Research PaperNo Access

Analysis and Design of Optimized Fractional Order Low-Pass Bessel Filter

Advanced Electronics Lab, Department of Electronics and Communication Engineering, Faculty of Technology (University of Delhi) New Delhi 110078, India

E-mail Address: soniashu.14@gmail.com

Search for more papers by this author

and

Maneesha Gupta

https://orcid.org/0000-0003-2495-678X

Advanced Electronics Lab, Department of Electronics and Communication Engineering, Netaji Subhas University of Technology (Formerly NSIT) New Delhi 110078, India

E-mail Address: Maneeshapub@gmail.com

Corresponding author.

Search for more papers by this author

https://doi.org/10.1142/S0218126621500353Cited by:16 (Source: Crossref)

Abstract

This paper approximates the behavior of low-pass Bessel filter in fractional domain using the Interior search algorithm (ISA). A detailed analysis has been done with sensitivity analysis, W-plane stability and absolute percentage error (gain and cut-off frequency) to study the low-pass fractional order filter. The work focuses on the analysis and design of fractional filter with two cases. In the first case, the design and simulation of $(1 + α)$ $(1 + α)$ order low-pass Bessel filter has been done using MATLAB for $α$ $α$ value ranging from 0.1 to 0.9. SPICE simulation of 1.2, 1.5 and 1.9 order low-pass Bessel filter using fractional order capacitor of order $α$ $α$ with Tow–Thomas biquad have been performed. In the second case, low-pass ( $α + β)$ $α + β)$ order Bessel filter has been simulated and designed using MATLAB, where $α$ $α$ and $β$ $β$ are two fractional order elements of a different order. SPICE simulation for different values of $α$ $α$ and $β$ $β$ have been done using two fractional order capacitors of $α$ $α$ and $β$ $β$ order with Tow–Thomas biquad.

This paper was recommended by Regional Editor Emre Salman.

Keywords:

