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Resonance

In physics, resonance refers to a wide class of phenomena that arise as a result of matching temporal or spatial periods of oscillatory objects. For an oscillatory dynamical systems driven by a time-varying external force, resonance occurs when the frequency of the external force coincides with the natural frequency of the system. Resonance can occur in various systems, such as mechanical, electrical, or acoustic systems, and it is desirable in certain applications, such as musical instruments or radio receivers. Resonance can also be undesirable, leading to excessive vibrations or even structural failure in some cases.

All systems, including molecular systems and particles, tend to vibrate at a natural frequency depending upon their structure; this frequency is known as a resonant frequency or resonance frequency. When an oscillating force, an external vibration, is applied at a resonant frequency of a dynamic system, object, or particle, the outside vibration will cause the system to oscillate at a higher amplitude (with more force) than when the same force is applied at other, non-resonant frequencies.

The resonant frequencies of a system can be identified when the response to an external vibration creates an amplitude that is a relative maximum within the system. Small periodic forces that are near a resonant frequency of the system have the ability to produce large amplitude oscillations in the system due to the storage of vibrational energy.

Resonance phenomena occur with all types of vibrations or waves: there is mechanical resonance, orbital resonance, acoustic resonance, electromagnetic resonance, nuclear magnetic resonance (NMR), electron spin resonance (ESR) and resonance of quantum wave functions. Resonant systems can be used to generate vibrations of a specific frequency (e.g., musical instruments), or pick out specific frequencies from a complex vibration containing many frequencies (e.g., filters).

The term resonance (from Latin resonantia, 'echo', from resonare, 'resound') originated from the field of acoustics, particularly the sympathetic resonance observed in musical instruments, e.g., when one string starts to vibrate and produce sound after a different one is struck.

Overview
Resonance occurs when a system is able to store and easily transfer energy between two or more different storage modes (such as kinetic energy and potential energy in the case of a simple pendulum). However, there are some losses from cycle to cycle, called damping. When damping is small, the resonant frequency is approximately equal to the natural frequency of the system, which is a frequency of unforced vibrations. Some systems have multiple, distinct, resonant frequencies.

Examples

A familiar example is a playground swing, which acts as a pendulum. Pushing a person in a swing in time with the natural interval of the swing (its resonant frequency) makes the swing go higher and higher (maximum amplitude), while attempts to push the swing at a faster or slower tempo produce smaller arcs. This is because the energy the swing absorbs is maximized when the pushes match the swing's natural oscillations.

Resonance occurs widely in nature, and is exploited in many devices. It is the mechanism by which virtually all sinusoidal waves and vibrations are generated. For example, when hard objects like metal, glass, or wood are struck, there are brief resonant vibrations in the object. Light and other short wavelength electromagnetic radiation is produced by resonance on an atomic scale, such as electrons in atoms. Other examples of resonance include:

 * Timekeeping mechanisms of modern clocks and watches, e.g., the balance wheel in a mechanical watch and the quartz crystal in a quartz watch
 * Tidal resonance of the Bay of Fundy
 * Acoustic resonances of musical instruments and the human vocal tract
 * Shattering of a crystal wineglass when exposed to a musical tone of the right pitch (its resonant frequency)
 * Friction idiophones, such as making a glass object (glass, bottle, vase) vibrate by rubbing around its rim with a fingertip
 * Electrical resonance of tuned circuits in radios and TVs that allow radio frequencies to be selectively received
 * Creation of coherent light by optical resonance in a laser cavity
 * Orbital resonance as exemplified by some moons of the Solar System's giant planets and resonant groups such as the plutinos
 * Material resonances in atomic scale are the basis of several spectroscopic techniques that are used in condensed matter physics
 * Electron spin resonance
 * Mössbauer effect
 * Nuclear magnetic resonance

Linear systems
Resonance manifests itself in many linear and nonlinear systems as oscillations around an equilibrium point. When the system is driven by a sinusoidal external input, a measured output of the system may oscillate in response. The ratio of the amplitude of the output's steady-state oscillations to the input's oscillations is called the gain, and the gain can be a function of the frequency of the sinusoidal external input. Peaks in the gain at certain frequencies correspond to resonances, where the amplitude of the measured output's oscillations are disproportionately large.

Since many linear and nonlinear systems that oscillate are modeled as harmonic oscillators near their equilibria, a derivation of the resonant frequency for a driven, damped harmonic oscillator is shown. An RLC circuit is used to illustrate connections between resonance and a system's transfer function, frequency response, poles, and zeroes. Building off the RLC circuit example, these connections for higher-order linear systems with multiple inputs and outputs are generalized.

The driven, damped harmonic oscillator
Consider a damped mass on a spring driven by a sinusoidal, externally applied force. Newton's second law takes the form

where m is the mass, x is the displacement of the mass from the equilibrium point, F0 is the driving amplitude, ω is the driving angular frequency, k is the spring constant, and c is the viscous damping coefficient. This can be rewritten in the form

where
 * $\omega_0 = \sqrt{k /m}$ is called the undamped angular frequency of the oscillator or the natural frequency,
 * $$\zeta = \frac{c}{2\sqrt{mk}}$$ is called the damping ratio.

Many sources also refer to ω0 as the resonant frequency. However, as shown below, when analyzing oscillations of the displacement x(t), the resonant frequency is close to but not the same as ω0. In general the resonant frequency is close to but not necessarily the same as the natural frequency. The RLC circuit example in the next section gives examples of different resonant frequencies for the same system.

The general solution of Equation ($$) is the sum of a transient solution that depends on initial conditions and a steady state solution that is independent of initial conditions and depends only on the driving amplitude F0, driving frequency ω, undamped angular frequency ω0, and the damping ratio ζ. The transient solution decays in a relatively short amount of time, so to study resonance it is sufficient to consider the steady state solution.

It is possible to write the steady-state solution for x(t) as a function proportional to the driving force with an induced phase change φ,

where $$ \varphi = \arctan\left(\frac{2\omega \omega_0\zeta}{\omega^2 - \omega_0^2} \right) + n\pi.$$

The phase value is usually taken to be between −180° and 0 so it represents a phase lag for both positive and negative values of the arctan argument.

Resonance occurs when, at certain driving frequencies, the steady-state amplitude of x(t) is large compared to its amplitude at other driving frequencies. For the mass on a spring, resonance corresponds physically to the mass's oscillations having large displacements from the spring's equilibrium position at certain driving frequencies. Looking at the amplitude of x(t) as a function of the driving frequency ω, the amplitude is maximal at the driving frequency $$\omega_r = \omega_0 \sqrt{1 - 2\zeta^2}.$$

ωr is the resonant frequency for this system. Again, the resonant frequency does not equal the undamped angular frequency ω0 of the oscillator. They are proportional, and if the damping ratio goes to zero they are the same, but for non-zero damping they are not the same frequency. As shown in the figure, resonance may also occur at other frequencies near the resonant frequency, including ω0, but the maximum response is at the resonant frequency.

Also, ωr is only real and non-zero if $\zeta < 1 / \sqrt{2}$, so this system can only resonate when the harmonic oscillator is significantly underdamped. For systems with a very small damping ratio and a driving frequency near the resonant frequency, the steady state oscillations can become very large.

The pendulum
For other driven, damped harmonic oscillators whose equations of motion do not look exactly like the mass on a spring example, the resonant frequency remains $$\omega_r = \omega_0 \sqrt{1 - 2\zeta^2},$$ but the definitions of ω0 and ζ change based on the physics of the system. For a pendulum of length ℓ and small displacement angle θ, Equation ($$) becomes $$ m\ell\frac{\mathrm{d}^2\theta}{\mathrm{d}t^2} = F_0 \sin(\omega t)-mg\theta-c\ell\frac{\mathrm{d}\theta}{\mathrm{d}t}$$

and therefore
 * $$\omega_0 = \sqrt{\frac{g}{\ell}},$$
 * $$\zeta = \frac{c}{2m}\sqrt{\frac{\ell}{g}}.$$

RLC series circuits
Consider a circuit consisting of a resistor with resistance R, an inductor with inductance L, and a capacitor with capacitance C connected in series with current i(t) and driven by a voltage source with voltage vin(t). The voltage drop around the circuit is

Rather than analyzing a candidate solution to this equation like in the mass on a spring example above, this section will analyze the frequency response of this circuit. Taking the Laplace transform of Equation ($$), $$sLI(s) + RI(s) + \frac{1}{sC}I(s) = V_\text{in}(s),$$ where I(s) and Vin(s) are the Laplace transform of the current and input voltage, respectively, and s is a complex frequency parameter in the Laplace domain. Rearranging terms, $$I(s) = \frac{s}{s^2L + Rs + \frac{1}{C}} V_\text{in}(s).$$

Voltage across the capacitor
An RLC circuit in series presents several options for where to measure an output voltage. Suppose the output voltage of interest is the voltage drop across the capacitor. As shown above, in the Laplace domain this voltage is $$V_\text{out}(s) = \frac{1}{sC}I(s)$$ or $$V_\text{out}= \frac{1}{LC(s^2 + \frac{R}{L}s + \frac{1}{LC})} V_\text{in}(s).$$

Define for this circuit a natural frequency and a damping ratio, $$ \omega_0 = \frac{1}{\sqrt{LC}},$$ $$ \zeta = \frac{R}{2}\sqrt{\frac{C}{L}}.$$

The ratio of the output voltage to the input voltage becomes $$H(s) \triangleq \frac{V_\text{out}(s)}{V_\text{in}(s)} = \frac{\omega_0^2}{s^2 + 2\zeta\omega_0s + \omega_0^2}$$

H(s) is the transfer function between the input voltage and the output voltage. This transfer function has two poles–roots of the polynomial in the transfer function's denominator–at

and no zeros–roots of the polynomial in the transfer function's numerator. Moreover, for $ζ ≤ 1$, the magnitude of these poles is the natural frequency ω0 and that for $ζ < 1/$\sqrt{2}$$, our condition for resonance in the harmonic oscillator example, the poles are closer to the imaginary axis than to the real axis.

