Nullor Equivalents of Active Devices for Symbolic Circuit Analysis | Circuits, Systems, and Signal Processing Skip to main content
Log in

Nullor Equivalents of Active Devices for Symbolic Circuit Analysis

  • Published:
Circuits, Systems, and Signal Processing Aims and scope Submit manuscript

Abstract

The new pathological elements, the voltage mirror (VM) and current mirror (CM), have shown advantages in analog behavioral modeling and circuit synthesis. Recently, the floating mirror elements have been used to derive pathological sections to ideally represent various popular analog signal processing properties that involve differential or multiple single-ended signals. In order to take advantage of the symbolic nodal analysis (NA) of nullor-mirror networks, we present the nullor equivalents of a differential voltage cell, a differential voltage conveying cell, and a current replication cell in this paper. The proposed nullor equivalents can be used to represent many popular active devices in performing symbolic NA. Two representative filter circuits containing differential characteristics of active devices are given to verify the feasibility. We expect them to be used within an analog design automation environment to enhance circuit analysis and modeling.

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

Access this article

Subscribe and save

Springer+ Basic
¥17,985 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (Japan)

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. I.A. Awad, A.M. Soliman, Inverting second generation current conveyors: the missing building blocks, CMOS realizations and applications. Int. J. Electron. 86, 413–432 (1999)

    Article  Google Scholar 

  2. I.A. Awad, A.M. Soliman, On the voltage mirrors and current mirrors. Int. J. Circuit Theory Appl. 32(3), 79–81 (2002)

    Google Scholar 

  3. L.T. Bruton, RC Active Circuits: Theory and Design (Prentice-Hall, Englewood Cliffs, 1980)

    Google Scholar 

  4. W. Chiu, S.I. Liu, H.W. Tsao, J.J. Chen, CMOS differential difference current conveyors and their applications. IEE Proc., Circuits Devices Syst. 143(2), 91–96 (1996)

    Article  MATH  Google Scholar 

  5. H. Floberg, Symbolic Analysis in Analog Integrated Circuit Design (Kluwer Academic, Boston, 1997)

    Book  MATH  Google Scholar 

  6. G. Gielen, P. Wambacq, W.M. Sansen, Symbolic analysis methods and applications for analog circuits: a tutorial overview. Proc. IEEE 82(2), 287–304 (1994)

    Article  Google Scholar 

  7. D.G. Haigh, T.J.W. Clarke, P.M. Radmore, Symbolic framework for linear active circuits based on port equivalence using limit variables. IEEE Trans. Circuits Syst. I 53(9), 2011–2024 (2006)

    Article  MathSciNet  Google Scholar 

  8. M.A. Ibrahim, H. Kuntman, O. Cicekoglu, New second-order low-pass, high-pass and band-pass filters employing minimum number of active and passive elements, in Proc. Int. Symp. Signal Circuits Syst. (2003), pp. 557–560

    Google Scholar 

  9. P. Kumar, R. Senani, Bibliography on nullors and their applications in circuit analysis, synthesis and design. Analog Integr. Circuits Signal Process. 33(1), 65–76 (2002)

    Article  Google Scholar 

  10. A. Leuciuc, Using nullors for realisation of inverse transfer functions and characteristics. Electron. Lett. 33, 949–951 (1997)

    Article  Google Scholar 

  11. B. Metin, K. Pal, O. Cicekoglu, All-pass filters using DDCC- and MOSFET-based electronic resistor. Int. J. Circuit Theory Appl. 39(8), 881–891 (2011)

    Google Scholar 

  12. S. Minaei, C. Temizyurek, Dual input all-pass filter using DVCC, in Proc. Int. Symp. Signal Circuits Syst. (2003), pp. 477–480

    Google Scholar 

  13. R.A. Saad, A.M. Soliman, A new approach for using the pathological mirror elements in the ideal representation of active devices. Int. J. Circuit Theory Appl. 38(2), 148–178 (2010)

    MATH  Google Scholar 

  14. R.A. Saad, A.M. Soliman, Generation modeling, and analysis of CCII-based gyrators using the generalized symbolic framework for linear active circuits. Int. J. Circuit Theory Appl. 36(3), 289–309 (2008)

    Article  MATH  Google Scholar 

  15. R.A. Saad, A.M. Soliman, On the systematic synthesis of CCII-based floating simulators. Int. J. Circuit Theory Appl. 38(9), 935–967 (2010)

