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Jitter

In electronics and telecommunications, jitter is the deviation from true periodicity of a presumably periodic signal, often in relation to a reference clock signal. In clock recovery applications it is called timing jitter. Jitter is a significant, and usually undesired, factor in the design of almost all communications links.

Jitter can be quantified in the same terms as all time-varying signals, e.g., root mean square (RMS), or peak-to-peak displacement. Also, like other time-varying signals, jitter can be expressed in terms of spectral density.

Jitter period is the interval between two times of maximum effect (or minimum effect) of a signal characteristic that varies regularly with time. Jitter frequency, the more commonly quoted figure, is its inverse. ITU-T G.810 classifies deviation lower frequencies below 10 Hz as wander and higher frequencies at or above 10 Hz as jitter.

Jitter may be caused by electromagnetic interference and crosstalk with carriers of other signals. Jitter can cause a display monitor to flicker, affect the performance of processors in personal computers, introduce clicks or other undesired effects in audio signals, and cause loss of transmitted data between network devices. The amount of tolerable jitter depends on the affected application.

Metrics
For clock jitter, there are three commonly used metrics:

 * Absolute jitter
 * The absolute difference in the position of a clock's edge from where it would ideally be.

 * Maximum time interval error (MTIE)
 * Maximum error committed by a clock under test in measuring a time interval for a given period of time.

 * Period jitter (a.k.a. cycle jitter)
 * The difference between any one clock period and the ideal or average clock period. Period jitter tends to be important in synchronous circuitry such as digital state machines where the error-free operation of the circuitry is limited by the shortest possible clock period (average period less maximum cycle jitter), and the performance of the circuitry is set by the average clock period. Hence, synchronous circuitry benefits from minimizing period jitter, so that the shortest clock period approaches the average clock period.

 * Cycle-to-cycle jitter
 * The difference in duration of any two adjacent clock periods. It can be important for some types of clock generation circuitry used in microprocessors and RAM interfaces.

In telecommunications, the unit used for the above types of jitter is usually the unit interval (UI) which quantifies the jitter in terms of a fraction of the transmission unit period. This unit is useful because it scales with clock frequency and thus allows relatively slow interconnects such as T1 to be compared to higher-speed internet backbone links such as OC-192. Absolute units such as picoseconds are more common in microprocessor applications. Units of degrees and radians are also used.

If jitter has a Gaussian distribution, it is usually quantified using the standard deviation of this distribution. This translates to an RMS measurement for a zero-mean distribution. Often, jitter distribution is significantly non-Gaussian. This can occur if the jitter is caused by external sources such as power supply noise. In these cases, peak-to-peak measurements may be more useful. Many efforts have been made to meaningfully quantify distributions that are neither Gaussian nor have a meaningful peak level. All have shortcomings but most tend to be good enough for the purposes of engineering work.

In computer networking, jitter can refer to packet delay variation, the variation (statistical dispersion) in the delay of the packets.

Types
One of the main differences between random and deterministic jitter is that deterministic jitter is bounded and random jitter is unbounded.

Random jitter
Random jitter, also called Gaussian jitter, is unpredictable electronic timing noise. Random jitter typically follows a normal distribution due to being caused by thermal noise in an electrical circuit.

Deterministic jitter
Deterministic jitter is a type of clock or data signal jitter that is predictable and reproducible. The peak-to-peak value of this jitter is bounded, and the bounds can easily be observed and predicted. Deterministic jitter has a known non-normal distribution. Deterministic jitter can either be correlated to the data stream (data-dependent jitter) or uncorrelated to the data stream (bounded uncorrelated jitter). Examples of data-dependent jitter are duty-cycle dependent jitter (also known as duty-cycle distortion) and intersymbol interference.

Total jitter
Total jitter (T) is the combination of random jitter (R) and deterministic jitter (D) and is computed in the context to a required bit error rate (BER) for the system:

in which the value of n is based on the BER required of the link.

A common BER used in communication standards such as Ethernet is 10−12.

Sampling jitter
In analog-to-digital and digital-to-analog conversion of signals, the sampling is normally assumed to be periodic with a fixed period—the time between every two samples is the same. If there is jitter present on the clock signal to the analog-to-digital converter or a digital-to-analog converter, the time between samples varies and instantaneous signal error arises. The error is proportional to the slew rate of the desired signal and the absolute value of the clock error. The effect of jitter on the signal depends on the nature of the jitter. Random jitter tends to add broadband noise while periodic jitter tends to add errant spectral components, "birdys". In some conditions, less than a nanosecond of jitter can reduce the effective bit resolution of a converter with a Nyquist frequency of 22 kHz to 14 bits.

Sampling jitter is an important consideration in high-frequency signal conversion, or where the clock signal is especially prone to interference.

In digital antenna arrays ADC and DAC jitters are the important factors determining the direction of arrival estimation accuracy and the depth of jammers suppression.

Packet jitter in computer networks
In the context of computer networks, packet jitter or packet delay variation (PDV) is the variation in latency as measured in the variability over time of the end-to-end delay across a network. A network with constant delay has no packet jitter. Packet jitter is expressed as an average of the deviation from the network mean delay. PDV is an important quality of service factor in assessment of network performance.

Transmitting a burst of traffic at a high rate followed by an interval or period of lower or zero rate transmission may also be seen as a form of jitter, as it represents a deviation from the average transmission rate. However, unlike the jitter caused by variation in latency, transmitting in bursts may be seen as a desirable feature, e.g. in variable bitrate transmissions.

Video and image jitter
Video or image jitter occurs when the horizontal lines of video image frames are randomly displaced due to the corruption of synchronization signals or electromagnetic interference during video transmission. Model-based dejittering study has been carried out under the framework of digital image and video restoration.

Testing
Jitter in serial bus architectures is measured by means of eye patterns. There are standards for jitter measurement in serial bus architectures. The standards cover jitter tolerance, jitter transfer function and jitter generation, with the required values for these attributes varying among different applications. Where applicable, compliant systems are required to conform to these standards.

Testing for jitter and its measurement is of growing importance to electronics engineers because of increased clock frequencies in digital electronic circuitry to achieve higher device performance. Higher clock frequencies have commensurately smaller eye openings, and thus impose tighter tolerances on jitter. For example, modern computer motherboards have serial bus architectures with eye openings of 160 picoseconds or less. This is extremely small compared to parallel bus architectures with equivalent performance, which may have eye openings on the order of 1000 picoseconds.

Jitter is measured and evaluated in various ways depending on the type of circuit under test. In all cases, the goal of jitter measurement is to verify that the jitter will not disrupt normal operation of the circuit.

Testing of device performance for jitter tolerance may involve injection of jitter into electronic components with specialized test equipment.

A less direct approach—in which analog waveforms are digitized and the resulting data stream analyzed—is employed when measuring pixel jitter in frame grabbers.

Anti-jitter circuits
Anti-jitter circuits (AJCs) are a class of electronic circuits designed to reduce the level of jitter in a clock signal. AJCs operate by re-timing the output pulses so they align more closely to an idealized clock. They are widely used in clock and data recovery circuits in digital communications, as well as for data sampling systems such as the analog-to-digital converter and digital-to-analog converter. Examples of anti-jitter circuits include phase-locked loop and delay-locked loop.

Jitter buffers
Jitter buffers or de-jitter buffers are buffers used to counter jitter introduced by queuing in packet-switched networks to ensure continuous playout of an audio or video media stream transmitted over the network. The maximum jitter that can be countered by a de-jitter buffer is equal to the buffering delay introduced before starting the play-out of the media stream. In the context of packet-switched networks, the term packet delay variation is often preferred over jitter.

Some systems use sophisticated delay-optimal de-jitter buffers that are capable of adapting the buffering delay to changing network characteristics. The adaptation logic is based on the jitter estimates computed from the arrival characteristics of the media packets. Adjustments associated with adaptive de-jittering involves introducing discontinuities in the media play-out which may be noticeable to the listener or viewer. Adaptive de-jittering is usually carried out for audio play-outs that include voice activity detection that allows the lengths of the silence periods to be adjusted, thus minimizing the perceptual impact of the adaptation.

Dejitterizer
A dejitterizer is a device that reduces jitter in a digital signal. A dejitterizer usually consists of an elastic buffer in which the signal is temporarily stored and then retransmitted at a rate based on the average rate of the incoming signal. A dejitterizer may not be effective in removing low-frequency jitter (wander).

Filtering and decomposition
A filter can be designed to minimize the effect of sampling jitter.

A jitter signal can be decomposed into intrinsic mode functions (IMFs), which can be further applied for filtering or dejittering.

title: Jitter


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Joint multichannel trunking and switching system

The Joint multichannel trunking and switching system is that composite multichannel trunking and switching system formed from assets of the Services, the Defense Communications System, other available systems, and/or assets controlled by the Joint Chiefs of Staff to provide an operationally responsive, survivable communication system, preferably in a mobile/transportable/recoverable configuration, for the joint force commander in an area of operations.

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


text: Talk:Journal/Attribution

title: Talk:Journal/Attribution


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Justify

Justify may refer to:
 * Justify (horse), winner of the 2018 U.S. Thoroughbred Triple Crown (Kentucky Derby, Preakness Stakes, and Belmont Stakes)
 * Justify (ANSI), an ANSI escape sequence
 * "Justify" (ATB song)
 * "Justify" (The Rasmus song)
 * "Justify", a song by The Red Jumpsuit Apparatus

title: Justify


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Kendall effect

In telecommunications the Kendall effect is a spurious pattern or other distortion in a facsimile.

It is caused by unwanted modulation products which arise from the transmission of the carrier signal, and appear in the form of a rectified baseband that interferes with the lower sideband of the carrier.

