Arabian Journal for Science and Engineering

, Volume 44, Issue 3, pp 1933–1948 | Cite as

Analog Realization of Electronically Tunable Fractional-Order Differ-Integrators

  • Divya GoyalEmail author
  • Pragya Varshney
Research Article - Electrical Engineering


This paper presents simple structures of fractional-order differentiators and fractional-order integrators. For these structures, both current mode and voltage mode designs have been implemented for differential input signals. The analog realizations of these fractional circuits use a single active element, the Differential Voltage Current Conveyor Transconductance Amplifier (DVCCTA), and a capacitive fractor. The passive elements present in the capacitive fractor are arranged in parallel RC ladder topology with their consecutive values in geometric progression. In the proposed structures, the capacitive fractor and the resistances connected at different ports of DVCCTA are all grounded, hence, making the designs simpler and less sensitive to the parasitic effects. Apart from this, the other key features of these designs are—electronically tunable, high dynamic range, robust and accurate. Simulations of all the four models are performed using TSMC \(0.25\,\upmu \hbox {m}\) technology in MentorGraphics. The non-ideal analysis of DVCCTA device and Monte Carlo analysis have been studied to validate the robustness of these models. The results obtained are in compliance with their corresponding ideal responses. Comparisons with other active element-based structures have been presented to substantiate the work proposed in this paper.