    Article  MATH  Google Scholar 

  16. R.A. Saad, A.M. Soliman, Use of mirror elements in the active device synthesis by admittance matrix expansion. IEEE Trans. Circuits Syst. I 55(9), 2726–2735 (2008)

    Article  MathSciNet  Google Scholar 

  17. C. Sanchez-Lopez, F.V. Fernandez, E. Tlelo-Cuautle, S.X.-D. Tan, Pathological element-based active device models and their application to symbolic analysis. IEEE Trans. Circuits Syst. I 58(6), 1382–1395 (2011)

    Article  MathSciNet  Google Scholar 

  18. H. Schmid, Approximating the universal active element. IEEE Trans. Circuits Syst. II 47(11), 1160–1169 (2000)

    Article  Google Scholar 

  19. A.M. Soliman, Applications of voltage and current unity gain cells in nodal admittance matrix expansion. IEEE Circuits Syst. Mag. 9(4), 29–42 (2009)

    Article  MathSciNet  Google Scholar 

  20. A.M. Soliman, Adjoint network theorem and floating elements in the NAM. J. Circuits Syst. Comput. 18, 597–616 (2009)

    Article  Google Scholar 

  21. A.M. Soliman, On the DVCC and the BOCCII as adjoint elements. J. Circuits Syst. Comput. 18(6), 1017–1032 (2009)

    Article  MathSciNet  Google Scholar 

  22. A.M. Soliman, Pathological representation of the two-output CCII and ICCII family and application. Int. J. Circuit Theory Appl. 39(6), 589–606 (2011)

    Article  Google Scholar 

  23. A.M. Soliman, R.A. Saad, The voltage mirror–current mirror pair as a universal element. Int. J. Circuit Theory Appl. 38(8), 787–795 (2009)

    Google Scholar 

  24. J.A. Svoboda, Current conveyors, operational amplifiers and nullor. IEE Proc., Circuits Devices Syst. 136(6), 317–322 (1989)

    Article  Google Scholar 

  25. J.A. Svoboda, Using nullors to analyse linear networks. Int. J. Circuit Theory Appl. 14, 169–180 (1986)

    Article  MATH  Google Scholar 

  26. E. Tlelo-Cuautle, C. Sanchez-Lopez, D. Moro-Frias, Symbolic analysis of (MO)(I)CCI(II)(III)-based analog circuits. Int. J. Circuit Theory Appl. 38(6), 649–659 (2010)

    Google Scholar 

  27. E. Tlelo-Cuautle, C. Sanchez-Lopez, E. Martinez-Romero, S.X.-D. Tan, Symbolic analysis of analog circuits containing voltage mirrors and current mirrors. Analog Integr. Circuits Signal Process. 65(1), 89–95 (2010)

    Article  Google Scholar 

  28. E. Tlelo-Cuautle, E. Martinez-Romero, C. Sanchez-Lopez, S.X.-D. Tan, Symbolic formulation method for mixed-mode analog circuits using nullors, in Proc. IEEE Int. Conf. Electron. Circuits Syst. (2009), pp. 856–859

    Google Scholar 

  29. E. Tlelo-Cuautle, M.A. Duarte-Villasenor, I. Guerra-Gomez, Automatic synthesis of VFs and VMs by applying genetic algorithms. Circuits Syst. Signal Process. 27(3), 391–403 (2008)

    Article  Google Scholar 

  30. H.Y. Wang, S.H. Chang, Y.L. Jeang, C.Y. Huang, Rearrangement of mirror elements. Analog Integr. Circuits Signal Process. 49, 87–90 (2006)

    Article  Google Scholar 

  31. H.Y. Wang, W.C. Huang, N.H. Chiang, Symbolic nodal analysis of circuits using pathological elements. IEEE Trans. Circuits Syst. II 57(11), 874–877 (2010)

    Article  Google Scholar 

  32. V.L. Wrick, W.J. Choyke, C.F. Tzeng, Symbolic analysis of circuits containing active elements. Electron. Lett. 17(20), 754–756 (1981)

    Article  Google Scholar 

  33. E. Yuce, Voltage-mode multifunction filters employing a single DVCC and grounded capacitors. IEEE Trans. Instrum. Meas. 58(7), 2216–2221 (2009)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Hung-Yu Wang.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Huang, WC., Wang, HY., Cheng, PS. et al. Nullor Equivalents of Active Devices for Symbolic Circuit Analysis. Circuits Syst Signal Process 31, 865–875 (2012). https://doi.org/10.1007/s00034-011-9364-z

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00034-011-9364-z

Keywords

Navigation