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
Summary
This paper introduces an electronic circuit capable of generating a set of functions, some of them known in digital systems as the logical operators AND, OR, XOR, and so on. Using two inputs,
u1 and
u2, the circuit provides 16 possible output combinations. The main idea of the electronic design is based on an RC network, operational amplifiers, and voltage comparators. On the other hand, mathematically, the stable system response is used as a surface where
u1 and
u2 are coordinate axes forming a plane, which intersects this surface, and the output
y can be seen as a circle surrounding some fixed points over this plane. The mathematical approach on this paper is intended as a groundwork for a multiple input reconfigurable logic gate that could be embedded in more complex systems. The procedure to obtain an XOR gate, represented by the
ffalse(6false) function, is explained to illustrate the circuit behavior. Results of the 16 implemented functions are shown in Appendices B and C.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.