Abstract
This paper briefly describes a recent discovery that occurred during the study of the simplest mathematical model of a class C amplifier with a bipolar transistor. It is proved both numerically and experimentally that chaos can be observed in this simple network structure under three conditions: (1) the transistor is considered non-unilateral, (2) bias point provides cubic polynomial feedforward and feedback transconductance, and (3) the LC tank has very high resonant frequency. Moreover, chaos is generated by an autonomous class C amplifier; i.e., an isolated system without a driving force is analyzed. By the connection of a harmonic input signal, much more complex behavior can be observed. Additionally, due to the high degree of generalization of the amplifier cell, similar fundamental circuits can be ordinarily found as subparts of typical building blocks of a radio frequency signal path.
Highlights
A significant number of research papers have been focused on numerical analysis of conventional electrical circuits from the viewpoint of chaos evolution
A routine known as approximate entropy [1,2,3] can be used to measure self-similarity of the data sequence produced by any dynamical system
The same method can be utilized for optimization, i.e., to increase robustness of the chaotic operational regime [10], to find the parameter subspace leading to chaos [11] in the analyzed dynamical system, or to replace parts of chaotic oscillators without changing of global dynamics [12]
Summary
A significant number of research papers have been focused on numerical analysis of conventional electrical circuits from the viewpoint of chaos evolution. The general definition of chaos speaks about long-time unpredictable behavior, dense state attractors with a fractal dimension, generated waveforms with increased entropy, and extreme sensitivity to small changes in initial conditions. The time sequence can be used for calculation of the largest Lyapunov exponent as well; see [4,5] for more details. Spectra of Lyapunov exponents can be calculated using linearization of the flow along the evolved state trajectory [6,7,8,9]. Some recent papers were focused on analysis and circuit
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