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Frequency Mixing
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. Mixers are widely used to shift signals from one frequency range to another, a process known as heterodyning, for convenience in transmission or further signal processing. For example, a key component of a superheterodyne receiver is a mixer used to move received signals to a common intermediate frequency. Frequency mixers are also used to modulate a carrier signal in radio transmitters. Types The essential characteristic of a mixer is that it produces a component in its output which is the product of the two input signals. Both active and passive circuits can realize mixers. Passive mixers use one or more diodes and ...
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Radio Society Of Great Britain
The Radio Society of Great Britain (RSGB) is the United Kingdom's recognised national society for amateur radio operators. The society was founded in 1913 as the London Wireless Club, making it one of the oldest organisations of its kind in the world. Through its work, it represent the interests of the UK's 80,000 licensed radio amateurs in the United Kingdom and certain dependent territories of the United Kingdom at the International Amateur Radio Union, acting as a medium for communication between the licensed operators and the UK government. Role The RSGB has traditionally acted as the organisation through which its members interact with the telecommunications regulatory authority of the United Kingdom, Ofcom. Although Ofcom has used its web site to solicit opinions directly from all amateur radio enthusiasts and other interested parties, the RSGB continues to advise and to seek to influence Ofcom on the likely impact of proposed changes in many areas – from decisions on ...
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Modulator
In electronics and telecommunications, modulation is the process of varying one or more properties of a periodic waveform, called the ''carrier signal'', with a separate signal called the ''modulation signal'' that typically contains information to be transmitted. For example, the modulation signal might be an audio signal representing sound from a microphone, a video signal representing moving images from a video camera, or a digital signal representing a sequence of binary digits, a bitstream from a computer. The carrier is higher in frequency than the modulation signal. In radio communication the modulated carrier is transmitted through space as a radio wave to a radio receiver. Another purpose is to transmit multiple channels of information through a single communication medium, using frequency-division multiplexing (FDM). For example in cable television which uses FDM, many carrier signals, each modulated with a different television channel, are transported through a sing ...
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Product Detector
A product detector is a type of demodulator used for AM and SSB signals. Rather than converting the envelope of the signal into the decoded waveform like an envelope detector, the product detector takes the product of the modulated signal and a local oscillator, hence the name. A product detector is a frequency mixer. Product detectors can be designed to accept either IF or RF frequency inputs. A product detector which accepts an IF signal would be used as a demodulator block in a superheterodyne receiver, and a detector designed for RF can be combined with an RF amplifier and a low-pass filter into a direct-conversion receiver. A simple product detector The simplest form of product detector mixes (or heterodynes) the RF or IF signal with a locally derived carrier (the Beat Frequency Oscillator, or BFO) to produce an audio frequency copy of the original audio signal and a mixer product at twice the original RF or IF frequency. This high-frequency component can then be fi ...
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Dc Offset
In signal processing, when describing a periodic function in the time domain, the DC bias, DC component, DC offset, or DC coefficient is the mean amplitude of the waveform. If the mean amplitude is zero, there is no DC bias. A waveform with no DC bias is known as a ''DC balanced'' or ''DC free'' waveform. Origin The term originates in electronics, where ''DC'' refers to a direct current voltage. In contrast, various other non-DC frequencies are analogous to superimposed alternating current (AC) voltages or currents, hence called ''AC components'' or ''AC coefficients''. Applications In the design of electronic amplifier circuits, every active device has biasing to set its ''operating point'', the steady state current and voltage on the device when no signal is applied. In bipolar transistor biasing, for example, a network of resistors is used to apply a small amount of DC to the base terminal of the transistor. The AC signal is applied at the same terminal and is amplified. Th ...
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Prosthaphaeresis
Prosthaphaeresis (from the Greek ''προσθαφαίρεσις'') was an algorithm used in the late 16th century and early 17th century for approximate multiplication and division using formulas from trigonometry. For the 25 years preceding the invention of the logarithm in 1614, it was the only known generally applicable way of approximating products quickly. Its name comes from the Greek ''prosthesis'' (πρόσθεσις) and ''aphaeresis'' (ἀφαίρεσις), meaning addition and subtraction, two steps in the process.Prosthaphaeresis
by Brian Borchers


History and motivation

In 16th-century Europe, celestial navigation of ships on long voyages relied heavily on

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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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Taylor Series
In mathematics, the Taylor series or Taylor expansion of a function is an infinite sum of terms that are expressed in terms of the function's derivatives at a single point. For most common functions, the function and the sum of its Taylor series are equal near this point. Taylor series are named after Brook Taylor, who introduced them in 1715. A Taylor series is also called a Maclaurin series, when 0 is the point where the derivatives are considered, after Colin Maclaurin, who made extensive use of this special case of Taylor series in the mid-18th century. The partial sum formed by the first terms of a Taylor series is a polynomial of degree that is called the th Taylor polynomial of the function. Taylor polynomials are approximations of a function, which become generally better as increases. Taylor's theorem gives quantitative estimates on the error introduced by the use of such approximations. If the Taylor series of a function is convergent, its sum is the limit of the ...
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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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Non-linearity
In mathematics and science, a nonlinear system is a system in which the change of the output is not proportional to the change of the input. Nonlinear problems are of interest to engineers, biologists, physicists, mathematicians, and many other scientists because most systems are inherently nonlinear in nature. Nonlinear dynamical systems, describing changes in variables over time, may appear chaotic, unpredictable, or counterintuitive, contrasting with much simpler linear systems. Typically, the behavior of a nonlinear system is described in mathematics by a nonlinear system of equations, which is a set of simultaneous equations in which the unknowns (or the unknown functions in the case of differential equations) appear as variables of a polynomial of degree higher than one or in the argument of a function which is not a polynomial of degree one. In other words, in a nonlinear system of equations, the equation(s) to be solved cannot be written as a linear combination of the un ...
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Optical Heterodyne Detection
Optical heterodyne detection is a method of extracting information encoded as modulation of the phase, frequency or both of electromagnetic radiation in the wavelength band of visible or infrared light. The light signal is compared with standard or reference light from a "local oscillator" (LO) that would have a fixed offset in frequency and phase from the signal if the latter carried null information. "Heterodyne" signifies more than one frequency, in contrast to the single frequency employed in homodyne detection. The comparison of the two light signals is typically accomplished by combining them in a photodiode detector, which has a response that is linear in energy, and hence quadratic in amplitude of electromagnetic field. Typically, the two light frequencies are similar enough that their difference or beat frequency produced by the detector is in the radio or microwave band that can be conveniently processed by electronic means. This technique became widely applicable to top ...
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Nonlinear Optics
Nonlinear optics (NLO) is the branch of optics that describes the behaviour of light in ''nonlinear media'', that is, media in which the polarization density P responds non-linearly to the electric field E of the light. The non-linearity is typically observed only at very high light intensities (when the electric field of the light is >108 V/m and thus comparable to the atomic electric field of ~1011 V/m) such as those provided by lasers. Above the Schwinger limit, the vacuum itself is expected to become nonlinear. In nonlinear optics, the superposition principle no longer holds. History The first nonlinear optical effect to be predicted was two-photon absorption, by Maria Goeppert Mayer for her PhD in 1931, but it remained an unexplored theoretical curiosity until 1961 and the almost simultaneous observation of two-photon absorption at Bell Labs and the discovery of second-harmonic generation by Peter Franken ''et al.'' at University of Michigan, both shortly after the constru ...
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