Skip to main content
Log in

The design of multiple feedback topology Chebyshev low-pass active filter with average differential evolution algorithm

  • Original Article
  • Published:
Neural Computing and Applications Aims and scope Submit manuscript


This study presents the design of a tenth-order multiple feedback Chebyshev low-pass filter (MF-C-LPF). Component selection and gain calculation of filters are generally achieved over long periods of time using traditional methods. For 1-dB and 3-dB gains, the component values of the filter were optimized for both continuous and discrete values using four different metaheuristic algorithms. In the first case where continuous values were used, component values were accepted as ideal and unlimited in order to minimize gains. In the second case, industrial E196 series component values were used to transform the design problem into a discrete optimization problem. In this case where the design problem became more complex, the performance of the metaheuristic algorithms was compared. The literature review shows that this study is the first attempt to design a 10th-order MF-C-LPF for E196 series values. The average differential evolution algorithm is proposed to determine the optimal component values of the tenth-order MF-C-LPF. The performance of the proposed method was compared with three commonly used algorithms (PSO, CSS and DE). The optimal filter component values and quality factors (Q) were presented for each stage. We believe that the quality factor values will be a reference for future studies.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18

Similar content being viewed by others


  1. Lacanette K (2010) A basic introduction to filters: active, passive, and switched-capacitor. Texas Instruments National Semiconductor Application Note. Accessed 4 May 2019

  2. Schaumann R, Van Valkengurg ME (2010) Design of analog filters. Oxford University Press, Oxford

    Google Scholar 

  3. Tseng CC, Lee SL (2017) Closed-form designs of digital fractional order Butterworth filters using discrete transforms. Signal Process 137:80–97.

    Article  Google Scholar 

  4. Yao SN, Collins T, Jancovic P (2012) Hybrid method for designing digital Butterworth filters. Comput Electr Eng 38(4):811–818.

    Article  Google Scholar 

  5. Thammawongsa N, Phromloungsri R, Jamsai M, Pornsuwancharoen N (2012) Design elliptic low pass filter with inductively compensated parallel-coupled lines. Procedia Eng 32:550–555.

    Article  Google Scholar 

  6. Ding S, Bian W, Sun T, Xue Y (2017) Fingerprint enhancement rooted in the spectra diffusion by the aid of the 2D adaptive Chebyshev band-pass filter with orientation-selective. Inf Sci 415–416:233–246.

    Article  MathSciNet  MATH  Google Scholar 

  7. Karam LJ, McClellan JH (1999) Chebyshev digital FIR filter design. Signal Process 76(1):17–36.

    Article  MATH  Google Scholar 

  8. Vaezi A, Gharaklili FG (2018) Synthesis and design of an LPF with wide-stop band and high rejection level. AEU Int J Electron Commun 95:139–145.

    Article  Google Scholar 

  9. Goh C, Li Y (2001) GA automated design and synthesis of analog circuits with practical constraints. In: Proceedings of the congress on evolutionary computation, pp 170–177

  10. Vural RA, Yildirim T, Kadioglu T, Basargan A (2012) Performance evaluation of evolutionary algorithms for optimal filter design. IEEE Trans Evol Comput 16(1):135–147.

    Article  Google Scholar 

  11. Gholami-Boroujeny S, Eshghi M (2012) Non-linear active noise cancellation using a bacterial foraging optimisation algorithm. IET Signal Proc 6(4):364–373.

    Article  Google Scholar 

  12. De BP, Kar R, Mandal D, Ghoshal SP (2015) Optimal selection of components value for analog active filter design using simplex particle swarm optimization. Int J Mach Learn Cyber 6(4):621–636.

    Article  Google Scholar 

  13. Doğan B, Ölmez T (2015) Vortex search algorithm for the analog active filter component selection problem. AEU Int J Electron Commun 69(9):1243–1253.

    Article  Google Scholar 

  14. Reja AH, Al-Salih AAM, Ahmad SN (2017) A matematerialized design for 7th order type-I Chebyshev LPF. Mater Today Proc 4:10383–10389

    Article  Google Scholar 

  15. Bose D, Biswas S, Vasilakos AV, Laha S (2014) Optimal filter design using an improved artificial bee colony algorithm. Inf Sci 281:443–461.

    Article  MathSciNet  Google Scholar 

  16. Prommee P, Thongdit P, Angkeaw K (2017) Log-domain high-order low-pass and band-pass filters. AEU Int J Electron Commun 79:234–242.