The Kendall effect occurs principally when the single-sideband width is greater than half of the facsimile carrier frequency.

title: Kendall effect


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K-factor

K-factor or K factor may refer to:

Engineering and technology

 * K-factor (aeronautics), the number of pulses expected for every one volumetric unit of fluid passing through a given flow meter
 * K-factor (centrifugation), relative pelleting efficiency of a given centrifuge rotor
 * K factor (crude oil refining), a system for classifying crude oil
 * K-factor (fire protection), formula used to calculate the discharge rate from a fire system nozzle
 * K factor (traffic engineering), the proportion of annual average daily traffic occurring in an hour

Mathematics and statistics

 * K-factor (actuarial), the ratio of the value of deferrable expenses to the value of estimated gross profits
 * k-factor (graph theory), a spanning k-regular subgraph in graph theory

Telecommunications

 * K-factor, the circular segment of earth profile that blocks off long-distance communications in line-of-sight propagation

Other uses

 * K-factor (Elo rating system), a constant used in Elo rating system
 * K-factor (marketing), the growth rate of websites, apps, or a customer base
 * K-factor (sheet metal), the ratio of location of the neutral line to the material thickness
 * The K Factor, a fictional TV show within Harry Hill's TV Burp
 * Bondi k-factor, the "k" in Bondi k-calculus

title: K-factor


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Label (disambiguation)

A label is any kind of tag attached to something so as to identify the object or its content. It may refer to:

 * Label, an identifier
 * Labelling, describing someone or something in a word or short phrase

Physical tags

 * Clothing label, referring either to a clothing brand, or to a physical tag on clothing
 * Museum label, for exhibitions in museums
 * Packaging and labelling, in industry

Arts, entertainment, and media

 * Label (TV series), an Indian web series
 * Labels, a 1930 travel book by Evelyn Waugh
 * "Labels", a song by GZA on the album Liquid Swords
 * Labels, a French record label created by Virgin Records, later a division of EMI Music France absorbed now into Warner Music.
 * Record label, a brand and a trademark associated with the marketing of music recordings and music videos
 * "Labels" (Dexter's Laboratory), an episode of Dexter's Laboratory

Computing

 * Label (command), a shell command
 * Label (control), a component of user interfaces
 * Label (computer science)
 * Tape label, human and/or machine readable metadata used by tape storage equipment
 * Label, in machine learning, a desired output for a given input in a dataset
 * Automatic label placement, computer methods of placing labels automatically on a map or chart
 * Labels, the parts of a domain name that are not "dots"
 * Revision tag, a textual label associated with a specific revision of a project

Other uses in science and technology

 * Isotopic labeling, a technique for tracking the passage of a sample of substance through a system
 * Labeling theory, or social reaction theory, a theory in sociology which ascribes labelling of people to control and identification of deviant behavior

Other uses

 * Label (heraldry), a charge closely resembling the strap with pendants which, from the saddle, crossed the horse's chest
 * Label, an older term for a long thin device, in particular, a ruler as on an astrolabe, circumferentor, or similar instrument
 * Label mould or hood mould, architectural moulding above windows to throw-off rainwater
 * Labeling (map design), or cartographic labeling, a form of typography that strongly deals with form, style, weight and size of type on a map
 * The Label language, an Oceanic language spoken in Papua New Guinea
 * Label (philately)

title: Label (disambiguation)


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Lambert's cosine law

In optics, Lambert's cosine law says that the radiant intensity or luminous intensity observed from an ideal diffusely reflecting surface or ideal diffuse radiator is directly proportional to the cosine of the angle θ between the observer's line of sight and the surface normal; I = I0 cos θ. The law is also known as the cosine emission law or Lambert's emission law. It is named after Johann Heinrich Lambert, from his Photometria, published in 1760.

A surface which obeys Lambert's law is said to be Lambertian, and exhibits Lambertian reflectance. Such a surface has the same radiance/luminance when viewed from any angle. This means, for example, that to the human eye it has the same apparent brightness. It has the same radiance because, although the emitted power from a given area element is reduced by the cosine of the emission angle, the solid angle, subtended by surface visible to the viewer, is reduced by the very same amount. Because the ratio between power and solid angle is constant, radiance (power per unit solid angle per unit projected source area) stays the same.

Lambertian scatterers and radiators
When an area element is radiating as a result of being illuminated by an external source, the irradiance (energy or photons /time/area) landing on that area element will be proportional to the cosine of the angle between the illuminating source and the normal. A Lambertian scatterer will then scatter this light according to the same cosine law as a Lambertian emitter. This means that although the radiance of the surface depends on the angle from the normal to the illuminating source, it will not depend on the angle from the normal to the observer. For example, if the moon were a Lambertian scatterer, one would expect to see its scattered brightness appreciably diminish towards the terminator due to the increased angle at which sunlight hit the surface. The fact that it does not diminish illustrates that the moon is not a Lambertian scatterer, and in fact tends to scatter more light into the oblique angles than a Lambertian scatterer.

The emission of a Lambertian radiator does not depend on the amount of incident radiation, but rather from radiation originating in the emitting body itself. For example, if the sun were a Lambertian radiator, one would expect to see a constant brightness across the entire solar disc. The fact that the sun exhibits limb darkening in the visible region illustrates that it is not a Lambertian radiator. A black body is an example of a Lambertian radiator.

Details of equal brightness effect
The situation for a Lambertian surface (emitting or scattering) is illustrated in Figures 1 and 2. For conceptual clarity we will think in terms of photons rather than energy or luminous energy. The wedges in the circle each represent an equal angle dΩ, of an arbitrarily chosen size, and for a Lambertian surface, the number of photons per second emitted into each wedge is proportional to the area of the wedge.

The length of each wedge is the product of the diameter of the circle and cos(θ). The maximum rate of photon emission per unit solid angle is along the normal, and diminishes to zero for θ = 90°. In mathematical terms, the radiance along the normal is I photons/(s·m2·sr) and the number of photons per second emitted into the vertical wedge is I dΩ dA. The number of photons per second emitted into the wedge at angle θ is I cos(θ) dΩ dA.

Figure 2 represents what an observer sees. The observer directly above the area element will be seeing the scene through an aperture of area dA0 and the area element dA will subtend a (solid) angle of dΩ0, which is a portion of the observer's total angular field-of-view of the scene. Since the wedge size dΩ was chosen arbitrarily, for convenience we may assume without loss of generality that it coincides with the solid angle subtended by the aperture when "viewed" from the locus of the emitting area element dA. Thus the normal observer will then be recording the same I dΩ dA photons per second emission derived above and will measure a radiance of

I_0=\frac{I\, d\Omega\, dA}{d\Omega_0\, dA_0} $$ photons/(s·m2·sr).

The observer at angle θ to the normal will be seeing the scene through the same aperture of area dA0 (still corresponding to a dΩ wedge) and from this oblique vantage the area element dA is foreshortened and will subtend a (solid) angle of dΩ0 cos(θ). This observer will be recording I cos(θ) dΩ dA photons per second, and so will be measuring a radiance of

I_0=\frac{I \cos(\theta)\, d\Omega\, dA}{d\Omega_0\, \cos(\theta)\, dA_0} =\frac{I\, d\Omega\, dA}{d\Omega_0\, dA_0} $$ photons/(s·m2·sr),

which is the same as the normal observer.

Relating peak luminous intensity and luminous flux
In general, the luminous intensity of a point on a surface varies by direction; for a Lambertian surface, that distribution is defined by the cosine law, with peak luminous intensity in the normal direction. Thus when the Lambertian assumption holds, we can calculate the total luminous flux, $$F_\text{tot}$$, from the peak luminous intensity, $$I_{\max}$$, by integrating the cosine law: $$\begin{align} F_\text{tot} &= \int_0^{2\pi} \int_0^{\pi/2} \cos(\theta) \, I_{\max}\, \sin(\theta)\,d\theta\,d\phi\\ &= 2\pi\cdot I_{\max}\int_0^{\pi/2}\cos(\theta)\sin(\theta)\,d\theta \\ &= 2\pi\cdot I_{\max}\int_0^{\pi/2}\frac{\sin(2\theta)}{2}\,d\theta \end{align}$$ and so
 * $$F_\text{tot}=\pi\,\mathrm{sr}\cdot I_{\max}$$

where $$\sin(\theta)$$ is the determinant of the Jacobian matrix for the unit sphere, and realizing that $$I_{\max}$$ is luminous flux per steradian. Similarly, the peak intensity will be $$1/(\pi\,\mathrm{sr})$$ of the total radiated luminous flux. For Lambertian surfaces, the same factor of $$\pi\,\mathrm{sr}$$ relates luminance to luminous emittance, radiant intensity to radiant flux, and radiance to radiant emittance. Radians and steradians are, of course, dimensionless and so "rad" and "sr" are included only for clarity.

Example: A surface with a luminance of say 100 cd/m2 (= 100 nits, typical PC monitor) will, if it is a perfect Lambert emitter, have a luminous emittance of 100π lm/m2. If its area is 0.1 m2 (~19" monitor) then the total light emitted, or luminous flux, would thus be 31.4 lm.

title: Lambert's cosine law


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Launch angle

In fiber optic telecommunications, the launch angle has the following meanings:

 * The angle, with respect to the normal, at which a light ray emerges from a surface.
 * The beam divergence at an emitting surface, such as that of a light-emitting diode (LED), laser, lens, prism, or optical fiber end face.
 * At an end face of an optical fiber, the angle between an input ray and the fiber axis. If the end face of the fiber is perpendicular to the fiber axis, the launch angle is equal to the angle of incidence.

In baseball, the "launch angle" is the angle, with respect to the ground level at home plate, at which a batted ball leaves the bat.

title: Launch angle


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Launch numerical aperture

In telecommunications, launch numerical aperture (LNA) is the numerical aperture of an optical system used to couple (launch) power into an optical fiber.

LNA may differ from the stated NA of a final focusing element if, for example, that element is underfilled or the focus is other than that for which the element is specified. LNA is one of the parameters that determine the initial distribution of power among the modes of an optical fiber.

title: Launch numerical aperture


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Layer

Layer or layered may refer to:

Arts, entertainment, and media

 * Layers (Kungs album)
 * Layers (Les McCann album)
 * Layers (Royce da 5′9″ album)
 * “Layers”, the title track of Royce da 5′9″’s sixth studio album
 * Layer, a female Maverick Hunter in the Mega Man X series
 * Layer, an element in a digital painting
 * Layer (film), a 2022 Russian film

Science

 * Stratum, a layer of rock or soil with internally consistent characteristics
 * Thermocline, a layer within a body of water where the temperature changes rapidly with depth
 * Layer, an area in the neocortex with specific structure and connection pattern among neurons

Computing

 * Layer (object-oriented design), a group of classes that have the same set of link-time module dependencies to other modules
 * Layers (digital image editing), used in digital image editing to separate different elements of an image
 * Layers, in 2D computer graphics
 * Abstraction layer, a way of hiding the implementation details of a particular set of functionality
 * Internet protocol suite layers
 * OSI model layers
 * Layer element, a deprecated -like tag, unique to Netscape 4 browsers
 * Layer of objects, a term in CAD
 * Map layer, a set of graphical information, especially in geographic information systems
 * Layer (deep learning), a structure in the architecture of a deep learning model, which take information from the previous layers and then pass information to the next layer

Electronics

 * Layer (electronics), a single thickness of some material covering a surface
 * Dual layer recording, a DVD layer
 * F region, or Appleton Layer in telecommunications

Other uses

 * Layer, a tier of archaeological deposits in an excavation
 * Layer hen, a hen raised to produce eggs
 * Layer cake, a cake consisting of stacked layers
 * Layered, Inc., an American software company
 * Layered clothing, the wearing of multiple layers of clothing for practical or fashion purposes
 * Layered hair, a popular hair-styling technique
 * Walter Francis Layer (1907-1965), American politician and U.S. Marine Corps colonel

title: Layer


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Layered system

In telecommunication, a layered system is a system in which components are grouped, i.e., layered, in a hierarchical arrangement, such that lower layers provide functions and services that support the functions and services of higher layers.

Systems of ever-increasing complexity and capability can be built by adding or changing the layers to improve overall system capability while using the components that are still in place.

title: Layered system


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Leaky mode

A leaky mode or tunneling mode in an optical fiber or other waveguide is a mode having an electric field that decays monotonically for a finite distance in the transverse direction but becomes oscillatory everywhere beyond that finite distance. Such a mode gradually "leaks" out of the waveguide as it travels down it, producing attenuation even if the waveguide is perfect in every respect. In order for a leaky mode to be definable as a mode, the relative amplitude of the oscillatory part (the leakage rate) must be sufficiently small that the mode substantially maintains its shape as it decays.

Leaky modes correspond to leaky rays in the terminology of geometric optics. The propagation of light through optical fibre can take place via meridional rays or skew rays. These skew rays suffer only partial reflection while meridional rays are completely guided. Thus the modes allowing propagation of skew rays are called leaky modes. Some optical power is lost into clad due to these modes.

title: Leaky mode


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Linear polarization

In electrodynamics, linear polarization or plane polarization of electromagnetic radiation is a confinement of the electric field vector or magnetic field vector to a given plane along the direction of propagation. The term linear polarization (French: polarisation rectiligne) was coined by Augustin-Jean Fresnel in 1822. See polarization and plane of polarization for more information.

The orientation of a linearly polarized electromagnetic wave is defined by the direction of the electric field vector. For example, if the electric field vector is vertical (alternately up and down as the wave travels) the radiation is said to be vertically polarized.

Mathematical description
The classical sinusoidal plane wave solution of the electromagnetic wave equation for the electric and magnetic fields is (cgs units)
 * $$ \mathbf{E} ( \mathbf{r}, t ) = |\mathbf{E}| \mathrm{Re} \left \{  |\psi\rangle  \exp \left [ i \left  ( kz-\omega t  \right ) \right ] \right \}  $$

 * $$ \mathbf{B} ( \mathbf{r}, t ) = \hat { \mathbf{z} } \times \mathbf{E} ( \mathbf{r} , t )/c  $$

for the magnetic field, where k is the wavenumber,

 * $$ \omega_{ }^{ } = c k$$

is the angular frequency of the wave, and $$ c $$ is the speed of light.

Here $$ \mid\mathbf{E}\mid    $$ is the amplitude of the field and

 * $$  |\psi\rangle  \ \stackrel{\mathrm{def}}{=}\  \begin{pmatrix} \psi_x  \\ \psi_y   \end{pmatrix} =   \begin{pmatrix} \cos\theta \exp \left ( i \alpha_x \right )   \\ \sin\theta \exp \left ( i \alpha_y \right )   \end{pmatrix}   $$

is the Jones vector in the x-y plane.

The wave is linearly polarized when the phase angles $$ \alpha_x^{ }, \alpha_y $$ are equal,

 * $$   \alpha_x =  \alpha_y \ \stackrel{\mathrm{def}}{=}\   \alpha    $$.

This represents a wave polarized at an angle $$ \theta   $$ with respect to the x axis. In that case, the Jones vector can be written

 * $$  |\psi\rangle  =   \begin{pmatrix} \cos\theta    \\ \sin\theta   \end{pmatrix} \exp \left ( i \alpha \right )   $$.

The state vectors for linear polarization in x or y are special cases of this state vector.

If unit vectors are defined such that

 * $$  |x\rangle  \ \stackrel{\mathrm{def}}{=}\    \begin{pmatrix} 1    \\ 0  \end{pmatrix}    $$

and

 * $$  |y\rangle  \ \stackrel{\mathrm{def}}{=}\    \begin{pmatrix} 0    \\ 1  \end{pmatrix}    $$

then the polarization state can be written in the "x-y basis" as

 * $$  |\psi\rangle  =  \cos\theta \exp \left ( i \alpha \right ) |x\rangle + \sin\theta \exp \left ( i \alpha \right ) |y\rangle = \psi_x |x\rangle + \psi_y |y\rangle $$.

title: Linear polarization


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Line code

In telecommunication, a line code is a pattern of voltage, current, or photons used to represent digital data transmitted down a communication channel or written to a storage medium. This repertoire of signals is usually called a constrained code in data storage systems. Some signals are more prone to error than others as the physics of the communication channel or storage medium constrains the repertoire of signals that can be used reliably.

Common line encodings are unipolar, polar, bipolar, and Manchester code.

Transmission and storage
After line coding, the signal is put through a physical communication channel, either a transmission medium or data storage medium. The most common physical channels are:
 * the line-coded signal can directly be put on a transmission line, in the form of variations of the voltage or current (often using differential signaling).
 * the line-coded signal (the baseband signal) undergoes further pulse shaping (to reduce its frequency bandwidth) and then is modulated (to shift its frequency) to create an RF signal that can be sent through free space.
 * the line-coded signal can be used to turn on and off a light source in free-space optical communication, most commonly used in an infrared remote control.
 * the line-coded signal can be printed on paper to create a bar code.
 * the line-coded signal can be converted to magnetized spots on a hard drive or tape drive.
 * the line-coded signal can be converted to pits on an optical disc.

Some of the more common binary line codes include:

Each line code has advantages and disadvantages. Line codes are chosen to meet one or more of the following criteria:
 * Minimize transmission hardware
 * Facilitate synchronization
 * Ease error detection and correction
 * Achieve a target spectral density
 * Eliminate a DC component

Disparity
Most long-distance communication channels cannot reliably transport a DC component. The DC component is also called the disparity, the bias, or the DC coefficient. The disparity of a bit pattern is the difference in the number of one bits vs the number of zero bits. The running disparity is the running total of the disparity of all previously transmitted bits. The simplest possible line code, unipolar, gives too many errors on such systems, because it has an unbounded DC component.

Most line codes eliminate the DC component – such codes are called DC-balanced, zero-DC, or DC-free. There are three ways of eliminating the DC component:

 * Use a constant-weight code. Each transmitted code word in a constant-weight code is designed such that every code word that contains some positive or negative levels also contains enough of the opposite levels, such that the average level over each code word is zero. Examples of constant-weight codes include Manchester code and Interleaved 2 of 5.
 * Use a paired disparity code. Each code word in a paired disparity code that averages to a negative level is paired with another code word that averages to a positive level. The transmitter keeps track of the running DC buildup, and picks the code word that pushes the DC level back towards zero. The receiver is designed so that either code word of the pair decodes to the same data bits. Examples of paired disparity codes include alternate mark inversion, 8b/10b and 4B3T.
 * Use a scrambler. For example, the scrambler specified in for 64b/66b encoding.

Polarity
Bipolar line codes have two polarities, are generally implemented as RZ, and have a radix of three since there are three distinct output levels (negative, positive and zero). One of the principle advantages of this type of code is that it can eliminate any DC component. This is important if the signal must pass through a transformer or a long transmission line.

Unfortunately, several long-distance communication channels have polarity ambiguity. Polarity-insensitive line codes compensate in these channels. There are three ways of providing unambiguous reception of 0 and 1 bits over such channels:
 * Pair each code word with the polarity-inverse of that code word. The receiver is designed so that either code word of the pair decodes to the same data bits. Examples include alternate mark inversion, Differential Manchester encoding, coded mark inversion and Miller encoding.
 * differential coding each symbol relative to the previous symbol. Examples include MLT-3 encoding and NRZI.
 * Invert the whole stream when inverted syncwords are detected, perhaps using polarity switching

Run-length limited codes
For reliable clock recovery at the receiver, a run-length limitation may be imposed on the generated channel sequence, i.e., the maximum number of consecutive ones or zeros is bounded to a reasonable number. A clock period is recovered by observing transitions in the received sequence, so that a maximum run length guarantees sufficient transitions to assure clock recovery quality.

RLL codes are defined by four main parameters: m, n, d, k. The first two, m/n, refer to the rate of the code, while the remaining two specify the minimal d and maximal k number of zeroes between consecutive ones. This is used in both telecommunication and storage systems that move a medium past a fixed recording head.

Specifically, RLL bounds the length of stretches (runs) of repeated bits during which the signal does not change. If the runs are too long, clock recovery is difficult; if they are too short, the high frequencies might be attenuated by the communications channel. By modulating the data, RLL reduces the timing uncertainty in decoding the stored data, which would lead to the possible erroneous insertion or removal of bits when reading the data back. This mechanism ensures that the boundaries between bits can always be accurately found (preventing bit slip), while efficiently using the media to reliably store the maximal amount of data in a given space.

Early disk drives used very simple encoding schemes, such as RLL (0,1) FM code, followed by RLL (1,3) MFM code which were widely used in hard disk drives until the mid-1980s and are still used in digital optical discs such as CD, DVD, MD, Hi-MD and Blu-ray using EFM and EFMPLus codes. Higher density RLL (2,7) and RLL (1,7) codes became the de facto standards for hard disks by the early 1990s.

Synchronization
Line coding should make it possible for the receiver to synchronize itself to the phase of the received signal. If the clock recovery is not ideal, then the signal to be decoded will not be sampled at the optimal times. This will increase the probability of error in the received data.

Biphase line codes require at least one transition per bit time. This makes it easier to synchronize the transceivers and detect errors, however, the baud rate is greater than that of NRZ codes.

Other considerations
A line code will typically reflect technical requirements of the transmission medium, such as optical fiber or shielded twisted pair. These requirements are unique for each medium, because each one has different behavior related to interference, distortion, capacitance and attenuation.

Common line codes

 * 2B1Q
 * 4B3T
 * 4B5B
 * 6b/8b encoding
 * 8b/10b encoding
 * 64b/66b encoding
 * 128b/130b encoding
 * Alternate mark inversion (AMI)
 * Coded mark inversion (CMI)
 * EFMPlus, used in DVDs
 * Eight-to-fourteen modulation (EFM), used in compact discs
 * Hamming code
 * Hybrid ternary code
 * Manchester code and differential Manchester
 * Mark and space
 * MLT-3 encoding
 * Modified AMI codes: B8ZS, B6ZS, B3ZS, HDB3
 * Modified frequency modulation, Miller encoding and delay encoding
 * Non-return-to-zero (NRZ)
 * Non-return-to-zero, inverted (NRZI)
 * Pulse-position modulation (PPM)
 * Return-to-zero (RZ)
 * TC-PAM

Optical line codes

 * Alternate-Phase Return-to-Zero (APRZ)
 * Carrier-Suppressed Return-to-Zero (CSRZ)
 * Three of Six, Fiber Optical (TS-FO)

title: Line code


text:
Link

Link or Links may refer to:

Places

 * Link, West Virginia, an unincorporated community in the US
 * Link River, Klamath Falls, Oregon, US

People with the name

 * Link (singer) (Lincoln Browder, born 1964), American R&B singer
 * Link (surname)
 * Charles Lincoln "Link" Neal III of Rhett & Link (born 1978), American comedian and YouTuber
 * Link Wray (1929–2005), American rock-and-roll guitarist

Devices

 * Link, a single element of a chain
 * Link-and-pin coupler

Computing

 * Hyperlink, from one electronic document to another
 * link (Unix), command-line program to link directory entries
 * , a type of HTML element
 * Link, in a linked list
 * Linker (computing), converts object files to executable
 * Links (web browser)
 * Microsoft Office Assistant Links, an animated cat
 * Link layer in computer networking
 * ln (Unix), command-line program to create a link to a file
 * Chainlink (blockchain), a cryptocurrency

Data networks

 * Link (Indonesia), an interbank network
 * LINK (UK), a cash machine network
 * Link+, for interlibrary loan in California and Nevada, US

Mathematics

 * Simplicial link, a set of simplices "surrounding" a given vertex in a simplicial complex.
 * Link (knot theory), a collection of knots entangled with one another
 * Link function in statistics

Other uses in science and technology

 * Link (Mars), a rock outcrop
 * Link or linking col, used in determining topographic prominence
 * Telecommunications link, communication channel between two or more devices

Fictional characters

 * Link (The Legend of Zelda), in The Legend of Zelda media
 * Link (The Matrix), in Matrix media
 * Link, in the 1993 novel Stone Cold
 * Link (Linkovitch Chomofsky), in the 1992 film Encino Man
 * Link Hogthrob, in The Muppets
 * Link Larkin, in the musical Hairspray

Games

 * Links (series), computer-simulated golf game by Access Software
 * Pokémon Link!, a 2005 puzzle game for the Nintendo DS

Music

 * "Link" (L'Arc-en-Ciel song), 2005
 * "Link" (Porno Graffitti song), 2007
 * Links (Kerfuffle album), a 2006 album by English folk band Kerfuffle
 * Links (Mark Murphy album), a 2001 album by Mark Murphy
 * The Link (album), by French death metal band Gojira

Periodicals

 * Link (magazine), a free publication of The Greenville News in Greenville, South Carolina, US
 * Links (magazine), a US golf magazine
 * The Link (newspaper), a student newspaper at Concordia University, Canada
 * The Link, the newsletter of the organization Americans for Middle East Understanding

Television

 * Link TV, US network
 * The Link (game show), UK, 2014–2015
 * The Link (TV program), US, 2011 documentary
 * The Link, a TV series by aptn Kids, Canada
 * Link: Eat, Love, Kill, a 2022 South Korean television series

Other uses in arts, entertainment, and media

 * Link (film), a 1986 horror movie featuring a super-intelligent, murderous orangutan
 * WLNK (formerly 107.9 the Link), a radio station in Charlotte, North Carolina, US

Businesses

 * Air Link, New South Wales, Australia
 * Hong Kong Link, toll tunnels and bridges company
 * Link REIT, Hong Kong real estate investment trust
 * The Link (retailer), UK mobile phone retailer
 * Link Aviation Devices, a manufacturer of aircraft simulator, now a subsidiary of L3 Technologies

Other organizations and programs

 * HOL LiNK program (Literacy and Numeracy Knowledge), by Hands On Learning Australia
 * Liberty in North Korea (LiNK), a refugee resettling group
 * Link Campus University, Rome, Italy
 * LINKS units, later student volunteering units, of St John Ambulance in England and Wales
 * Local involvement networks (LINks), National Health Service England
 * Project LINK, a UN project to build global macroeconomic models
 * The Link (UK organization) for "Anglo-German friendship", UK, 1937
 * The Links, a social and service organization of American Black women

Transportation systems

 * Link bus rapid transit, a planned line in Rochester, Minnesota, US
 * Link bus services, Auckland, New Zealand
 * Link light rail, Seattle, Washington, US
 * Terminal Link, Toronto Airport, Canada
 * San Leandro LINKS, a bus service, California, US

Other uses

 * Link (unit), surveying length unit
 * Link, a single sausage in a string
 * Links (golf), a coastal golf course
 * The Link (skyscraper), France
 * The Links, the mascot of Lincoln High School (Lincoln, Nebraska)

title: Link


text:
Link level

For computer networking, Link level: In the hierarchical structure of a primary or secondary station, the conceptual level of control or data processing logic that controls the data link.

Note: Link-level functions provide an interface between the station high-level logic and the data link. Link-level functions include (a) transmit bit injection and receive bit extraction, (b) address and control field interpretation, (c) command response generation, transmission and interpretation, and (d) frame check sequence computation and interpretation.

title: Link level


text:
Link quality analysis

In adaptive high-frequency (HF) radio, link quality analysis (LQA) is the overall process by which measurements of signal quality are made, assessed, and analyzed.

In LQA, signal quality is determined by measuring, assessing, and analyzing link parameters, such as bit error ratio (BER), and the levels of the ratio of signal-plus-noise-plus-distortion to noise-plus-distortion (SINAD). Measurements are stored at—and exchanged between—stations, for use in making decisions about link establishment.

For adaptive HF radio, LQA is automatically performed and is usually based on analyses of pseudo-BERs and SINAD readings.

title: Link quality analysis


text:
Load

Load or LOAD may refer to:

Aeronautics and transportation

 * Load factor (aeronautics), the ratio of the lift of an aircraft to its weight
 * Passenger load factor, the ratio of revenue passenger miles to available seat miles of a particular transportation operation (e.g. a flight)

Biology and medicine

 * Afterload, the maximum effect of a heartbeat driving blood mass out of the heart into the aorta and pulmonary arteries
 * Genetic load, of a population
 * Late-onset Alzheimer's disease (acronym: LOAD), a chronic neurodegenerative disease
 * Parasite load, of an organism
 * Viral load, of organisms and populations

Computing and electricity

 * Load (computing), a measure of how much processing a computer performs
 * Electrical load, a device connected to the output of a circuit
 * Electronic load, a simulated electrical load used for testing purposes
 * Invade-a-Load, was a fast loader routine used in software for the Commodore 64 computer; it was used in commercial computer games
 * Load balancing (computing), or load distribution, a method that improves the distribution of workloads across multiple computing resources
 * Load balancing (electrical power), or load distribution, the storing of excess electrical power by power stations during low demand periods, for release as demand rises
 * Load cell, a transducer that is used to create an electrical signal
 * Load factor (computer science), the ratio of the number of records to the number of addresses within a data structure
 * Load factor (electrical), the average power divided by the peak power over a period of time
 * Load file, the file used to import data into a database or to link images
 * Load management, also known as demand side management (DSM), the process of balancing the supply of electricity on the network with the electrical load
 * Load testing, the process of putting demand on a system and measuring its response

Mechanics, construction, and architecture

 * Add-on factor, or load factor, floor area, floor space, or floorspace, is the area (measured as square feet or square metres) taken up by a building or part of it
 * Mechanical load, the external mechanical resistance against which a machine, such as a motor or engine, acts
 * Structural load, forces which apply to a structure
 * Wind load
 * Moving load, this is the load that changes in time the place to which is applied

Music

 * Load Records, an American experimental independent record label
 * Load (album), the 6th album released by the band Metallica
 * Loads (album), a 1995 compilation of the British pop group Happy Mondays

Places

 * Load, Kentucky
 * Load Brook, a hamlet in England

Other uses

 * The Load, a 2018 Serbian war film
 * Cargo, paraphernalia being transported
 * Factor loadings, in statistics, the exposure to specific factors or components in Factor Analysis or Principal Component Analysis
 * Load fund, a mutual fund with a type of commission known as a load
 * Load, a sexual slang term for semen

title: Load


text:
Loading characteristic

In multichannel telephone systems, the loading characteristic is a plot, for the busy hour, of the equivalent mean power and the peak power as a function of the number of voice channels.

The equivalent power of a multichannel signal referred to the zero transmission level point is a function of the number of channels and has for its basis a specified voice channel mean power.

title: Loading characteristic


text:
Loading coil

A loading coil or load coil is an inductor that is inserted into an electronic circuit to increase its inductance. The term originated in the 19th century for inductors used to prevent signal distortion in long-distance telegraph transmission cables. The term is also used for inductors in radio antennas, or between the antenna and its feedline, to make an electrically short antenna resonant at its operating frequency.

The concept of loading coils was discovered by Oliver Heaviside in studying the problem of slow signalling speed of the first transatlantic telegraph cable in the 1860s. He concluded additional inductance was required to prevent amplitude and time delay distortion of the transmitted signal. The mathematical condition for distortion-free transmission is known as the Heaviside condition. Previous telegraph lines were overland or shorter and hence had less delay, and the need for extra inductance was not as great. Submarine communications cables are particularly subject to the problem, but early 20th century installations using balanced pairs were often continuously loaded with iron wire or tape rather than discretely with loading coils, which avoided the sealing problem.

Loading coils are historically also known as Pupin coils after Mihajlo Pupin, especially when used for the Heaviside condition and the process of inserting them is sometimes called pupinization.

Telephone lines
A common application of loading coils is to improve the voice-frequency amplitude response characteristics of the twisted balanced pairs in a telephone cable. Because twisted pair is a balanced format, half the loading coil must be inserted in each leg of the pair to maintain the balance. It is common for both these windings to be formed on the same core. This increases the flux linkages, without which the number of turns on the coil would need to be increased. Despite the use of common cores, such loading coils do not comprise transformers, as they do not provide coupling to other circuits.

Loading coils inserted periodically in series with a pair of wires reduce the attenuation at the higher voice frequencies up to the cutoff frequency of the low-pass filter formed by the inductance of the coils (plus the distributed inductance of the wires) and the distributed capacitance between the wires. Above the cutoff frequency, attenuation increases rapidly. The shorter the distance between the coils, the higher the cut-off frequency. The cutoff effect is an artifact of using lumped inductors. With loading methods using continuous distributed inductance there is no cutoff.

Without loading coils, the line response is dominated by the resistance and capacitance of the line with the attenuation gently increasing with frequency. With loading coils of exactly the right inductance, neither capacitance nor inductance dominate: the response is flat, waveforms are undistorted and the characteristic impedance is resistive up to the cutoff frequency. The coincidental formation of an audio frequency filter is also beneficial in that noise is reduced.

DSL
With loading coils, signal attenuation of a circuit remains low for signals within the passband of the transmission line but increases rapidly for frequencies above the audio cutoff frequency. If the telephone line is subsequently reused to support applications that require higher frequencies, such as in analog or digital carrier systems or digital subscriber line (DSL), loading coils must be removed or replaced. Using coils with parallel capacitors forms a filter with the topology of an m-derived filter and a band of frequencies above the cut-off is also passed. Without removal, for subscribers at an extended distance, e.g., over 4 miles (6.4 km) from the central office, DSL cannot be supported.

Carrier systems
American early and middle 20th century telephone cables had load coils at intervals of a mile (1.61 km), usually in coil cases holding many. The coils had to be removed to pass higher frequencies, but the coil cases provided convenient places for repeaters of digital T-carrier systems, which could then transmit a 1.5 Mbit/s signal that distance. Due to narrower streets and higher cost of copper, European cables had thinner wires and used closer spacing. Intervals of a kilometer allowed European systems to carry 2 Mbit/s.

Radio antenna
Another type of loading coil is used in radio antennas. Monopole and dipole radio antennas are designed to act as resonators for radio waves; the power from the transmitter, applied to the antenna through the antenna's transmission line, excites standing waves of voltage and current in the antenna element. To be “naturally” resonant, the antenna must have a physical length of one quarter of the wavelength of the radio waves used (or a multiple of that length, with odd multiples usually preferred). At resonance, the antenna acts electrically as a pure resistance, absorbing all the power applied to it from the transmitter.

In many cases, for practical reasons, it is necessary to make the antenna shorter than the resonant length, this is called an electrically short antenna. An antenna shorter than a quarter wavelength presents capacitive reactance to the transmission line. Some of the applied power is reflected back into the transmission line and travels back toward the transmitter. The two currents at the same frequency running in opposite directions causes standing waves on the transmission line, measured as a standing wave ratio (SWR) greater than one. The elevated currents waste energy by heating the wire, and can even overheat the transmitter.

To make an electrically short antenna resonant, a loading coil is inserted in series with the antenna. The coil is built to have an inductive reactance equal and opposite to the capacitive reactance of the short antenna, so the combination of reactances cancels. When so loaded the antenna presents a pure resistance to the transmission line, preventing energy from being reflected. The loading coil is often placed at the base of the antenna, between it and the transmission line (base loading), but for more efficient radiation, it is sometimes inserted near the midpoint of the antenna element (center loading).

Loading coils for powerful transmitters can have challenging design requirements, especially at low frequencies. The radiation resistance of short antennas can be very low, as low a few ohms in the LF or VLF bands, where antennas are commonly short and inductive loading is most needed. Because resistance in the coil winding is comparable to, or exceeds the radiation resistance, loading coils for extremely electrically short antennas must have extremely low AC resistance at the operating frequency. To reduce skin effect losses, the coil is often made of tubing or Litz wire, with single layer windings, with turns spaced apart to reduce proximity effect resistance. They must often handle high voltages. To reduce power lost in dielectric losses, the coil is often suspended in air supported on thin ceramic strips. The capacitively loaded antennas used at low frequencies have extremely narrow bandwidths, and therefore if the frequency is changed the loading coil must be adjustable to tune the antenna to resonance with the new transmitter frequency. Variometers are often used.

Bulk power transmission
To reduce losses due to high capacitance on long-distance bulk power transmission lines, inductance can be introduced to the circuit with a flexible AC transmission system (FACTS), a static VAR compensator, or a static synchronous series compensator. Series compensation can be thought of as an inductor connected to the circuit in series if it is supplying inductance to the circuit.

Campbell equation
The Campbell equation is a relationship due to George Ashley Campbell for predicting the propagation constant of a loaded line. It is stated as;

 * $$\cosh \left(\gamma'd\right) = \cosh (\gamma d) + \frac{Z}{2Z_0} \sinh (\gamma d)$$

where,

 * $$\gamma \!\,$$ is the propagation constant of the unloaded line
 * $$\gamma ' \!\,$$ is the propagation constant of the loaded line
 * $$d \!\,$$ is the interval between coils on the loaded line
 * $$Z \!\,$$ is the impedance of a loading coil and
 * $$Z_0 \!\,$$ is the characteristic impedance of the unloaded line.

A more engineer friendly rule of thumb is that the approximate requirement for spacing loading coils is ten coils per wavelength of the maximum frequency being transmitted. This approximation can be arrived at by treating the loaded line as a constant k filter and applying image filter theory to it. From basic image filter theory the angular cutoff frequency and the characteristic impedance of a low-pass constant k filter are given by;

 * $$\omega_c = \frac{1}{\sqrt{L_{\frac{1}{2}} C_{\frac{1}{2}}}}$$ and,  $$Z_0 = \sqrt{\frac{L_{\frac{1}{2}}}{C_{\frac{1}{2}}}}$$

where $L_{\frac{1}{2}}$ and $$C_{\frac{1}{2}}$$ are the half section element values.

From these basic equations the necessary loading coil inductance and coil spacing can be found;

 * $$L = \frac{Z_0}{\omega_c}$$ and,  $$d = \frac{2}{\omega_c Z_0 C}$$

where C is the capacitance per unit length of the line.

Expressing this in terms of number of coils per cutoff wavelength yields;

 * $$\frac{\lambda_c}{d} = \pi v Z_0 C$$

where v is the velocity of propagation of the cable in question.

Since $v = {1 \over Z_0 C}$ then

 * $$\frac{\lambda_c}{d} = \pi$$.

Campbell arrived at this expression by analogy with a mechanical line periodically loaded with weights described by Charles Godfrey in 1898 who obtained a similar result. Mechanical loaded lines of this sort were first studied by Joseph-Louis Lagrange (1736–1813).

The phenomenon of cutoff whereby frequencies above the cutoff frequency are not transmitted is an undesirable side effect of loading coils (although it proved highly useful in the development of filters). Cutoff is avoided by the use of continuous loading since it arises from the lumped nature of the loading coils.

Oliver Heaviside
The origin of the loading coil can be found in the work of Oliver Heaviside on the theory of transmission lines. Heaviside (1881) represented the line as a network of infinitesimally small circuit elements. By applying his operational calculus to the analysis of this network he discovered (1887) what has become known as the Heaviside condition. This is the condition that must be fulfilled in order for a transmission line to be free from distortion. The Heaviside condition is that the series impedance, Z, must be proportional to the shunt admittance, Y, at all frequencies. In terms of the primary line coefficients the condition is:

 * $$\frac{R}{G}=\frac{L}{C}$$

where:

 * $$R$$ is the series resistance of the line per unit length
 * $$L$$ is the series self-inductance of the line per unit length
 * $$G$$ is the shunt leakage conductance of the line insulator per unit length
 * $$C$$ is the shunt capacitance between the line conductors per unit length

Heaviside was aware that this condition was not met in the practical telegraph cables in use in his day. In general, a real cable would have,

 * $$\frac{R}{G} \gg \frac{L}{C}$$

This is mainly due to the low value of leakage through the cable insulator, which is even more pronounced in modern cables which have better insulators than in Heaviside's day. In order to meet the condition, the choices are therefore to try to increase G or L or to decrease R or C. Decreasing R requires larger conductors. Copper was already in use in telegraph cables and this is the very best conductor available short of using silver. Decreasing R means using more copper and a more expensive cable. Decreasing C would also mean a larger cable (although not necessarily more copper). Increasing G is highly undesirable; while it would reduce distortion, it would at the same time increase the signal loss. Heaviside considered, but rejected, this possibility which left him with the strategy of increasing L as the way to reduce distortion.

Heaviside immediately (1887) proposed several methods of increasing the inductance, including spacing the conductors further apart and loading the insulator with iron dust. Finally, Heaviside made the proposal (1893) to use discrete inductors at intervals along the line. However, he never succeeded in persuading the British GPO to take up the idea. Brittain attributes this to Heaviside's failure to provide engineering details on the size and spacing of the coils for particular cable parameters. Heaviside's eccentric character and setting himself apart from the establishment may also have played a part in their ignoring of him.

John Stone
John S. Stone worked for the American Telephone & Telegraph Company (AT&T) and was the first to attempt to apply Heaviside's ideas to real telecommunications. Stone's idea (1896) was to use a bimetallic iron-copper cable which he had patented. This cable of Stone's would increase the line inductance due to the iron content and had the potential to meet the Heaviside condition. However, Stone left the company in 1899 and the idea was never implemented. Stone's cable was an example of continuous loading, a principle that was eventually put into practice in other forms, see for instance Krarup cable later in this article.

George Campbell
George Campbell was another AT&T engineer working in their Boston facility. Campbell was tasked with continuing the investigation into Stone's bimetallic cable, but soon abandoned it in favour of the loading coil. His was an independent discovery: Campbell was aware of Heaviside's work in discovering the Heaviside condition, but unaware of Heaviside's suggestion of using loading coils to enable a line to meet it. The motivation for the change of direction was Campbell's limited budget.

Campbell was struggling to set up a practical demonstration over a real telephone route with the budget he had been allocated. After considering that his artificial line simulators used lumped components rather than the distributed quantities found in a real line, he wondered if he could not insert the inductance with lumped components instead of using Stone's distributed line. When his calculations showed that the manholes on telephone routes were sufficiently close together to be able to insert the loading coils without the expense of either having to dig up the route or lay in new cables he changed to this new plan. The very first demonstration of loading coils on a telephone cable was on a 46-mile length of the so-called Pittsburgh cable (the test was actually in Boston, the cable had previously been used for testing in Pittsburgh) on 6 September 1899 carried out by Campbell himself and his assistant. The first telephone cable using loaded lines put into public service was between Jamaica Plain and West Newton in Boston on 18 May 1900.

Campbell's work on loading coils provided the theoretical basis for his subsequent work on filters which proved to be so important for frequency-division multiplexing. The cut-off phenomena of loading coils, an undesirable side-effect, can be exploited to produce a desirable filter frequency response.

Michael Pupin
Michael Pupin, inventor and Serbian immigrant to the USA, also played a part in the story of loading coils. Pupin filed a rival patent to the one of Campbell's. This patent of Pupin's dates from 1899. There is an earlier patent (1894, filed December 1893) which is sometimes cited as Pupin's loading coil patent but is, in fact, something different. The confusion is easy to understand, Pupin himself claims that he first thought of the idea of loading coils while climbing a mountain in 1894, although there is nothing from him published at that time.

Pupin's 1894 patent "loads" the line with capacitors rather than inductors, a scheme that has been criticised as being theoretically flawed and never put into practice. To add to the confusion, one variant of the capacitor scheme proposed by Pupin does indeed have coils. However, these are not intended to compensate the line in any way. They are there merely to restore DC continuity to the line so that it may be tested with standard equipment. Pupin states that the inductance is to be so large that it blocks all AC signals above 50 Hz. Consequently, only the capacitor is adding any significant impedance to the line and "the coils will not exercise any material influence on the results before noted".

Legal battle
Heaviside never patented his idea; indeed, he took no commercial advantage of any of his work. Despite the legal disputes surrounding this invention, it is unquestionable that Campbell was the first to actually construct a telephone circuit using loading coils. There also can be little doubt that Heaviside was the first to publish and many would dispute Pupin's priority.

AT&T fought a legal battle with Pupin over his claim. Pupin was first to patent but Campbell had already conducted practical demonstrations before Pupin had even filed his patent (December 1899). Campbell's delay in filing was due to the slow internal machinations of AT&T.

However, AT&T foolishly deleted from Campbell's proposed patent application all the tables and graphs detailing the exact value of inductance that would be required before the patent was submitted. Since Pupin's patent contained a (less accurate) formula, AT&T was open to claims of incomplete disclosure. Fearing that there was a risk that the battle would end with the invention being declared unpatentable due to Heaviside's prior publication, they decided to desist from the challenge and buy an option on Pupin's patent for a yearly fee so that AT&T would control both patents. By January 1901 Pupin had been paid $200,000 ($13 million in 2011 ) and by 1917, when the AT&T monopoly ended and payments ceased, he had received a total of $455,000 ($25 million in 2011 ).

Benefit to AT&T
The invention was of enormous value to AT&T. Telephone cables could now be used to twice the distance previously possible, or alternatively, a cable of half the previous quality (and cost) could be used over the same distance. When considering whether to allow Campbell to go ahead with the demonstration, their engineers had estimated that they stood to save $700,000 in new installation costs in New York and New Jersey alone. It has been estimated that AT&T saved $100 million in the first quarter of the 20th century. Heaviside, who began it all, came away with nothing. He was offered a token payment but would not accept, wanting the credit for his work. He remarked ironically that if his prior publication had been admitted it would "interfere ... with the flow of dollars in the proper direction ...".

Submarine cables
Distortion is a particular problem for submarine communication cables, partly because their great length allows more distortion to build up, but also because they are more susceptible to distortion than open wires on poles due to the characteristics of the insulating material. Different wavelengths of the signal travel at different velocities in the material causing dispersion. It was this problem on the first transatlantic telegraph cable that motivated Heaviside to study the problem and find the solution. Loading coils solve the dispersion problem, and the first use of them on a submarine cable was in 1906 by Siemens and Halske in a cable across Lake Constance.

There are a number of difficulties using loading coils with heavy submarine cables. The bulge of the loading coils could not easily pass through the cable laying apparatus of cable ships and the ship had to slow down during the laying of a loading coil. Discontinuities where the coils were installed caused stresses in the cable during laying. Without great care, the cable might part and would be difficult to repair. A further problem was that the material science of the time had difficulties sealing the joint between coil and cable against ingress of seawater. When this occurred the cable was ruined. Continuous loading was developed to overcome these problems, which also has the benefit of not having a cutoff frequency.

Krarup cable
A Danish engineer, Carl Emil Krarup, invented a form of continuously loaded cable which solved the problems of discrete loading coils. Krarup cable has iron wires continuously wound around the central copper conductor with adjacent turns in contact with each other. This cable was the first use of continuous loading on any telecommunication cable. In 1902, Krarup both wrote his paper on this subject and saw the installation of the first cable between Helsingør (Denmark) and Helsingborg (Sweden).

Permalloy cable
Even though the Krarup cable added inductance to the line, this was insufficient to meet the Heaviside condition. AT&T searched for a better material with higher magnetic permeability. In 1914, Gustav Elmen discovered permalloy, a magnetic nickel-iron annealed alloy. In c. 1915, Oliver E. Buckley, H. D. Arnold, and Elmen, all at Bell Labs, greatly improved transmission speeds by suggesting a method of constructing submarine communications cable using permalloy tape wrapped around the copper conductors.

The cable was tested in a trial in Bermuda in 1923. The first permalloy cable placed in service connected New York City and Horta (Azores) in September 1924. Permalloy cable enabled signalling speed on submarine telegraph cables to be increased to 400 words/min at a time when 40 words/min was considered good. The first transatlantic cable achieved only two words/min.

Mu-metal cable
Mu-metal has similar magnetic properties to permalloy but the addition of copper to the alloy increases the ductility and allows the metal to be drawn into wire. Mu-metal cable is easier to construct than permalloy cable, the mu-metal being wound around the core copper conductor in much the same way as the iron wire in Krarup cable. A further advantage with mu-metal cable is that the construction lends itself to a variable loading profile whereby the loading is tapered towards the ends.

Mu-metal was invented in 1923 by the Telegraph Construction and Maintenance Company, London, who made the cable, initially, for the Western Union Telegraph Co. Western Union were in competition with AT&T and the Western Electric Company who were using permalloy. The patent for permalloy was held by Western Electric which prevented Western Union from using it.

Patch loading
Continuous loading of cables is expensive and hence is only done when absolutely necessary. Lumped loading with coils is cheaper but has the disadvantages of difficult seals and a definite cutoff frequency. A compromise scheme is patch loading whereby the cable is continuously loaded in repeated sections. The intervening sections are left unloaded.

Current practice
Loaded cable is no longer a useful technology for submarine communication cables, having first been superseded by co-axial cable using electrically powered in-line repeaters and then by fibre-optic cable. Manufacture of loaded cable declined in the 1930s and was then superseded by other technologies post-World War 2. Loading coils can still be found in some telephone landlines today but new installations use more modern technology.

title: Loading coil


text:
Lobe

Lobe may refer to:

People with the name

 * Lobe (surname)

Science and healthcare

 * Lobe (anatomy)
 * Lobe, a large-scale structure of a radio galaxy
 * Glacial lobe, a lobe-shaped glacier
 * Lobation, a characteristic of the nucleus of certain biological cells
 * Acoustic lobe, radiation pattern exhibited by multi-driver loudspeakers
 * Delta lobe or deltaic lobe, the projection of a river delta mouth into standing water
 * Roche lobe, the region of space around a star in a binary system within which orbiting material is gravitationally bound to that star
 * Sidelobe, an identifiable segment of an antenna radiation pattern
 * Grating lobe, a sidelobe that is much higher than all other side lobes, approximately the same as the main beam — exists only in phased arrays
 * Main lobe, the lobe containing the maximum power

Other uses

 * Lobe, an oblong protrusion from a camshaft
 * The Lobe, a character in Freakazoid!
 * Lobes (album), a 2023 album by We Are Scientists

title: Lobe


text:
Local access and transport area

Local access and transport area (LATA) is a term used in U.S. telecommunications regulation. It represents a geographical area of the United States under the terms of the Modification of Final Judgment (MFJ) entered by the United States District Court for the District of Columbia in Civil Action number 82-0192 or any other geographic area designated as a LATA in the National Exchange Carrier Association, Inc. Tariff FCC No. 4. that precipitated the breakup of the original AT&T into the "Baby Bells" or created since that time for wireline regulation.

Generally, a LATA represents an area within which a divested Regional Bell Operating Company (RBOC) is permitted to offer exchange telecommunications and exchange access services. Under the terms of the MFJ, the RBOCs are generally prohibited from providing services that originate in one LATA and terminate in another.

LATA boundaries tend to be drawn around markets, and not necessarily along existing state or area code borders. Some LATAs cross over state boundaries, such as those for the New York metropolitan area and Greenwich, Connecticut; Chicago, Illinois; Portland, Oregon; and areas between Maryland, Virginia, and West Virginia. Area codes and LATAs do not necessarily share boundaries; many LATAs exist in multiple area codes, and many area codes exist in multiple LATAs.

Originally, the LATAs were grouped into regions within which one particular RBOC was allowed to provide services. The LATAs in each of these regions are numbered beginning with the same digit. Generally, the LATAs were associated with carriers or other indications in the following manner:

In addition to this list, two local carriers were made independent: Cincinnati Bell in the Cincinnati area, and SNET (a former unit of AT&T, sold to Frontier) in Connecticut. These were assigned LATAs in the 9xx range.

Since the breakup of the original AT&T in 1984, however, some amount of deregulation, as well as a number of phone company mergers, have blurred the significance of these regions. A number of new LATAs have been formed within these regions since their inception, most beginning with the digit 9.

LATAs contribute to an often confusing aspect of long-distance telephone service. Due to the various and overlapping regulatory limitations and inter-business arrangements, phone companies typically provide differing types of “long distance” service, each with potentially different rates: Given the complexity of the legal and financial issues involved in each distinction, many long-distance companies tend to not explain the details of these different rates, which can lead to billing questions from surprised customers.
 * within same LATA, within same state
 * within same LATA, between different states
 * between different LATAs, within same state
 * between different LATAs, between different states

Local carriers have various alternative terms for LATAs such as “Service Area” by Pacific Bell in California, or “Regional Calling Area” by Verizon in Maryland.

To facilitate the sharing of Telcordia telephone routing databases between countries, LATAs were later defined for the provinces of Canada, the other countries and territories of the North American Numbering Plan, and Mexico. Aside from U.S. territories, LATAs have no regulatory purpose in these areas. In 2000, the Canadian Radio-television and Telecommunications Commission eliminated all Canadian provincial LATAs in favor of a single LATA for Canada (888).

No LATAs exist with a second digit of 0 or 1, which distinguished them from traditional area codes.

US state LATAs
The city or place name given with some LATAs is the name given to identify the LATA, not the limit of its boundary. Generally this is the most significant metropolitan area in the LATA. In some cases, a LATA is named after the largest phone exchange in the LATA that was historically served by an RBOC. For example, the largest city in the Pahrump LATA in Nevada is Las Vegas. Since Las Vegas was not historically served by an RBOC, the LATA is named after the smaller town of Pahrump, which was historically served by Nevada Bell (now AT&T Inc.). Also, listing under a state does not necessarily limit the LATA's territory to that state; there may be overlaps as well as enclaves. Areas that include notable portions of other states are explained, but not all LATA state overlaps may be detailed.

LATA boundaries are not always solidly defined. Inter-carrier agreements, change proposals to the Federal Communications Commission (FCC), and new wiring developments into rural areas can and do often alter the effective borders between LATAs. Many sources on LATA boundary information conflict with each other at detailed levels. Telcordia data may provide the most up-to-date details of LATA inclusions.

Alabama

 * 476 Birmingham
 * 477 Huntsville
 * 478 Montgomery
 * Includes Georgetown, Georgia
 * 480 Mobile
 * Includes areas of Mississippi north of Pascagoula
 * Includes parts of northern Escambia County, Florida in the Century and Walnut Hill areas

Alaska

 * 832

Arizona

 * 666 Phoenix
 * Includes Winterhaven, California
 * Includes Spirit Mountain, Nevada
 * Includes Glen Canyon, Utah
 * 668 Tucson
 * Includes Rodeo and Virden, New Mexico
 * 980 Navajo Nation (Arizona portion)
 * Includes southwestern San Juan County, Utah

Arkansas

 * 526 Fort Smith
 * Includes part of Oklahoma from Pocola to Moffett
 * Includes section of Oklahoma from Colcord to Watts
 * Includes small part of Barry County, Missouri
 * Includes area of Oklahoma near Maysville, Arkansas
 * Includes area of Oklahoma near Uniontown, Arkansas
 * 528 Little Rock
 * Includes Watson, Oklahoma
 * 530 Pine Bluff
 * Includes Junction City, Louisiana

California

 * 722 San Francisco
 * 724 Chico
 * 726 Sacramento
 * 728 Fresno
 * 730 Los Angeles
 * Includes La Paz County, Arizona
 * 732 San Diego
 * 734 Bakersfield
 * 736 Monterey
 * 738 Stockton
 * 740 San Luis Obispo
 * 973 Palm Springs

Colorado

 * 656 Denver
 * 658 Colorado Springs

Connecticut

 * 920

Washington, D.C.

 * 236
 * Includes the west portion of the West Bay of Maryland, as far north as Damascus, Maryland (roughly Montgomery, Prince George's, Charles, and St. Mary's counties of Maryland)
 * Includes the northeasternmost portion of Virginia, from Sterling to just north of Fredericksburg (roughly Northern Virginia)

Florida

 * 448 Pensacola
 * Includes Clear Springs, Wing and Florala, Alabama
 * 450 Panama City
 * Includes a small portion of Georgia near Tallahassee
 * 452 Jacksonville
 * 454 Gainesville
 * 456 Daytona Beach
 * 458 Orlando
 * 460 Southeast Florida
 * 939 Fort Myers
 * 952 Tampa
 * 953 Tallahassee
 * Florida is a special case in which state regulators have also assigned 5-digit LATA codes which overlay the Federally-assigned 3-digit LATAs. See map on the right for details. Some carriers refer to these by the 3-digit LATA, others by the 5-digit.

Georgia

 * 438 Atlanta
 * Includes portion of Alabama from Oakland to Huguley
 * Includes Phenix City, Alabama
 * Includes Ranburne, Alabama
 * 440 Savannah
 * Includes part of southern South Carolina as far north as Hardeeville and Hilton Head Island
 * 442 Augusta
 * Includes Aiken County and Edgefield County, South Carolina
 * 444 Albany
 * 446 Macon

Hawaii

 * 834

Idaho

 * 652 Southern Idaho
 * Includes Malheur County, Oregon, especially the Ontario area
 * Includes Jackpot, Jarbidge, and Owyhee, Nevada
 * Includes Alta and Border, Wyoming
 * 960 Coeur d'Alene
 * Includes part of northwest Montana as far east as Eureka and as far south as Libby
 * Includes Pullman, Washington and surrounding area
 * Includes Pend Oreille County, Washington

Illinois

 * 358 Chicago
 * Includes Lake County and Newton County, Indiana, especially the Gary, Indiana area
 * Includes Demotte, Hebron, and Lakes of the Four Seasons, Indiana
 * Extends into Wisconsin Salem Township
 * 360 Rockford
 * Extends into Wisconsin near Apple River, Illinois
 * 362 Cairo
 * 364 Sterling
 * 366 Forrest
 * 368 Peoria
 * 370 Champaign
 * May include areas of Indiana near Danville, Illinois
 * 374 Springfield
 * 376 Quincy
 * 976 Mattoon
 * 977 Macomb
 * 978 Olney

Indiana

 * 330 Evansville
 * 332 South Bend
 * 334 Auburn-Huntington
 * 336 Indianapolis
 * Extends into Illinois near Dana, Indiana
 * 338 Bloomington
 * 937 Richmond
 * Includes Union City, Ohio
 * 938 Terre Haute
 * Includes Edgar and Clark counties of Illinois
 * May include Robinson, Illinois

Iowa

 * 630 Sioux City
 * Extends into Minnesota near incorporated areas of Iowa along its length
 * Includes the eastern portions of Dakota and Thurston counties of Nebraska
 * Includes North Sioux City, South Dakota, and extends into South Dakota near Akron and Hawarden, Iowa
 * 632 Des Moines
 * Extends into Missouri from Andover, Missouri to south of Davis City, Iowa
 * 634 Davenport
 * Includes portion of Illinois as far as Geneseo and Aledo
 * Includes the Galena, Illinois area
 * 635 Cedar Rapids

Kansas

 * 524 Kansas City (see Missouri for details)
 * 532 Wichita
 * 534 Topeka

Kentucky

 * 462 Louisville
 * Includes the central southern area of Indiana around Salem
 * 464 Owensboro
 * 466 Winchester

Louisiana

 * 492 Baton Rouge
 * 486 Shreveport
 * 488 Lafayette
 * 490 New Orleans

Maine

 * 120

Maryland

 * 236 see Washington, D.C.; most of this LATA is actually in Maryland
 * 238 Baltimore
 * 240 Hagerstown
 * Includes the easternmost part of West Virginia around Martinsburg as far as Route 9
 * Includes the northwestern part of the Eastern Panhandle of West Virginia including Keyser, from Grant County to Short Gap
 * Includes area of Pennsylvania just north of Hancock, Maryland
 * 242 Salisbury

Massachusetts

 * 126 Western Massachusetts
 * 128 Eastern Massachusetts

Michigan

 * 340 Detroit
 * 342 Upper Peninsula of Michigan
 * Includes portion of Wisconsin around Iron Mountain, Michigan as far as Rhinelander and Townsend, Wisconsin
 * 344 Saginaw
 * 346 Lansing
 * 348 Grand Rapids

Minnesota

 * 620 Rochester
 * 624 Duluth
 * 626 St. Cloud
 * 628 Minneapolis
 * 636 Brainerd, Minnesota-Fargo, North Dakota

Mississippi

 * 482 Jackson
 * Includes parts of Alabama around Columbus, Mississippi
 * 484 Biloxi

Missouri

 * 520 St. Louis
 * Includes part of south-central Illinois southwest of Springfield.
 * 521 Westphalia (per locallingguide.com, includes Columbia MO)
 * 522 Springfield
 * 524 Kansas City
 * Includes eastern portion of Kansas as far out as U.S. 73 and U.S. 59 and south as far as U.S. 54
 * 521 Central Missouri: Columbia and surrounding areas

Montana

 * 648 Great Falls
 * 650 Billings
 * 963 Kalispell (historical)
 * note: LATA 963 appears on many LATA lists, and at least one map, but is no longer a separate LATA-equivalent area. It is now part of LATA 648.

Nebraska

 * 644 Omaha
 * 646 Grand Island
 * 958 Lincoln

Nevada

 * 720 Reno
 * May include Alpine, Verdi and Coleville, California
 * 721 Pahrump

New Hampshire

 * 122
 * Includes part of Vermont around Groton
 * Includes part of Maine around Kittery and Wilsons Mills

New Jersey

 * 220 Atlantic Coastal New Jersey
 * 222 Delaware Valley
 * 224 North Jersey

New Mexico

 * 664

New York

 * 132 New York City and surrounding metropolitan area
 * Includes Greenwich, Connecticut
 * 133 Poughkeepsie
 * Includes Milford, Pennsylvania and surrounding area
 * 134 Albany
 * Includes Hancock, Massachusetts
 * 136 Syracuse
 * 138 Binghamton
 * Includes Sayre, Pennsylvania and surrounding area
 * 140 Buffalo
 * Includes Ulysses, Pennsylvania and surrounding area
 * 921 Fishers Island
 * 974 Rochester

North Carolina

 * 420 Asheville
 * 422 Charlotte
 * Includes York County and Lancaster County, South Carolina
 * 424 Greensboro-Winston-Salem area
 * 426 Raleigh
 * 428 Wilmington
 * 949 Fayetteville
 * 951 Rocky Mount

North Dakota

 * 636 Brainerd, Minnesota-Fargo, North Dakota
 * 638 Bismarck
 * Includes portions of Montana near Beach and Homesteaders Gap, North Dakota

Ohio

 * 320 Cleveland
 * 322 Youngstown
 * 324 Columbus
 * 325 Akron
 * 326 Toledo
 * 328 Dayton
 * 922 Cincinnati
 * Includes Rising Sun, Indiana and surrounding area
 * Includes the northern tip of Kentucky as far south as Williamstown
 * 923 Lima-Mansfield

Oklahoma

 * 536 Oklahoma City
 * 538 Tulsa

Oregon

 * 670 Eugene
 * 672 Portland
 * Includes Southwestern Washington from Willapa Bay to Goldendale

Pennsylvania

 * 226 Harrisburg
 * 228 Philadelphia
 * 230 Altoona
 * 232 Wilkes-Barre/Scranton
 * 234 Pittsburgh
 * 924 Erie

Rhode Island

 * 130 Rhode Island

South Carolina

 * 430 Greenville
 * Includes Polk County, North Carolina
 * 432 Florence
 * 434 Columbia
 * 436 Charleston

South Dakota

 * 640

Tennessee

 * 468 Memphis
 * Includes part of Mississippi from south of Memphis to as far south as Hernando
 * 470 Nashville
 * 472 Chattanooga
 * Includes northwestern tip of Georgia
 * 474 Knoxville
 * 956 Bristol-Kingsport-Johnson City
 * Includes part of Virginia from Abingdon to Wytheville

Texas

 * 540 El Paso
 * 542 Midland
 * 544 Lubbock
 * 546 Amarillo
 * Includes the southern half of the Oklahoma Panhandle
 * 548 Wichita Falls
 * 550 Abilene
 * 552 Dallas
 * 554 Longview
 * Includes Miller County, Arkansas
 * 556 Waco
 * 558 Austin
 * 560 Houston
 * 562 Beaumont
 * 564 Corpus Christi
 * 566 San Antonio
 * 568 Brownsville
 * 570 Hearne
 * 961 San Angelo

