No Access

Reconfigurable Fractional-Order Filter with Electronically Controllable Slope of Attenuation, Pole Frequency and Type of Approximation

Jan Jerabek

Department of Telecommunications, Brno University of Technology, Technicka 12, Brno, 616 00, Czech Republic

E-mail Address: jerabekj@feec.vutbr.cz

Corresponding author.

Search for more papers by this author

Roman Sotner

Department of Telecommunications, Brno University of Technology, Technicka 12, Brno, 616 00, Czech Republic

E-mail Address: sotner@feec.vutbr.cz

Search for more papers by this author

Jan Dvorak

Department of Telecommunications, Brno University of Technology, Technicka 12, Brno, 616 00, Czech Republic

E-mail Address: dvorakjan@phd.feec.vutbr.cz

Search for more papers by this author

Josef Polak

Department of Telecommunications, Brno University of Technology, Technicka 12, Brno, 616 00, Czech Republic

E-mail Address: xpolak24@phd.feec.vutbr.cz

Search for more papers by this author

David Kubanek

Department of Telecommunications, Brno University of Technology, Technicka 12, Brno, 616 00, Czech Republic

E-mail Address: kubanek@feec.vutbr.cz

Search for more papers by this author

Norbert Herencsar

Department of Telecommunications, Brno University of Technology, Technicka 12, Brno, 616 00, Czech Republic

E-mail Address: herencsn@feec.vutbr.cz

Search for more papers by this author

, and

Jaroslav Koton

Department of Telecommunications, Brno University of Technology, Technicka 12, Brno, 616 00, Czech Republic

E-mail Address: koton@feec.vutbr.cz

Search for more papers by this author

https://doi.org/10.1142/S0218126617501572Cited by:50 (Source: Crossref)

Abstract

This paper presents design of electronically reconfigurable fractional-order filter that is able to be configured to operate as fractional-order low-pass filter (FLPF) or fractional-order high-pass filter (FHPF). Its slope of attenuation between pass band and stop band, i.e., order of the filter, is electronically adjustable in the range between 1 and 2. Also, pole frequency can be electronically controlled independently with respect to other tuned parameters. Moreover, particular type of approximation can be also controlled electronically. This feature set is available both for FLPF and FHPF-type of response. Presented structure of the filter is based on well-known follow-the-leader feedback (FLF) topology adjusted in our case for utilization with just simple active elements operational transconductance amplifiers (OTAs) and adjustable current amplifiers (ACAs), both providing possibility to control its key parameter electronically. This paper explains how reconfigurable third-order FLF topology is used in order to approximate both FLPF and FHPF in concerned frequency band of interest. Design is supported by PSpice simulations for three particular values of order of the filter (1.25, 1.5, 1.75), for several values of pole frequency and for two particular types of approximation forming the shape of both the magnitude and phase response. Moreover, theoretical presumptions are successfully confirmed by laboratory measurements with prepared prototype based on behavioral modeling.

This paper was recommended by Regional Editor Piero Malcovati.

Keywords:

References

1. M. Ortigueira, An introduction to the fractional continuous-time linear systems: The 21st century systems, IEEE Circuits Syst. Mag. 8 (2008) 19–26. Google Scholar
2. A. S. Elwakil, Fractional-order circuits and systems: An emerging interdisciplinary research area, IEEE Circuits Syst. Mag. 10 (2010) 40–50. Google Scholar
3. T. Freeborn , A survey of fractional-order circuit models for biology and biomedicine, IEEE J. Emerg. Sel. Top. Circuits Syst. 3 (2013) 416–424. Crossref, Web of Science, Google Scholar
4. A. S. Elwakil and B. Maundy , Extracting the Cole–Cole impedance model parameters without direct impedance measurement, Electron. Lett. 46 (2010) 1367–1368. Crossref, Web of Science, Google Scholar
5. T. J. Freeeborn, A. Elwakil and B. Maundy , Electrode location impact on Cole-impedance parameters using magnitude-only measurements, Proc. 59th IEEE Int. Midwest Symposium on Circuits and Systems, Abu Dhabi, UAE, 16–19 October 2016, pp. 21–24. Google Scholar
6. J. Valsa, P. Dvorak and M. Friedel , Network model of CPE, Radioengineering 20 (2011) 619–626. Web of Science, Google Scholar
7. J. Valsa and J. Vlach , RC models of a constant phase element, Int. J. Circuit Theory Appl. 41 (2013) 59–67. Crossref, Web of Science, Google Scholar
8. B. M. Vinagre, I. Podlubny, A. Hernandez and V. Feliu , Some approximations of fractional order operators used in control theory and applications, Fractional Calc. Appl. Anal. 3 (2000) 231–248. Google Scholar
9. J. Petrzela, T. Gotthans and Z. Hrubos , General review of the passive networks with fractional-order dynamics, Proc. Int. Conf. Circuits, Systems, Control, Signals, Barcelona, Spain, 17–19 October 2012, pp. 172–177. Google Scholar
10. J. Petrzela , Analog continuous-time filtering extended to fractional-order network elements, Proc. 36th Int. Conf. Telecommunications and Signal Processing TSP, Rome, Italy, 2–4 July 2013, pp. 417–421. Google Scholar
11. J. Petrzela , Fundamental analog cells for fractional-order two-port synthesis, Proc. 23rd Int. Conf. Radioelektronika, Pardubice, Czech Republic, 17–18 April 2013, pp. 182–187. Google Scholar
12. J. Petrzela , A note on fractional-order two-terminal devices in filtering applications, Proc. 24th Int. Conf. Radioelektronika, Bratislava, Slovakia, 2014, pp. 1–4. Google Scholar
13. M. Tripathy, D. Mondal, K. Biswas and S. Sen , Experimental studies on realization of fractional inductors and fractional-order bandpass filters, Int. J. Circuit Theory Appl. 43 (2015) 1183–1196. Crossref, Web of Science, Google Scholar
14. I. Dimeas, G. Tsirimokou, C. Psychalinos and A. Elwakil , Realization of fractional-order capacitor and inductor emulators using current feedback operational amplifiers, Proc. Int. Symp. on Nonlinear Theory and its Applications NOLTA, Hong Kong, China, 1–4 December 2015, pp. 237–240. Google Scholar
15. G. Tsirimokou, C. Psychalinos, A. S. Elwakil and K. N. Salama , Experimental verification of on-chip CMOS fractional-order capacitor emulators, Electron. Lett. 52 (2016) 1298–1300. Crossref, Web of Science, Google Scholar
16. G. Tsirimokou, C. Psychalinos and A. S. Elwakil , Emulation of a constant phase element using operational transconductance amplifiers, Analog Integr. Circuits Signal Process. 85 (2015) 413–423. Crossref, Web of Science, Google Scholar
17. G. Tsirimokou, C. Laoudias and C. Psychalinos , 0.5-V fractional-order companding filters, Int. J. Circuit Theory Appl. 43 (2015) 1105–1126. Crossref, Web of Science, Google Scholar
18. G. Tsirimokou and C. Psychalinos , Ultra-low voltage fractional-order circuits using current mirrors, Int. J. Circuit Theory Appl. 44 (2016) 109–126. Crossref, Web of Science, Google Scholar
19. T. Freeborn, B. Maundy and A. Elwakil , Field programmable analogue array implementation of fractional step filters, IET Circuits Devices Syst. 4 (2010) 514–524. Crossref, Web of Science, Google Scholar
20. B. Maundy, A. Elwakil and T. Freeborn , On the practical realization of higher-order filters with fractional stepping, Signal Process. 91 (2011) 484–491. Crossref, Web of Science, Google Scholar
21. R. Sotner, J. Jerabek, J. Petrzela and T. Dostal , Simple approach for synthesis of fractional-order grounded immittances based on OTAs, Proc. Int. Conf. Telecommunications and Signal Processing TSP, Vienna, Austria, 27–29 June 2016, pp. 563–568. Google Scholar
22. R. Sotner, J. Jerabek, N. Herencsar, J. Petrzela, T. Dostal and K. Vrba , First-order adjustable transfer sections for synthesis suitable for special purposes in constant phase block approximation, Int. J. Electron. Commun. 69 (2015) 1334–1345. Crossref, Web of Science, Google Scholar
23. M. Krishna, S. Das, K. Biswas and B. Goswami , Fabrication of a fractional order capacitor with desired specifications: A study on process identification and characterization, IEEE Trans. Electron Devices 58 (2011) 4067–4073. Crossref, Web of Science, Google Scholar
24. A. M. Elshurafa, M. N. Almadhoun, K. N. Salama and H. N. Alshareef , Microscale electrostatic fractional capacitors using reduced graphene oxide percolated polymer composites, Appl. Phys. Lett. 102 (2013) 232901. Crossref, Web of Science, Google Scholar
25. A. Adhikary, M. Khanra, S. Sen and K. Biswas , Realization of carbon nanotube based electrochemical fractor, Proc. IEEE Int. Symp. on Circuits and Systems ISCAS, Lisbon, Portugal, 24–27 May 2015, pp. 2329–2332. Google Scholar
