Generalized Single Stage Class C Amplifier: Analysis from the Viewpoint of Chaotic Behavior

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.

Evidence of Strange Attractors in Class C Amplifier with Single Bipolar Transistor: Polynomial and Piecewise-Linear Case

“…Recent papers [ 20 , 21 ] have revealed the existence of strange attractors in a fundamental stage of class C amplifier with a single bipolar transistor. However, the bipolar transistor in this paper is assumed to have linear forward trans-conductance y 21 ( v 1 ), while work [ 20 ] assumes a cubic polynomial for both functions y 12 ( v 2 ), y 21 ( v 1 ). Therefore, all seven distinct chaotic cases revealed in this manuscript are algebraically simpler than the single example proposed in paper [ 20 ].…”

“…However, the bipolar transistor in this paper is assumed to have linear forward trans-conductance y 21 ( v 1 ), while work [ 20 ] assumes a cubic polynomial for both functions y 12 ( v 2 ), y 21 ( v 1 ). Therefore, all seven distinct chaotic cases revealed in this manuscript are algebraically simpler than the single example proposed in paper [ 20 ]. In contrast, paper [ 21 ] deals with smooth nonlinear function y 21 ( v 1 ) and presents strange attractors discovered for only two shapes of forward trans-conductance.…”

“…Readers can pick and use our dynamical system that fits a specific application. In general, the upcoming sections represent more comprehensive analysis of the class C amplifier than case study [ 20 ]. Simple circuits with one or two transistors are analyzed in paper [ 22 ], again from the viewpoint of the evolution of chaotic behavior.…”

Hyperchaotic Self-Oscillations of Two-Stage Class C Amplifier With Generalized Transistors

“…Both forward y21 and backward y12 transconductance are considered as nonzero and could be scalar nonlinear functions. The latter property is assumed in paper [47] where y21(v1) and y12(v2) are cubic polynomial functions and single GBT-based amplifier is addressed. New shapes of the chaotic attractors are reported also for the case where y21 is linear and y12(v2) is the only nonlinearity.…”

Binary Memory Implemented by Using Variable Gain Amplifiers With Multipliers

“…Logic circuits are also not excluded from potentially chaotic systems [29]. Recent paper presents evolution of chaos in fundamental class C amplifier having single bipolar transistor [30]. Several very simple chaotic circuits with one or two bipolar transistors and three accumulation elements are discussed in [31].…”