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Feedback Modelling in Amplifier Circuits Using Open-Loop Transfer Functions

Received: 10 July 2022     Accepted: 25 July 2022     Published: 29 July 2022
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Abstract

Negative feedback is an established technique used to improve the quality of an amplifier. The modelling of the closed-loop circuit is a complex procedure that, if not done properly, may give erroneous results. A new method for modelling amplifiers that use negative feedback over a broad frequency range is presented. The method overcomes the main difficulties of the two-port analysis, namely the identification of the feedback type and the determination of the feedback network loading to the open-loop amplifier. Compared to other methods, it is more suitable for handling frequency-dependent quantities. All topologies are treated as voltage amplifiers. The open-loop amplifier is described by three open-loop transfer functions. The theoretical context of the non-ideal op amp is used to derive the closed-loop quantities, discriminating between the non-inverting and the inverting case. The proposed method provides accurate results over a broad range of frequencies. The poles and the zeros can be readily calculated as well as the loop gain, to examine the stability of the amplifier. It can account for complex loads and frequency-dependent gain-setting resistors. Another advantage is that once the open-loop transfer functions are known, other closed-loop configurations can be computed with no additional effort. Circuit complexity has not been found to be a problem. The proposed modelling technique has been used in the class for a number of years with undergraduate students responding positively to it.

Published in Journal of Electrical and Electronic Engineering (Volume 10, Issue 4)
DOI 10.11648/j.jeee.20221004.13
Page(s) 149-157
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2022. Published by Science Publishing Group

Keywords

Feedback Circuits, Loop-Gain, Two-Port Analysis, Return Ratio

References
[1] Millman, J., Grabel, A. (1987). Microelectronics, New York, McGraw-Hill.
[2] Gray, P. R., Hurst, P. J., Lewis, S. H., Meyer, R. G. (2001). Analysis and Design of Analog Integrated Circuits, New York, John Wiley & Sons, Inc.
[3] Sedra, A. S., Smith, K. C. (2003). Microelectronic Circuits, Oxford University Press.
[4] Marrero, J. (2005). Simplified analysis of feedback amplifiers, IEEE Trans. on Educ., 48 (1), 53-59. doi: 10.1109/TE.2004.832878.
[5] Yeung, K. S. (1982). An alternative approach for analyzing feedback amplifiers, IEEE Trans. on Educ., 25 (4), 132-136. doi: 10.1109/TE.1982.4321568.
[6] Bode, H. W. (1945). Network Analysis and Feedback Amplifier Design, New York, Van Nostrad.
[7] Rosenstark, S. (1974). A simplified method of feedback amplifiers analysis, IEEE Trans. on Education, 127 (4), 192-198. doi: 10.1109/TE.1974.4320925.
[8] Blackman, R. B. (1943). Effect of feedback on impedance, Bell System Technical Journal, 22, 269-277. doi: 10.1002/j.1538-7305.1943.tb00443.x.
[9] Hakim, S. S. (1966). Feedback Circuit Analysis, New York, Wiley.
[10] Nicolic, B., Marjanovic, S. (1998). A general method of feedback amplifier analysis, IEEE Int. Symp. Circuits Systems, Monterey, CA, 1998, pp. 415-418. doi: 10.1109/ISCAS.1998.704038.
[11] Davis, A. M. (1981). A general method for analyzing feedback amplifiers, IEEE Trans. On Educ., E-24, 291-293. doi: 10.1109/TE.1981.4321514.
[12] Ochoa, A. (1998). A systematic approach to the analysis of general and feedback circuits and systems using signal flow graphs and driving point impedance, IEEE Trans. Circuits. Syst. 45 (2), 187-195. doi: 10.1109/82.661648.
[13] Pellegrini, B. (2009). Improved feedback theory, IEEE Trans. Circuits Syst., 56 (9), 1949-1959. doi: 10.1109/TCSI.2008.2011591.
[14] Cunha, T. R, Pedro, J. C., Lima, E. G., (2008). Low-Pass Equivalent Feedback Topology for Power Amplifier Modeling, 2008 IEEE MTT-S International Microwave Symposium Digest, 1445-1448.
[15] Yang, H., (2012). Modeling, Analysis and Design of Feedback Operational Amplifier for Undergraduate Studies in Electrical Engineering, TELKOMNIKA Indonesian J. of Elec. Eng, 10 (8), 2295-2304. doi: 10.11591/telkomnika.v10i8.1609.
[16] Gu, L., He, L., Liu, Y., Sheng, Z., Wang, W., (2012). An Analysis Method for Negative Feedback Amplifier Network Based on Dual-port Network Model, Proceedings of the 2012 International Conference on Computer Application and System Modeling (ICCASM 2012), pp. 61-64. doi: 10.2991/ICCASM.2012.15.
Cite This Article
  • APA Style

