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Electronically Tunable Fractional Order Filter

  • Research Article - Computer Engineering and Computer Science
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Abstract

In this paper, an electronically tunable resistorless fractional order filter (FOF) based on operational transconductance amplifier (OTA) is presented. It uses two fractional capacitors (FC) of same order and provides fractional order low-pass filter and fractional order band-pass filter responses simultaneously. Mathematical formulations are outlined for various critical frequencies and transfer function sensitivities for presented FOF. The FCs of orders 0.5 and 0.9 are considered for illustrating the proposal. The FCs are realized using the fourth-order continued fraction expansion-based RC ladder and are characterized using SPICE simulations. Functional verification of presented FOF with FC of orders 0.5 and 0.9 is exhibited through SPICE simulations. The OTA is implemented using \(0.5\,\upmu \hbox {m}\) CMOS technology model parameters. Electronic tunability of half power and right-phase frequencies of presented FOF is achieved through bias current variation of OTA. The transfer functions’ sensitivity with respect to various circuit parameters is also examined through simulations, and it is found that the values remain well within unity for most of the circuit parameters. Furthermore, the presented FOF is attractive from integration viewpoint as it achieves tunability via bias current variation in contrast to tuning through resistor variation in existing FOFs.

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References

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

    Article  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)

    Article  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)

    Article  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 \(\text{PI}^{\uplambda}\text{D}^{\upmu}\) controller circuit. In: IEEE Conference on ECTICON (2012). doi:10.1109/ECTICON.2012.6254136

  8. Geddes, L.A.; Baker, L.E.: Principles of Applied Biomedical Instrumentation, 3rd edn. Wiely, 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)

    Article  Google Scholar 

  10. 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 

  11. 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)

    Article  Google Scholar 

  12. Freeborn, T.J.; Maundy, B.; Elwakil, A.: Fractional resonance-based \(\text{RL}_{\upbeta}\text{C}_{\upalpha}\) filters. Math. Probl. Eng. 2013, 1–10 (2013)

  13. Soltan, A.; Radwan, A.G.; Soliman, A.M.: Butterworth passive filter in the fractional-order. Int. Conf. Microelectron. (ICM) 23, 1–5 (2011)

    Google Scholar 

  14. Radwan, A.: Stability analysis of the fractional-order \(\text{RL}_{\upbeta}\text{C}_{\upalpha}\) circuit. J. Fract. Calc. Appl. 3(1), 1–15 (2012)

    Google Scholar 

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

    Article  Google Scholar 

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

  17. Soltan, A.; Radwan, A.G.; Soliman, A.M.: Fractional order sallen-key and KHN filters stability and poles allocation. Circuits Syst. Signal Process. 34(5), 1461–1480 (2014)

    Article  MATH  Google Scholar 

  18. Said, L.A.; Ismail, S.M.; Radwan, A.G.; Madian, A.H.; El-Yazeed, M.F.A.; Soliman, A.M.: On The Optimization of Fractional Order Low-Pass filters. Circuits Syst. Signal Process. 35(6), 2017–2039 (2016)

    Article  MathSciNet  Google Scholar 

  19. Freeborn, T.; Maundy, B.; Elwakil, A.S.: Approximated fractional order Chebyshev lowpass filters. Math. Probl. Eng. 2015, 1–7 (2015)

  20. Freeborn, T.J.; Maundy, B.; Elwakil, A.: Fractional-step Tow-Thomas biquad filters, nonlinear theory and its applications. IEICE (NOLTA) 3(3), 357–374 (2012)

    Article  Google Scholar 

  21. Soltan, A.; Radwan, A.G.; Soliman, A.M.: CCII based fractional filters of different orders. J. Adv. Res. 5(2), 157–164 (2014)

    Article  Google Scholar 

  22. Soltan, A.; Radwan, A.G.; Soliman A.M.: CCII based KHN fractional order filter. In: IEEE-Midwest Symposium on Circuits and Systems (MWSCAS), pp. 197–200 (2013)

  23. AbdelAty, A.M.; Soltan, A.; Ahmed, W.A.; Radwan A.G.: Low pass filter design based on fractional power Chebyshev polynomial. In: IEEE International Conference on Electronics, Circuits, and Systems (ICECS) (2015). doi:10.1109/ICECS.2015.7440236

  24. Freeborn, T.J.; Elwakil, A.S.; Maundy, B.: Approximated fractional-order inverse Chebyshev lowpass filters. Circuits Syst. Signal Process. 35(6), 1973–1982 (2016)

    Article  MathSciNet  Google Scholar 

  25. Ahmadi, P.; Maundy, B.; Elwakil, A.S.; Belostostski, L.: High-quality factor asymmetric-slope band pass filters: a fractional-order capacitor approach. IET Circuits Devices Syst. 6(3), 187–197 (2012)

    Article  Google Scholar 

  26. Tsirimokou, G.; Laoudias, C.; Psychalinos, C.: 0.5-V fractional-order companding filters. Int. J. Circuit Theory Appl. (2014). doi:10.1002/cta.1995

  27. Tsirimokou, G.; Psychalinos, C.: Ultra-low voltage fractional order differentiator and integrator topologies an application for handling noisy ECGs. Analog Integerated Circuits Signal Process. 81(2), 393–405 (2014)

