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Investigation of a Heterogeneous RLC Lattice with Triangular Topology, Excited by a Lumped Voltage Source

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Abstract

Heterogeneous triangular network composed of resistors, capacitors and inductors gives a genuine electrical model for analyzing many engineering and physical problems. Here, we discuss various designs of RLC electrical circuits possessing a triangular topology. The theoretical formulation uses the WCIP technique. The proposed method rests on the definition of the incident and reflected waves from the voltage and current on each circuit branch. The use of the auxiliary source concept makes the execution of the employed technique simple and increments the capacity and effectiveness of the strategy for treating more intricate circuits. The mathematical formulation is subdivided into two definition domains: a spatial domain expresses the network architecture and imposes the boundary conditions, and a spectral one which characterizes the periodicity laws and describes the coupling of the electrical elements. The relationships formulated are resolved by an iterative process where the spectral and spatial equations are repeated up to the convergence. In numerical example, the results obtained by the WCIP method, for a resistors network of triangular topology, show good conformance with the analytical solutions. The method has also demonstrated its performances for investigating various designs of heterogeneous RLC lattice with triangular topology including the heterogeneous RL, RC and RLC circuits, perturbed RC circuits and a composite RLC circuit excited by vertical and horizontal lumped sources.

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Data Availability Statement

The datasets generated during and/or analyzed during the current study are available from the first author on reasonable request.

References

  1. M. Aouaichia, N. McCullen, C.R. Bowen, Understanding the anomalous frequency responses of composite materials using very large random resistor capacitor networks. Eur. Phys. J. B 90(39), 1–16 (2017)

    Google Scholar 

  2. J.H. Asad, Infinite simple 3d cubic network of identical capacitors. Mod. Phys. Lett. B 27(15), 1350112 (2013)

    Article  Google Scholar 

  3. J.H. Asad, A.A. Diab, M.Q. Owaidat, J.M. Khalifeh, Perturbed infinite 3d simple cubic network of identical capacitors. ACTA Phys. Pol. A 126(3), 777–781 (2014)

    Article  Google Scholar 

  4. D. Atkinson, F. Van Steenwijk, Infinite resistive lattices. Am. J. Phys. 67(6), 486–492 (1999)

    Article  Google Scholar 

  5. J. Cserti, Application of the lattice green function for calculating the resistance of an infinite network of resistors. Am. J. Phys. 68(10), 896–906 (2000)

    Article  Google Scholar 

  6. J. Cserti, G. Szécheny, G. David, Uniform tiling with electrical resistors. J. Phys. A. Math. Theor. 44, 215201 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  7. X. Dong, S. He, V. Stojanovic, Robust fault detection filter design for a class of discrete-time conic-type non-linear Markov jump systems with jump fault signals. IET Cont. Theory Appl. 14(14), 1912–1919 (2020)

    Article  Google Scholar 

  8. A.P. Fitz, R.J. Green, Fingerprint classification using a hexagonal fast Fourier transform. Pattern Recogn. 29(10), 1587–1597 (1979)

    Article  Google Scholar 

  9. T. Hanyu, T. Endoh, D. Suzuki, H. Koike, Y. Ma, N. Onizawa, M. Natsui, S. Ikeda, H. Ohno, Standby power free integrated circuits using magnetic tunnel junction based very large scale integration computing. Am. J. Phys. 104(10), 1844–1863 (2016)

    Google Scholar 

  10. R.S. Hijjawi, J.H. Asad, A.J. Sakaji, J.M. Khalifeh, Perturbation of an infinite network of identical capacitors. Int. J. Mod. Phys. B 21(2), 199–209 (2007)

    Article  MATH  Google Scholar 

  11. J. Iness, A. Noemen, A. Taoufik, B. Henri, An efficient algorithm for electromagnetic scattering by a set of perfect conducting cylindrical objects using the artificial neural network. Int. J. Rad. Freq. Aided Eng. 29(4), 192–199 (2018)

    Google Scholar 

  12. J. Iness, A. Noemen, A. Taoufik, B. Henri, Radiation pattern and scattering parameter for multilayer cylindrical loop antenna using the iterative method wcip. Int. J. Electron. Commun. 101, 192–199 (2019)

    Article  Google Scholar 

  13. N.S. Izmailian, R. Kenna, A generalised formulation of the Laplacian approach to resistor networks. J. Stat. Mech. Theor. 9, 09016 (2014)

    Google Scholar 

  14. N.S. Izmailian, H. Ming-Chang, Asymptotic expansion for the resistance between two maximally separated nodes on an m by n resistor network. Phys. Rev. E 82, 011125 (2010)

    Article  Google Scholar 

  15. L. Liu, H. Moayedi, A.S.A. Rashid, S.S.A. Rahman, H. Nguyen, Optimizing an artificial neural network model with genetic algorithm predicting load-settlement behaviours of ecofriendly raft pile foundation system. Eng. Comput. 36, 421–433 (2020)

    Article  Google Scholar 

  16. R.M. Mersereau, The processing of hexagonally sampled two dimensional signals. Proc. IEEE 67(6), 930–949 (1979)

    Article  Google Scholar 

  17. P. Miettinen, M. Honkala, J. Roos, M. Valtonen, Partitioning-based realizable model order reduction method for RLC circuits. IEEE Trans. Comput. Aided Des. Integr. Circuit Syst. 30(3), 374–387 (2015)

    Article  Google Scholar 

  18. H. Moayedi, A. Moatamediyan, H. Nguyen, X.N. Bui, D.T. Bui, A.S.A. Rashid, Prediction of ultimate bearing capacity through various novel evolutionary and neural network models. Eng. Comput. 36, 671–687 (2020)

    Article  Google Scholar 

  19. A. Mohamed, A. Hervé, B. Henri, A new iterative method for scattering problems. Euro. Micro. Conf., EuMC ’95’, BOLOGNE (Italy) (4–7 September 1995)

  20. A. Noemen, V. Didier, Design and analysis of two layers RLC network of rectangular topology by wave concept iterative process method. Int. J. Numer. Model. Electron. e2805, 1–17 (2020)

    Google Scholar 

  21. A. Noemen, B. Henri, Wave concept iterative process method for multiple loop antennas around a spherical media. IET Microw., Ant. Propag. 13(5), 666–674 (2019)

    Article  Google Scholar 

  22. A. Noemen, B. Henri, The wave concept iterative process (wcip) method for electrical circuit network with triangular and hexagonal topology. Int. J. Circuit. Theor. Appl. 47, 1340–1356 (2019)

    Google Scholar 

  23. A. Noemen, A. Taoufik, B. Henri, Analysis of multilayered cylindrical structures using a full wave method. Prog. Electromagn. Res. 85, 425–438 (2008)

    Article  Google Scholar 

  24. A. Noemen, A. Taoufik, B. Henri, S. Bruno, B. Ouannas, Wave concept iterative process method for electromagnetic or photonic jets: numerical and experimental results. IEEE Trans. Ant. Propag. 63(5), 4857–4867 (2015)

    MathSciNet  MATH  Google Scholar 

  25. A. Noemen, B. Tarek, A. Taoufik, B. Henri, Investigation of electromagnetic scattering by arbitrarily shaped structures using the wave concept iterative process. J. Microw., Optoelectron. Electr. Appl. 7(1), 192–199 (2008)

    Google Scholar 

  26. M.Q. Owaidat, M. Alsboul, A. Qwasmeh, Two point resistance on hypercubic lattices with second nearest neighbor resistors. J. Phys. A Math. 74, 38–44 (2018)

    Google Scholar 

  27. M.Q. Owaidat, J.H. Asad, Resistance calculation of three-dimensional triangular and hexagonal prism lattices. Eur. Phys. J. PLus 131(309), P09016 (2016)

    Google Scholar 

  28. M.Q. Owaidat, J.H. Asad, T. Zhi-Zhong, Resistance computation of generalized decorated square and simple cubic network lattices. Results Phys. 12, 1621–1627 (2019)

    Article  Google Scholar 

  29. M.Q. Owaidat, R.S. Hijjawi, J.H. Asad, J.M. Khalifeh, The two-point capacitance of infinite triangular and honeycomb networks. Eur. Phys. J. Appl. Phys. 68, 10102 (2014)

    Article  Google Scholar 

  30. I.N. Sh, R. Kenna, F.Y. Wu, The two point resistance of a resistor network: a new formulation and application to the cobweb network. J. Phys. A: Math. Theor. 47, 035003 (2014)

    Article  MATH  Google Scholar 

  31. W. Sidina, B. Damienne, B. Henri, P. Gamand, A new full-wave hybrid differential integral approach for the investigation of multilayer structures including non uniformly doped diffusions. IEEE Trans., Microw. Theory Techn. 53(1), 204–214 (2005)

    Google Scholar 

  32. J.T. Sloan, M.A.K. Othman, F. Capolino, Theory of double ladder lumped circuits. IEEE Trans. Circuit Syst. 65(1), 3–13 (2018)

    Article  Google Scholar 

  33. V. Stojanovic, N. Nedic, Identification of time-varying OE models in presence of non-Gaussian noise: application to pneumatic servo drives. Int. J. Robust. Nonlinear Cont. 26(18), 3974–3995 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  34. V. Stojanovic, N. Nedic, D. Prsic, L. Dubonjic, V. Djordjevic, Application of cuckoo search algorithm to constrained control problem of a parallel robot platform. Int. J. Adv. Manuf. Tech. 87, 2497–2507 (2016)

    Article  Google Scholar 

  35. V. Stojanovic, D. Prsic, Robust identification for fault detection in the presence of non-Gaussian noises: application to hydraulic servo drives. Nonlinear Dyn. 100, 2299–2313 (2020)

    Article  Google Scholar 

  36. H. Tao, P. Wang, Y. Chen, V. Stojanovic, H. Yang, An unsupervised fault diagnosis method for rolling bearing using STFT and generative neural networks. J. Frank. Inst. 357(11), 7286–7307 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  37. F.Y. Wu, Theory of resistor networks: the two-point resistance. J. Phys. A 37, 6653–6673 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  38. E. Zhao, Topological circuits of inductors and capacitors. Anal. Phys. 18(9), 289–313 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  39. T. Zhi-Zhong, Resistance network model. Xidian Uni. Press, Xin, China 91, 8–88 (2011)

  40. T. Zhi-Zhong, Formula of equivalent resistance about infinite plane rectangular network and its application. J. Nantong Univ. (Natural Sci.) 11, 86–94 (2012)

    Google Scholar 

  41. T. Zhi-Zhong, Recursion transform approach to compute the resistance of a resistor network with an arbitrary boundary. Chin. Phys. 24, 020503 (2015)

    Article  Google Scholar 

  42. T. Zhi-Zhong, Recursion transform method for computing resistance of the complex resistor network with three arbitrary boundaries. Phys. Rev. E 91, 052122 (2015)

    Article  MathSciNet  Google Scholar 

  43. T. Zhi-Zhong, Recursion transform method to a non regular mxn cobweb with an arbitrary longitude. Sci. Rep. 5, 11266 (2015)

    Article  Google Scholar 

  44. T. Zhi-Zhong, Theory on resistance of mxn cobweb network and its application. Int. J. Circuit Theor. Appl. 43, 1687–1702 (2015)

    Article  Google Scholar 

  45. T. Zhi-Zhong, Two point resistance of an mxn resistors network with an arbitrary boundary and its application in RLC network. Chin. Phys. B 25(5), 050504 (2016)

    Article  Google Scholar 

  46. T. Zhi-Zhong, Two point resistance of a non-regular cylindrical network with a zero resistor axis and two arbitrary boundaries. Commun. Theor. Phys. 67(3), 280–288 (2017)

    Article  MATH  Google Scholar 

  47. T. Zhi-Zhong, Z. Qing-Hua, Calculation of the equivalent resistance and impedance of the cylindrical network based on recursion transform method. Acta Phys. Sin. 66(7), 070501 (2017)

    Article  Google Scholar 

  48. L. Zhou, T. Zhi-Zhong, Q. hua Zhang, A fractional order multifunctional n step honeycomb RLC circuit network. Front. Inform. Technol. Electron 18(8), 1186–1196 (2017)

    Article  Google Scholar 

  49. R. Zhou, D. Chen, Fractional order 2xn RLC circuit network. Ann. Phys. 24(9), 1550142 (2015)

    Google Scholar 

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Authors and Affiliations

  1. Communication System Laboratory, El Manar University of Tunis, 1002, Tunis, Tunisia

    Noemen Ammar

  2. Signal, Image and Technology of Information Laboratory, El Manar University of Tunis, 1002, Tunis, Tunisia

    Gabzili Hanen

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  1. Noemen Ammar
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  2. Gabzili Hanen
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Correspondence to Gabzili Hanen.

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Ammar, N., Hanen, G. Investigation of a Heterogeneous RLC Lattice with Triangular Topology, Excited by a Lumped Voltage Source. Circuits Syst Signal Process 40, 3655–3683 (2021). https://doi.org/10.1007/s00034-021-01651-7

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  • DOI: https://doi.org/10.1007/s00034-021-01651-7

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