Design of a Fractional Order Low-pass Filter Using a Differential Voltage Current Conveyor

Authors

  • Battula Tirumala Krishna Department of Electronics and Communication Engineering, Lincoln University College, Petaling Jaya, Malaysia https://orcid.org/0000-0002-8316-7310
  • Midhunchakkaravathy Janarthanan Department of Electronics and Communication Engineering, Lincoln University College, Petaling Jaya, Malaysia

DOI:

https://doi.org/10.26636/jtit.2023.169123

Keywords:

current conveyor, differential voltage, differentiator, fractional order, integrator, RC network, simulation

Abstract

In this paper, an active implementation of a differential voltage current conveyor (DVCC) based on a low-pass filter operating in the fractional order domain is presented. The transfer function for a fractional order system is dependent on the rational approximation of sα. Different methods used for calculating the rational approximation, including Carlson, Elkhazalil, and curve fitting, are evaluated here. Finally, to validate the theoretical results, a fractional order Butterworth filter is simulated in the Pspice environment using the 0.5 micrometer CMOS technology with an R-C network-based fractional order capacitor. Additionally, using the Monte Carlo analysis, the impact of current and voltage faults on DVCC response is investigated. It has been inferred that realization with a wider bandwidth is possible.

Downloads

Download data is not yet available.

References

K.B. Oldham and J. Spanier, The Fractional Calculus. New York, USA: Academic Press, 1974 (ISBN: 9780486450018).
View in Google Scholar

G. Carlson and C. Halijak, "Approximation of fractional capacitors (1/s) (1/n) by a regular Newton process", IEEE Transactions on Circuit Theory, vol. 11, no. 2, pp. 210–213, 1964 https://doi.org/10.1109/TCT.1964.1082270 DOI: https://doi.org/10.1109/TCT.1964.1082270
View in Google Scholar

B.T. Krishna, "Studies on fractional order differentiators and integrators: A survey", Signal Processing, vol. 91, no. 3, pp. 386–426, 2011 https://doi.org/10.1016/j.sigpro.2010.06.022 DOI: https://doi.org/10.1016/j.sigpro.2010.06.022
View in Google Scholar

A. Yüce and N. Tan, "Electronic realization technique for fractional order integrators", The Journal of Engineering, vol. 2020, no. 5, pp. 157–167, 2020 https://doi.org/10.1049/joe.2019.1024 DOI: https://doi.org/10.1049/joe.2019.1024
View in Google Scholar

B.T. Krishna, "Realization of fractance device using fifth order approximation", Communications on Applied Electronics (CAE), vol. 7, no. 34, pp. 1–5, 2020 https://doi.org/10.5120/cae2020652 869. DOI: https://doi.org/10.5120/cae2020652869
View in Google Scholar

Y. Wei, Y-Q. Chen, Y. Wei, and X. Zhang, "Consistent approximation of fractional order operators", Journal of Dynamic Systems, Measurement and Control, vol. 143, no. 8, 2021 https://doi.org/10.1115/1.4050393 DOI: https://doi.org/10.1115/1.4050393
View in Google Scholar

A. Kartci et al., "Synthesis and optimization of fractional order elements using a genetic algorithm", IEEE Access, vol. 7, pp. 80233–80246, 2019 https://doi.org/10.1109/ACCESS.2019.2923166 DOI: https://doi.org/10.1109/ACCESS.2019.2923166
View in Google Scholar

A.K. Mahmood and S.A.R. Saleh, "Realization of fractional order differentiator by analogue electronic circuit", International Journal of Advances in Engineering & Technology, vol. 8, no. 1, pp. 1939–1951, 2015 https://doi.org/10.7323/ijaet/v8_iss1 DOI: https://doi.org/10.7323/ijaet/v8_iss1
View in Google Scholar

S. Kapoulea, C. Psychalinos, and A.S. Elwakil, "FPAA-based reization of filters with fractional Laplace operators of different orders", Fractal and Fract., vol. 5, no. 4, pp. 218–228, 2021 https://doi.org/10.3390/fractalfract5040218 DOI: https://doi.org/10.3390/fractalfract5040218
View in Google Scholar

M.S. Semary, M.E. Fouda, H.N. Hassana, and A.G. Radwan, "Realization of fractional-order capacitor based on passive symmetric network", Journal of Advanced Research, vol. 18, pp. 147–159, 2019 https://doi.org/10.1016/j.jare.2019.02.004 DOI: https://doi.org/10.1016/j.jare.2019.02.004
View in Google Scholar

V. Alimisis, Ch. Dimas, G. Pappas, and P.P. Sotiriadis, "Analog realization of fractional-order skin-electrode model for tetrapolar bio-impedance measurements", Technologies, vol. 8, no. 4, 2020, p. 61 https://doi.org/10.3390/technologies8040061 DOI: https://doi.org/10.3390/technologies8040061
View in Google Scholar

N. Mijat, D. Jurisic, G.S. Moschytz, "Analog modeling of fractional-order elements: A classical circuit theory approach", IEEE Access, vol. 9, pp. 110309–10331, 2021 https://doi.org/10.1109/ACCESS.2021.3101160 DOI: https://doi.org/10.1109/ACCESS.2021.3101160
View in Google Scholar

A.K. Mahmood and S.A.R. Saleh, "Realization of fractional-order proportional-integral-derivative controller using fractance circuit", JEA Journal of Electrical Engineering, vol. 2, no. 1, pp. 1–11, 2018 https://doi.org/10.13140/RG.2.2.30942.69445
View in Google Scholar

S. Holm, T. Holm, and Ø.G. Martinsen, "Simple circuit equivalents for the constant phase element", PLoS ONE, vol. 16, no. 3, 2021 https://doi.org/10.1371/journal.pone.0248786 DOI: https://doi.org/10.1371/journal.pone.0248786
View in Google Scholar

P. Prommee, N. Wongprommoon, and R. Sotner, "Frequency tunability of fractance device based on OTA-C", in 42nd International Conference on Telecommunications and Signal Processing (TSP2019), Budapest, Hungary, 2019 https://doi.org/10.1109/TSP.20 19.8768816 DOI: https://doi.org/10.1109/TSP.2019.8768816
View in Google Scholar

P. Prommee, P. Pienpichayapong, N. Manositthichai, and N. Wongprommoon, "OTA-based tunable fractional-order devices for biomedical engineering", AEU – International Journal of Electronics and Communications, vol. 128, pp. 1–13, 2021 https://doi.org/10.1016/j.aeue.2020.153520 DOI: https://doi.org/10.1016/j.aeue.2020.153520
View in Google Scholar

S.K. Mishra, M. Gupta, and D.K. Upadhyay, "Active realization of fractional order Butterworth lowpass filter using DVCC", Journal of King Saud University, vol. 32, no. 2, pp. 158–165, 2020 https://doi.org/10.1016/j.jksues.2018.11.005 DOI: https://doi.org/10.1016/j.jksues.2018.11.005
View in Google Scholar

D.K. Upadhyay and S.K. Mishra, "Fractional order microwave low-pass band-pass filter", in 2015 Annual IEEE India Conference (INDICON), New Delhi, India, 2015 https://doi.org/10.1109/INDI-CON.2015.7443282 DOI: https://doi.org/10.1109/INDICON.2015.7443282
View in Google Scholar

N. Shrivastava and P. Varshney, "Implementation of Carlson based fractional differentiation in control of fractional plants", I.J. Intelligent Systems and Applications, vol. 10, no. 9, pp. 66–74, 2018 https://doi.org/10.5815/ijisa.2018.09.08 DOI: https://doi.org/10.5815/ijisa.2018.09.08
View in Google Scholar

R. El-Khazali, I.M. Batiha, and S. Momani, "Approximation of fractional-order operators", in Fractional Calculus. ICFDA 2018, P. Agarwal, D. Baleanu, Y. Chen, S. Momani, and J. Machado, Eds. Springer Proceedings in Mathematics & Statistics, vol. 303. Singapore: Springer https://doi.org/10.1007/978-981-15-0430-3_8 DOI: https://doi.org/10.1007/978-981-15-0430-3_8
View in Google Scholar

K. Bingi, R. Ibrahim, M. Karsiti, S. Hassam, and V. Harindran, "Frequency response based curve fitting approximation of fractional-order PID controllers", International Journal of Applied Mathematics and Computer Science, vol. 29, no. 2, pp. 311–326, 2019 https://doi.org/10.2478/amcs-2019-0023 DOI: https://doi.org/10.2478/amcs-2019-0023
View in Google Scholar

Cover page of vol. 2 2023 issue

Downloads

Published

2023-06-30

Issue

No. 2 (2023)

Section

ARTICLES FROM THIS ISSUE

License

Copyright (c) 2023 Journal of Telecommunications and Information Technology

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

[1]
B. T. Krishna and M. Janarthanan, “Design of a Fractional Order Low-pass Filter Using a Differential Voltage Current Conveyor”, JTIT, vol. 92, no. 2, pp. 17–21, Jun. 2023, doi: 10.26636/jtit.2023.169123.