    Spyros Loutridis. (2022). Feedback Modelling in Amplifier Circuits Using Open-Loop Transfer Functions. Journal of Electrical and Electronic Engineering, 10(4), 149-157. https://doi.org/10.11648/j.jeee.20221004.13

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    ACS Style

    Spyros Loutridis. Feedback Modelling in Amplifier Circuits Using Open-Loop Transfer Functions. J. Electr. Electron. Eng. 2022, 10(4), 149-157. doi: 10.11648/j.jeee.20221004.13

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    AMA Style

    Spyros Loutridis. Feedback Modelling in Amplifier Circuits Using Open-Loop Transfer Functions. J Electr Electron Eng. 2022;10(4):149-157. doi: 10.11648/j.jeee.20221004.13

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  • @article{10.11648/j.jeee.20221004.13,
      author = {Spyros Loutridis},
      title = {Feedback Modelling in Amplifier Circuits Using Open-Loop Transfer Functions},
      journal = {Journal of Electrical and Electronic Engineering},
      volume = {10},
      number = {4},
      pages = {149-157},
      doi = {10.11648/j.jeee.20221004.13},
      url = {https://doi.org/10.11648/j.jeee.20221004.13},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.jeee.20221004.13},
      abstract = {Negative feedback is an established technique used to improve the quality of an amplifier. The modelling of the closed-loop circuit is a complex procedure that, if not done properly, may give erroneous results. A new method for modelling amplifiers that use negative feedback over a broad frequency range is presented. The method overcomes the main difficulties of the two-port analysis, namely the identification of the feedback type and the determination of the feedback network loading to the open-loop amplifier. Compared to other methods, it is more suitable for handling frequency-dependent quantities. All topologies are treated as voltage amplifiers. The open-loop amplifier is described by three open-loop transfer functions. The theoretical context of the non-ideal op amp is used to derive the closed-loop quantities, discriminating between the non-inverting and the inverting case. The proposed method provides accurate results over a broad range of frequencies. The poles and the zeros can be readily calculated as well as the loop gain, to examine the stability of the amplifier. It can account for complex loads and frequency-dependent gain-setting resistors. Another advantage is that once the open-loop transfer functions are known, other closed-loop configurations can be computed with no additional effort. Circuit complexity has not been found to be a problem. The proposed modelling technique has been used in the class for a number of years with undergraduate students responding positively to it.},
     year = {2022}
    }
    

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  • TY  - JOUR
    T1  - Feedback Modelling in Amplifier Circuits Using Open-Loop Transfer Functions
    AU  - Spyros Loutridis
    Y1  - 2022/07/29
    PY  - 2022
    N1  - https://doi.org/10.11648/j.jeee.20221004.13
    DO  - 10.11648/j.jeee.20221004.13
    T2  - Journal of Electrical and Electronic Engineering
    JF  - Journal of Electrical and Electronic Engineering
    JO  - Journal of Electrical and Electronic Engineering
    SP  - 149
    EP  - 157
    PB  - Science Publishing Group
    SN  - 2329-1605
    UR  - https://doi.org/10.11648/j.jeee.20221004.13
    AB  - Negative feedback is an established technique used to improve the quality of an amplifier. The modelling of the closed-loop circuit is a complex procedure that, if not done properly, may give erroneous results. A new method for modelling amplifiers that use negative feedback over a broad frequency range is presented. The method overcomes the main difficulties of the two-port analysis, namely the identification of the feedback type and the determination of the feedback network loading to the open-loop amplifier. Compared to other methods, it is more suitable for handling frequency-dependent quantities. All topologies are treated as voltage amplifiers. The open-loop amplifier is described by three open-loop transfer functions. The theoretical context of the non-ideal op amp is used to derive the closed-loop quantities, discriminating between the non-inverting and the inverting case. The proposed method provides accurate results over a broad range of frequencies. The poles and the zeros can be readily calculated as well as the loop gain, to examine the stability of the amplifier. It can account for complex loads and frequency-dependent gain-setting resistors. Another advantage is that once the open-loop transfer functions are known, other closed-loop configurations can be computed with no additional effort. Circuit complexity has not been found to be a problem. The proposed modelling technique has been used in the class for a number of years with undergraduate students responding positively to it.
    VL  - 10
    IS  - 4
    ER  - 

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Author Information
  • Department of Electrical and Computer Engineering, Polytechnic School, University of Thessaly, Volos, Greece

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