Integrator Differentiator Differential input Fractional Fractor Current conveyor 


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  1. 1.
    Biolek, D.; Senani, R.; Biolkova, V.; Kolka, Z.: Active elements for analog signal processing: classification, review, and new proposals. Radioengineering 17, 15–32 (2008)Google Scholar
  2. 2.
    Patranabis, D.; Ghosh, D.: Integrators and differentiators with current conveyors. IEEE Trans. Circuits Syst. 31, 567–9 (1984)CrossRefGoogle Scholar
  3. 3.
    Lee, J.Y.; Tsao, H.W.: True RC integrators based on current conveyors with tunable time constants using active control and modified loop technique. IEEE Trans. Instrum. Meas. 41, 709–14 (1992)CrossRefGoogle Scholar
  4. 4.
    Liu, S.I.; Hwang, Y.S.: Dual-input differentiators and integrators with tunable time constants using current conveyors. IEEE Trans. Instrum. Meas. 43(4), 650–4 (1994)CrossRefGoogle Scholar
  5. 5.
    Kumar P.; Verma R.: Realization of a novel current mode fully differential PID (FDPID) controller. In: IEEE 5th India International Conference on Power Electronics (IICPE), Dec 2012. pp. 1–5 (2012)Google Scholar
  6. 6.
    Erdal, C.; Kuntman, H.; Kafali, S.: A current controlled conveyor based proportional-integral-derivative (PID) controller. IU J. Electr. Electron. Eng. 4(2), 1243–8 (2004)Google Scholar
  7. 7.
    Yuce, E.; Minaei, S.: New CCII-based versatile structure for realizing PID controller and instrumentation amplifier. Microelectron. J. 41(5), 311–6 (2010)CrossRefGoogle Scholar
  8. 8.
    Srisakultiew, S.; Siripruchyanun, M.: A synthesis of electronically controllable current-mode PI, PD and PID controllers employing CCCDBAs. Circuits Syst. 4(3), 287 (2013)CrossRefGoogle Scholar
  9. 9.
    Lawanwisut S.; Srisakultiew S.; Siripruchyanun M.: A synthesis of low component count for current-mode PID, PI and PD controllers employing single CCTA and Grounded elements. In: 2015 IEEE 38th International Conference on Telecommunications and Signal Processing (TSP), July 2015. pp. 1–5 (2015)Google Scholar
  10. 10.
    Mahmoud, S.A.: Low voltage wide range CMOS differential voltage current conveyor and its applications. Contemp. Eng. Sci. 1(3), 105–26 (2008)MathSciNetGoogle Scholar
  11. 11.
    Tangsrirat, W.: Floating simulator with a single DVCCTA. Indian J. Eng. Mater. Sci. 20, 79–86 (2013)Google Scholar
  12. 12.
    Nandi, R.; Das, S.; Venkateswaran, P.: Floating lossless immittance functions using DVCCTA. Int. J. Electron. Lett. 4(1), 117–26 (2016)CrossRefGoogle Scholar
  13. 13.
    Chien, H.C.; Chen, C.Y.: CMOS realization of single-resistance-controlled and variable frequency dual-mode sinusoidal oscillators employing a single DVCCTA with all-grounded passive components. Microelectron. J. 45(2), 226–38 (2014)CrossRefGoogle Scholar
  14. 14.
    Pandey, N.; Pandey, R.: Approach for third order quadrature oscillator realisation. IET Circuits Devices Syst. 9(3), 161–71 (2015)CrossRefGoogle Scholar
  15. 15.
    Pandey, N.; Arora, S.; Takkar, R.; Pandey, R.: DVCCCTA-based implementation of mutually coupled circuit. ISRN Electron. 2012, 1–6 (2012)Google Scholar
  16. 16.
    Lee, C.N.: Independently tunable mixed-mode universal biquad filter with versatile input/output functions. AEU Int. J. Electron. Commun. 70(8), 1006–19 (2016)CrossRefGoogle Scholar
  17. 17.
    Khateb, F.; Kubánek, D.; Tsirimokou, G.; Psychalinos, C.: Fractional-order filters based on low-voltage DDCCs. Microelectron. J. 50, 50–9 (2016)CrossRefGoogle Scholar
  18. 18.
    Phatsornsiri, P.; Kumngern, M.; Lamun, P.: A voltage-mode universal biquadratic filter using DDCCTA. J. Circuits Syst. Comput. 25(05), 1650034–57 (2016)CrossRefGoogle Scholar
  19. 19.
    Tangsrirat, W.; Channumsin, O.; Pukkalanun, T.: Resistorless realization of electronically tunable voltage-mode SIFO-type universal filter. Microelectron. J. 44(3), 210–5 (2013)CrossRefGoogle Scholar
  20. 20.
    Chen, H.P.; Hwang, Y.S.; Ku, Y.T.; Lin, T.J.: Voltage-mode biquadratic filters using single DDCCTA. AEU Int. J. Electron. Commun. 70(10), 1403–11 (2016)CrossRefGoogle Scholar
  21. 21.
    Kuntman H.H.; Uygur A.: New possibilities and trends in circuit design for analog signal processing. In: 2012 IEEE International Conference on Applied Electronics (AE), Sept 2012. pp. 1–9 (2012)Google Scholar
  22. 22.
    Nezha M.; Massinissa T.; Jean-Claude T.: Physical interpretation and initialization of the fractional integrator. In: 2014 IEEE International Conference on Fractional Differentiation and Its Applications (ICFDA) June 2014. pp. 1–6 (2014)Google Scholar
  23. 23.
    Petras, I.; Sierociuk, D.; Podlubny, I.: Identification of parameters of a half-order system. IEEE Trans. Signal Process. 60(10), 5561–6 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Sierociuk, D.; Podlubny, I.; Petras, I.: Experimental evidence of variable-order behavior of ladders and nested ladders. IEEE Trans. Control Syst. Technol. 21(2), 459–66 (2013)CrossRefGoogle Scholar
  25. 25.
    Mondal, D.; Biswas, K.: Performance study of fractional order integrator using single-component fractional order element. IET Circuits Devices Syst. 5(4), 334–42 (2011)CrossRefGoogle Scholar
  26. 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(02), 361–86 (2009)CrossRefGoogle Scholar
  27. 27.
    Podlubny, I.; Petraš, I.; Vinagre, B.M.; O’leary, P.; Dorčák, L’.: Analogue realizations of fractional-order controllers. Nonlinear Dyn. 29(1), 281–96 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  28. 28.
