A novel high-frequency interpretation of a general purpose Op-Amp-based negative resistance for chaotic vibrations in a simple a priori nonchaotic circuit

Abstract

A novel model of general purpose operational amplifiers is made to approximate, at best, the equivalent circuit for real model at high-frequency. With this new model, it appears that certain oscillators, usually studied under ideal considerations or using many existing real models of operational amplifiers, have hidden subtle and attractive chaotic dynamics that have previously been unknown. These can now be revealed. With the new considerations, a “two-component” circuit, consisting simply of a capacitor in parallel with a nonmodified (and usually presented as a linear, negative) resistance, tends to exhibit chaotic signals. P-Spice and laboratory experimental results are in good agreement with the theoretical predictions.

Keywords

Operational amplifiers high frequency simplest chaotic circuit relaxation oscillator negative resistance hidden chaos

Get full access to this article

View all access options for this article.

References

Bendixson

(1901) Sur les courbes dfinies par des quations diffrentielles. Acta Mathematica 24: 1–88.

Chen

Djidjeli

Price

(2006) Computing Lyapunov exponents based on the solution expression of the variational system. Applied Mathematics and Computation 174: 982–996.

Chua

(1971) Memristor the missing circuit element. IEEE T Circ Theory 18: 507–519.

Chua

(1992) The genesis of Chuas circuit. Stuttgart: Hirzel-Verlag, AE 46: 507–519.

Farmer

(1982) Chaotic attractor of an infinite-dimensional dynamical system. Physica D 4: 366–393.

Fullagar D (1968) A New High Performance Monolithic Operational Amplifier. Fairchild Semiconductor Application Brief, May 1968 (The uA741 IC op amp).

Hayes

Horowitz

(1991) Student Manual For The Art Of Electronics, Cambridge: Cambridge University Press.

Horowitz

Hill

(1990) The Art Of Electronics (2nd edition), Cambridge: Cambridge University Press.

Ikeda

Matsumoto

(1987) High-dimensional chaotic behaviour in system with time-delayed feedback. Physica D 29: 223–235.

10.

Jung

(2005) Op Amp Applications Handbook, Burlington: Elsevier.

11.

Karki J (1998) Understanding Operational Amplifier Specifications - Mixed Signal and Analog Operational Amplifiers (Digital Signal Processing Solutions, WHITE PAPER: SLOA011). Texas Instruments.

12.

Karki J (2000) Effect of parasitic capacitance in op amp circuits - Mixed Signal Products (Application report, WHITE PAPER: SLOA013A). Texas Instruments, Dallas, Texas. Available at: http://www.ti.com.cn/cn/lit/an/sloa013a/sloa013a.pdf (accessed 10 May 2015).

13.

Kegne

Kenmogne

. On the modeling and nonlinear dynamics of autonomous Silva-Young type chaotic oscillators with flat power spectrum. Chaos. 24(043134): 1054–1500.

14.

Kuendiger T, Schrey J, Taha I et al. (2001) Cadence Op-amp schematic design tutorial for TSMC CMOSP35. Available at: http://ece.nitdgp.ac.in/˜akmal/ec9053/OpAmp-Final _cadence_LAB.pdf (accessed 10 May 2015).

15.

Kitio Kwuimy

Nataraj

Litak

(2011) Melnikov's criteria, parametric control of chaos, and stationary chaos occurrence in systems with asymmetric potential subjected to multiscale type excitation. Chaos: An Interdisciplinary Journal of Nonlinear Science 21(043113): 1–12.

16.

Leonov

Kuznetsov

(2013) Hidden attractors in dynamical systems: From hidden oscillations in HILBERT-KOLMOGOROV, Aizerman, and Kalman problems to hidden chaotic attractor in Chua circuits. Int J Bifurcation Chaos 23(1330002): 1–69.

17.

Louodop

Fotsin

Bowong

Kammogne

AST

(2014) Adaptive time-delay synchronization of chaotic systems with uncertainties using a nonlinear feedback coupling. Journal of Vibration and Control 20: 815–826.

18.

Lumbroso

(1995) Circuits lectroniques 92 problmes rsolus, classes suprieures MPSI.PCSI.PTSI, 2nd ed. Paris: Dunod.

19.

Mackey

Glass

(1977) Oscillation and chaos in physiological control system. Science 197: 287–289.

20.

Malvino

Bates

(2007) Electronic Principles (7th edition), India: McGraw-Hill Education.

21.

Mancini R (2012) Op amp for every one. Available at: http://web.mit.edu/6.101/www/reference/op_amps_everyone.pdf (accessed 10 May 2015).

22.

Merkin

(1997) Introduction to the Theory of Stability, New York: Springer.

23.

Muthuswamy

Chua

(2010) Simplest chaotic circuit. Int J. Bifurcat Chaos 20: 1567–80.

24.

Muthuswamy B, Przybylski A, Feilbach C and Mossbrucker J (2012) Two element chaotic and hyperchaotic circuits. In: 4th International Interdisciplinary Symposium on Chaos and Complex Systems, Antalya, Turkey, 30 April 2012. Available at: http://www.harpgroup.org/fpgaMemoryDevices/TwoElementChaoticAndHyperChaoticCircuits-CCS2012.pdf (accessed 10 May 2015).

25.

Mykolaitis

Tamasevicius

Bumeliene

(2005) Application of ultrafast Schottky diodes to high megahertz chaotic oscillators. Acta Physica Polonica A 107: 365–368.

26.

National Semiconductor Application Note 31 (1978) Op Amp Circuit Collection. Available at: http://www.padocss.com/download~54264182335b7ba5128b464b (accessed 10 May 2015).

27.

Pham

Buscarino

Fortuna

Frasca

(2013) Simple memristive time-delay chaotic systems. Int J Bifurcat Chaos 23(1350073): 1–9.

28.

Piper

Sprott

(2010) Simple autonomous chaotic circuits. IEEE Transactions on Ciruits and Systems-II: Express Briefs 57: 730–734.

29.

Strukov

Snider

Stewart

Williams

(2008) The missing memristor found. Nature 453: 80–83.

30.

Tchitnga

Fotsin

Nana

Louodop Fotso

Woafo

(2012) Hartley's oscillator: The simplest chaotic two-component circuit. Chaos, Solitons & Fractals 45: 306–313.

31.

Wolff C, Kenney JG and Carley LR (1997) CAD for the analysis and design of AS converters. In: Norsworthy SR, Schreier R and Temes GC (eds) Delta-Sigma Data Converters: Theory, Design and Simulation, IEEE Press, 1997, pp.447–467.