Evaluating H(s) along the imaginary axis $s = iω$, the transfer function describes the frequency response of this circuit. Equivalently, the frequency response can be analyzed by taking the Fourier transform of Equation ($$) instead of the Laplace transform. The transfer function, which is also complex, can be written as a gain and phase, $$ H(i\omega) = G(\omega)e^{i\Phi(\omega)}.$$

A sinusoidal input voltage at frequency ω results in an output voltage at the same frequency that has been scaled by G(ω) and has a phase shift Φ(ω). The gain and phase can be plotted versus frequency on a Bode plot. For the RLC circuit's capacitor voltage, the gain of the transfer function H(iω) is

Note the similarity between the gain here and the amplitude in Equation ($$). Once again, the gain is maximized at the resonant frequency $$\omega_r = \omega_0 \sqrt{1 - 2\zeta^2}.$$

Here, the resonance corresponds physically to having a relatively large amplitude for the steady state oscillations of the voltage across the capacitor compared to its amplitude at other driving frequencies.

Voltage across the inductor
The resonant frequency need not always take the form given in the examples above. For the RLC circuit, suppose instead that the output voltage of interest is the voltage across the inductor. As shown above, in the Laplace domain the voltage across the inductor is $$V_\text{out}(s) = sLI(s),$$ $$V_\text{out}(s) = \frac{s^2}{s^2 + \frac{R}{L}s + \frac{1}{LC}} V_\text{in}(s),$$ $$V_\text{out}(s) = \frac{s^2}{s^2 + 2\zeta\omega_0s + \omega_0^2} V_\text{in}(s),$$

using the same definitions for ω0 and ζ as in the previous example. The transfer function between Vin(s) and this new Vout(s) across the inductor is $$H(s) = \frac{s^2}{s^2 + 2\zeta\omega_0s + \omega_0^2}.$$

This transfer function has the same poles as the transfer function in the previous example, but it also has two zeroes in the numerator at. Evaluating H(s) along the imaginary axis, its gain becomes $$ G(\omega) = \frac{\omega^2}{\sqrt{\left(2\omega\omega_0\zeta\right)^2 + (\omega_0^2 - \omega^2)^2}}.$$

Compared to the gain in Equation ($$) using the capacitor voltage as the output, this gain has a factor of ω2 in the numerator and will therefore have a different resonant frequency that maximizes the gain. That frequency is $$\omega_r = \frac{\omega_0}{\sqrt{1 - 2\zeta^2}},$$

So for the same RLC circuit but with the voltage across the inductor as the output, the resonant frequency is now larger than the natural frequency, though it still tends towards the natural frequency as the damping ratio goes to zero. That the same circuit can have different resonant frequencies for different choices of output is not contradictory. As shown in Equation ($$), the voltage drop across the circuit is divided among the three circuit elements, and each element has different dynamics. The capacitor's voltage grows slowly by integrating the current over time and is therefore more sensitive to lower frequencies, whereas the inductor's voltage grows when the current changes rapidly and is therefore more sensitive to higher frequencies. While the circuit as a whole has a natural frequency where it tends to oscillate, the different dynamics of each circuit element make each element resonate at a slightly different frequency.

Voltage across the resistor
Suppose that the output voltage of interest is the voltage across the resistor. In the Laplace domain the voltage across the resistor is $$V_\text{out}(s) = RI(s),$$ $$V_\text{out}(s) = \frac{Rs}{L\left(s^2 + \frac{R}{L}s + \frac{1}{LC}\right)} V_\text{in}(s),$$

and using the same natural frequency and damping ratio as in the capacitor example the transfer function is $$H(s) = \frac{2\zeta\omega_0s}{s^2 + 2\zeta\omega_0s+\omega_0^2}.$$

This transfer function also has the same poles as the previous RLC circuit examples, but it only has one zero in the numerator at s = 0. For this transfer function, its gain is $$ G(\omega) = \frac{2\zeta\omega_0\omega}{\sqrt{\left(2\omega\omega_0\zeta\right)^2 + (\omega_0^2 - \omega^2)^2}}.$$

The resonant frequency that maximizes this gain is $$\omega_r = \omega_0,$$ and the gain is one at this frequency, so the voltage across the resistor resonates at the circuit's natural frequency and at this frequency the amplitude of the voltage across the resistor equals the input voltage's amplitude.

Antiresonance
Some systems exhibit antiresonance that can be analyzed in the same way as resonance. For antiresonance, the amplitude of the response of the system at certain frequencies is disproportionately small rather than being disproportionately large. In the RLC circuit example, this phenomenon can be observed by analyzing both the inductor and the capacitor combined.

Suppose that the output voltage of interest in the RLC circuit is the voltage across the inductor and the capacitor combined in series. Equation ($$) showed that the sum of the voltages across the three circuit elements sums to the input voltage, so measuring the output voltage as the sum of the inductor and capacitor voltages combined is the same as vin minus the voltage drop across the resistor. The previous example showed that at the natural frequency of the system, the amplitude of the voltage drop across the resistor equals the amplitude of vin, and therefore the voltage across the inductor and capacitor combined has zero amplitude. We can show this with the transfer function.

The sum of the inductor and capacitor voltages is $$V_\text{out}(s) = (sL+\frac{1}{sC})I(s),$$ $$V_\text{out}(s) = \frac{s^2+\frac{1}{LC}}{s^2 + \frac{R}{L}s + \frac{1}{LC}} V_\text{in}(s).$$

Using the same natural frequency and damping ratios as the previous examples, the transfer function is $$H(s) = \frac{s^2+\omega_0^2}{s^2 + 2\zeta\omega_0s + \omega_0^2}.$$

This transfer has the same poles as the previous examples but has zeroes at

Evaluating the transfer function along the imaginary axis, its gain is $$G(\omega) = \frac{\omega_0^2-\omega^2}{\sqrt{\left(2\omega\omega_0\zeta\right)^2 + (\omega_0^2 - \omega^2)^2}}.$$

Rather than look for resonance, i.e., peaks of the gain, notice that the gain goes to zero at ω = ω0, which complements our analysis of the resistor's voltage. This is called antiresonance, which has the opposite effect of resonance. Rather than result in outputs that are disproportionately large at this frequency, this circuit with this choice of output has no response at all at this frequency. The frequency that is filtered out corresponds exactly to the zeroes of the transfer function, which were shown in Equation ($$) and were on the imaginary axis.

Relationships between resonance and frequency response in the RLC series circuit example
These RLC circuit examples illustrate how resonance is related to the frequency response of the system. Specifically, these examples illustrate:
 * How resonant frequencies can be found by looking for peaks in the gain of the transfer function between the input and output of the system, for example in a Bode magnitude plot
 * How the resonant frequency for a single system can be different for different choices of system output
 * The connection between the system's natural frequency, the system's damping ratio, and the system's resonant frequency
 * The connection between the system's natural frequency and the magnitude of the transfer function's poles, pointed out in Equation ($$), and therefore a connection between the poles and the resonant frequency
 * A connection between the transfer function's zeroes and the shape of the gain as a function of frequency, and therefore a connection between the zeroes and the resonant frequency that maximizes gain
 * A connection between the transfer function's zeroes and antiresonance

The next section extends these concepts to resonance in a general linear system.

Generalizing resonance and antiresonance for linear systems
Next consider an arbitrary linear system with multiple inputs and outputs. For example, in state-space representation a third order linear time-invariant system with three inputs and two outputs might be written as $$\begin{bmatrix} \dot{x}_1 \\ \dot{x}_2 \\ \dot{x}_3 \end{bmatrix} = A \begin{bmatrix} x_1(t) \\ x_2(t) \\ x_3(t) \end{bmatrix} + B \begin{bmatrix} u_1(t) \\ u_2(t) \\ u_3(t) \end{bmatrix},$$ $$\begin{bmatrix} y_1(t) \\ y_2(t) \end{bmatrix} = C \begin{bmatrix} x_1(t) \\ x_2(t) \\ x_3(t) \end{bmatrix} + D \begin{bmatrix} u_1(t) \\ u_2(t) \\ u_3(t) \end{bmatrix},$$ where ui(t) are the inputs, xi(t) are the state variables, yi(t) are the outputs, and A, B, C, and D are matrices describing the dynamics between the variables.

This system has a transfer function matrix whose elements are the transfer functions between the various inputs and outputs. For example, $$ \begin{bmatrix} Y_1(s) \\ Y_2(s) \end{bmatrix} = \begin{bmatrix} H_{11}(s) & H_{12}(s) & H_{13}(s) \\ H_{21}(s) & H_{22}(s) & H_{23}(s) \end{bmatrix} \begin{bmatrix} U_1(s) \\ U_2(s) \\ U_3(s) \end{bmatrix}. $$

Each Hij(s) is a scalar transfer function linking one of the inputs to one of the outputs. The RLC circuit examples above had one input voltage and showed four possible output voltages–across the capacitor, across the inductor, across the resistor, and across the capacitor and inductor combined in series–each with its own transfer function. If the RLC circuit were set up to measure all four of these output voltages, that system would have a 4×1 transfer function matrix linking the single input to each of the four outputs.

Evaluated along the imaginary axis, each Hij(iω) can be written as a gain and phase shift, $$H_{ij}(i\omega) = G_{ij}(\omega)e^{i\Phi_{ij}(\omega)}.$$

Peaks in the gain at certain frequencies correspond to resonances between that transfer function's input and output, assuming the system is stable.

Each transfer function Hij(s) can also be written as a fraction whose numerator and denominator are polynomials of s. $$H_{ij}(s) = \frac{N_{ij}(s)}{D_{ij}(s)}.$$

The complex roots of the numerator are called zeroes, and the complex roots of the denominator are called poles. For a stable system, the positions of these poles and zeroes on the complex plane give some indication of whether the system can resonate or antiresonate and at which frequencies. In particular, any stable or marginally stable, complex conjugate pair of poles with imaginary components can be written in terms of a natural frequency and a damping ratio as $$s = -\zeta\omega_0 \pm i\omega_0\sqrt{1-\zeta^2},$$ as in Equation ($$). The natural frequency ω0 of that pole is the magnitude of the position of the pole on the complex plane and the damping ratio of that pole determines how quickly that oscillation decays. In general,
 * Complex conjugate pairs of poles near the imaginary axis correspond to a peak or resonance in the frequency response in the vicinity of the pole's natural frequency. If the pair of poles is on the imaginary axis, the gain is infinite at that frequency.
 * Complex conjugate pairs of zeroes near the imaginary axis correspond to a notch or antiresonance in the frequency response in the vicinity of the zero's frequency, i.e., the frequency equal to the magnitude of the zero. If the pair of zeroes is on the imaginary axis, the gain is zero at that frequency.