    Article  Google Scholar 

  28. Maundy, B.; Elwakil, A.S.; Freeborn, T.J.: On the Practical realization of higher order filters with fractional stepping. Signal Process. 91(3), 484–491 (2011)

    Article  MATH  Google Scholar 

  29. Jerabek, J.; Sotner, R.; Dvorak, J.; Langhammer, L.; Koton, J.: Fractional-order high-pass filter with electronically adjustable parameters. In: IEEE International Conference on Applied Electronics (2016). doi:10.1109/AE.2016.7577253

  30. Tsirimokou, G.; Psychalinos, C.; Elwakil, A.S.: Fractional-order electronically controlled generalized filters. Int. J. Circuit Theory Appl. (2016). doi:10.1002/cta.2250

    Google Scholar 

  31. Khateb, F.; Kubanek, D.; Tsirimokou, G.; Psychalinos, C.: Fractional-order filters based on low-voltage DDCCs. Microelectron. J. 50, 50–59 (2016)

    Article  Google Scholar 

  32. Li, M.: Approximating ideal filters by systems of fractional order. Comput. Math. Methods Med. 2012, 1–6 (2012)

    MathSciNet  Google Scholar 

  33. Tripathy, M.C.; Biswas, K.; Sen, S.: A design example of a fractional-order Kerwin-Huelsman-Newcomb biquad filter with two fractional capacitors of different order. Circuits Syst. Signal Process. 32, 1523–1536 (2013)

    Article  MathSciNet  Google Scholar 

  34. 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)

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

  36. 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)

    Article  MathSciNet  Google Scholar 

  37. Tripathy, M.C.; Mondal, D.; Biswas, K.; Sen, S.: Experimental studies on realization of fractional inductors and fractional-order bandpass filters. Int. J. Circuit Theory Appl. 43(9), 1183–1196 (2014)

    Article  Google Scholar 

  38. Helie, T.: Simulation of fractional-order low-pass filters. IEEE/ACM Trans. Audio Speech Lang. Process. 22(11), 1636–1647 (2014)

    Article  Google Scholar 

  39. Biolek, D.; Senani, R.; Biolkova, V.; Kolka, Z.: Active elements for analog signal processing: classification, review, and new proposals. Radioengineering 17(4), 15–32 (2008)

    Google Scholar 

  40. Ranjan, R.K.; Yalla, S.P.; Sorya, S.; Paul, S.K.: Active comb filter using operational transconductance amplifier. Act. Passiv. Electron. Compon. (2014). doi:10.1155/2014/587932

    Google Scholar 

  41. Ananda Mohan, P.V.: VLSI Analog Filters: Active RC, OTA-C and SC. Birkhauer, Boston (2013)

    Book  MATH  Google Scholar 

  42. Kamat, D.V.: Ananda Mohan, P.V.; Gopalakrishna Prabhu, K.: Active-RC filters using two-stage OTAs with and without feed-forward compensation. IET Circuits Devices Syst. 5(6), 527–535 (2011)

    Article  Google Scholar 

  43. Li, Y.A.: Electronically tunable current-mode biquadratic filter and four-phase quadrature oscillator. Microelectron. J. 45(3), 330–335 (2014)

    Article  Google Scholar 

  44. Li, Y.N.: On the systematic synthesis of OTA-based wien oscillators. AEU Int. J. Electron. Commun. 67(9), 754–760 (2013)

  45. Sotner, R.; Jerabek, J.; Herencsar, N.; Vrba, K.; Dostal, T.: Features of multi-loop structures with OTAs and adjustable current amplifier for second-order multiphase/ quadrature oscillators. AEU Int. J. Electron. Commun. 69(5), 814–822 (2015)

    Article  Google Scholar 

  46. Senani, R.; Gupta, M.; Bhaskar, D.R.; Singh, A.K.: Generation of equivalent forms of operational transconductance amplifier-RC sinusoidal oscillators: the nullor approach. IET J. Eng. (2014). doi:10.1049/joe.2013.0200

    Google Scholar 

  47. Senani, R.; Bhaskar, D.R.; Gupta, M.; Singh, A.K.: Canonic OTA-C sinusoidal oscillators: generation of new grounded-capacitor versions. Am. J. Electr. Electron. Eng. 3(6), 137–146 (2015)

    Google Scholar 

  48. Krishna, B.T.: Studies on fractional-order differentiators and integrators: a survey. Signal Process. 91(3), 386–426 (2011)

    Article  MATH  Google Scholar 

  49. Sumi, Y.; Tsukutani, T.; Tsunetsugu, H.; Yabuki, N.: Electrical tunable multiple-mode universal biquadratic circuits. In: International Conference on Computer Application and Industrial Electronics (2010). doi:10.1109/ICCAIE.2010.5735109

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Authors and Affiliations

  1. Department of Electronics and Communication Engineering, Delhi Technological University Delhi, Delhi, India

    Rakesh Verma, Neeta Pandey & Rajeshwari Pandey

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  1. Rakesh Verma
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  2. Neeta Pandey
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  3. Rajeshwari Pandey
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Correspondence to Neeta Pandey.

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Verma, R., Pandey, N. & Pandey, R. Electronically Tunable Fractional Order Filter. Arab J Sci Eng 42, 3409–3422 (2017). https://doi.org/10.1007/s13369-017-2500-8

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  • DOI: https://doi.org/10.1007/s13369-017-2500-8

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