Utah

 * 660 Utah
 * May include Mesquite and Partoun, Nevada
 * May include Fredonia and Colorado City, Arizona
 * 981 Navajo Nation (Utah portion)

Vermont

 * 124 Vermont
 * Includes West Lebanon and West Chesterfield, New Hampshire

Virginia

 * 236 Arlington, Fairfax, Prince William, and Stafford counties, and enclosed cities. See Washington, D.C.
 * 244 Roanoke
 * 246 Culpeper
 * 248 Richmond
 * 250 Lynchburg
 * 252 Norfolk
 * 927 Harrisonburg
 * 928 Charlottesville
 * 929 Edinburg
 * 932 (Shared with WV)

Washington

 * 674 Seattle
 * 676 Spokane
 * Includes parts of Oregon including Milton-Freewater and Troy
 * Includes a section of Idaho from Lewiston to Grangeville, up to Troy, and Elk City
 * Includes Tensed, Idaho

West Virginia

 * 254 Charleston
 * 256 Clarksburg
 * 240 Martinsburg
 * 932 (overlap with VA)

Wisconsin

 * 350 Northeast Wisconsin
 * Includes the southern corner of Michigan's Upper Peninsula
 * 352 Northwest Wisconsin
 * 354 Southwest Wisconsin
 * 356 Southeast Wisconsin

Wyoming

 * 654 Wyoming

U.S. territory LATAs

 * American Samoa - 884
 * Guam - 871
 * Northern Mariana Islands - 870
 * Puerto Rico - 820
 * U.S. Virgin Islands - 822
 * Wake Island - 836

Non-U.S. LATAs (non-regulatory)

 * Mexico - 838
 * Bahamas - 824
 * Jamaica - 826
 * Dominican Republic - 828
 * Other Caribbean - 830
 * Canada - 888

Canada
As LATAs exist for US regulatory purposes, where they serve as a demarcation between intra-LATA calls (handled by regional Bell operating companies) and inter-LATA calls (handled by interstate long-distance carriers such as AT&T), they have no legal significance in Canada.

As of 2000, all of Canada (except for non-geographic numbers) is identified as LATA 888.

The use of this LATA set to identify individual provinces is therefore deprecated:
 * Alberta - 881, 884
 * British Columbia - 886
 * Manitoba - 888
 * New Brunswick - 890
 * Newfoundland - 885
 * Nova Scotia/P.E.I. - 887, 889
 * Ontario - 851
 * Quebec - 850, 883
 * Saskatchewan - 891
 * Yukon Territory - 892

Local interconnection region
Canada does define local interconnection regions (LIR's), which determine where points of interconnection (POI) must be provided by competing local exchange and mobile carriers to provide local number portability. A Canadian LIR is geographically smaller than a US LATA, typically comparable in size to a small city's flat-rate local calling area or to an entire large regional municipality. In areas where a small-city Digital Multiplex System controls a group of remote switching centres, one for each surrounding village, the local interconnect region normally includes each exchange in the city plus all downstream remotes of those exchanges. In a Toronto-sized city, the LIR will include only the city itself.

While the LIRs resemble local calling areas in geographic size, there are some key differences:
 * LIR's normally do not include incumbent local independent telephone company exchanges in locations not opened to competition, where the independent numbers are currently not portable.
 * LIR's do not cross provincial boundaries. Lloydminster has an LIR for each province, as does Ottawa-Hull.
 * LIR's closely follow network topology, which often does not match a local flat-rate calling area as local calling is defined by arbitrary regulatory constructs.

One example: The tiny unincorporated village of Beebe Plain, divided by the Quebec-Vermont border, is served by +1-819-876 Rock Island, Quebec, Canada (a remote station controlled from Magog) and +1-802-873 Derby Line, Vermont, USA (a remote station controlled from St. Johnsbury). Magog and St. Johnsbury are both a long-distance call from anywhere in Beebe Plain, even though Canadian subscribers can place local calls to Sherbrooke, US subscribers can locally call Newport and an international call within the village is local. An LIR assignment which follows network topology places the Canadian remote station in Magog's LIR, not Sherbrooke's LIR.

title: Local access and transport area


text: Local battery

title: Local battery


text:
Local call

In telephony, the term local call has the following meanings:

 * 1) Any call using a single switching center; that is, not traveling to another telephone network;
 * 2) A call made within a local calling area as defined by the local exchange carrier;
 * 3) Any call for which an additional charge, i.e., toll charge, is not billed to the calling or called party, or (depending on the country) for which this charge is reduced because it is a short-distance call (e.g. within a town or local metropolitan area).

Typically, local calls have shorter numbers than long-distance calls, as the area code may not be required. However, this is not true in parts of the United States and Canada that are subject to overlay plans or many countries in Europe that require closed dialing plans.

Toll free (e.g. "800" numbers in the United States) are not necessarily local calls; despite being free to the caller, any charge due for the distance of the connection is charged to the called party.

Commercial users who make or accept many long-distance calls to or from a particular distant place may make them as local calls by use of a foreign exchange service. Such an "FX" line also allows people in the distant place to call by using a telephone number local to them.

title: Local call


text:
Log-periodic antenna

A log-periodic antenna (LP), also known as a log-periodic array or log-periodic aerial, is a multi-element, directional antenna designed to operate over a wide band of frequencies. It was invented by John Dunlavy in 1952.

The most common form of log-periodic antenna is the log-periodic dipole array or LPDA, The LPDA consists of a number of half-wave dipole driven elements of gradually increasing length, each consisting of a pair of metal rods. The dipoles are mounted close together in a line, connected in parallel to the feedline with alternating phase. Electrically, it simulates a series of two- or three-element Yagi–Uda antennas connected together, each set tuned to a different frequency.

LPDA antennas look somewhat similar to Yagi antennas, in that they both consist of dipole rod elements mounted in a line along a support boom, but they work in very different ways. Adding elements to a Yagi increases its directionality, or gain, while adding elements to an LPDA increases its frequency response, or bandwidth.

One large application for LPDAs is in rooftop terrestrial television antennas, since they must have large bandwidth to cover the wide television bands of roughly 54–88 and 174–216 MHz in the VHF and 470–890 MHz in the UHF while also having high gain for adequate fringe reception. One widely used design for television reception combined a Yagi for UHF reception in front of a larger LPDA for VHF.

Basic concept
The LPDA normally consists of a series of half wave dipole "elements" each consisting of a pair of metal rods, positioned along a support boom lying along the antenna axis. The elements are spaced at intervals following a logarithmic function of the frequency, known as d or sigma. The length of the successive elements and the spacing between them gradually decrease along the boom. The relationship between the lengths is a function known as tau. Sigma and tau are the key design elements of the LPDA design. The radiation pattern of the antenna is unidirectional, with the main lobe along the axis of the boom, off the end with the shortest elements. Each dipole element is resonant at a wavelength approximately equal to twice its length. The bandwidth of the antenna, the frequency range over which it has near-maximum gain, is approximately between the resonant frequencies of the longest and shortest elements.

Every element in the LPDA antenna is a driven element, that is, connected electrically to the feedline. A parallel wire transmission line usually runs along the central boom, and each successive element is connected in opposite phase to it. The feedline can often be seen zig-zagging across the support boom holding the elements. Another common construction method is to use two parallel central support booms that also acts as the transmission line, mounting the dipoles on the alternate booms. Other forms of the log-periodic design replace the dipoles with the transmission line itself, forming the log-periodic zig-zag antenna. Many other forms using the transmission wire as the active element also exist.

The Yagi and the LPDA designs look very similar at first glance, as they both consist of a number of dipole elements mounted along a support boom. The Yagi, however, has only a single driven element connected to the transmission line, usually the second one from the back of the array, the remaining elements are parasitic. The Yagi antenna differs from the LPDA in having a very narrow bandwidth.

In general terms, at any given frequency the log-periodic design operates somewhat similar to a three-element Yagi antenna; the dipole element closest to resonant at the operating frequency acts as a driven element, with the two adjacent elements on either side as director and reflector to increase the gain, the shorter element in front acting as a director and the longer element behind as a reflector. However, the system is somewhat more complex than that, and all the elements contribute to some degree, so the gain for any given frequency is higher than a Yagi of the same dimensions as any one section of the log-periodic. However, a Yagi with the same number of elements as a log-periodic would have far higher gain, as all of those elements are improving the gain of a single driven element. In its use as a television antenna, it was common to combine a log-periodic design for VHF with a Yagi for UHF, with both halves being roughly equal in size. This resulted in much higher gain for UHF, typically on the order of 10 to 14 dB on the Yagi side and 6.5 dB for the log-periodic. But this extra gain was needed anyway in order to make up for a number of problems with UHF signals.

It should be strictly noted that the log-periodic shape, according to the IEEE definition, does not align with broadband property for antennas. The broadband property of log-periodic antennas comes from its self-similarity. A planar log-periodic antenna can also be made self-complementary, such as logarithmic spiral antennas (which are not classified as log-periodic per se but among the frequency independent antennas that are also self-similar) or the log-periodic toothed design. Y. Mushiake found, for what he termed "the simplest self-complementary planar antenna," a driving point impedance of η0/2=188.4 Ω at frequencies well within its bandwidth limits.

History
John Dunlavy invented the log-periodic antenna in 1952 while working for the United States Air Force but was not credited with it due to its "Secret" classification. The University of Illinois at Urbana–Champaign had patented the Isbell and Mayes–Carrel antennas and licensed the design as a package exclusively to JFD Electronics in New York. Channel Master and Blonder Tongue Labs ignored the patents and produced a wide range of antennas based on that design. Lawsuits regarding the antenna patent, which the U.I. Foundation lost, evolved into the 1971 Blonder-Tongue Doctrine. This precedent governs patent litigation.

Short wave broadcast antennas
The log-periodic is commonly used as a transmitting antenna in high power shortwave broadcasting stations because its broad bandwidth allows a single antenna to transmit on frequencies in multiple bands. The log-periodic zig-zag design with up to 16 sections has been used. These large antennas are typically designed to cover 6 to 26 MHz but even larger ones have been built which operate as low as 2 MHz. Power ratings are available up to 500 kW. Instead of the elements being driven in parallel, attached to a central transmission line, the elements are driven in series, adjacent elements connected at the outer edges. The antenna shown here would have about 14 dBi gain. An antenna array consisting of two such antennas, one above the other and driven in phase has a gain of up to 17 dBi. Being log-periodic, the antenna's main characteristics (radiation pattern, gain, driving point impedance) are almost constant over its entire frequency range, with the match to a 300 Ω feed line achieving a standing wave ratio of better than 2:1 over that range.

title: Log-periodic antenna