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Small-Signal Fractional-Order Model of PN Junction Long-Base Diode

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Abstract

Most models of PN junction diode are mathematical models rather than circuit models, and there is a necessary trade-off between model versatility and accuracy. The small-signal fractional-order circuit model of PN junction long-base diode based upon the device’s physical operating principles and fractional-order vector fitting is obtained. This model consists of fractional elements and traditional elements; at the same time, the conventional diffusion model, that is two-element diode model, is included as a special one. In particular, only two model parameters, inverse saturation current and minority carrier lifetime of the PN junction diode, need to be extracted for formulating fractional-order model. And it is proved that the simulation effect is perfect by comparing the normalized admittances of different diode models. So the efficiency and accuracy of the model can be greatly improved compared with the high-speed dynamic model of PN junction diode. The presented equivalent model is shown to be capable of reproducing the frequency-dependent characteristics of PN junction long-base diode, and it can be applied to different small-signal circuit environments. Finally, experiment of junction diode can also validate the efficiency of the small-signal fractional model.

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References

  1. A. Ahmad, Ph Auriol, C. Kieny, Shell-form power transformer modeling at high frequencies. IEEE Trans. Magn. 30(5), 3729–3732 (1994)

    Article  Google Scholar 

  2. F. Boulgamh, M. Remram, A. Djouambi, Small-signal fractional-order modeling of PN junction diode, in Recent Advances in Electrical Engineering and Control Applications (Springer, Berlin, 2017), pp. 247–255

  3. F. Boulgamh, M. Remram, A. Djouambi, Fractional behaviour of PN junction diode under AC-small-signal conditions, in ICEERE 2018, LNEE, ed. by Hajji et al., vol. 519 (2019), pp. 283–289. https://doi.org/10.1007/978-981-13-1405-6_34

  4. L.O. Chua, Device modeling via nonlinear circuit elements. IEEE Trans. Circuits Syst. 27(11), 1014–1044 (1980)

    Article  MathSciNet  Google Scholar 

  5. L.O. Chua, C.C. Chen, High-speed non-linear circuit models for p–n junction diodes. Int. J. Circuit Theory Appl. 16(2), 157–190 (1988)

    Article  Google Scholar 

  6. L.O. Chua, P.M. Lin, Computer-Aided Analysis of Electronic Circuits, Algorithms and Computational Techniques (Computer-Aided Analysis of Electronic Circuits, California, 1975)

    MATH  Google Scholar 

  7. A. Dervisoglu, L.O. Chua, Modelling non-linear devices exhibiting frequency-dependent capacitances and inductances. Int. J. Circuits Theor. Appl. 13, 133–148 (1985)

    Article  Google Scholar 

  8. L. Dorčák, J. Terpák, I. Petráš, et al., Comparison of the electronic realization of the fractional-order system and its model, in Proceedings of IEEE International Conference on the 13th International Carpathian Control Conference, High Tatras, Slovakia (2012), pp. 119–124

  9. A. Dzielinski, G. Sarwas, D. Sierociuk, et al., Frequency response based identification of fractional-order dynamical systems, in Proceeding of IEEE International Conference on Carpathian Control, 2011 12th, Velke Karlovice, Czech Republic (2011), pp. 98–102

  10. A. Dzielinski, D. Sierociuk, Ultracapacitor modelling and control using discrete fractional-order state-space model. Acta Montan. Slovaca 13(1), 136–145 (2008)

    MATH  Google Scholar 

  11. A. Dzielinski, D. Sierociuk, G. Sarwas, Some applications of fractional-order calculus. Bull. Polish Acad. Sci. Tech. Sci. 58(4), 583–592 (2010)

    MATH  Google Scholar 

  12. A. Elwakil, Fractional-order circuits and systems: an emerging interdisciplinary research area. IEEE Circuits Syst. Mag. 10(4), 40–50 (2010)

    Article  Google Scholar 

  13. B. Gustavsen, Improving the pole relocating properties of vector fitting. IEEE Trans. Power Delivery 21(3), 1587–1592 (2006)

    Article  Google Scholar 

  14. B. Gustavsen, A. Semlyen, Rational approximation of frequency domain responses by vector fitting. IEEE Trans. Power Deliv. 14, 1052–1061 (1999)

    Article  Google Scholar 

  15. A. Jalloul, J.C. Trigeassou, K. Jelassi et al., Fractional-order modeling of rotor skin effect in induction machines. Int. J. Comput. Sci. Issues 8(4), 801–813 (2011)