In the RLC circuit example, the first generalization relating poles to resonance is observed in Equation ($$). The second generalization relating zeroes to antiresonance is observed in Equation ($$). In the examples of the harmonic oscillator, the RLC circuit capacitor voltage, and the RLC circuit inductor voltage, "poles near the imaginary axis" corresponds to the significantly underdamped condition ζ < 1/$$\sqrt{2}$$.

Standing waves
A physical system can have as many natural frequencies as it has degrees of freedom and can resonate near each of those natural frequencies. A mass on a spring, which has one degree of freedom, has one natural frequency. A double pendulum, which has two degrees of freedom, can have two natural frequencies. As the number of coupled harmonic oscillators increases, the time it takes to transfer energy from one to the next becomes significant. Systems with very large numbers of degrees of freedom can be thought of as continuous rather than as having discrete oscillators.

Energy transfers from one oscillator to the next in the form of waves. For example, the string of a guitar or the surface of water in a bowl can be modeled as a continuum of small coupled oscillators and waves can travel along them. In many cases these systems have the potential to resonate at certain frequencies, forming standing waves with large-amplitude oscillations at fixed positions. Resonance in the form of standing waves underlies many familiar phenomena, such as the sound produced by musical instruments, electromagnetic cavities used in lasers and microwave ovens, and energy levels of atoms.

Standing waves on a string
When a string of fixed length is driven at a particular frequency, a wave propagates along the string at the same frequency. The waves reflect off the ends of the string, and eventually a steady state is reached with waves traveling in both directions. The waveform is the superposition of the waves.

At certain frequencies, the steady state waveform does not appear to travel along the string. At fixed positions called nodes, the string is never displaced. Between the nodes the string oscillates and exactly halfway between the nodes–at positions called anti-nodes–the oscillations have their largest amplitude.

For a string of length $$L$$ with fixed ends, the displacement $$y(x,t)$$ of the string perpendicular to the $$x$$-axis at time $$t$$ is $$ y(x,t) = 2y_\text{max}\sin(kx) \cos(2\pi ft), $$

where
 * $$y_\text{max}$$ is the amplitude of the left- and right-traveling waves interfering to form the standing wave,
 * $$k$$ is the wave number,
 * $$f$$ is the frequency.

The frequencies that resonate and form standing waves relate to the length of the string as $$ f = \frac{nv}{2L}, $$ $$ n = 1,2,3,\dots$$

where $$v$$ is the speed of the wave and the integer $$n$$ denotes different modes or harmonics. The standing wave with $ω_{0} = 1 rad/s$ oscillates at the fundamental frequency and has a wavelength that is twice the length of the string. The possible modes of oscillation form a harmonic series.

Resonance in complex networks
A generalization to complex networks of coupled harmonic oscillators shows that such systems have a finite number of natural resonant frequencies, related to the topological structure of the network itself. In particular, such frequencies result related to the eigenvalues of the network's Laplacian matrix. Let $${\bf A}$$ be the adjacency matrix describing the topological structure of the network and $${\bf L}={\bf K}-{\bf A}$$ the corresponding Laplacian matrix, where $${\bf K}={\rm diag}\, \{ k_{i}\}$$ is the diagonal matrix of the degrees of the network's nodes. Then, for a network of classical and identical harmonic oscillators, when a sinusoidal driving force $$f(t)=F_{0}\sin \omega t$$ is applied to a specific node, the global resonant frequencies of the network are given by $$\omega_{i}=\sqrt{1+\mu_{i}}$$ where $$\mu_{i}$$ are the eigenvalues of the Laplacian $${\bf L}$$.

Mechanical and acoustic

Mechanical resonance is the tendency of a mechanical system to absorb more energy when the frequency of its oscillations matches the system's natural frequency of vibration than it does at other frequencies. It may cause violent swaying motions and even catastrophic failure in improperly constructed structures including bridges, buildings, trains, and aircraft. When designing objects, engineers must ensure the mechanical resonance frequencies of the component parts do not match driving vibrational frequencies of motors or other oscillating parts, a phenomenon known as resonance disaster.

Avoiding resonance disasters is a major concern in every building, tower, and bridge construction project. As a countermeasure, shock mounts can be installed to absorb resonant frequencies and thus dissipate the absorbed energy. The Taipei 101 building relies on a 660 t—a tuned mass damper—to cancel resonance. Furthermore, the structure is designed to resonate at a frequency that does not typically occur. Buildings in seismic zones are often constructed to take into account the oscillating frequencies of expected ground motion. In addition, engineers designing objects having engines must ensure that the mechanical resonant frequencies of the component parts do not match driving vibrational frequencies of the motors or other strongly oscillating parts.

Clocks keep time by mechanical resonance in a balance wheel, pendulum, or quartz crystal.

The cadence of runners has been hypothesized to be energetically favorable due to resonance between the elastic energy stored in the lower limb and the mass of the runner.

Acoustic resonance is a branch of mechanical resonance that is concerned with the mechanical vibrations across the frequency range of human hearing, in other words sound. For humans, hearing is normally limited to frequencies between about 20 Hz and 20,000 Hz (20 kHz), Many objects and materials act as resonators  with resonant frequencies within this range, and when struck vibrate mechanically, pushing on the surrounding air to create sound waves. This is the source of many percussive sounds we hear.

Acoustic resonance is an important consideration for instrument builders, as most acoustic instruments use resonators, such as the strings and body of a violin, the length of tube in a flute, and the shape of, and tension on, a drum membrane.

Like mechanical resonance, acoustic resonance can result in catastrophic failure of the object at resonance. The classic example of this is breaking a wine glass with sound at the precise resonant frequency of the glass, although this is difficult in practice.

International Space Station
The rocket engines for the International Space Station (ISS) are controlled by an autopilot. Ordinarily, uploaded parameters for controlling the engine control system for the Zvezda module make the rocket engines boost the International Space Station to a higher orbit. The rocket engines are hinge-mounted, and ordinarily the crew does not notice the operation. On January 14, 2009, however, the uploaded parameters made the autopilot swing the rocket engines in larger and larger oscillations, at a frequency of 0.5 Hz. These oscillations were captured on video, and lasted for 142 seconds.

Electrical

Electrical resonance occurs in an electric circuit at a particular resonant frequency when the impedance of the circuit is at a minimum in a series circuit or at maximum in a parallel circuit (usually when the transfer function peaks in absolute value). Resonance in circuits are used for both transmitting and receiving wireless communications such as television, cell phones and radio.

Optical
An optical cavity, also called an optical resonator, is an arrangement of mirrors that forms a standing wave cavity resonator for light waves. Optical cavities are a major component of lasers, surrounding the gain medium and providing feedback of the laser light. They are also used in optical parametric oscillators and some interferometers. Light confined in the cavity reflects multiple times producing standing waves for certain resonant frequencies. The standing wave patterns produced are called "modes". Longitudinal modes differ only in frequency while transverse modes differ for different frequencies and have different intensity patterns across the cross-section of the beam. Ring resonators and whispering galleries are examples of optical resonators that do not form standing waves.

Different resonator types are distinguished by the focal lengths of the two mirrors and the distance between them; flat mirrors are not often used because of the difficulty of aligning them precisely. The geometry (resonator type) must be chosen so the beam remains stable, i.e., the beam size does not continue to grow with each reflection. Resonator types are also designed to meet other criteria such as minimum beam waist or having no focal point (and therefore intense light at that point) inside the cavity.

Optical cavities are designed to have a very large Q factor. A beam reflects a large number of times with little attenuation—therefore the frequency line width of the beam is small compared to the frequency of the laser.

Additional optical resonances are guided-mode resonances and surface plasmon resonance, which result in anomalous reflection and high evanescent fields at resonance. In this case, the resonant modes are guided modes of a waveguide or surface plasmon modes of a dielectric-metallic interface. These modes are usually excited by a subwavelength grating.

Orbital
In celestial mechanics, an orbital resonance occurs when two orbiting bodies exert a regular, periodic gravitational influence on each other, usually due to their orbital periods being related by a ratio of two small integers. Orbital resonances greatly enhance the mutual gravitational influence of the bodies. In most cases, this results in an unstable interaction, in which the bodies exchange momentum and shift orbits until the resonance no longer exists. Under some circumstances, a resonant system can be stable and self-correcting, so that the bodies remain in resonance. Examples are the 1:2:4 resonance of Jupiter's moons Ganymede, Europa, and Io, and the 2:3 resonance between Pluto and Neptune. Unstable resonances with Saturn's inner moons give rise to gaps in the rings of Saturn. The special case of 1:1 resonance (between bodies with similar orbital radii) causes large Solar System bodies to clear the neighborhood around their orbits by ejecting nearly everything else around them; this effect is used in the current definition of a planet.

Atomic, particle, and molecular
Nuclear magnetic resonance (NMR) is the name given to a physical resonance phenomenon involving the observation of specific quantum mechanical magnetic properties of an atomic nucleus in the presence of an applied, external magnetic field. Many scientific techniques exploit NMR phenomena to study molecular physics, crystals, and non-crystalline materials through NMR spectroscopy. NMR is also routinely used in advanced medical imaging techniques, such as in magnetic resonance imaging (MRI).

All nuclei containing odd numbers of nucleons have an intrinsic magnetic moment and angular momentum. A key feature of NMR is that the resonant frequency of a particular substance is directly proportional to the strength of the applied magnetic field. It is this feature that is exploited in imaging techniques; if a sample is placed in a non-uniform magnetic field then the resonant frequencies of the sample's nuclei depend on where in the field they are located. Therefore, the particle can be located quite precisely by its resonant frequency.

Electron paramagnetic resonance, otherwise known as electron spin resonance (ESR), is a spectroscopic technique similar to NMR, but uses unpaired electrons instead. Materials for which this can be applied are much more limited since the material needs to both have an unpaired spin and be paramagnetic.

The Mössbauer effect is the resonant and recoil-free emission and absorption of gamma ray photons by atoms bound in a solid form.

Resonance in particle physics appears in similar circumstances to classical physics at the level of quantum mechanics and quantum field theory. Resonances can also be thought of as unstable particles, with the formula in the Universal resonance curve section of this article applying if Γ is the particle's decay rate and Ω is the particle's mass M. In that case, the formula comes from the particle's propagator, with its mass replaced by the complex number M + iΓ. The formula is further related to the particle's decay rate by the optical theorem.

