; Elwakil, A.S.; Belostotski, L.: High-quality factor asymmetric-slope band-pass lters: a fractional order capacitor approach. IET Circuits Devices Syst. 6, 187–97 (2012)

    Google Scholar 

  41. Freeborn, T.J.; Maundy, B.; Elwakil, A.S.: Fractional-step Tow–Thomas biquad lters. Nonlinear Theor. Appl. 3, 357–74 (2012)

    Google Scholar 

  42. Bertsias, P.; Psychalinos, C.; Elwakil, A. S.; Maundy, B. J.: Simple multi-function fractional-order filter designs. In: IEEE conference on MOCAST (2019). https://doi.org/10.1109/MOCAST.2019.8741674

  43. Dvorak, J.; Jerabek, J.; Polesakova, Z.; Langhammer, L.; Blazek, P.: Multifunctional electronically recongurable and tunable fractional-order lter. Elektronika IR Elektrotechnika 25(1), 26–30 (2018)

    Google Scholar 

  44. Verma, R.; Pandey, N.; Pandey, R.: Electronically tunable fractional order filter. Arab. J. Sci. Eng. 42, 3409–3422 (2017)

    Google Scholar 

  45. Bhat, M.V.; Bhat, S.S.S.; Kamath, D.V.: Gm-C current mode fractional all pass filter of order (0¡alpha¡1), In: IEEE Conference ICECA (2019). https://doi.org/10.1109/ICECA.2019.8822183

  46. Mahata, S.; Saha, S.K.; Kar, R.; Mandal, D.: Optimal design of fractional order low pass butterworth lter with accurate magnitude response. Digit. Signal Process, 72, 96–114 (2018)

    Google Scholar 

  47. Soni, A.; Sreejeth, N.; Saxena, V.; Gupta, M.: Series optimized fractional order low pass butterworth filter. Arab. J. Sci. Eng. (2019). https://doi.org/10.1007/s13369-019-04225-7

    Article  Google Scholar 

  48. Kaur, G.; Ansari, A.Q.; Hashmi, M.S.: Analysis and investigation of CDBA based fractional-order filters. Analog Integr. Circuits Signal Process. (2020). https://doi.org/10.1007/s10470-020-01683-0

    Article  Google Scholar 

  49. Tsirimokou, G.; Psychalinos, C.: Ultra-low voltage fractional-order circuits using current mirrors. Int. J. Circuits Theor. Appl. 44, 109–26 (2016)

    Google Scholar 

  50. Jerabek, J.; Sotner, R.; Dvorak, J.; Langhammer, L.; Koton, J.: Fractional-order high-pass lter with electronically adjustable parameters. In: International Conference on Applied Electronics, pp. 111–116, (2016). https://doi.org/10.1109/AE.2016.7577253

  51. Koton, J.; Kubanek, D.; Sladok, O.; Vrba, K.: Fractional-order low- and high-pass lters using UVCs. J. Circuits Syst. Comput. 26(12), 1–23 (2017)

    Google Scholar 

  52. Maundy, B.; Elwakil, A.S.; Freeborn, T.J.: On the practical realization of higher order lters with fractional stepping. Signal Process. 91(3), 484–91 (2011)

    MATH  Google Scholar 

  53. Khateb, F.; Kubanek, D.; Tsirimokou, G.; Psychalinos, C.: Fractional-order lter based on low-voltage DDCCs. Microelectron. J. 50, 50–59 (2011)

    Google Scholar 

  54. Tsirimokou, G.; Koumousi, S.; Psychalinos, C.: Design of fractional-order lters using current feedback operational ampliers. J. Eng. Sci. Technol. Rev. 9(4), 77–81 (2016)

    Google Scholar 

  55. Langhammer, L.; Dvorak, J.; Jerabek, J.; Koton, J.; Sotner, R.: Fractional-order low-pass lter with electronic tunability of its order and pole frequency. J. Electr. Eng. Slovak. 69(1), 3–13 (2018)

    Google Scholar 

  56. Jerabek, J.; Sotner, R.; Dvorak, J.; Polak, J.; Kubanek, D.; Herencsar, N.; Koton, J.: Recongurable fractional-order lter with electronically controllable slope of attenuation, pole frequency and type of approximation. J. Circuits Syst. Comput. 26(10), 1–21 (2017)

    Google Scholar 

  57. Dvorak, J.; Langhammer, L.; Jerabek, J.; Koton, J.; Sotner, R.; Polak, J.: Synthesis and analysis of electronically adjustable fractional-order low-pass lter. J. Circuits Syst. Comput. 27(2), 1850032-(1-18) (2018)