    Google Scholar 

  16. A.K. Kamath, J.R. Gandhi, A.S. Bohra, A.V. Goel, D.U. Patil, O.V. Kulkarni, J.O. Chandle. Modeling of transformer characteristics using fractional-order transfer functions, in Proceedings of IEEE International Conference on Control and Automation, ICCA, Christchurch, New Zealand (2009), pp. 2123–2128

  17. S.M. Krakauer, Harmonic generation, rectification, and lifetime evaluation with the step recovery diode. Proc. IRE 50(7), 1665–1676 (1962)

    Article  Google Scholar 

  18. B.J. Li, H.Y. Liu, A solving method of overdetermined system. J. Sheng yang Univ. Technol. 24(1), 76–77 (2002)

    Google Scholar 

  19. J.G. Linvill, Lumped models of transistors and diodes, in Proceedings of IEEE International Conference on Proceedings of the IRE (1958), pp. 1141–1152

  20. X. Liu, G.S. Liang, An algorithm for fractional-order system identification, in Processing of IEEE International Conference on Computational Science and Engineering, Chengdu, China (2015), pp. 66–71

  21. J.A.T. Machado, A.M.S.F. Galhano, Fractional-order inductive phenomena based on the skin effect. Nonlinear Dyn. 68(1–2), 107–115 (2010)

    MathSciNet  Google Scholar 

  22. R. Mansouri, M. Bettayeb, T. Djamah, S. Djennoune, Vector fitting fractional system identification using particle swarm optimization. Appl. Math. Comput. 206(2), 510–520 (2008)

    MathSciNet  MATH  Google Scholar 

  23. D.W. Marquardt, An algorithm for least squares estimation of non-linear parameters. J. Soc. Ind. Appl. Math. 11(2), 431–441 (1963)

    Article  Google Scholar 

  24. R.S. Muller, T.L. Kamins, Device Electronics for Integrated Circuits (Wiley, New York, 1977)

    Google Scholar 

  25. Nano Dot Tek™, What is fractance and why is it useful?. Nano Dot Tek™. Report NDT. 24 (2007), pp. 11–37. http://www.nanodottek.com

  26. R.F. Pierret, P. Hall, Semiconductor Device Fundamentals (United States Edition, USA, 1996)

    Google Scholar 

  27. Y. Pu, Research on the Application of Fractional Calculus in Modern Signal Analysis and Processing (Sichuan University, Chengdu, 2006)

    Google Scholar 

  28. L.D. Pulfrey, Understanding Modern Transistors and Diodes (Cambridge University Press, Cambridge, 2010)

    Book  Google Scholar 

  29. M. Richard, D.M. Ortigueira, P. Igor, T. Juan, On the fractional signals and systems. Signal Process. 91, 350–371 (2011)

    Article  Google Scholar 

  30. S.M. Sze, K.K. Ng, Physics of Semiconductor Devices, 2nd edn. (Wiley, New York, 1981)

    Google Scholar 

  31. J.A. Tenreiro Machado, A.M. Lopes, Fractional-order modeling of a diode. Commun. Nonlinear Sci. Number Simul. 70, 343–353 (2019)

    Article  MathSciNet  Google Scholar 

  32. P.P. Wang, F.H. Branin, Jr., Multi-section network modeling of junction diodes, in Proceedings of 4th Annual Pittsburg Conference on Modeling and Simulation, Pittsburg, Penn (1973)

  33. S. Westerlund, L. Ekstam, Capacitor theory. IEEE Trans. Dielectr. Electr. Insul. 1(5), 826–839 (1994)

    Article  Google Scholar 

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Acknowledgements

This research was supported in part by the Natural Science Foundation of Hebei Province under Grant No. E2018502121 and the Natural Science Foundation of Beijing Municipality under Grant No. 3192039.

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  1. Department of Electric Engineering, North China Electric Power University, No. 619 Yong Hua North Street, Baoding, 071003, China

    Guishu Liang, Hao Shen & Xin Liu

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  1. Guishu Liang
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  2. Hao Shen
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  3. Xin Liu
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Correspondence to Hao Shen.

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Liang, G., Shen, H. & Liu, X. Small-Signal Fractional-Order Model of PN Junction Long-Base Diode. Circuits Syst Signal Process 39, 3350–3371 (2020). https://doi.org/10.1007/s00034-019-01340-6

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