Disadvantages
A column of soldiers marching in regular step on a narrow and structurally flexible bridge can set it into dangerously large amplitude oscillations. On April 12, 1831, the Broughton Suspension Bridge near Salford, England collapsed while a group of British soldiers were marching across. Since then, the British Army has had a standing order for soldiers to break stride when marching across bridges, to avoid resonance from their regular marching pattern affecting the bridge.

Vibrations of a motor or engine can induce resonant vibration in its supporting structures if their natural frequency is close to that of the vibrations of the engine. A common example is the rattling sound of a bus body when the engine is left idling.

Structural resonance of a suspension bridge induced by winds can lead to its catastrophic collapse. Several early suspension bridges in Europe and United States were destroyed by structural resonance induced by modest winds. The collapse of the Tacoma Narrows Bridge on 7 November 1940 is characterized in physics as a classic example of resonance. It has been argued by Robert H. Scanlan and others that the destruction was instead caused by aeroelastic flutter, a complicated interaction between the bridge and the winds passing through it—an example of a self oscillation, or a kind of "self-sustaining vibration" as referred to in the nonlinear theory of vibrations.

Q factor
The Q factor or quality factor is a dimensionless parameter that describes how under-damped an oscillator or resonator is, and characterizes the bandwidth of a resonator relative to its center frequency. A high value for Q indicates a lower rate of energy loss relative to the stored energy, i.e., the system is lightly damped. The parameter is defined by the equation: $$ Q =2\pi \text{ } \frac{ \text{ maximum energy stored}}{ \text{total energy lost per cycle at resonance}} $$.

The higher the Q factor, the greater the amplitude at the resonant frequency, and the smaller the bandwidth, or range of frequencies around resonance occurs. In electrical resonance, a high-Q circuit in a radio receiver is more difficult to tune, but has greater selectivity, and so would be better at filtering out signals from other stations. High Q oscillators are more stable.

Examples that normally have a low Q factor include door closers (Q=0.5). Systems with high Q factors include tuning forks (Q=1000), atomic clocks and lasers (Q≈1011).

Universal resonance curve

The exact response of a resonance, especially for frequencies far from the resonant frequency, depends on the details of the physical system, and is usually not exactly symmetric about the resonant frequency, as illustrated for the simple harmonic oscillator above. For a lightly damped linear oscillator with a resonance frequency Ω, the intensity of oscillations I when the system is driven with a driving frequency ω is typically approximated by a formula that is symmetric about the resonance frequency: $$I(\omega) \equiv |\chi|^2 \propto \frac{1}{(\omega - \Omega)^2 + \left( \frac{\Gamma}{2} \right)^2 }.$$

Where the susceptibility $$\chi(\omega) $$ links the amplitude of the oscillator to the driving force in frequency space: $$ x(\omega) = \chi(\omega) F(\omega) $$

The intensity is defined as the square of the amplitude of the oscillations. This is a Lorentzian function, or Cauchy distribution, and this response is found in many physical situations involving resonant systems. $ζ = 0.4$ is a parameter dependent on the damping of the oscillator, and is known as the linewidth of the resonance. Heavily damped oscillators tend to have broad linewidths, and respond to a wider range of driving frequencies around the resonant frequency. The linewidth is inversely proportional to the Q factor, which is a measure of the sharpness of the resonance.

In radio engineering and electronics engineering, this approximate symmetric response is known as the universal resonance curve, a concept introduced by Frederick E. Terman in 1932 to simplify the approximate analysis of radio circuits with a range of center frequencies and Q values.

title: Resonance


text:
Response

Response may refer to:
 * Call and response (music), musical structure
 * Reaction (disambiguation)
 * Request–response
 * Output or response, the result of telecommunications input
 * Response (liturgy), a line answering a versicle
 * Response (music) or antiphon, a response to a psalm or other part of a religious service
 * Response, a phase in emergency management
 * Response rate (survey)

Proper names and titles

 * Response, a print and online magazine of Christian thought published by Seattle Pacific University
 * Response (album), a studio album by Phil Wickham
 * Response (company), a call centre company based in Scotland
 * The Response (film)
 * The National War Memorial (Canada), titled The Response
 * The Northumberland Fusiliers Memorial in Newcastle upon Tyne, titled "The Response"

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Response


text:
Response time (technology)

In technology, response time is the time a system or functional unit takes to react to a given input.

Computing
In computing, the responsiveness of a service, how long a system takes to respond to a request for service, is measured through the response time. That service can be anything from a memory fetch, to a disk IO, to a complex database query, or loading a full web page. Ignoring transmission time for a moment, the response time is the sum of the service time and wait time. The service time is the time it takes to do the work you requested. For a given request the service time varies little as the workload increases – to do X amount of work it always takes X amount of time. The wait time is how long the request had to wait in a queue before being serviced and it varies from zero, when no waiting is required, to a large multiple of the service time, as many requests are already in the queue and have to be serviced first.

With basic queueing theory math you can calculate how the average wait time increases as the device providing the service goes from 0-100% busy. As the device becomes busier, the average wait time increases in a non-linear fashion. The busier the device is, the more dramatic the response time increases will seem as you approach 100% busy; all of that increase is caused by increases in wait time, which is the result of all the requests waiting in queue that have to run first.

Transmission time gets added to response time when your request and the resulting response has to travel over a network and it can be very significant. Transmission time can include propagation delays due to distance (the speed of light is finite), delays due to transmission errors, and data communication bandwidth limits (especially at the last mile) slowing the transmission speed of the request or the reply.

Developers can reduce the response time of a system (for end users or not) using program optimization techniques.

Real-time systems
In real-time systems the response time of a task or thread is defined as the time elapsed between the dispatch (time when task is ready to execute) to the time when it finishes its job (one dispatch). Response time is different from WCET which is the maximum time the task would take if it were to execute without interference. It is also different from deadline which is the length of time during which the task's output would be valid in the context of the specific system. And it has a relation to the TTFB, which is the time between the dispatch and the time when the response starts.

Display technologies
Response time is the amount of time a pixel in a display takes to change. It is measured in milliseconds (ms). Lower numbers mean faster transitions and therefore fewer visible image artifacts. Display monitors with long response times would create display motion blur around moving objects, making them unacceptable for rapidly moving images. Response times are usually measured from grey-to-grey transitions, based on a VESA industry standard from the 10% to the 90% points in the pixel response curve.

In fast paced competitive games such as Counter-Strike, the response time of a display is crucial for optimal performance. Displays that have a lower response time are more responsive to player input and produce less visual errors when displaying a rapidly changing image, making low response time important for competitive gaming. Most modern monitors that are marketed for gaming have a response time of 1ms, although it is not uncommon to see <1ms response time in high end monitors, and >1ms response time on less expensive monitors or monitors that have a higher resolution.

title: Response time (technology)


text:
Responsivity

Responsivity is a measure of the input–output gain of a detector system. In the specific case of a photodetector, it measures the electrical output per optical input.

A photodetector's responsivity is usually expressed in units of amperes or volts per watt of incident radiant power. For a system that responds linearly to its input, there is a unique responsivity. For nonlinear systems, the responsivity is the local slope. Many common photodetectors respond linearly as a function of the incident power.

Responsivity is a function of the wavelength of the incident radiation and of the sensor's properties, such as the bandgap of the material of which the photodetector is made. One simple expression for the responsivity R of a photodetector in which an optical signal is converted into an electric current (known as a photocurrent) is
 * $$R=\eta\frac{q}{hf}\approx\eta\frac{\lambda_{(\mu m)}}{1.23985(\mu m\times W/A)}$$

where $$\eta$$ is the quantum efficiency (the conversion efficiency of photons to electrons) of the detector for a given wavelength, $$q$$ is the electron charge, $$f$$ is the frequency of the optical signal, and $$h$$ is the Planck constant. This expression is also given in terms of $$\lambda$$, the wavelength of the optical signal, and has the unit of amperes per watt (A/W).

The term responsivity is also used to summarize input–output relationship in non-electrical systems. For example, a neuroscientist may measure how neurons in the visual pathway respond to light. In this case, responsivity summarizes the change in the neural response per unit signal strength. The responsivity in these applications can have a variety of units. The signal strength typically is controlled by varying either intensity (intensity-response function) or contrast (contrast-response function). The neural response measure depends on the part of the nervous system under study. For example, at the level of the retinal cones, the response might be in photocurrent. In the central nervous system the response is usually spikes per second. In functional neuroimaging, the response measure is usually BOLD contrast. The responsivity units reflect the relevant stimulus and physiological units.

When describing an amplifier, the more common term is gain.

Deprecated synonym sensitivity. A system's sensitivity is the inverse of the stimulus level required to produce a threshold response, with the threshold typically chosen just above the noise level.

title: Responsivity


text:
Restoration

Restoration is the act of restoring something to its original state. This may refer to:
 * Conservation and restoration of cultural property
 * Audio restoration
 * Conservation and restoration of immovable cultural property
 * Film restoration
 * Image restoration
 * Textile restoration
 * Restoration ecology
 * Environmental restoration

Restoration may also refer to:

Film and television

 * The Restoration (1909 film), a film by D.W. Griffith starring Mary Pickford
 * The Restoration (1910 film), an American silent short drama produced by the Thanhouser Company
 * The Restoration (2020 film), a Peruvian comedy film
 * Restoration (1995 film), a film by Michael Hoffman starring Robert Downey Jr
 * Restoration (2011 film), an Israeli film by Yossi Madmoni
 * Restoration (2016 film), an Australian science fiction thriller by Stuart Willis
 * Restoration (TV series), a BBC TV series
 * "Restoration" (Arrow), an episode of Arrow

History

 * Kenmu Restoration (1333) in Japan
 * Portuguese Restoration War (1640–1668)
 * Stuart Restoration (1660) in England, Wales and associated realms
 * Restoration (Ireland)
 * Restoration (Scotland)
 * Restoration in the English colonies
 * Restoration and Regeneration in Switzerland (1814–1830)
 * First Restoration in France (1814)
 * Bourbon Restoration in France (1815)
 * Restoration (Peru) (1839–1841), also called the Peruvian Restoration
 * Dominican Restoration War (1863–1865)
 * Meiji Restoration (1868) in Japan
 * Restoration (Spain) (1874–1931), also called the Bourbon Restoration
 * Manchu Restoration (1917) in China

Literature

 * Restoration comedy, English comedy written and performed in the English Restoration period of 1660–1710
 * Restoration (Berg novel), a 2002 novel by Carol Berg
 * Restoration (Ólafsson novel), a 2012 novel by Ólafur Jóhann Ólafsson
 * Restoration (Tremain novel), a 1989 novel by Rose Tremain set during the English Revolution
 * Restoration (newspaper), a Catholic newspaper published by the Madonna House Apostolate

Music

 * Restorations (band), an American rock band
 * Restoration (EP), an EP by Haken
 * Restoration (Lecrae album)
 * Restoration, half of the Revamp & Restoration double tribute album to Elton John and Bernie Taupin

Religion

 * Church of God (Restoration), denomination rooted in the holiness movement
 * Restoration (Latter Day Saints), doctrine of the Latter Day Saint movement
 * Restoration branches, independent Latter Day Saints organizations
 * Restoration Movement, a Christian movement originating in the 19th century that seeks to restore the doctrine and practice of the early church

Ships

 * HMS Restoration (1678), a third rate built by Betts
 * HMS Restoration (1706), a third rate

Other uses

 * Dental restoration
 * Restoration Hardware, a hardware store
 * Restoration style
 * Restoration of the Monarchy, a fashion label by Eric Villency
 * Foreskin restoration, the process of regaining some of the tissue lost in circumcision

title: Restoration


text:
Return loss

In telecommunications, return loss is a measure in relative terms of the power of the signal reflected by a discontinuity in a transmission line or optical fiber. This discontinuity can be caused by a mismatch between the termination or load connected to the line and the characteristic impedance of the line. It is usually expressed as a ratio in decibels (dB);

 * $$RL(\mathrm{dB}) = 10 \log_{10} {P_\mathrm i \over P_\mathrm r}$$
 * where RL(dB) is the return loss in dB, Pi is the incident power and Pr is the reflected power.

Return loss is related to both standing wave ratio (SWR) and reflection coefficient (Γ). Increasing return loss corresponds to lower SWR. Return loss is a measure of how well devices or lines are matched. A match is good if the return loss is high. A high return loss is desirable and results in a lower insertion loss.

From a certain perspective 'Return Loss' is a misnomer. The usual function of a transmission line is to convey power from a source to a load with minimal loss. If a transmission line is correctly matched to a load, the reflected power will be zero, no power will be lost due to reflection, and 'Return Loss' will be infinite. Conversely if the line is terminated in an open circuit, the reflected power will be equal to the incident power; all of the incident power will be lost in the sense that none of it will be transferred to a load, and RL will be zero. Thus the numerical values of RL tend in the opposite sense to that expected of a 'loss'.

Sign
As defined above, RL will always be positive, since Pr can never exceed Pi. However, return loss has historically been expressed as a negative number, and this convention is still widely found in the literature. Strictly speaking, if a negative sign is ascribed to RL, the ratio of reflected to incident power is implied;

 * $$RL'(\mathrm{dB}) = 10 \log_{10} {P_\mathrm r \over P_\mathrm i}$$
 * where RL'(dB) is the negative of RL(dB).

In practice, the sign ascribed to RL is largely immaterial. If a transmission line includes several discontinuities along its length, the total return loss will be the sum of the RLs caused by each discontinuity, and provided all RLs are given the same sign, no error or ambiguity will result. Whichever convention is used, it will always be understood that Pr can never exceed Pi.

Electrical
In metallic conductor systems, reflections of a signal traveling down a conductor can occur at a discontinuity or impedance mismatch. The ratio of the amplitude of the reflected wave Vr to the amplitude of the incident wave Vi is known as the reflection coefficient $$\Gamma$$.

 * $$\mathit \Gamma = {V_\mathrm r \over V_\mathrm i}$$

Return loss is the negative of the magnitude of the reflection coefficient in dB. Since power is proportional to the square of the voltage, return loss is given by,

 * $$RL(\mathrm{dB}) = -20 \log_{10} \left| \mathit \Gamma \right|$$

where the vertical bars indicate magnitude. Thus, a large positive return loss indicates the reflected power is small relative to the incident power, which indicates good impedance match between transmission line and load.

If the incident power and the reflected power are expressed in 'absolute' decibel units, (e.g., dBm), then the return loss in dB can be calculated as the difference between the incident power Pi (in absolute decibel units) and the reflected power Pr (also in absolute decibel units),

 * $$RL(\mathrm{dB}) = P_\mathrm i(\mathrm{dB}) - P_\mathrm r(\mathrm{dB})\,$$

Optical
In optics (particularly in fiber optics) a loss that takes place at discontinuities of refractive index, especially at an air-glass interface such as a fiber endface. At those interfaces, a fraction of the optical signal is reflected back toward the source. This reflection phenomenon is also called "Fresnel reflection loss," or simply "Fresnel loss."

Fiber optic transmission systems use lasers to transmit signals over optical fiber, and a low optical return loss (ORL) can cause the laser to stop transmitting correctly. The measurement of ORL is becoming more important in the characterization of optical networks as the use of wavelength-division multiplexing increases. These systems use lasers that have a lower tolerance for ORL, and introduce elements into the network that are located in close proximity to the laser.

 * $$\text{ORL}(\mathrm{dB}) = 10 \log_{10} {P_\mathrm i \over P_\mathrm r}$$

where $$\scriptstyle P_\mathrm r$$ is the reflected power and $$\scriptstyle P_\mathrm i$$ is the incident, or input, power.

title: Return loss


text:
RF power margin

In telecommunication, the term RF power margin has the following meanings:

 * 1) The amount of transmitter power above that which is computed by the link designer as the minimum required to meet specified link performance. The RF power margin allows for uncertainties in (a) empirical components of the signal level prediction method, (b) terrain characteristics, (c) atmospheric conditions, and (d) equipment performance parameters.
 * 2) At any given time in an operational link, the reserve transmitter power over that which is required to maintain specified link performance.

title: RF power margin


text:
Ringaround

In telecommunication, the term ringaround has the following meanings:

 * 1) The improper routing of a call back through a switching center already engaged in attempting to complete the same call.
 * 2) In secondary surveillance radar, the presence of false targets declared as a result of transponder interrogation by side lobes of the interrogating antenna.

title: Ringaround


text:
Ringdown

In telephony, ringdown is a method of signaling an operator in which telephone ringing current is sent over the line to operate a lamp or cause the operation of a self-locking relay known as a drop.

Ringdown is used in manual operation, and is distinguished from automatic signaling by dialing a number. The signal consists of a continuous or pulsed alternating current (AC) signal transmitted over the line. It may be used with or without a telephone switchboard. The term originated in magneto telephone signaling in which cranking the magneto generator, either integrated into the telephone set or housed in a connected ringer box, would not only ring its bell but also cause a drop to fall down at the telephone exchange switchboard, marked with the number of the line to which the magneto telephone instrument was connected. At the end of the conversation, one participant would crank to ring off, signaling the operator to take down the connection. In modern British English, "ring off" still means ending a telephone conversation, though it is of course done by other means. Ring off is also used figuratively to indicate no longer communicating with a person.

The last ringdown telephone exchange in the United States was located at Bryant Pond, Maine, had 400+ subscribers, and converted to dial service in October 1983.

Ringdown operator
In telephone systems where calls from distant automated exchanges arrive for manual subscribers or non-dialable points, there often would be a ringdown operator (reachable from the distant operator console by dialling NPA+181) who would manually ring the desired subscriber on a party line or toll station. On some systems, this function was carried out by the inward operator (NPA+121). In both cases, this is a telephone operator at the destination who provides assistance solely to other operators on inbound toll calls; the ringdown operator nominally cannot be dialed directly by the subscriber.

Non-operator use
In an application not involving a telephone operator, a two-point automatic ringdown circuit, or ringdown, has a telephone at each end. When the telephone at one end goes off-hook, the phone at the other end instantly rings. No dialing is involved and therefore telephone sets without dials are sometimes used.

Many ringdown circuits work in both directions. In some cases a circuit is designed to work in one direction only. That is, going off-hook at one end (end A) rings the other (end B). Going off-hook at end B has no effect at end A.

Ringdown features are often part of a key telephone system. In the wire spring relay key service units of the Bell System 1A2, a model 216 automatic ringdown was used to operate the circuit. In the 400-series units, a number of different KTUs operate (supervise) a ringdown, including the model 415. In other situations, the ringdown is powered and operated by equipment inside the telephone exchange.

In the case of enterprises with a private branch exchange (PBX) switch, the ringdown can be operated by the PBX key. The switch is programmed to ring a specific extension (the called phone) when a defined extension (the calling phone) goes off-hook. The PBX does not offer dial tone to the calling extension: it only detects on-hook or off-hook status.

Voice over IP adapters can be networked and configured to provide automatic ringdown by selecting a dial plan which replaces the empty string with a predefined number or SIP address, dialed immediately. (Some Cisco VoIP phones and analog adapters treat a dial plan of (S0 <:1234567890>) as a hotline configuration which dials 1-234-567890 zero seconds after the telephone is taken off-hook, for instance).

These circuits are used:

 * over high-volume routes where one site calls another very frequently.
 * Example: an information desk and the information desk staff supervisor's desk.

 * where a tamper-proof ability to call from one point to another is needed.
 * Example: a phone used to summon a taxicab to an airport or hotel.

 * where a limited ability to contact one entity (but no ability to make outside calls) is desired.
 * Example: a "house phone" in a hotel lobby to the live operator at the hotel's switchboard

 * where the public, or users that are not trained in using a specific office telephone system, must place calls.
 * Example: the after-hours phone to reach the watchman from the front door at a warehouse.

 * in locations where emergencies are handled and the time required to dial digits would cause an unacceptable delay in handling of an emergency.
 * Example: an airport control tower to the airport's fire station or fire dispatch center.
 * Example: Independent System Operator (ISO) communication to a power plant.

 * in situations where the called party needs to be certain of who is calling.
 * Example: a hospital emergency department and an ambulance dispatch center.

In some cases, automatic ringdown circuits have one-to-many configurations. When one phone goes off-hook, a group of phones is made to ring simultaneously.

In cases where one or both ends of the circuit terminate in a key telephone system, a well designed system will have no hold feature on the ringdown circuit unless supervision provides a Calling Party Control (CPC) signal.

PLAR
Private line automatic ringdown (PLAR) is a type of analog signaling often used in telephone-based systems. When a device is taken off-hook, ringing voltage is automatically applied to a circuit to alert other stations on the line. When answered on another station, a call is maintained over the circuit. The telephone company switch is not involved in the process, making this a private line.

title: Ringdown


text:
Ringer equivalence number

The ringer equivalence number (REN) is a telecommunications measure that represents the electrical loading effect of a telephone ringer on a telephone line. In the United States, ringer equivalence was first defined by U.S. Code of Federal Regulations, Title 47, Part 68, based on the load that a standard Bell System model 500 telephone represented, and was later determined in accordance with specification ANSI/TIA-968-B (August 2009). Measurement systems analogous to the REN exist internationally.

Definition
The ringer equivalence of 1 represents the loading effect of a single traditional telephone ringing circuit, such as that within the Western Electric model 500 telephone. The ringer equivalence of modern telephone equipment may be significantly lower than 1. For example, externally powered electronic ringing telephones may have a value as low as 0.1, while modern line-powered telephones, in which the ringer is powered from the telephone line, typically have a REN of approximately 0.8.

In the United States, the FCC Part 68 specification defined REN 1 as equivalent to a 6930 Ω resistor in series with an 8 μF (microfarad) capacitor. The modern ANSI/TIA-968-B specification (August 2009) defines it as an impedance of 7000 Ω at 20  Hz (type A ringer), or 8000  Ω from 15  Hz to 68  Hz (type B ringer).

Maximum ringer equivalence
The total ringer load on a subscriber line is the sum of the ringer equivalences of all devices (phone, fax, a separate answerphone, etc.) connected to the line. This represents the overall loading effect of the subscriber equipment on the central office ringing current source. Subscriber telephone lines are usually limited to support a ringer equivalence of 5, per the federal specifications.

If the total allowable ringer load is exceeded, the phone circuit may fail to ring or otherwise malfunction. For example, call waiting, caller ID, and ADSL services are often affected by high ringer load.

Some analog telephone adapters for Internet telephony require analog telephones with low REN, for example, the AT&T 210 is a basic phone which does not require an external electrical connection and has a REN of 0.9B.

International specifications
In the United Kingdom a maximum of 4 is allowed on any British Telecom (BT) line.

In Australia a maximum of 3 is allowed on any Telstra or Optus Line.

In Canada it is called a load number (LN); which must not exceed 100. The LN of each device represents the percentage of total load allowed.

In Europe 1 REN used to be equivalent to an 1800 Ω resistor in series with a 1 μF capacitor. The latest ETSI specification (2003–09) calls for 1 REN to be greater than 16 kΩ at 25 Hz and 50 Hz.

title: Ringer equivalence number


text:
Ring latency

In a ring network, such as Token Ring, ring latency is the time required for a signal to propagate once around the ring. Ring latency may be measured in seconds or in bits at the data transmission rate. Ring latency includes signal propagation delays in the ring medium, the drop cables, and the data stations connected to the ring network.

title: Ring latency


text:
Round-trip delay

In telecommunications, round-trip delay (RTD) or round-trip time (RTT) is the amount of time it takes for a signal to be sent plus the amount of time it takes for acknowledgement of that signal having been received. This time delay includes propagation times for the paths between the two communication endpoints. In the context of computer networks, the signal is typically a data packet. RTT is commonly used interchangeably with ping time, which can be determined with the ping command. However, ping time may differ from experienced RTT with other protocols since the payload and priority associated with ICMP messages used by ping may differ from that of other traffic.

End-to-end delay is the length of time it takes for a signal to travel in one direction and is often approximated as half the RTT.

Protocol design
RTT is a measure of the amount of time taken for an entire message to be sent to a destination and for a reply to be sent back to the sender. The time to send the message to the destination in its entirety is known as the network latency, and thus RTT is twice the latency in the network plus a processing delay at the destination. The other sources of delay in a network that make up the network latency are processing delay in transmission, propagation time, transmission time and queueing time. Propagation time is dependent on distance. Transmission time for a message is proportional to the message size divided by the bandwidth. Thus higher bandwidth networks will have lower transmission time, but the propagation time will remain unchanged, and so RTT does fall with increased bandwidth, but the delay increasingly represents propagation time.

Networks with both high bandwidth and a high RTT (and thus high bandwidth-delay product) can have large amounts of data in transit at any given time. Such long fat networks require a special protocol design. One example is the TCP window scale option.

The RTT was originally estimated in TCP by:

 * $$\mathrm{RTT} = \alpha \cdot \mathrm{old\_RTT} + (1 - \alpha) \cdot \mathrm{new\_round\_trip\_sample}$$

where $$\alpha$$ is constant weighting factor ($$0 \leq \alpha < 1$$). Choosing a value for $$\alpha$$ close to 1 makes the weighted average immune to changes that last a short time (e.g., a single segment that encounters long delay). Choosing a value for $$\alpha$$ close to 0 makes the weighted average respond to changes in delay very quickly. This was improved by the Jacobson/Karels algorithm, which takes standard deviation into account as well. Once a new RTT is calculated, it is entered into the equation above to obtain an average RTT for that connection, and the procedure continues for every new calculation.

Wi-Fi
Accurate round-trip time measurements over Wi-Fi using IEEE 802.11mc are the basis for the Wi-Fi positioning system.

title: Round-trip delay


text:
Routing indicator

In telecommunication, the term routing indicator (RI) has the following meanings:

 * 1) In a message header, an address, i.e., group of characters, that specifies routing instructions for the transmission of the message to its final destination.

A Routing Indicator is a group of letters assigned to identify a station within a tape relay network to facilitate routing of traffic. It indicates the status of the station and may indicate its geographical area. The following factors are reflected in routing indicator assignment:

 * (a) National or international affiliation and service (when required) of the station.
 * (b) The geographical area in which the station is located or area from which it is served.
 * (c) Network status of the station, i.e., major or minor relay, or tributary stations.

Routing indicators consist of not less than four, and not more than seven letters, including suffixes. The intent of allocated letters and of letter position is as follows:

 * First Letter - The letter R or the letter “Q” appears as the first letter and distinguishes strategic/worldwide routing indicators from call signs, address groups and theater routing indicators.
 * Second Letter - this letter, in conjunction with the first letter, identifies the nation or international alliance to which allotted.
 * Third Letter - This letter position serves the following purposes:
 * 1) Normally identifies the geographical area in which a station is located or from which it is served.
 * 2) Exceptionally, may be used by nations or international alliances irrespective of geographical area for specific alternative purposes, such as when the capacity of assigned second letters is insufficient to meet the requirement, or when more than one geographical area is involved as in the case of a tributary actively connected to two different major relay stations. In conjunction with the second letter “J”, may be reallocated, on a national basis, to a country not listed.
 * Fourth Letter - This letter position serves a dual purpose as follows:
 * 1) Indicates major relay stations, as generated by assignment requirements.
 * 2) Identifies the service or other national/international entity, as shown in the delineation table.

 * (e) Fifth and Following Letters - These letters and positions, when added to the four letters of a major relay routing indicator, designate the minor relay or tributary stations of that major relay station.

title: Routing indicator


text:
Rubidium standard

A rubidium standard or rubidium atomic clock is a frequency standard in which a specified hyperfine transition of electrons in rubidium-87 atoms is used to control the output frequency.

Synopsis
The Rb standard is the most inexpensive, compact, and widely produced atomic clock, used to control the frequency of television stations, cell phone base stations, in test equipment, and global navigation satellite systems like GPS. Commercial rubidium clocks are less accurate than caesium atomic clocks, which serve as primary frequency standards, so a rubidium clock is usually used as a secondary frequency standard.

Commercial rubidium frequency standards operate by disciplining a crystal oscillator to the rubidium hyperfine transition of 6.8 GHz ($6,834,682,610.904 Hz$). The intensity of light from a rubidium discharge lamp that reaches a photodetector through a resonance cell will drop by about 0.1% when the rubidium vapor in the resonance cell is exposed to microwave power near the transition frequency. The crystal oscillator is stabilized to the rubidium transition by detecting the light dip while sweeping an RF synthesizer (referenced to the crystal) through the transition frequency.

title: Rubidium standard


text:
Rural radio service

Rural radiotelephone service (RRTS) provides basic, analog communications service between locations deemed so remote that traditional wireline service or service by other means is not feasible. RRTS uses channelized radio to provide radiotelephone services such as Basic Exchange Telephone Radio Service between a fixed subscriber location and a remote central office, private line service between a two fixed locations or interconnection between two or more central offices. RRTS does not enable mobile communications.

Licensing
In the United States, the Federal Communications Commission issues initial rural radiotelephone service licenses on a site-by-site basis. Once a license is issued, the licensee can sell or lease the license to another party.

The FCC service rules for rural radiotelephone are filed in 47 C.F.R. part 22 subpart F.

Technical information
In the United States, the ULS radio service code and description for rural radiotelephone licenses is CR – Rural Radiotelephone. The licensed spectrum is divided in 44 channels of 20 kHz each.

title: Rural radio service


text:
Saturation

Saturation, saturated, unsaturation or unsaturated may refer to:

Chemistry

 * Saturated and unsaturated compounds, a classification of compounds related to their ability to resist addition reactions
 * Degree of unsaturation
 * Saturated fat or saturated fatty acid
 * Unsaturated fat or unsaturated fatty acid
 * Non-susceptibility of an organometallic compound to oxidative addition
 * Saturation of protein binding sites
 * Saturation of enzymes with a substrate
 * Saturation of a solute in a solution, as related to the solute's maximum solubility at equilibrium
 * Supersaturation, where the concentration of a solute exceeds its maximum solubility at equilibrium
 * Undersaturation, where the concentration of a solute is less than its maximum solubility at equilibrium

Biology

 * Oxygen saturation, a clinical measure of the amount of oxygen in a patient's blood
 * Saturation pollination, a pollination technique
 * Saturated mutagenesis, a form of site-directed mutagenesis
 * Saturation (genetic), the observed number of mutations relative to the maximum amount possible
 * Ocean saturation, more than 2.3 billion years ago: see "Great Oxygenation Event"
 * Environmental saturation, environmental resistance to population growth: see "Logistic function" and "Carrying capacity"

Physics

 * Colorfulness § Saturation, see also: "Saturation intent", a rendering intent in color management
 * Thermodynamic state at lower temperature bound of superheated steam
 * Saturation (magnetic), the state when a magnetic material is fully magnetized
 * Saturated fluid or saturated vapor, contains as much thermal energy as it can without boiling or condensing
 * Saturated steam
 * Dew point, which is a temperature that occurs when atmospheric relative humidity reaches 100% and the air is saturated with moisture
 * Saturated absorption, a set-up that enables the precise determination of the transition frequency of an atom between its ground state and an optically excited state

Electronics

 * Saturation velocity, the maximum velocity charge carrier in a semiconductor attains in the presence of very high electric fields
 * Saturation, a region of operation of a
 * Saturation current, limit of flowing current through a device

Hydrology

 * Saturated zone, below the groundwater table
 * Unsaturated zone, above the groundwater table
 * Soil saturation, water content in a soil

Mathematics

 * Saturation (commutative algebra), the inverse image of the localization of an ideal or submodule
 * Saturated model, a concept in mathematical logic
 * Saturation arithmetic, in arithmetic, a version of arithmetic in which all operations are limited to fixed range
 * Saturation (graph theory), a categorization of vertices in graph theory
 * Saturated measure, if every locally measurable set is also measurable
 * Saturated multiplicatively closed sets, a concept in ring theory

Music

 * "Saturation (song)", a 1997 single by Australian group The Superjesus
 * Saturation (Urge Overkill album), 1993
 * Saturation (Vas Deferens Organization album), 1996
 * Saturation (Brockhampton album), 2017 (Also see Saturation II and Saturation III)

Other uses

 * Market saturation, in economics
 * Saturation diving

title: Saturation


text:
Scan

Scan, SCAN or Scanning may refer to:

Computing and electronics

 * Graham scan, an algorithm for finding the convex hull of a set of points in the plane
 * 3D scanning, of a real-world object or environment to collect three dimensional data
 * Counter-scanning, in physical micro and nanotopography measuring instruments like scanning probe microscope
 * Elevator algorithm or SCAN, a disk scheduling algorithm
 * Image scanning, an optical scan of images, printed text, handwriting or an object
 * Optical character recognition, optical recognition of printed text or printed sheet music
 * Port scanner, in computer networking
 * Prefix sum, an operation on lists that is also known as the scan operator
 * Raster scan, the rectangular pattern of image capture and reconstruction in television
 * Scan chain, a type of manufacturing test used with integrated circuits
 * Scan line, one line in a raster scanning pattern
 * Screen reading, on computers to quickly locate text elements and images
 * Shared Check Authorization Network (SCAN), a database of bad check writers and collection agency for bad checks
 * Space Communications and Navigation Program (SCaN), by NASA

Medical

 * Schedules for Clinical Assessment in Neuropsychiatry (SCAN), a set of psychiatric diagnostic tools by WHO
 * DMSA scan, a radionuclide scan used in kidney studies
 * Medical imaging, of the interior of a body
 * Medical ultrasound, the medical procedure for examining internal structures, especially when applied to developing foetuses in the womb
 * CT scan (computed tomography scan)
 * Magnetic resonance imaging, MRI scan
 * Switch access scanning, a technique that allows users with motor impairments to use a computer using switch access
 * Partner-assisted scanning, a technique that allows a person with severe disabilities to communicate

Businesses

 * Scan Furniture, a former US chain in Washington, D.C., US
 * SCAN Health Plan, not-for-profit health care company based in Long Beach, California, US
 * Scan AB or Scan Foods UK Ltd, the Swedish and UK subsidiaries of the Finnish HKScan
 * Seattle Community Access Network, a former TV channel in Seattle, Washington, US
 * Scan (company), a software company based in Provo, Utah, US

Publishing

 * Social Cognitive and Affective Neuroscience, a scientific journal
 * Scanning (journal), a scanning microscopy scientific journal published by Hindawi
 * Scan: Journal of Media Arts Culture, former online journal published by Macquarie University, Sydney, Australia
 * SCAN (newspaper), the student newspaper at Lancaster University, UK

Other uses

 * Scansion, in poetry
 * Scan reading, a method of speed reading
 * Scientific content analysis (SCAN), a disputed technique
 * "Scan" (Prison Break episode), an episode of the television series Prison Break

title: Scan


text:
Schematic

A schematic, or schematic diagram, is a designed representation of the elements of a system using abstract, graphic symbols rather than realistic pictures. A schematic usually omits all details that are not relevant to the key information the schematic is intended to convey, and may include oversimplified elements in order to make this essential meaning easier to grasp, as well as additional organization of the information.

For example, a subway map intended for passengers may represent a subway station with a dot. The dot is not intended to resemble the actual station at all but aims to give the viewer information without unnecessary visual clutter. A schematic diagram of a chemical process uses symbols in place of detailed representations of the vessels, piping, valves, pumps, and other equipment that compose the system, thus emphasizing the functions of the individual elements and the interconnections among them and suppresses their physical details. In an electronic circuit diagram, the layout of the symbols may not look anything like the circuit as it appears in the physical world: instead of representing the way the circuit looks, the schematic aims to capture, on a more general level, the way it works. This may be contrasted with a wiring diagram, which preserves the spatial relationships between each of its components.

Types
Schematics and other types of diagrams, e.g., {|style="width:100%"
 * style="vertical-align:top; width:25px;"|
 * style="vertical-align:top;"|

Electrical and electronic industry

In electrical and electronic industry, a schematic diagram is often used to describe the design of equipment. Schematic diagrams are often used for the maintenance and repair of electronic and electromechanical systems. While schematics were traditionally drawn by hand, using standardized templates or pre-printed adhesive symbols, today electronic design automation software (EDA or "electrical CAD") is often used.

In electronic design automation, until the 1980s schematics were virtually the only formal representation for circuits. More recently, with the progress of computer technology, other representations were introduced and specialized computer languages were developed, since with the explosive growth of the complexity of electronic circuits, traditional schematics are becoming less practical. For example, hardware description languages are indispensable for modern digital circuit design.

Schematics for electronic circuits are prepared by designers using EDA (electronic design automation) tools called schematic capture tools or schematic entry tools. These tools go beyond simple drawing of devices and connections. Usually they are integrated into the whole design flow and linked to other EDA tools for verification and simulation of the circuit under design.

Programmable logic controllers (PLC) can be programmed using ladder diagrams.

In electric power systems design, a schematic drawing called a one-line diagram is frequently used to represent substations, distribution systems or even whole electrical power grids. These diagrams simplify and compress the details that would be repeated on each phase of a three-phase system, showing only one element instead of three. Electrical diagrams for switchgear often have common device functions designate by standard function numbers. Another type of diagram used for power systems is a three-line diagram.

For analysis purposes of a power system, from the one-line diagram, if the system is balanced, an equivalent per-phase (or single-phase) schematic diagram can be obtained. If all of the parameters are represented as impedances and voltage sources, the equivalent per-phase schematic diagram is called an impedance diagram. If all of the parameters are represented as admittances and current sources, the equivalent per-phase schematic diagram is called an admittance diagram.

If the power system is unbalanced, but it is linear (or can be approximated by a linear system), then Fortescue's theorem (symmetrical components) can be applied. In this way, from the one-line diagram, three different per-phase schematic diagrams are obtained, known as sequence diagrams: positive sequence diagram, negative sequence diagram, and zero sequence diagram. Each of these diagrams can be represented as an impedance diagram or as an admittance diagram.

Schematics in repair manuals
Schematic diagrams are used extensively in repair manuals to help users understand the interconnections of parts, and to provide graphical instruction to assist in dismantling and rebuilding mechanical assemblies. Many automotive and motorcycle repair manuals devote a significant number of pages to schematic diagrams.

title: Schematic


text:
Scrambler

In telecommunications, a scrambler is a device that transposes or inverts signals or otherwise encodes a message at the sender's side to make the message unintelligible at a receiver not equipped with an appropriately set descrambling device. Whereas encryption usually refers to operations carried out in the digital domain, scrambling usually refers to operations carried out in the analog domain. Scrambling is accomplished by the addition of components to the original signal or the changing of some important component of the original signal in order to make extraction of the original signal difficult. Examples of the latter might include removing or changing vertical or horizontal sync pulses in television signals; televisions will not be able to display a picture from such a signal. Some modern scramblers are actually encryption devices, the name remaining due to the similarities in use, as opposed to internal operation.

In telecommunications and recording, a scrambler (also referred to as a randomizer) is a device that manipulates a data stream before transmitting. The manipulations are reversed by a descrambler at the receiving side. Scrambling is widely used in satellite, radio relay communications and PSTN modems. A scrambler can be placed just before a FEC coder, or it can be placed after the FEC, just before the modulation or line code. A scrambler in this context has nothing to do with encrypting, as the intent is not to render the message unintelligible, but to give the transmitted data useful engineering properties.

A scrambler replaces sequences (referred to as whitening sequences) with other sequences without removing undesirable sequences, and as a result it changes the probability of occurrence of vexatious sequences. Clearly it is not foolproof as there are input sequences that yield all-zeros, all-ones, or other undesirable periodic output sequences. A scrambler is therefore not a good substitute for a line code, which, through a coding step, removes unwanted sequences.

Purposes of scrambling
A scrambler (or randomizer) can be either:
 * 1) An algorithm that converts an input string into a seemingly random output string of the same length (e.g., by pseudo-randomly selecting bits to invert), thus avoiding long sequences of bits of the same value; in this context, a randomizer is also referred to as a scrambler.
 * 2) An analog or digital source of unpredictable (i.e., high entropy), unbiased, and usually independent (i.e., random) output bits. A "truly" random generator may be used to feed a (more practical) deterministic pseudo-random random number generator, which extends the random seed value.

There are two main reasons why scrambling is used:

 * To enable accurate timing recovery on receiver equipment without resorting to redundant line coding. It facilitates the work of a timing recovery circuit (see also clock recovery), an automatic gain control and other adaptive circuits of the receiver (eliminating long sequences consisting of '0' or '1' only).
 * For energy dispersal on the carrier, reducing inter-carrier signal interference. It eliminates the dependence of a signal's power spectrum upon the actual transmitted data, making it more dispersed to meet maximum power spectral density requirements (because if the power is concentrated in a narrow frequency band, it can interfere with adjacent channels due to the intermodulation (also known as cross-modulation) caused by non-linearities of the receiving tract).

