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Application of Inductive Topological Transfer Function Generation for a Cascaded Low-Pass Filter

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Abstract

This work presents applications of an inductive topological approach in the calculation of the transfer function of a cascading network control system. The method provides a very versatile and effective way of counting all the graphs that contribute and of translating them into their algebraic contribution. The contributing graphs are very simple and reflect the morphology of the original control system signal flow graph. Application of the method and results are presented for an n-cell RC network. We derive an analytical formula relating ω(3 dB) to the filter size (n) and R j C j (j=1,2,…,n). This formula can be used for designing preset frequency range self-loaded LP filters by varying their size. We also derive general expressions for the sensitivities which we use to observe a sensitivity-insensitivity filter transition for various frequency ranges, relaxation times, and, most importantly, filter sizes.

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References

  1. S. Butterworth, On the theory of filter amplifiers. Exp. Wirel. Wirel. Eng. 7(85), 536–541 (1930)

    Google Scholar 

  2. B. Chen, Topological patterns identification for sneak circuit analysis, in Proceedings of 8th International Conference on Reliability, Maintainability and Safety (2009), pp. 133–137

    Google Scholar 

  3. L.O. Chua, C.W. Wu, On the universe of stable cellular neural networks. Int. J. Circuit Theory Appl. 20, 497–517 (1992)

    Article  MATH  Google Scholar 

  4. S. Djordjević, P.M. Petković, Reordering in topology decision diagram method for symbolic circuit analysis, in Proceedings of 25th International Conference on Microelectronics, vol. 2 (2006), pp. 447–450

    Google Scholar 

  5. R.P. Feynman, Quantum Electrodynamics (Addison-Wesley, Reading, 1962)

    MATH  Google Scholar 

  6. B.A. Francis, M. Vidyasagar, Algebraic and topological aspects of the regulator problem for lumped linear systems. Automatica 19(1), 87–90 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  7. M. Iordache, L. Dumitriu, Network function generation for MIMO systems, in Proceedings of 11th International Conference on Optimization of Electrical and Electronic Equipment (2008), pp. 27–32

    Google Scholar 

  8. M. Iordache, L. Dumitriu, The generalized topological formula for transfer function generation by two-graph tree enumeration. Analog Integr. Circuits Signal Process. 47(1), 85–100 (2006)

    Article  Google Scholar 

  9. G.D. Mahan, Many Particle Physics (Physics of Solids and Liquids) (Springer, New York, 2000)

    Book  Google Scholar 

  10. A. Marascu, L. Dumitriu, M. Iordache, D. Niculae, Tolerance analysis for Chebysev filters, in 4th European Conference on Circuits and Systems for Communications (2008), pp. 133–137

    Google Scholar 

  11. D. Marcuse, Principles of Quantum Electronics (Academic Press, New York, 1980)

    Google Scholar 

  12. D. Marcuse, Engineering Quantum Electrodynamics (Harcourt Brace Jovanovich, New York, 1970)

    Google Scholar 

  13. S. Mason, H. Zimmerman, Electronic Circuits, Signals and Systems (Wiley, New York, 1960)

    Google Scholar 

  14. K.K. Pang, Synthesis of optimum RC phase-shift network. IEEE Trans. Circuit Theory CT-17(3), 352–357 (1970)

    Article  Google Scholar 

  15. C.B. Sharpe, A general Tchebycheff rational function, in Proceedings of the IRE (1954), pp. 454–457

    Google Scholar 

  16. R.E. Showalter, C.H. Snyder, A distributed RC network model with dielectric loss. IEEE Trans. Circuits Syst. CAS-33(7), 707–710 (1986)

    Article  Google Scholar 

  17. M.A. Styblinski, B.D. Meyer, Signal flow graphs vs fuzzy cognitive maps in application to qualitative circuit analysis. Int. J. Man-Mach. Stud. 35(2), 175–186 (1991)

    Article  Google Scholar 

  18. G. Vecris, J.J. Quinn, Novel diagrammatic method for analysis of finite periodic and aperiodic multilayer structures. Solid State Commun. 76(8), 1071–1076 (1990)

    Article  Google Scholar 

  19. G. Vecris, J.J. Quinn, Novel diagrammatic method for analyzing the surface electronic modes of finite multilayer structures. Appl. Surf. Sci. 48–49, 319–323 (1991)

    Article  Google Scholar 

  20. G.E. Vekris, C.K. Manavis, W. Balachandran, M. Hadjinicolaou, V. Syrris, N.N. Kyriakoudis, Network cascaded control system transfer function generation using an inductive topological method, in The 19th Mediterranean Conference on Control and Automation (2011)

    Google Scholar 

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Authors and Affiliations

  1. Department of Electronics, Technological Educational Institute of Thessaloniki, P.O. Box 141, 57400, Thessaloniki, Greece

    Georgios E. Vekris, Vassilis Syrris, Christos K. Manavis & Nikolaos N. Kyriakoudis

  2. School of Engineering and Design, Brunel University, West London, UK

    Christos K. Manavis, Wamadeva Balachandran & Marios Hadjinicolaou

Authors
  1. Georgios E. Vekris
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  2. Vassilis Syrris
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  3. Christos K. Manavis
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  4. Wamadeva Balachandran
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  5. Marios Hadjinicolaou
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  6. Nikolaos N. Kyriakoudis
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Correspondence to Vassilis Syrris.

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Vekris, G.E., Syrris, V., Manavis, C.K. et al. Application of Inductive Topological Transfer Function Generation for a Cascaded Low-Pass Filter. Circuits Syst Signal Process 32, 2667–2681 (2013). https://doi.org/10.1007/s00034-013-9608-1

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  • DOI: https://doi.org/10.1007/s00034-013-9608-1

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