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.
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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)
M.T. Abuelma’atti, Identification of cascadable current-mode filters and inverse-filters using single FTFN. Frequenz 54(11–12), 284–289 (2000)
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)
D.R. Bhaskar, M. Kumar, P. Kumar, Fractional order inverse filters using operational amplifier. Analog Integr. Circ. Signal Process. 97(1), 149–158 (2018)
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)
B. Chipipop, W. Surakampontorn, Realisation of current-mode FTFN-based inverse filter. Electron. Lett. 35(9), 690–692 (1999)
P. Duffett-Smith, Synthesis of lumped element, distributed, and planar filters. J. Atmos. Terr. Phys. 52(9), 811–812 (1990)
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)
T.J. Freeborn, A.S. Elwakil, B. Maundy, Approximated fractional-order inverse Chebyshev lowpass filters. Circ. Syst. Signal Process. 35(6), 1973–1982 (2015)
T.J. Freeborn, B. Maundy, A. Elwakil, Fractional-step Tow-Thomas biquad filters. Nonlinear Theory Appl. IEICE 3(3), 357–374 (2012)
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. 1–5
S. Gupta, D. Bhaskar, R. Senani, A. Singh, Inverse active filters employing CFOAS. Electr. Eng. 91(1), 23 (2009)
S. Gupta, D. Bhaskar, R. Senani, New analogue inverse filters realised with current feedback OP-AMPS. Int. J. Electron. 98(8), 1103–1113 (2011)
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)
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. 38–41
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. 1–5
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. 1–4
B. Krishna, Studies on fractional order differentiators and integrators: a survey. Signal Process. 91(3), 386–426 (2011)
A. Leuciuc, Using nullors for realisation of inverse transfer functions and characteristics. Electron. Lett. 33(11), 949–951 (1997)
G. Maione, Thiele’s continued fractions in digital implementation of noninteger differintegrators. Signal Image Video Process. 6(3), 401–410 (2012)
K. Matsuda, H. Fujii, H(infinity) optimized wave-absorbing control—analytical and experimental results. J. Guid. Control Dyn. 16(6), 1146–1153 (1993)
R. Pandey, N. Pandey, T. Negi, V. Garg, CDBA based universal inverse filter. ISRN Electronics (2013)
V. Patil, R. Sharma, Novel inverse active filters employing CFOAS. Int. J. Sci. Res. Dev. 3(7), 359–360 (2015)
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)
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)
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)
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)
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. 603–606
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)
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. 375–408
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)
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)
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)
A.K. Singh, A. Gupta, R. Senani, Otra-based multi-function inverse filter configuration. Adv. Electr. Electron. Eng. 15(5), 846–856 (2018)
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)
H.-Y. Wang, C.-T. Lee, Using nullors for realisation of current-mode FTFN-based inverse filters. Electron. Lett. 35(22), 1889–1890 (1999)
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)
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)
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)
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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.
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Hamed, E.M., Said, L.A., Madian, A.H. et al. On the Approximations of CFOA-Based Fractional-Order Inverse Filters. Circuits Syst Signal Process 39, 2–29 (2020). https://doi.org/10.1007/s00034-019-01155-5
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DOI: https://doi.org/10.1007/s00034-019-01155-5