Skip to main content
Log in

Piecewise Nonlinear Approach to the Implementation of Nonlinear Current Transfer Functions

Circuits, Systems, and Signal Processing Aims and scope Submit manuscript

Abstract

A piecewise nonlinear approach to the nonlinear circuit design has been proposed in this paper. It is to approximate a target nonlinear transfer function by a particular combination of selected nonlinear pieces. The pieces can be produced by one or more analog blocks involving nonlinear devices. This approach can be applied to design nonlinear circuits to implement various current transfer functions. By controlling the operation modes of the transistor pair in a simple current mirror, one can modulate the current transfer function in a radical or fine-tuning manner. It is thus possible for the same current mirror to generate very different nonlinear pieces in different sections of its input range. In order that the control is done automatically by the input current, or in other words, the operation of the transistors is made to be input-current-dependent in a controlled manner, a series structure of two transistors has been proposed to be incorporated in the current mirror. The dependency can be made different by placing the structure in different places of the current mirror and/or by making the two transistors complementary or not, which makes the variations of the nonlinear function. Several current mirrors have been designed. Each of them consists of a very small number of transistors and performs a defined nonlinear current transfer function. The circuits have been simulated with HSPICE to validate the functions. The successful results have been obtained and are presented in the paper.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19

References

  1. H. Amin, K.M. Curtis, B.R. Hayes-Gill, Piecewise linear approximation applied to nonlinear function of a neural network, in IEE Proceedings—Circuits, Devices and Systems, vol. 144 (1997), pp. 313–317

    Google Scholar 

  2. L.O. Chua, Nonlinear circuits. IEEE Trans. Circuits Syst. 31(1), 69–87 (1984)

    Article  MATH  Google Scholar 

  3. J.A. Galan, A.J. Lopez-Martin, R.G. Carvajal, J. Ramirez-Angulo, C. Rubia-Marcos, Super class-AB OTAs with adaptive biasing and dynamic output current scaling. IEEE Trans. Circuits Syst. I, Regul. Pap. 54(3), 449–457 (2007)

    Article  Google Scholar 

  4. F. Kronmueller, P. Zehnich, Operational transconductance amplifier with a non-linear current mirror for improved slew rate. US Patent 6414552/d, July 2002

  5. R.E. Mallory, Nonlinear current mirror for loop-gain control. US Patent 6181142, January 2001

  6. M. Parodi, M. Storace, P. Julian, Synthesis of multiport resistors with piecewise-linear characteristics: a mixed-signal architecture. Int. J. Circuit Theory Appl. 33(4), 307–319 (2005)

    Article  MATH  Google Scholar 

  7. T. Poggi, A. Sciutto, M. Storace, Piecewise linear implementation of nonlinear dynamical systems: from theory to practice. Electron. Lett. 45(19), 966–967 (2009)

    Article  Google Scholar 

  8. Y. Tsividis, C. McAdrew, Operation and Modeling of the MOS Transistor, 3rd edn. (Oxford University Press, Oxford, 2010)

    Google Scholar 

  9. E.A. Vittoz, Analog VLSI signal processing: why, where, and how? Analog Integr. Circuits Signal Process. 6, 27–44 (1994)

    Article  Google Scholar 

  10. C. Wang, Nonlinear current mirrors for analog and mixed signal processing, in Proc. IEEE Mid-West Symposium on Circuits and Systems (2011)

    Google Scholar 

  11. C. Wang, A simple scheme of current amplification for sensor applications, in Proc. IEEE International Conference on Electronic Devices and Solid State Circuits, Hong Kong (2005), pp. 647–650

    Google Scholar 

  12. C. Wang, Wide-dynamic-range and high-sensitivity current-to-voltage converters. Circuits Syst. Signal Process. 29(6), 1223–1236 (2010)

    Article  MATH  Google Scholar 

  13. B.M. Wilamowski, E.S. Ferre-Pikal, O. Kaynak, Low power, current mode CMOS circuits for synthesis of arbitrary nonlinear functions, in 9th NASA Symposium on VLSI Design (2000), pp. 7.3.1–7.3.8

    Google Scholar 

Download references

Acknowledgements

This work was supported in part by the Natural Sciences and Engineering Research Council (NSERC) of Canada and in part by the Regroupement Stratégique en Microélectronique du Québec (ReSMiQ).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Chunyan Wang.

Appendix

Appendix

The current transfer characteristic of i OUT versus i IN of the circuit shown in Fig. 10 features a positive di OUT /di IN in the lower part of the input range and a negative di OUT /di IN in the upper part. At the point i IN =I INP ,di OUT /di IN =0 and i OUT reaches its maximum value I PK . The value of I INP can be estimated based on i P =i N and i P =i P1,i P1 denoting the current in P 1, under the condition that all the transistors are in the saturation mode. To simplify the derivation, let us assume that N 1 and N 2 are identical, and P 1 and P R are also so, i.e., \(\beta_{N1}=\beta_{N2}=\beta_{n}=\mu_{n}C_{\mathrm{ox}}'\frac{W_{n}}{L_{n}}\) and \(\beta_{P1}=\beta_{PR}=\beta_{p}=\mu_{p}C_{\mathrm{ox}}'\frac{W_{p}}{L_{p}}\). Also we assume that 1+ λv DS is close to unity and the threshold voltage of P 1 is equal to that of P R , i.e., V t_P1V t_PR =V tp .

If I INP is expected to be of micro-Amperes, i P =i P1, and P R is in the saturation mode, we will have

As i P =i N and P R and N 2 are in the saturation mode, we have

As 2v GP V DD +v G , if \(\alpha =\sqrt{\frac{\beta _{n}}{\beta _{P}}}\) we will have

and I INP is given as

It should be noted that the simplest models for the saturation mode of MOS transistors have been used in the above derivation in order to formulate the relationship between I INP and other parameters such as V DD ,β n , and β p . Thus, the result can only be used as a guideline in the design to determine approximately the level I INP , not for a quantitative calculation of the value of I INP , even though the transistors are in strong inversion.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wang, C. Piecewise Nonlinear Approach to the Implementation of Nonlinear Current Transfer Functions. Circuits Syst Signal Process 32, 499–523 (2013). https://doi.org/10.1007/s00034-012-9479-x

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00034-012-9479-x

Keywords

Navigation