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Rich Dynamical Behavior in a Simple Chaotic Oscillator Based on Sallen Key High-Pass Filter

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Abstract

A chaotic oscillator has been designed based on a Sallen Key-type high-pass filter (HPF). The HPF has been converted to a chaotic oscillator using a parallel combination of a PN junction diode as a nonlinear element and an inductor as an energy storage element. The dynamics of the proposed system has been simulated numerically using fourth-order Runge–Kutta method. The circuit exhibits period-doubling route to chaos as well as period-adding route to chaos depending on the choice of system parameters. Striking features like antimonotonicity and coexistence of attractors are also observed. Bifurcation diagram, phase plane plots and spectrum of Lyapunov exponents have been employed to describe the chaotic behavior of the system. A hardware experiment has been carried out to verify the same in the laboratory using off-the-shelf components.

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Data Availability

All data generated or analyzed during this study are included in this article.

Abbreviations

C :

Capacitor

R 1, R 2, R a, R b :

Resistor

V 1, V 0 :

Voltage

k :

R1/2R2

ω 0 :

Frequency of oscillation

L :

Inductor

D :

General purpose diode

C D :

Diode parasitic transit capacitance

V CD :

Voltage across CD

I L :

Inductor current

I D :

Nonlinear diode current

R D :

Forward conductance resistance of the diode

V γ :

Forward voltage drop of the diode

ε :

C D /C

r :

R1/R2

b :

R12C/L

K D :

R 1 /R D

x, y, z, p :

Normalized state variables

a(p):

A piecewise linear function

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Authors and Affiliations

  1. Department of Physics, Bidhan Chandra College, Asansol, 713304, West Bengal, India

    Saumen Chakraborty

  2. Department of Physics, Raniganj Girls’ College, Searsole Rajbari, 713358, West Bengal, India

    Saumendra Sankar De Sarkar

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  1. Saumen Chakraborty
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Chakraborty, S., De Sarkar, S.S. Rich Dynamical Behavior in a Simple Chaotic Oscillator Based on Sallen Key High-Pass Filter. Circuits Syst Signal Process 42, 3835–3853 (2023). https://doi.org/10.1007/s00034-023-02325-2

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