References

1. A. S. Ali, A. G. Radwan and A. M. Soliman, Fractional order Butterworth filter: Active and passive realizations, IEEE J. Emerg. Sel. Topics Circuits Syst. 3 (2013) 346–354, https://doi.org/10.1109/JETCAS.2013.2266753. Web of Science, Google Scholar
2. A. Soltan, A. G. Radwan and A. M. Soliman, CCII based fractional filters of different orders, J. Adv. Res. 5 (2014) 157–164, https://doi.org/10.1016/j.jare.2013.01.007. Google Scholar
3. A. Soltan, A. G. Radwan and A. M. Soliman, Fractional order filter with two fractional elements of dependent orders, Microelect. J. 43 (2012) 818–827, https://doi.org/10.1016/j.mejo.2012.06.009. Web of Science, Google Scholar
4. T. J. Freeborn, Comparison of $(1 + α)$ $(1 + α)$ fractional order transfer functions to approximate low pass Butterworth magnitude responses, Circuits Syst. Signal Process. 35 (2016) 1983–2002, https://doi.org/10.1007/s00034-015-0226-y. Web of Science, Google Scholar
5. A. Soni and M. Gupta, Design of fractional order Butterworth filter using genetic algorithm, Proc. 2nd IEEE Int. Conf. on Power Electronics, Intelligent Control and Energy Systems (Delhi, India, 2018), pp. 1052–1055. Google Scholar
6. T. Khanna and D. K. Upadhyay, Design and realization of fractional order butterworth low pass filters, Proc. IEEE Int. Conf. on Signal Processing, Computing and Control (Waknaghat, 2015), pp. 356–361. Google Scholar
7. S. Mahata, S. K. Saha, R. Kar and D. Mandal, Optimal design of fractional order low pass Butterworth filter with accurate magnitude response, Digit Signal Process. 72 (2018) 96–114. Web of Science, Google Scholar
8. A. Soni, N. Sreejeth, V. Saxena and M. Gupta, Series optimized fractional order low pass Butterworth filter, Arab. J. Sci. Eng. 45 (2019) 1–15, https://doi.org/10.1007/s13369-019-04225-7. Web of Science, Google Scholar
9. A. Acharya, S. Das, I. Pan and S. Das, Extending the concept of analog Butterworth filter for fractional order systems, Signal Process. 94 (2013) 409–420, https://doi.org/10.1016/j.sigpro.2013.07.012. Web of Science, Google Scholar
10. L. A. Said, S. M. Ismail, A. G. Radwan, A. H. Madian, M. F. A. El-Yazeed and A. M. Soliman, On the optimization of fractional order low pass filters, Circuits Syst. Signal Process. 35 (2016) 2017–2039, https://doi.org/10.1007/s00034-016-0258-y. Web of Science, Google Scholar
11. T. J. Freeborn, B. Maundy and A. S. Elwakil, Approximated fractional order Chebyshev low pass filters, Hindawi Pub. Corp. 2015 (2015) 1–7, https://doi.org/10.1155/2015/832468. Google Scholar
12. A. Soni and M. Gupta, Performance evaluation of different order fractional Chebyshev filter using optimisation techniques, Int. J. Electron. Lett. 8 (2019) 1–18, https://doi.org/10.1080/21681724.2019.1584915. Google Scholar
13. T. J. Freeborn, A. S. Elwakil and B. Maundy, Approximated fractional order inverse Chebyshev low pass filters, Circuits Syst. Signal Process. 35 (2015) 1973–1982, https://doi.org/10.1007/s00034-015-0222-2. Web of Science, Google Scholar
14. D. K. Avdeeva, V. Y. E. Kazakov, N. M. Natalinova, M. L. Ivanov, M. A. Yuzhakova and N. V. Turushev, The simulation results of the high-pass and low-pass filter effect on the quality of micropotential recordings on the electrocardiogram, Biol. Med. 6 (2014) 1–10. Google Scholar
15. A. H. Gandomi, Interior search algorithm (ISA): A novel approach for global optimization, ISA Trans. 53 (2014) 1168–1183, https://doi.org/10.1016/j.isatra.2014.03.018. Web of Science, Google Scholar
16. B. Bentouati, S. Chettih and L. Chaib, Interior search algorithm for optimal power flow with non-smooth cost functions, Cogent Eng. 4 (2017) 1–17, https://doi.org/10.1080/23311916. 2017.1292598. Web of Science, Google Scholar
17. T. J. Freeborn, B. Maundy and A. S. Elwakil, Field programmable analogue array implementations of fractional step filters, IET Digit. Libr. IET Circu. Dev. Sys. 4 (2010) 514–524, https://doi.org/10.1049/iet-cds.2010.0141. Web of Science, Google Scholar
18. S. Mahata, S. K. Saha, R. Kar and D. Mandal, Approximation of fractional-order low-pass filter, IET Signal Process. 13 (2018) 112–124, https://doi.org/10.1049/iet-spr.2018.5128. Web of Science, Google Scholar
19. J. Dvorak, L. Langhammer, J. Jerabek, J. Koton, R. Sotner and J. Polak, Synthesis and analysis of electronically adjustable fractional-order low-pass filter, J. Circuit. Sys. Comp. 27 (2018) 3–13. Web of Science, Google Scholar
20. T. J. Freeborn, B. Maundy and A. Elwakil, Fractional resonance-based RL $_{β}$ $_{β}$ C $_{α}$ $_{α}$ filters, Hindawi Pub. Corp. 2013 (2013) 1–10, https://doi.org/10.1155/2013/726721. Google Scholar
21. T. J. Freeborn, B. Maundy and A. S. Elwakil, Fractional step Tow-Thomas biquad filters, Nonlinear Theory Appl. 3 (2012) 357–374, https://doi.org/10.1587/nolta.3.357. Google Scholar
22. M. C. 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, https://doi.org/10.1007/s00034-012-9539-2. Web of Science, Google Scholar
23. D. Kubanek and T. Freeborn, $(1 + α)$ $(1 + α)$ Fractional-order transfer functions to approximate low-pass magnitude responses with an arbitrary quality factor, Int. J. Electronics Commun. 83 (2017) 570–578, https://doi.org/10.1016/j.aeue.2017.04.031. Web of Science, Google Scholar
24. M. A. Al-Alaoui, Class of digital integrators and differentiators, IET Signal Process. 5 (2011) 251–260, https://doi.org/10.1049/iet-spr.2010.0107. Web of Science, Google Scholar