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A LR-Diode circuit exhibits non-linear behavior and demonstrates chaotic behavior. By adjusting the amplitude of the driving frequency one can see period doubling, and eventually chaos.
Chaos theory is an interdisciplinary area of scientific study and branch of mathematics focused on underlying patterns and deterministic laws of dynamical systems that are highly sensitive to initial conditions, and were once thought to have completely random states of disorder and irregularities. Chaos theory states that within the apparent randomness of chaotic complex systems, there are underlying patterns, interconnection, constant feedback loops, repetition, self-similarity, fractals, and self-organization. The butterfly effect, an underlying principle of chaos, describes how a small change in one state of a deterministic nonlinear system can result in large differences in a later state. A metaphor for this behavior is that a butterfly flapping its wings in Brazil can cause a tornado in Texas.
A diode is a two-terminal electronic component that conducts current primarily in one direction ; it has low resistance in one direction, and high resistance in the other.
An electrical network is an interconnection of electrical components or a model of such an interconnection, consisting of electrical elements. An electrical circuit is a network consisting of a closed loop, giving a return path for the current. Linear electrical networks, a special type consisting only of sources, linear lumped elements, and linear distributed elements, have the property that signals are linearly superimposable. They are thus more easily analyzed, using powerful frequency domain methods such as Laplace transforms, to determine DC response, AC response, and transient response.
A varistor is an electronic component with an electrical resistance that varies with the applied voltage. Also known as a voltage-dependent resistor (VDR), it has a nonlinear, non-ohmic current–voltage characteristic that is similar to that of a diode. Unlike a diode however, it has the same characteristic for both directions of traversing current. Traditionally, varistors were indeed constructed by connecting two rectifiers, such as the copper-oxide or germanium-oxide rectifier in antiparallel configuration. At low voltage the varistor has a high electrical resistance which decreases as the voltage is raised. Modern varistors are primarily based on sintered ceramic metal-oxide materials which exhibit directional behavior only on a microscopic scale. This type is commonly known as the metal-oxide varistor (MOV).
Electrical elements are conceptual abstractions representing idealized electrical components, such as resistors, capacitors, and inductors, used in the analysis of electrical networks. All electrical networks can be analyzed as multiple electrical elements interconnected by wires. Where the elements roughly correspond to real components, the representation can be in the form of a schematic diagram or circuit diagram. This is called a lumped-element circuit model. In other cases, infinitesimal elements are used to model the network, in a distributed-element model.
In electronics, a linear regulator is a voltage regulator used to maintain a steady voltage. The resistance of the regulator varies in accordance with both the input voltage and the load, resulting in a constant voltage output. The regulating circuit varies its resistance, continuously adjusting a voltage divider network to maintain a constant output voltage and continually dissipating the difference between the input and regulated voltages as waste heat. By contrast, a switching regulator uses an active device that switches on and off (oscilates) to maintain an average value of output. Because the regulated voltage of a linear regulator must always be lower than input voltage, efficiency is limited and the input voltage must be high enough to always allow the active device to drop some voltage.
In electronics, negative resistance (NR) is a property of some electrical circuits and devices in which an increase in voltage across the device's terminals results in a decrease in electric current through it.
In electronics, a mixer, or frequency mixer, is an electrical circuit that creates new frequencies from two signals applied to it. In its most common application, two signals are applied to a mixer, and it produces new signals at the sum and difference of the original frequencies. Other frequency components may also be produced in a practical frequency mixer.
A voltage regulator is a system designed to automatically maintain a constant voltage. A voltage regulator may use a simple feed-forward design or may include negative feedback. It may use an electromechanical mechanism, or electronic components. Depending on the design, it may be used to regulate one or more AC or DC voltages.
In electrical engineering and electronics, a network is a collection of interconnected components. Network analysis is the process of finding the voltages across, and the currents through, all network components. There are many techniques for calculating these values; however, for the most part, the techniques assume linear components. Except where stated, the methods described in this article are applicable only to linear network analysis.
Mitchell Jay Feigenbaum was an American mathematical physicist whose pioneering studies in chaos theory led to the discovery of the Feigenbaum constants.
Small-signal modeling is a common analysis technique in electronics engineering used to approximate the behavior of electronic circuits containing nonlinear devices with linear equations. It is applicable to electronic circuits in which the AC signals are small relative to the DC bias currents and voltages. A small-signal model is an AC equivalent circuit in which the nonlinear circuit elements are replaced by linear elements whose values are given by the first-order (linear) approximation of their characteristic curve near the bias point.
Chua's circuit is a simple electronic circuit that exhibits classic chaotic behavior. This means roughly that it is a "nonperiodic oscillator"; it produces an oscillating waveform that, unlike an ordinary electronic oscillator, never "repeats". It was invented in 1983 by Leon O. Chua, who was a visitor at Waseda University in Japan at that time. The ease of construction of the circuit has made it a ubiquitous real-world example of a chaotic system, leading some to declare it "a paradigm for chaos".
A clamper is an electronic circuit that fixes either the positive or the negative peak excursions of a signal to a defined voltage by adding a variable positive or negative DC voltage to it. The clamper does not restrict the peak-to-peak excursion of the signal (clipping); it moves the whole signal up or down so as to place its peaks at the reference level.
A linear circuit is an electronic circuit which obeys the superposition principle. This means that the output of the circuit F(x) when a linear combination of signals ax1(t) + bx2(t) is applied to it is equal to the linear combination of the outputs due to the signals x1(t) and x2(t) applied separately:
Large-signal modeling is a common analysis method used in electronic engineering to describe nonlinear devices in terms of the underlying nonlinear equations. In circuits containing nonlinear elements such as transistors, diodes, and vacuum tubes, under "large signal conditions", AC signals have high enough magnitude that nonlinear effects must be considered.
In graphical analysis of nonlinear electronic circuits, a load line is a line drawn on the characteristic curve, a graph of the current vs. the voltage in a nonlinear device like a diode or transistor. It represents the constraint put on the voltage and current in the nonlinear device by the external circuit. The load line, usually a straight line, represents the response of the linear part of the circuit, connected to the nonlinear device in question. The points where the characteristic curve and the load line intersect are the possible operating point(s) of the circuit; at these points the current and voltage parameters of both parts of the circuit match.
Electronics engineering is a sub-discipline of electrical engineering which emerged in the early 20th century and is distinguished by the additional use of active components such as semiconductor devices to amplify and control electric current flow. Previously electrical engineering only used passive devices such as mechanical switches, resistors, inductors and capacitors.
Passivity is a property of engineering systems, most commonly encountered in analog electronics and control systems. Typically, analog designers use passivity to refer to incrementally passive components and systems, which are incapable of power gain. In contrast, control systems engineers will use passivity to refer to thermodynamically passive ones, which consume, but do not produce, energy. As such, without context or a qualifier, the term passive is ambiguous.
In electronics and chaos theory, Chua's diode is a type of two-terminal, nonlinear active resistor which can be described with piecewise-linear equations. It is an essential part of Chua's circuit, a simple electronic oscillator circuit which exhibits chaotic oscillations and is widely used as an example for a chaotic system. It is implemented as a voltage-controlled, nonlinear negative resistor.
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