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Voltage Ladder
A voltage ladder is a simple electronic circuit consisting of several resistors connected in series with a voltage placed across the entire resistor network. Voltage ladders are useful for providing a set of successive voltage references, for instance for a flash analog-to-digital converter. How it works A voltage drop occurs across each resistor in the network causing each successive "rung" of the ladder (each node of the circuit) to have a higher voltage than the one before it. Ohm's law can be used to easily calculate the voltage at each node. Since the ladder is a series circuit, the current is the same throughout, and is given by the total voltage divided by the total resistance (V/Req), which is just the sum of each series resistor in the ladder. The voltage drop across any one resistor is now given simply by I*Rn, where I is the current calculated above, and Rn is the resistance of the resistor in question. The voltage referenced to ground at any node is simply the sum of ...
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Electronic Circuit
An electronic circuit is composed of individual electronic components, such as resistors, transistors, capacitors, inductors and diodes, connected by conductive wires or traces through which electric current can flow. It is a type of electrical circuit and to be referred to as ''electronic'', rather than ''electrical'', generally at least one active component must be present. The combination of components and wires allows various simple and complex operations to be performed: signals can be amplified, computations can be performed, and data can be moved from one place to another. Circuits can be constructed of discrete components connected by individual pieces of wire, but today it is much more common to create interconnections by photolithographic techniques on a laminated substrate (a printed circuit board or PCB) and solder the components to these interconnections to create a finished circuit. In an integrated circuit or IC, the components and interconnections are formed on t ...
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Resistor
A resistor is a passive two-terminal electrical component that implements electrical resistance as a circuit element. In electronic circuits, resistors are used to reduce current flow, adjust signal levels, to divide voltages, bias active elements, and terminate transmission lines, among other uses. High-power resistors that can dissipate many watts of electrical power as heat may be used as part of motor controls, in power distribution systems, or as test loads for generators. Fixed resistors have resistances that only change slightly with temperature, time or operating voltage. Variable resistors can be used to adjust circuit elements (such as a volume control or a lamp dimmer), or as sensing devices for heat, light, humidity, force, or chemical activity. Resistors are common elements of electrical networks and electronic circuits and are ubiquitous in electronic equipment. Practical resistors as discrete components can be composed of various compounds and forms. Resisto ...
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Series Circuit
Two-terminal components and electrical networks can be connected in series or parallel. The resulting electrical network will have two terminals, and itself can participate in a series or parallel topology. Whether a two-terminal "object" is an electrical component (e.g. a resistor) or an electrical network (e.g. resistors in series) is a matter of perspective. This article will use "component" to refer to a two-terminal "object" that participate in the series/parallel networks. Components connected in series are connected along a single "electrical path", and each component has the same current through it, equal to the current through the network. The voltage across the network is equal to the sum of the voltages across each component. Components connected in parallel are connected along multiple paths, and each component has the same voltage across it, equal to the voltage across the network. The current through the network is equal to the sum of the currents through each com ...
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Voltage
Voltage, also known as electric pressure, electric tension, or (electric) potential difference, is the difference in electric potential between two points. In a static electric field, it corresponds to the work needed per unit of charge to move a test charge between the two points. In the International System of Units, the derived unit for voltage is named ''volt''. The voltage between points can be caused by the build-up of electric charge (e.g., a capacitor), and from an electromotive force (e.g., electromagnetic induction in generator, inductors, and transformers). On a macroscopic scale, a potential difference can be caused by electrochemical processes (e.g., cells and batteries), the pressure-induced piezoelectric effect, and the thermoelectric effect. A voltmeter can be used to measure the voltage between two points in a system. Often a common reference potential such as the ground of the system is used as one of the points. A voltage can represent either a source ...
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Flash ADC
A flash ADC (also known as a direct-conversion ADC) is a type of analog-to-digital converter that uses a linear voltage ladder with a comparator at each "rung" of the ladder to compare the input voltage to successive reference voltages. Often these reference ladders are constructed of many resistors; however, modern implementations show that capacitive voltage division is also possible. The output of these comparators is generally fed into a digital encoder, which converts the inputs into a binary value (the collected outputs from the comparators can be thought of as a unary value). Benefits and drawbacks Flash converters are extremely fast compared to many other types of ADCs, which usually narrow in on the "correct" answer over a series of stages. Compared to these, a flash converter is also quite simple and, apart from the analog comparators, only requires logic for the final conversion to binary. For best accuracy, often a track-and-hold circuit is inserted in front of the A ...