Scramblers are essential components of physical layer system standards besides interleaved coding and modulation. They are usually defined based on linear-feedback shift registers (LFSRs) due to their good statistical properties and ease of implementation in hardware.

It is common for physical layer standards bodies to refer to lower-layer (physical layer and link layer) encryption as scrambling as well. This may well be because (traditional) mechanisms employed are based on feedback shift registers as well.

Some standards for digital television, such as DVB-CA and MPE, refer to encryption at the link layer as scrambling.

Additive (synchronous) scramblers

Additive scramblers (they are also referred to as synchronous) transform the input data stream by applying a pseudo-random binary sequence (PRBS) (by modulo-two addition). Sometimes a pre-calculated PRBS stored in the read-only memory is used, but more often it is generated by a linear-feedback shift register (LFSR).

In order to assure a synchronous operation of the transmitting and receiving LFSR (that is, scrambler and descrambler), a sync-word must be used.

A sync-word is a pattern that is placed in the data stream through equal intervals (that is, in each frame). A receiver searches for a few sync-words in adjacent frames and hence determines the place when its LFSR must be reloaded with a pre-defined initial state.

The additive descrambler is just the same device as the additive scrambler.

Additive scrambler/descrambler is defined by the polynomial of its LFSR (for the scrambler on the picture above, it is $$1+z^{-14}+z^{-15}$$) and its initial state.

Multiplicative (self-synchronizing) scramblers

Multiplicative scramblers (also known as feed-through) are called so because they perform a multiplication of the input signal by the scrambler's transfer function in Z-space. They are discrete linear time-invariant systems. A multiplicative scrambler is recursive, and a multiplicative descrambler is non-recursive. Unlike additive scramblers, multiplicative scramblers do not need the frame synchronization, that is why they are also called self-synchronizing. Multiplicative scrambler/descrambler is defined similarly by a polynomial (for the scrambler on the picture it is $$1+z^{-18}+z^{-23}$$), which is also a transfer function of the descrambler.

Comparison of scramblers
Scramblers have certain drawbacks:
 * Both types may fail to generate random sequences under worst-case input conditions.
 * Multiplicative scramblers lead to error multiplication during descrambling (i.e. a single-bit error at the descrambler's input will result in w errors at its output, where w equals the number of the scrambler's feedback taps).
 * Additive scramblers must be reset by the frame sync; if this fails, massive error propagation will result, as a complete frame cannot be descrambled. (Alternatively if you know what was sent, the scrambler can be synchronized)
 * The effective length of the random sequence of an additive scrambler is limited by the frame length, which is normally much shorter than the period of the PRBS. By adding frame numbers to the frame sync, it is possible to extend the length of the random sequence, by varying the random sequence in accordance with the frame number.

Noise
The first voice scramblers were invented at Bell Labs in the period just before World War II. These sets consisted of electronics that could mix two signals or alternatively "subtract" one signal back out again. The two signals were provided by a telephone and a record player. A matching pair of records was produced, each containing the same recording of noise. The recording was played into the telephone, and the mixed signal was sent over the wire. The noise was then subtracted out at the far end using the matching record, leaving the original voice signal intact. Eavesdroppers would hear only the noisy signal, unable to understand the voice.

One of those, used (among other duties) for telephone conversations between Winston Churchill and Franklin D. Roosevelt was intercepted and unscrambled by the Germans. At least one German engineer had worked at Bell Labs before the war and came up with a way to break them. Later versions were sufficiently different that the German team was unable to unscramble them. Early versions were known as "A-3" (from AT&T Corporation). An unrelated device called SIGSALY was used for higher-level voice communications.

The noise was provided on large shellac phonograph records made in pairs, shipped as needed, and destroyed after use. This worked, but was enormously awkward. Just achieving synchronization of the two records proved difficult. Post-war electronics made such systems much easier to work with by creating pseudo-random noise based on a short input tone. In use, the caller would play a tone into the phone, and both scrambler units would then listen to the signal and synchronize to it. This provided limited security, however, as any listener with a basic knowledge of the electronic circuitry could often produce a machine of similar-enough settings to break into the communications.

Cryptographic
It was the need to synchronize the scramblers that suggested to James H. Ellis the idea for non-secret encryption, which ultimately led to the invention of both the RSA encryption algorithm and Diffie–Hellman key exchange well before either was reinvented publicly by Rivest, Shamir, and Adleman, or by Diffie and Hellman.

The latest scramblers are not scramblers in the truest sense of the word, but rather digitizers combined with encryption machines. In these systems the original signal is first converted into digital form, and then the digital data is encrypted and sent. Using modern public-key systems, these "scramblers" are much more secure than their earlier analog counterparts. Only these types of systems are considered secure enough for sensitive data.

Voice inversion scrambling can be as simple as inverting the frequency bands around a static point to various complex methods of changing the inversion point randomly and in real time and using multiple bands.

The "scramblers" used in cable television are designed to prevent casual signal theft, not to provide any real security. Early versions of these devices simply "inverted" one important component of the TV signal, re-inverting it at the client end for display. Later devices were only slightly more complex, filtering out that component entirely and then adding it by examining other portions of the signal. In both cases the circuitry could be easily built by any reasonably knowledgeable hobbyist. (see Television encryption.)

Electronic kits for scrambling and descrambling are available from hobbyist suppliers. Scanner enthusiasts often use them to listen in to scrambled communications at car races and some public-service transmissions. It is also common in FRS radios. This is an easy way to learn about scrambling.

The term "scrambling" is sometimes incorrectly used when jamming is meant.

Descramble
Descramble in cable television context is the act of taking a scrambled or encrypted video signal that has been provided by a cable television company for premium television services, processed by a scrambler and then supplied over a coaxial cable and delivered to the household where a set-top box reprocesses the signal, thus descrambling it and making it available for viewing on the television set. A descrambler is a device that restores the picture and sound of a scrambled channel. A descrambler must be used with a cable converter box to be able to unencrypt all of the premium & pay-per-view channels of a Cable Television System.

External links and references

 * DVB framing structure, channel coding and modulation for 11/12 GHz satellite services (EN 300 421)
 * V.34 ITU-T recommendation
 * Intelsat Earth Station Standard IESS-308

title: Scrambler


text:
Screen

Screen or Screens may refer to:

Arts

 * Screen printing or silkscreening, a printing method
 * Big screen, a nickname for motion pictures
 * Split screen (filmmaking), showing two or more images side by side
 * Stochastic screening and Halftone photographic screening, methods of simulating grays with one-color printing

Filtration and selection processes

 * Screening (economics), the process of identifying or selecting members of a population based on one or more selection criteria
 * Screening (biology), idem, on a scientific basis,
 * of which a genetic screen is a procedure to identify a particular kind of phenotype
 * the Irwin screen is a toxicological procedure
 * Sieve, a mesh used to separate fine particles from coarse ones
 * Mechanical screening, a unit operation in material handling which separates product into multiple grades by particle size

Media and music

 * "Screen", a song by Twenty One Pilots from Vessel
 * Screen International, a film magazine covering the international film markets
 * Screen (journal), a film and television studies journal published by Oxford University Press
 * Screen (magazine), a weekly entertainment magazine from India
 * The Screen (cinematheque), a theatre in Santa Fe, New Mexico, US
 * Screenonline, online film and television magazine produced by the British Film Institute
 * Screens (album), a 2009 album by Mint Chicks
 * Screen (Australian TV series), Australian television series on Foxtel Arts channel
 * "Screens", a song by Weezer from their 2021 album OK Human

Media display

 * Electronic visual display, a cathode ray tube or liquid crystal display (LCD)
 * Touchscreen, a display device that also takes input via embedded pressure sensors
 * Projection screen, a viewing surface
 * Display device, an output device for presentation of information in visual form
 * Computer monitor, a monitor for use with a computer
 * Television set, a device that combines a tuner, display, and loudspeakers

Barriers, separation or partitioning

 * Window screen, a plastic or wire mesh that covers a window opening
 * Screen door, a mesh, wire or plastic, that covers a door opening
 * Fire screen, a device to put in front of a fireplace
 * Windbreak of trees or shrubs
 * Windshield (windscreen), protects the driver of a vehicle
 * Folding screen, a piece of decorative furniture
 * Rainscreen, in building construction
 * Rood screen, a partition in a church which separates the chancel from the nave
 * Smoke screen, smoke released in order to mask the movement or location of military units
 * Parclose screen, a partition in a church, separate from the Rood screen

Software

 * GNU Screen, a computer program which multiplexes computer terminals
 * Another name for "dynpro" in ABAP programs
 * Screen (image blending), a blending method for digital images
 * Yahoo! Screen, a video streaming service

Sports

 * Screen (sports), when a player obstructs the vision or motion of another player
 * Screen (ice hockey), obstruction of a goaltender's view of the puck
 * Screen pass, a type of offensive play in American football

Other

 * Screen (bridge), a device used in some Bridge games that visually separates partners at the table from each other
 * Electronic page, an interface, scene, page, or group of content on an electronic display device
 * Pat Screen, Louisiana State University football player and Mayor-President of East Baton Rouge Parish, Louisiana
 * The conductive screen around the inner conductor(s) of an electrical cable, usually either foil or braided wire
 * "The Verdant Braes of Screen", an Irish song in which the name Screen refers to Ballinascreen in County Londonderry, Northern Ireland
 * SCREEN Holdings, a Japanese company in the technology manufacturing sector

title: Screen


text:
Secondary frequency standard

In telecommunications, a secondary frequency standard is a frequency standard that does not have inherent accuracy, and therefore must be calibrated against a primary frequency standard.

Secondary standards include crystal oscillators and rubidium standards. A crystal oscillator depends for its frequency on its physical dimensions, which vary with fabrication and environmental conditions. A rubidium standard is a secondary standard even though it uses atomic transitions, because it takes the form of a gas cell through which an optical signal is passed. The gas cell has inherent inaccuracies because of gas pressure variations, including those induced by temperature variations. There are also variations in the concentrations of the required buffer gases, which variations cause frequency deviations.

title: Secondary frequency standard