26. P. Ushakov, A. Shadrin, D. Kubanek and J. Koton , Passive fractional-order components based on resistive-capacitive circuits with distributed parameters, Proc. 39th Int. Conf. Telecommunications and Signal Processing TSP, Vienna, Austria, 27–29 June 2016, pp. 638–642. Google Scholar
27. P. Ahmadi, B. Maundy, A. Elwakil and L. Belostotski , High-quality factor asymmetric-slope band-pass filters: A fractional-order capacitor approach, IET Circuits Devices Syst 6 (2012) 187–197. Crossref, Web of Science, Google Scholar
28. M. Tripathy, K. Biswas and S. Sen , A design example of a fractional-order Kerwin–Huelsman–Newcomb biquad filter with two fractional capacitors of different order, Circuits Syst. Signal Process. 32 (2013) 1523–1536. Crossref, Web of Science, Google Scholar
29. A. Ali, A. Radwan and A. Soliman , Fractional order Butterworth filter: Active and passive realizations, IEEE J. Emerg. Sel. Top. Circuits Syst. 3 (2013) 346–354. Crossref, Web of Science, Google Scholar
30. A. Soltan, A. G. Radwan and A. M. Soliman , Fractional order sallen-key and KHN filters: Stability and poles allocation, Circuits Syst. Signal Process. 34 (2015) 1461–1480. Crossref, Web of Science, Google Scholar
31. T. Freeborn, B. Maundy and A. Elwakil , Toward the realization of fractional step filters, Proc. IEEE Int. Symp. on Circuits and Systems ISCAS, Paris, France, 30 May–2 June 2010, pp. 1037–1040. Google Scholar
32. B. Maundy, A. Elwakil and T. Freeborn , On the practical realization of higher-order filters with fractional stepping, Signal Process. 91 (2011) 484–491. Crossref, Web of Science, Google Scholar
33. F. Khateb, D. Kubanek, G. Tsirimokou and C. Psychalinos , Fractional-order filters based on low-voltage DDCCs, Microelectron. J. 50 (2016) 50–59. Crossref, Web of Science, Google Scholar
34. G. Tsirimokou, C. Psychalinos and A. S. Elwakil , Fractional-order electronically controlled generalized filters, Int. J. Circuit Theory Appl. (2016), doi: 10.1002/cta.2250. Crossref, Web of Science, Google Scholar
35. J. Dvorak, L. Langhammer, J. Jerabek, J. Koton, R. Sotner and J. Polak , Electronically tunable fractional-order low-pass filter with current followers, Proc. 39th Int. Conf. Telecommunications and Signal Processing TSP, Vienna, Austria, 27–29 June 2016, pp. 587–592. Google Scholar
36. D. Biolek, R. Senani, V. Biolkova and Z. Kolka , Active elements for analog signal processing: Classification, review and new proposals, Radioengineering 17 (2008) 15–32. Web of Science, Google Scholar
37. J. Jerabek, J. Koton, R. Sotner and K. Vrba , Adjustable band-pass filter with current active elements: Two fully-differential and single-ended solutions, Analog Integr. Circuits Signal Process. 74 (2013) 129–139. Crossref, Web of Science, Google Scholar
38. G. E. Carlson and C. A. Halijak , Approximation of fractional capacitors (1/s) $\land$ (1/n) by a regular Newton process, IEEE Trans. Circuit Theory 11 (1964) 210–213. Crossref, Google Scholar
39. K. Matsuda and H. Fujii , H $_{\infty}$ –optimized wave-absorbing control: Analytical and experimental results, J. Guid. Control Dyn. 16 (1993) 1146–1153. Crossref, Web of Science, Google Scholar
40. A. Oustaloup , Systèmes Asservis Linéaires d’Ordre Fractionnaire: Théorie et Pratique (Masson, Paris, 1983). Google Scholar
41. A. Oustalou , La Dérivation Non Entière, Théorie, Synthèse et Applications (Hermes Science Publications, Paris, 1995). Google Scholar
42. A. Oustaloup, F. Levron, B. Mathieu and F. Nanot , Frequency-band complex non integer differentiator: Characterization and synthesis, IEEE Trans. Circuits Syst. I, Fundam. Theory Appl. 47 (2000) 25–39. Crossref, Google Scholar
43. A. Djouambi, A. Charef and A. Besançon , Optimal approximation, simulation and analog realization of the fundamental fractional order transfer function, Int. J. Appl. Math. Comput. Sci. 17 (2007) 455–462. Crossref, Web of Science, Google Scholar
44. C. Gruau, D. Picart, R. Belmas, E. Bouton, F. Delmaire-Sizes, J. Sabatier and H. Trumel , Ignition of a confined high explosive under low velocity impact, Int. J. Impact Eng. 36 (2009) 537–550. Crossref, Web of Science, Google Scholar
45. B. Krishna and K. Reddy , Active and passive realization of fractance device of order $1 ∕ 2$ , Active Passive Electron. Compon. 2008 (2008) 1–5. Crossref, Google Scholar
46. J. Jerabek and K. VRBA , SIMO type low-input and high-output impedance current- mode universal filter employing three universal current conveyors, AEU — Int. J. Electron. Commun. 64 (2010) 588–593. Crossref, Web of Science, Google Scholar
47. J. Jerabek, R. Sotner, D. Kubanek, J. Dvorak, L. Langhammer, N. Herencsar and K. Vrba , Fractional-order low-pass filter with electronically adjustable parameters, Proc. Int. Conf. Telecommunications and Signal Processing, Vienna, Austria, 27–29 June 2016, pp. 569–574. Google Scholar
48. J. Jerabek, R. Sotner, J. Dvorak, L. Langhammer and J. Koton , Fractional-order high-pass filter with electronically adjustable parameters, Proc. 2016 Int. Conf. Applied Electronics (AE), Pilsen, Czech Republic, 6–7 September 2016, pp. 111–116. Google Scholar
49. Datasheet EL2082 (Elantec), Current-mode multiplier (intersil, rev. D, 1996), http://www.intersil.com/content/dam/Intersil/documents/el20/el2082.pdf. Google Scholar