Application of dynamical system theory in LC harmonic oscillator circuits: A complement tool to the Barkhausen criterion

There are different types of electronic oscillators that have a wide variety of applications in areas such as computing, audio, communication, among others. One of these is the harmonic oscillators that generate an output sinusoidal signal. Due to the advantages of these, this paper proposes a methodology based on an analysis based on the dynamical system theory. This provides undergraduates a useful tool for a better understanding of the harmonic oscillators in order to design and implement accurately this kind of circuits. This tool complements the widely recognized Barkhausen criterion, which is a mathematical condition that must be satisfied by linear feedback oscillators. The analysis based on the dynamical system theory consists of obtaining a state matrix and its eigenvalues from the mathematical model of the oscillator circuits. The eigenvalues are adjusted to get an oscillator system, thus from this way, a set of conditions are derived. These conditions are complementary to those obtained by the Barkhausen criterion