    Charef, A.: Analogue realisation of fractional-order integrator, differentiator and fractional PI\(^{\lambda }\)D\(^{\mu }\) controller. IEE Proc. Control Theory Appl. 153(6), 714–20 (2006)CrossRefGoogle Scholar
  29. 29.
    Djouambi A.; Charef A.; Voda A.: Numerical simulation and identification of fractional systems using digital adjustable fractional order integrator. In: 2013 IEEE European Conference on Control (ECC) July 2013. pp. 2615–2620 (2013)Google Scholar
  30. 30.
    Adhikary, A.; Khanra, M.; Pal, J.; Biswas, K.: Realization of fractional order elements. INAE Lett. 2, 41–47 (2017)CrossRefGoogle Scholar
  31. 31.
    Khanra M.; Pal J.; Biswas K.: Rational approximation and analog realization of fractional order differentiator. In: 2011 IEEE International Conference on Process Automation, Control and Computing (PACC), July 2011. pp. 1–6 (2011)Google Scholar
  32. 32.
    Valsa, J.; Vlach, J.: RC models of a constant phase element. Int. J. Circuit Theory Appl. 41(1), 59–67 (2013)Google Scholar
  33. 33.
    Gonzalez E.A.; Petráš I.: Advances in fractional calculus: control and signal processing applications. In: 2015 IEEE 16th International Conference on Carpathian Control (ICCC), May 2015. pp. 147–152 (2015)Google Scholar
  34. 34.
    Abulencia G.L.; Abad AC.: Analog realization of a low-voltage two-order selectable fractional-order differentiator in a 0.35 um CMOS technology. In: 2015 IEEE International Conference on Humanoid, Nanotechnology, Information Technology, Communication and Control, Environment and Management (HNICEM), Dec 2015. pp. 1–6 (2015)Google Scholar
  35. 35.
    Gonzalez, E.; Dorčák, L’.; Monje, C.; Valsa, J.; Caluyo, F.; Petráš, I.: Conceptual design of a selectable fractional-order differentiator for industrial applications. Fract. Calc. Appl. Anal. 17(3), 697–716 (2014)CrossRefzbMATHGoogle Scholar
  36. 36.
    Krishna, B.T.: Studies on fractional order differentiators and integrators: a survey. Signal Process. 91(3), 386–426 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  37. 37.
    Hollmann, L.J.; Stevenson, R.L.: Pole-zero placement algorithm for the design of digital filters with fractional-order rolloff. Signal Process. 107, 218–29 (2015)CrossRefGoogle Scholar
  38. 38.
    Dhabale, A.S.; Dive, R.; Aware, M.V.; Das, S.: A new method for getting rational approximation for fractional order differintegrals. Asian J. Control 17(6), 2143–52 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  39. 39.
    Tsirimokou, G.; Koumousi, S.; Psychalinos, C.: Design of fractional-order filters using current feedback operational amplifiers. J. Eng. Sci. Technol. Rev. 9, 77–81 (2016)CrossRefGoogle Scholar
  40. 40.
    Verma, R.; Pandey, N.; Pandey, R.: Electronically tunable fractional order filter. Arab. J. Sci. Eng. 42, 3409–3422 (2017)CrossRefGoogle Scholar
  41. 41.
    Psychalinos, C.; Elwakil, A.; Maundy, B.; Allagui, A.: Analysis and realization of a switched fractional-order-capacitor integrator. Int. J. Circuit Theory Appl. 44(11), 2035–40 (2016)CrossRefGoogle Scholar
  42. 42.
    Caponetto, R.; Dongola, G.; Maione, G.; Pisano, A.: Integrated technology fractional order proportional-integral-derivative design. J. Vib. Control 20(7), 1066–75 (2014)MathSciNetCrossRefGoogle Scholar
  43. 43.
    Tsirimokou, G.; Psychalinos, C.: Ultra-low voltage fractional-order circuits using current mirrors. Int. J. Circuit Theory Appl. 44(1), 109–26 (2016)CrossRefGoogle Scholar
  44. 44.
    Vastarouchas, C.; Tsirimokou, G.; Freeborn, T.J.; Psychalinos, C.: Emulation of an electrical-analogue of a fractional-order human respiratory mechanical impedance model using OTA topologies. AEU Int. J. Electron. Commun. 78, 201–8 (2017)CrossRefGoogle Scholar
  45. 45.
    Dimeas I.; Tsirimokou G.; Psychalinos C.; Elwakil A.: Realization of fractional-order capacitor and inductor emulators using current feedback operational amplifiers. In: 2015 International Symposium on Nonlinear Theory and its Application (NOLTA), Dec 2015. pp. 237–240 (2015)Google Scholar
  46. 46.
    Sheng, H.; Sun, H.G.; Coopmans, C.; Chen, Y.Q.; Bohannan, G.W.: A physical experimental study of variable-order fractional integrator and differentiator. Eur. Phys. J. Spec. Top. 193(1), 93–104 (2011)CrossRefGoogle Scholar
  47. 47.
    Biswas, K.; Sen, S.; Dutta, P.K.: Realization of a constant phase element and its performance study in a differentiator circuit. IEEE Trans. Circuits Syst. II Expr. Br. 53(9), 802–6 (2006)CrossRefGoogle Scholar
  48. 48.
    Sarafraz, M.S.; Tavazoei, M.S.: Realizability of fractional-order impedances by passive electrical networks composed of a fractional capacitor and RLC components. IEEE Trans. Circuits Syst. I Regul. Pap. 62(12), 2829–35 (2015)MathSciNetCrossRefGoogle Scholar
  49. 49.
    Pu, Y.F.: Measurement units and physical dimensions of fractance-part I: Position of purely ideal fractor in Chua’s axiomatic circuit element system and fractional-order reactance of fractor in its natural implementation. IEEE Access 4, 3379–97 (2016)CrossRefGoogle Scholar
  50. 50.
    Yifei P.; Xiao Y.; Ke L.; Jiliu Z.; Ni Z.; Yi Z.; Xiaoxian P.: Structuring analog fractance circuit for 1/2 order fractional calculus. In: 2005 IEEE 6th International Conference on ASICON, 2005. pp. 1136–1139 (2005)Google Scholar

Copyright information

© King Fahd University of Petroleum & Minerals 2018

Authors and Affiliations

  1. 1.Division of Instrumentation and Control Engineering, Netaji Subhas Institute of TechnologyUniversity of DelhiDelhiIndia

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