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Voltage Drop
Voltage drop is the decrease of electrical potential along the path of a current flowing in an electrical circuit. Voltage drops in the internal resistance of the source, across conductors, across contacts, and across connectors are undesirable because some of the energy supplied is dissipated. The voltage drop across the electrical load is proportional to the power available to be converted in that load to some other useful form of energy. For example, an electric space heater may have a resistance of ten ohms, and the wires that supply it may have a resistance of 0.2 ohms, about 2% of the total circuit resistance. This means that approximately 2% of the supplied voltage is lost in the wire itself. An excessive voltage drop may result in the unsatisfactory performance of a space heater and overheating of the wires and connections. National and local electrical codes may set guidelines for the maximum voltage drop allowed in electrical wiring to ensure efficiency of distributi ...
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Runge's Phenomenon
In the mathematical field of numerical analysis, Runge's phenomenon () is a problem of oscillation at the edges of an interval that occurs when using polynomial interpolation with polynomials of high degree over a set of equispaced interpolation points. It was discovered by Carl David Tolmé Runge (1901) when exploring the behavior of errors when using polynomial interpolation to approximate certain functions. The discovery was important because it shows that going to higher degrees does not always improve accuracy. The phenomenon is similar to the Gibbs phenomenon in Fourier series approximations. Introduction The Weierstrass approximation theorem states that for every continuous function ''f''(''x'') defined on an interval 'a'',''b'' there exists a set of polynomial functions ''P''''n''(''x'') for ''n''=0, 1, 2, …, each of degree at most ''n'', that approximates ''f''(''x'') with uniform convergence over 'a'',''b''as ''n'' tends to infinity, that is, :\lim_ \left( \sup ...
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Ohm's Law
Ohm's law states that the current through a conductor between two points is directly proportional to the voltage across the two points. Introducing the constant of proportionality, the resistance, one arrives at the usual mathematical equation that describes this relationship: :I = \frac, where is the current through the conductor, ''V'' is the voltage measured ''across'' the conductor and ''R'' is the resistance of the conductor. More specifically, Ohm's law states that the ''R'' in this relation is constant, independent of the current. If the resistance is not constant, the previous equation cannot be called ''Ohm's law'', but it can still be used as a definition of static/DC resistance. Ohm's law is an empirical relation which accurately describes the conductivity of the vast majority of electrically conductive materials over many orders of magnitude of current. However some materials do not obey Ohm's law; these are called non-ohmic. The law was named after t ...
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Electric Current
An electric current is a stream of charged particles, such as electrons or ions, moving through an electrical conductor or space. It is measured as the net rate of flow of electric charge through a surface or into a control volume. The moving particles are called charge carriers, which may be one of several types of particles, depending on the conductor. In electric circuits the charge carriers are often electrons moving through a wire. In semiconductors they can be electrons or holes. In an electrolyte the charge carriers are ions, while in plasma, an ionized gas, they are ions and electrons. The SI unit of electric current is the ampere, or ''amp'', which is the flow of electric charge across a surface at the rate of one coulomb per second. The ampere (symbol: A) is an SI base unit. Electric current is measured using a device called an ammeter. Electric currents create magnetic fields, which are used in motors, generators, inductors, and transformers. In ordinary con ...
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Ground (electricity)
In electrical engineering, ground or earth is a reference point in an electrical circuit from which voltages are measured, a common return path for electric current, or a direct physical connection to the Earth. Electrical circuits may be connected to ground for several reasons. Exposed conductive parts of electrical equipment are connected to ground, to protect users from electrical shock hazard. If internal insulation fails, dangerous voltages may appear on the exposed conductive parts. Connecting exposed parts to ground will allow circuit breakers (or RCDs) to interrupt power supply in the event of a fault. In electric power distribution systems, a protective earth (PE) conductor is an essential part of the safety provided by the earthing system. Connection to ground also limits the build-up of static electricity when handling flammable products or electrostatic-sensitive devices. In some telegraph and power transmission circuits, the ground itself can be used as one condu ...
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Voltage Divider Rule
In electronics, a voltage divider (also known as a potential divider) is a passive linear circuit that produces an output voltage (''V''out) that is a fraction of its input voltage (''V''in). Voltage division is the result of distributing the input voltage among the components of the divider. A simple example of a voltage divider is two resistors connected in series, with the input voltage applied across the resistor pair and the output voltage emerging from the connection between them. Resistor voltage dividers are commonly used to create reference voltages, or to reduce the magnitude of a voltage so it can be measured, and may also be used as signal attenuators at low frequencies. For direct current and relatively low frequencies, a voltage divider may be sufficiently accurate if made only of resistors; where frequency response over a wide range is required (such as in an oscilloscope probe), a voltage divider may have capacitive elements added to compensate load capacitance ...
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