    Google Scholar 

  58. Verma, R.; Pandey, N.; Pandey, R.: CFOA based low pass and high pass fractional step filter realizations. AEU Int. J. Electron. Commun. 99, 161–176 (2019)

    Google Scholar 

  59. Nakagava, M.; Sorimachi, K.: Basic characteristics of a fractance device. IEICE Trans. Fundam. Electron. Commun. Comput. Sci. 75(12), 1814–1818 (1992)

    Google Scholar 

  60. Agambayev, A.; Farhat, M.; Patole, S.P.; Hassan, A.H.; Bagci, H.; Salama, K.N.: An ultra-broadbandsingle-component fractional-order capacitor using MoS2-ferroelectric polymer composite. Appl. Phys. Lett. 113, 093505 (2018)

    Google Scholar 

  61. Caponetto, R.; Graziani, S.; Pappalardo, F.L.; Sapuppo, F.: Experimental characterization of ionic polymermetal composite as a novel fractional order element. Adv. Math. Phys. 1–10, Article ID: 953695 (2013)

  62. Tu, S.; Jiang, Q.; Zhang, X.; Alshareef, H.N.: Solid state mxene based electrostatic fractional capacitors. Appl. Phys. Lett. 114(23), 232903 (2019)

    Google Scholar 

  63. Vinagre, B.M.; Podlubny, I.; Hernandez, A.; Feliu, V.: Some approximations of fractional order operators used in control theory and applications. Fract. Calc. Appl. Anal. 3(3), 945–950 (2000)

    MathSciNet  MATH  Google Scholar 

  64. El-Khazali, R.: On the biquadratic approximation of fractional order Laplacian operators. Analog Integr. Circuits Signal Process. 82(3), 503–517 (2015)

    Google Scholar 

  65. Xue, D.Y.; Zhao, C.; Chen, Y.Q.: A modified approximation method of fractional order system. In: IEEE Conference on Mechatronics and Automation, pp. 1043–1048, (2006)

  66. Muñiz-Montero, C.; García-Jiménez, L.V.; Sánchez-Gaspariano, L.A.; Sánchez-López, C.; Gonzalez-Diaz, V.R.; Tlelo-Cuautle, E.: New alternatives for analog implementation of fractional-order integrators, differentiators and PID controllers based on integer-order integrators. Nonlinear Dyn. 90(1), 241–256 (2017)

    MathSciNet  Google Scholar 

  67. Radwan, A.G.; Soliman, A.M.; Elwakil, A.S.; Sedeek, A.: On the stability of linear systems with fractional-order elements. Chaos Solitons Fractals 40(5), 2317–2328 (2009)

    MATH  Google Scholar 

  68. Tlelo-Cuautle, E.; Sanabria-Borbón, A.C.: Optimizing operational amplifiers by evolutionary algorithms and gm/Id method. Int. J. Electron. 103(10), 1665–1684 (2016)

    Google Scholar 

  69. Yan, Z.; Mak, P.; Martins, R.P.: Double recycling technique for folded-cascode OTA. Analog Integr. Circuits Signal Processing. 71, 137–141 (2012)

    Google Scholar 

  70. Joshi, A.; Shrimali, H.; Sharma, S.K.: Systematic design approach for a gain boosted telescopic OTA with cross-coupled capacitor. IET Circuits Devices Syst. 11(3), 225–231 (2017)

    Google Scholar 

  71. Dammak, H.D.; Bensalem, S.; Zouari, S.; Loulou, M.: Design of folded cascode OTA in different regions of operation through gm/ID methodology. Int. J. Electr. Comput. Eng. 2(9), 1741–1746 (2008)

    Google Scholar 

  72. Tsukutani, T.; Sumi, Y.; Fukui, Y.: Electronically controlled current-mode oscillators using MO-OTAs and grounded capacitors. Frequenz 60(11–12), 220–223 (2006)

    Google Scholar 

  73. Adhikary, A.; Sen, P.; Sen, S.; Biswas, K.: Design and performance study of dynamic fractors in any of the four quadrants. Circuits Syst. Signal Process. 35(6), 1909–1932 (2016)

    MathSciNet  Google Scholar 

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Varshney, G., Pandey, N. & Pandey, R. Electronically Tunable Multifunction Transadmittance-Mode Fractional-Order Filter. Arab J Sci Eng 46, 1067–1078 (2021). https://doi.org/10.1007/s13369-020-04841-8

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