    Article  Google Scholar 

  17. Bulut GG, Güler H, Özdemir MT (2017) Optimal selection of components in a sixth-order Butterworth low-pass filter with using grey wolf algorithm. Int J Electr Electron Data Commun 5(10):1–4

    Google Scholar 

  18. Nayak B, Choudhury TR, Misra B (2018) Component value selection for active filters based on minimization of GSP and E12 compatible using Grey Wolf and Particle Swarm Optimization. AEU Int J Electron Commun 87:48–53.

    Article  Google Scholar 

  19. Hiçdurmaz B, Durmuş B, Temurtaş H, Özyön S (2016) The prediction of butterworth type active filter parameters in low pass sallen key topology by backtracking search algorithm. In: Proceedings of 2nd international conference on engineering and natural sciences, vol. 9, pp 2422–2428

  20. Durmuş B, Hiçdurmaz B, Temurtaş H, Özyön S (2016) Defining the parameters of the high pass active filter by using backtracking search algorithm. In: Proceedings of 2nd international conference on engineering and natural sciences, vol. 9, pp 2429–2435

  21. Horrocks DH, Spittle MC (1993) Component value selection for active filters using genetic algorithms. Proc IEEE Workshop Natl Algorithms Signal Process 1(13):1–6

    Google Scholar 

  22. Kalinli A (2006) Component value selection for active filters using parallel tabu search algorithm. AEU Int J Electron Commun 60(1):85–92.

    Article  Google Scholar 

  23. Vural RA, Bozkurt U, Yildirim T (2013) Analog active filter component selection with nature inspired metaheuristics. AEU Int J Electron Commun 67(3):197–205.

    Article  Google Scholar 

  24. Durmuş B (2018) Optimal components selection for active filter design with average differential evolution algorithm. AEU Int J Electron Commun 94:293–302.

    Article  Google Scholar 

  25. Jiang M, Yang Z, Gan Z (2007) Optimal components selection for analog active filters using clonal selection algorithm. In: Proceedings of international conference on intelligent computing, pp 950–959

  26. Pactitis SA (2007) Active filters theory and design. CRC Press Taylor & Francis Group, Broken

    Google Scholar 

  27. Sallen RP, Key EL (1955) A practical method of designing RC active filters. IRE Trans Circuit Theory 2(1):74–85.

    Article  Google Scholar 

  28. Karki J (2002) Active low-pass filter design, Texas Instruments Application Report. Accessed 05 May 2019

  29. Kaveh A, Talatahari S (2010) A novel heuristic optimization method: charged system search. Acta Mech 213(3–4):267–289.

    Article  MATH  Google Scholar 

  30. Storn R, Price K (1997) Differential evolution—a simple and efficient heuristic for global optimization over continuous spaces. J Global Optim 11(4):341–359.

    Article  MathSciNet  MATH  Google Scholar 

  31. Kennedy J, Eberhart RC (1995) Particle swarm optimization. Proc IEEE Int Conf Neural Netw 4:1942–1948

    Article  Google Scholar 

  32. Kamboj VK, Bath SK, Dhillon JS (2016) Solution of non-convex load dispatch problem using grey wolf optimizer. Neural Comput Appl 27:1301–1316.

    Article  Google Scholar 

  33. Bala R, Ghosh S (2019) Optimal position and rating of DG in distribution networks by ABC-CS from load flow solutions illustrated by fuzzy-PSO. Neural Comput Appl 31:489–507.

    Article  Google Scholar 

  34. Cheng MY, Prayogo D (2017) A novel fuzzy adaptive teaching-learning-based optimization (FATLBO) for solving structural optimization problems. Eng Comput 33:55–69.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to Burhanettin Durmuş.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Human and animals rights

No experiments were performed that involved humans/animals.

Informed consent

No human participant-based experiments were performed so it is not needed.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.



See Tables 13, 14, 15 and 16.

Table 13 Component values of best solutions for filter design (1-dB ripple—continuous)
Table 14 Component values of best solutions for filter design (1-dB ripple—discrete)
Table 15 Component values of best solutions for filter design (3-dB ripple—continuous)
Table 16 Component values of best solutions for filter design (3-dB ripple—discrete)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Durmuş, B., Temurtaş, H. & Özyön, S. The design of multiple feedback topology Chebyshev low-pass active filter with average differential evolution algorithm. Neural Comput & Applic 32, 17097–17113 (2020).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: