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Overtone

An overtone is any resonant frequency above the fundamental frequency of a sound. (An overtone may or may not be a harmonic) In other words, overtones are all pitches higher than the lowest pitch within an individual sound; the fundamental is the lowest pitch. While the fundamental is usually heard most prominently, overtones are actually present in any pitch except a true sine wave. The relative volume or amplitude of various overtone partials is one of the key identifying features of timbre, or the individual characteristic of a sound.

Using the model of Fourier analysis, the fundamental and the overtones together are called partials. Harmonics, or more precisely, harmonic partials, are partials whose frequencies are numerical integer multiples of the fundamental (including the fundamental, which is 1 times itself). These overlapping terms are variously used when discussing the acoustic behavior of musical instruments. (See etymology below.) The model of Fourier analysis provides for the inclusion of inharmonic partials, which are partials whose frequencies are not whole-number ratios of the fundamental (such as 1.1 or 2.14179).

When a resonant system such as a blown pipe or plucked string is excited, a number of overtones may be produced along with the fundamental tone. In simple cases, such as for most musical instruments, the frequencies of these tones are the same as (or close to) the harmonics. Examples of exceptions include the circular drum – a timpani whose first overtone is about 1.6 times its fundamental resonance frequency, gongs and cymbals, and brass instruments. The human vocal tract is able to produce highly variable amplitudes of the overtones, called formants, which define different vowels.

Explanation
Most oscillators, from a plucked guitar string to a flute that is blown, will naturally vibrate at a series of distinct frequencies known as normal modes. The lowest normal mode frequency is known as the fundamental frequency, while the higher frequencies are called overtones. Often, when an oscillator is excited — for example, by plucking a guitar string — it will oscillate at several of its modal frequencies at the same time. So when a note is played, this gives the sensation of hearing other frequencies (overtones) above the lowest frequency (the fundamental).

Timbre is the quality that gives the listener the ability to distinguish between the sound of different instruments. The timbre of an instrument is determined by which overtones it emphasizes. That is to say, the relative volumes of these overtones to each other determines the specific "flavor", "color" or "tone" of sound of that family of instruments. The intensity of each of these overtones is rarely constant for the duration of a note. Over time, different overtones may decay at different rates, causing the relative intensity of each overtone to rise or fall independent of the overall volume of the sound. A carefully trained ear can hear these changes even in a single note. This is why the timbre of a note may be perceived differently when played staccato or legato.

A driven non-linear oscillator, such as the vocal folds, a blown wind instrument, or a bowed violin string (but not a struck guitar string or bell) will oscillate in a periodic, non-sinusoidal manner. This generates the impression of sound at integer multiple frequencies of the fundamental known as harmonics, or more precisely, harmonic partials. For most string instruments and other long and thin instruments such as a bassoon, the first few overtones are quite close to integer multiples of the fundamental frequency, producing an approximation to a harmonic series. Thus, in music, overtones are often called harmonics. Depending upon how the string is plucked or bowed, different overtones can be emphasized.

However, some overtones in some instruments may not be of a close integer multiplication of the fundamental frequency, thus causing a small dissonance. "High quality" instruments are usually built in such a manner that their individual notes do not create disharmonious overtones. In fact, the flared end of a brass instrument is not to make the instrument sound louder, but to correct for tube length “end effects” that would otherwise make the overtones significantly different from integer harmonics. This is illustrated by the following:

Consider a guitar string. Its idealized 1st overtone would be exactly twice its fundamental if its length were shortened by ½, perhaps by lightly pressing a guitar string at the 12th fret; however, if a vibrating string is examined, it will be seen that the string does not vibrate flush to the bridge and nut, but it instead has a small “dead length” of string at each end. This dead length actually varies from string to string, being more pronounced with thicker and/or stiffer strings. This means that halving the physical string length does not halve the actual string vibration length, and, hence, the overtones will not be exact multiples of a fundamental frequency. The effect is so pronounced that properly set up guitars will angle the bridge such that the thinner strings will progressively have a length up to few millimeters shorter than the thicker strings. Not doing so would result in inharmonious chords made up of two or more strings. Similar considerations apply to tube instruments.

Musical usage term

An overtone is a partial (a "partial wave" or "constituent frequency") that can be either a harmonic partial (a harmonic) other than the fundamental, or an inharmonic partial. A harmonic frequency is an integer multiple of the fundamental frequency. An inharmonic frequency is a non-integer multiple of a fundamental frequency.

An example of harmonic overtones: (absolute harmony)

Some musical instruments produce overtones that are slightly sharper or flatter than true harmonics. The sharpness or flatness of their overtones is one of the elements that contributes to their sound. Due to phase inconsistencies between the fundamental and the partial harmonic, this also has the effect of making their waveforms not perfectly periodic.

Musical instruments that can create notes of any desired duration and definite pitch have harmonic partials. A tuning fork, provided it is sounded with a mallet (or equivalent) that is reasonably soft, has a tone that consists very nearly of the fundamental, alone; it has a sinusoidal waveform. Nevertheless, music consisting of pure sinusoids was found to be unsatisfactory in the early 20th century.

Etymology
In Hermann von Helmholtz's classic "On The Sensations Of Tone" he used the German "Obertöne" which was a contraction of "Oberpartialtöne", or in English: "upper partial tones". According to Alexander Ellis (in pages 24–25 of his English translation of Helmholtz), the similarity of German "ober" to English "over" caused a Prof. Tyndall to mistranslate Helmholtz' term, thus creating "overtone". Ellis disparages the term "overtone" for its awkward implications. Because "overtone" makes the upper partials seem like such a distinct phenomena, it leads to the mathematical problem where the first overtone is the second partial. Also, unlike discussion of "partials", the word "overtone" has connotations that have led people to wonder about the presence of "undertones" (a term sometimes confused with "difference tones" but also used in speculation about a hypothetical "undertone series").

"Overtones" in choral music
In barbershop music, a style of four-part singing, the word overtone is often used in a related but particular manner. It refers to a psychoacoustic effect in which a listener hears an audible pitch that is higher than, and different from, the fundamentals of the four pitches being sung by the quartet. The barbershop singer's "overtone" is created by the interactions of the upper partial tones in each singer's note (and by sum and difference frequencies created by nonlinear interactions within the ear). Similar effects can be found in other a cappella polyphonic music such as the music of the Republic of Georgia and the Sardinian cantu a tenore. Overtones are naturally highlighted when singing in a particularly resonant space, such as a church; one theory of the development of polyphony in Europe holds that singers of Gregorian chant, originally monophonic, began to hear the overtones of their monophonic song and to imitate these pitches - with the fifth, octave, and major third being the loudest vocal overtones, it is one explanation of the development of the triad and the idea of consonance in music.

The first step in composing choral music with overtone singing is to discover what the singers can be expected to do successfully without extensive practice. The second step is to find a musical context in which those techniques could be effective, not mere special effects. It was initially hypothesized that beginners would be able to:

 * glissando through the partials of a given fundamental, ascending or descending, fast, or slow
 * use vowels/text for relative pitch gestures on indeterminate partials specifying the given shape without specifying particular partials
 * improvise on partials of the given fundamental, ad lib., freely, or in giving style or manner
 * find and sustain a particular partial (requires interval recognition)
 * by extension, move to an adjacent partial, above or below, and alternate between the two

Singers should not be asked to change the fundamental pitch while overtone singing and changing partials should always be to an adjacent partial. When a particular partial is to be specified, time should be allowed (a beat or so) for the singers to get the harmonics to "speak" and find the correct one.

String instruments
String instruments can also produce multiphonic tones when strings are divided in two pieces or the sound is somehow distorted. The sitar has sympathetic strings which help to bring out the overtones while one is playing. The overtones are also highly important in the tanpura, the drone instrument in traditional North and South Indian music, in which loose strings tuned at octaves and fifths are plucked and designed to buzz to create sympathetic resonance and highlight the cascading sound of the overtones.

Western string instruments, such as the violin, may be played close to the bridge (a technique called "sul ponticello " or "am Steg") which causes the note to split into overtones while attaining a distinctive glassy, metallic sound. Various techniques of bow pressure may also be used to bring out the overtones, as well as using string nodes to produce natural harmonics. On violin family instruments, overtones can be played with the bow or by plucking. Scores and parts for Western violin family instruments indicate where the performer is to play harmonics. The most well-known technique on a guitar is playing flageolet tones or using distortion effects. The ancient Chinese instrument the guqin contains a scale based on the knotted positions of overtones. The Vietnamese đàn bầu functions on flageolet tones. Other multiphonic extended techniques used are prepared piano, prepared guitar and 3rd bridge.

Wind instruments
Wind instruments manipulate the overtone series significantly in the normal production of sound, but various playing techniques may be used to produce multiphonics which bring out the overtones of the instrument. On many woodwind instruments, alternate fingerings are used. "Overblowing ", or adding intensely exaggerated air pressure, can also cause notes to split into their overtones. In brass instruments, multiphonics may be produced by singing into the instrument while playing a note at the same time, causing the two pitches to interact - if the sung pitch is at specific harmonic intervals with the played pitch, the two sounds will blend and produce additional notes by the phenomenon of sum and difference tones.

Non-western wind instruments also exploit overtones in playing, and some may highlight the overtone sound exceptionally. Instruments like the didgeridoo are highly dependent on the interaction and manipulation of overtones achieved by the performer changing their mouth shape while playing, or singing and playing simultaneously. Likewise, when playing a harmonica or pitch pipe, one may alter the shape of their mouth to amplify specific overtones. Though not a wind instrument, a similar technique is used for playing the jaw harp: the performer amplifies the instrument's overtones by changing the shape, and therefore the resonance, of their vocal tract.

Brass Instruments
Brass instruments originally had no valves, and could only play the notes in the natural overtone, or harmonic series.

Brass instruments still rely heavily on the overtone series to produce notes: the tuba typically has 3-4 valves, the tenor trombone has 7 slide positions, the trumpet has 3 valves, and the French horn typically has 4 valves. Each instrument can play (within their respective ranges) the notes of the overtone series in different keys with each fingering combination (open, 1, 2, 12, 123, etc). The role of each valve or rotor (excluding trombone) is as follows: 1st valve lowers major 2nd, 2nd valve lowers minor 2nd, 3rd valve-lowers minor 3rd, 4th valve-lowers perfect 4th (found on piccolo trumpet, certain euphoniums, and many tubas). The French horn has a trigger key that opens other tubing and is pitched a perfect fourth higher; this allows for greater ease between different registers of the instrument. Valves allow brass instruments to play chromatic notes, as well as notes within the overtone series (open valve = C overtone series, 2nd valve = B overtone series on the C Trumpet) by changing air speed and lip vibrations.

The tuba, trombone, and trumpet play notes within the first few octaves of the overtone series, where the partials are farther apart. The French horn sounds notes in a higher octave of the overtone series, so the partials are closer together and make it more difficult to play the correct pitches and partials.

Overtone singing
Overtone singing is a traditional form of singing in many parts of the Himalayas and Altay; Tibetans, Mongols and Tuvans are known for their overtone singing. In these contexts it is often referred to as throat singing or khoomei, though it should not be confused with Inuit throat singing, which is produced by different means. There is also the possibility to create the overtone out of fundamental tones without any stress on the throat.

Also, the overtone is very important in singing to take care of vocal tract shaping, to improve color, resonance, and text declamation. During practice overtone singing, it helps the singer to remove unnecessary pressure on the muscle, especially around the throat. So if one can "find" a single overtone, then one will know where the sensation needs to be in order to bring out vocal resonance in general, helping to find the resonance in one's own voice on any vowel and in any register.

Overtones in music composition
The primacy of the triad in Western harmony comes from the first four partials of the overtone series. The eighth through fourteenth partials resemble the equal tempered acoustic scale:

When this scale is rendered as a chord, it is called the lydian dominant thirteenth chord. This chord appears throughout Western music, but is notably used as the basis of jazz harmony, features prominently in the music of Franz Liszt, Claude Debussy, Maurice Ravel, and appears as the Mystic chord in the music of Alexander Scriabin.

Because the overtone series rises infinitely from the fundamental with no periodicity, in Western music the equal temperament scale was designed to create synchronicity between different octaves. This was achieved by de-tuning certain intervals, such as the perfect fifth. A true perfect fifth is 702 cents above the fundamental, but equal temperament flattens it by two cents. The difference is only barely perceptible, and allows both for the illusion of the scale being in-tune with itself across multiple octaves, and for tonalities based on all 12 chromatic notes to sound in-tune.

Western classical composers have also made use of the overtone series through orchestration. In his treatise "Principles of Orchestration," Russian composer Nikolai Rimsky-Korsakov says the overtone series "may serve as a guide to the orchestral arrangement of chords". Rimsky-Korsakov then demonstrates how to voice a C major triad according to the overtone series, using partials 1, 2, 3, 4, 5, 6, 8, 10, 12, and 16.

In the 20th century, exposure to non-Western music and further scientific acoustical discoveries led some Western composers to explore alternate tuning systems. Harry Partch for example designed a tuning system that divides the octave into 43 tones, with each tone based on the overtone series. The music of Ben Johnston uses many different tuning systems, including his String Quartet No. 5 which divides the octave into more than 100 tones.

Spectral music is a genre developed by Gérard Grisey and Tristan Murail in the 1970s and 80s, under the auspices of IRCAM. Broadly, spectral music deals with resonance and acoustics as compositional elements. For example, in Grisey's seminal work Partiels, the composer used a sonogram to analyze the true sonic characteristics of the lowest note on a tenor trombone (E2). The analysis revealed which overtones were most prominent from that sound, and Partiels was then composed around the analysis. Another seminal spectral work is Tristan Murail's Gondwana for orchestra. This work begins with a spectral analysis of a bell, and gradually transforms it into the spectral analysis of a brass instrument. Other spectralists and post-spectralists include Jonathan Harvey, Kaija Saariaho, and Georg Friedrich Haas.

John Luther Adams is known for his extensive use of the overtone series, as well as his tendency to allow musicians to make their own groupings and play at their own pace to alter the sonic experience. For example, his piece Sila: The Breath of the World can be played by 16 to 80 musicians and are separated into their own groups. The piece is set on sixteen "harmonic clouds" that are grounded on the first sixteen overtones of low B-flat. Another example is John Luther Adam's piece Everything That Rises, which grew out of his piece Sila: The Breath of the World. Everything That Rises is a piece for string quartet that has sixteen harmonic clouds that are built off of the fundamental tone (C0)

title: Overtone


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Packet-switching node

A packet-switching node is a node in a packet-switching network that contains data switches and equipment for controlling, formatting, transmitting, routing, and receiving data packets.

Note: In the Defense Data Network (DDN), a packet-switching node is usually configured to support up to thirty-two X.25 56 kbit/s host connections, as many as six 56 kbit/s interswitch trunk (IST) lines to other packet-switching nodes, and at least one Terminal Access Controller (TAC).

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

title: Packet-switching node


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Paired disparity code

In telecommunication, a paired disparity code is a line code in which at least one of the data characters is represented by two codewords of opposite disparity that are used in sequence so as to minimize the total disparity of a longer sequence of digits.

A particular codeword of any line code can either have no disparity (the average weight of the codeword is zero), negative disparity (the average weight of the codeword is negative), or positive disparity (the average weight of the codeword is positive).

In a paired disparity code, every codeword that averages to a negative level (negative disparity) is paired with some other codeword that averages to a positive level (positive disparity).

In a system that uses a paired disparity code, the transmitter must keep track of the running DC buildup – the running disparity –  and always pick the codeword that pushes the DC level back towards zero. The receiver is designed so that either codeword of the pair decodes to the same data bits.

Most line codes use either a paired disparity code or a constant-weight code.

The simplest paired disparity code is alternate mark inversion signal. Other paired disparity codes include 8b/10b, 8B12B, the modified AMI codes, coded mark inversion, and 4B3T.

The digits may be represented by disparate physical quantities, such as two different frequencies, phases, voltage levels, magnetic polarities, or electrical polarities, each one of the pair representing a 0 or a 1.

title: Paired disparity code


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Title 47 CFR Part 68

Title 47 CFR Part 68 is a section of the Code of Federal Regulations of the United States that regulate the direct electrical connection of telecommunications equipment and customer premises wiring with the public switched telephone network, certain private line services, and connection of private branch exchange (PBX) equipment to certain telecommunication interfaces.

Scope

 * The direct connection of telecommunications equipment and customer premises wiring with the public switched telephone network and certain private line services, such as
 * foreign exchange lines at the customer premises end
 * the station end of off-premises stations associated with PBX and Centrex services
 * trunk-to-station tie lines at the trunk end only
 * switched service network station lines, i.e., common control switching arrangements
 * The direct connection of
 * all PBX and similar systems to private line services for tie trunk type interfaces,
 * off-premises station lines, and (3) automatic identified outward dialing (AIOD) and message registration.

Part 68 rules provide the technical and procedural standards under which direct electrical connection of customer-provided telephone equipment, systems, and protective apparatus may be made to the nationwide network without causing harm and without a requirement for protective circuit arrangements in the service-provider networks.

The equivalent European regulation is called TBR21.

title: Title 47 CFR Part 68


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Party line

Party line or Party Line may refer to:

 * Party line (politics), the agenda of a political party
 * Party line (telephony), a system where multiple telephone customers are connected to the same phone line

Film and television

 * Party Line (film), a 1988 indie film
 * "Party Line" (SMW episode), a 1991 episode of Super Mario World
 * "Party Line" (The Shield), a 2008 episode of The Shield

Music

 * Partyline, a Washington, D.C.-based band
 * "Party Line" (the Kinks song), 1966
 * "Party Line" (Andrea True Connection song), 1976
 * "Party Line" (Wanessa song), 2010
 * Party Line, a 1982 album by the Powder Blues Band
 * "The Party Line", a 2015 song by Belle and Sebastian from Girls in Peacetime Want to Dance

Other uses

 * The Party Line (radio), a topical sitcom on BBC Radio 4
 * Party Line, a call-in radio program on WBTG AM 1290 in Sheffield, Alabama
 * Chat line, a service to meet talk with other people via telephone

title: Party line


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Passband

A passband is the range of frequencies or wavelengths that can pass through a filter. For example, a radio receiver contains a bandpass filter to select the frequency of the desired radio signal out of all the radio waves picked up by its antenna. The passband of a receiver is the range of frequencies it can receive when it is tuned into the desired frequency (channel).

A bandpass-filtered signal (that is, a signal with energy only in a passband), is known as a bandpass signal, in contrast to a baseband signal. The bandpass filter usually has two band-stop filters.

Filters

In telecommunications, optics, and acoustics, a passband (a band-pass filtered signal) is the portion of the frequency spectrum that is transmitted (with minimum relative loss or maximum relative gain) by some filtering device. In other words, it is a band of frequencies which passes through some filter or a set of filters. The accompanying figure shows a schematic of a waveform being filtered by a bandpass filter consisting of a highpass and a lowpass filter.

Radio receivers generally include a tunable band-pass filter with a passband that is wide enough to accommodate the bandwidth of the radio signal transmitted by a single station.

Digital transmission
There are two main categories of digital communication transmission methods: baseband and passband.

 * In baseband transmission, line coding is utilized, resulting in a pulse train or digital pulse amplitude modulated (PAM) signal. This is typically used over non-filtered wires such as fiber optical cables and short-range copper links, for example: V.29 (EIA/TIA-232), V.35, IEEE 802.3, SONET/SDH.
 * In passband transmission, digital modulation methods are employed so that only a limited frequency range is used in some bandpass filtered channel. Passband transmission is typically utilized in wireless communication and in bandpass filtered channels such as POTS lines. It also allows for frequency-division multiplexing. The digital bitstream is converted first into an equivalent baseband signal, and then to a RF signal. On the receiver side a demodulator is used to detect the signal and reverse the modulation process. A combined equipment for modulation and demodulation is called a modem.

Details
In general, there is an inverse relationship between the width of a filter's passband and the time required for the filter to respond to new inputs. Broad passbands yield faster response times. This is a consequence of the mathematics of Fourier analysis.

The limiting frequencies of a passband are defined as those at which the relative intensity or power decreases to a specified fraction of the maximum intensity or power. This decrease in power is often specified to be the half-power points, i.e., 3 dB below the maximum power.

The difference between the limiting frequencies is called the bandwidth, and is expressed in hertz (in the optical regime, in nanometers or micrometers of differential wavelength).

The related term "bandpass" is an adjective that describes a type of filter or filtering process; it is frequently confused with "passband", which refers to the actual portion of affected spectrum. These two words are both compound words that follow the English rules of formation: the primary meaning is the latter part of the compound, while the modifier is the first part. Hence, one may correctly say 'A dual bandpass filter has two passbands'.

title: Passband


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Path loss

Path loss, or path attenuation, is the reduction in power density (attenuation) of an electromagnetic wave as it propagates through space. Path loss is a major component in the analysis and design of the link budget of a telecommunication system.

This term is commonly used in wireless communications and signal propagation. Path loss may be due to many effects, such as free-space loss, refraction, diffraction, reflection, aperture-medium coupling loss, and absorption. Path loss is also influenced by terrain contours, environment (urban or rural, vegetation and foliage), propagation medium (dry or moist air), the distance between the transmitter and the receiver, and the height and location of antennas.

Causes
Path loss normally includes propagation losses caused by the natural expansion of the radio wave front in free space (which usually takes the shape of an ever-increasing sphere), absorption losses (sometimes called penetration losses), when the signal passes through media not transparent to electromagnetic waves, diffraction losses when part of the radiowave front is obstructed by an opaque obstacle, and losses caused by other phenomena.

The signal radiated by a transmitter may also travel along many and different paths to a receiver simultaneously; this effect is called multipath. Multipath waves combine at the receiver antenna, resulting in a received signal that may vary widely, depending on the distribution of the intensity and relative propagation time of the waves and bandwidth of the transmitted signal. The total power of interfering waves in a Rayleigh fading scenario varies quickly as a function of space (which is known as small scale fading). Small-scale fading refers to the rapid changes in radio signal amplitude in a short period of time or distance of travel.

Loss exponent
In the study of wireless communications, path loss can be represented by the path loss exponent, whose value is normally in the range of 2 to 4 (where 2 is for propagation in free space, 4 is for relatively lossy environments and for the case of full specular reflection from the earth surface—the so-called flat earth model). In some environments, such as buildings, stadiums and other indoor environments, the path loss exponent can reach values in the range of 4 to 6. On the other hand, a tunnel may act as a waveguide, resulting in a path loss exponent less than 2.

Path loss is usually expressed in dB. In its simplest form, the path loss can be calculated using the formula

 * $$L = 10 n \log_{10}(d)+C$$

where $$L$$ is the path loss in decibels, $$n$$ is the path loss exponent, $$d$$ is the distance between the transmitter and the receiver, usually measured in meters, and $$C$$ is a constant which accounts for system losses.

Radio engineer formula
Radio and antenna engineers use the following simplified formula (derived from the Friis Transmission Formula) for the signal path loss between the feed points of two isotropic antennas in free space:

Path loss in dB:
 * $$L = 20 \log_{10}\left(\frac{4\pi d} \lambda \right) $$

where $$L$$ is the path loss in decibels, $$\lambda$$ is the wavelength and $$d$$ is the transmitter-receiver distance in the same units as the wavelength. Note the power density in space has no dependency on $$\lambda$$; The variable $$\lambda$$ exists in the formula to account for the effective capture area of the isotropic receiving antenna.

Prediction
Calculation of the path loss is usually called prediction. Exact prediction is possible only for simpler cases, such as the above-mentioned free space propagation or the flat-earth model. For practical cases the path loss is calculated using a variety of approximations.

Statistical methods (also called stochastic or empirical) are based on measured and averaged losses along typical classes of radio links. Among the most commonly used such methods are Okumura–Hata, the COST Hata model, W.C.Y.Lee, etc. These are also known as radio wave propagation models and are typically used in the design of cellular networks and public land mobile networks (PLMN). For wireless communications in the very high frequency (VHF) and ultra high frequency (UHF) frequency band (the bands used by walkie-talkies, police, taxis and cellular phones), one of the most commonly used methods is that of Okumura–Hata as refined by the COST 231 project. Other well-known models are those of Walfisch–Ikegami, W. C. Y. Lee, and Erceg. For FM radio and TV broadcasting the path loss is most commonly predicted using the ITU model as described in P.1546 (successor to P.370) recommendation.

Deterministic methods based on the physical laws of wave propagation are also used; ray tracing is one such method. These methods are expected to produce more accurate and reliable predictions of the path loss than the empirical methods; however, they are significantly more expensive in computational effort and depend on the detailed and accurate description of all objects in the propagation space, such as buildings, roofs, windows, doors, and walls. For these reasons they are used predominantly for short propagation paths. Among the most commonly used methods in the design of radio equipment such as antennas and feeds is the finite-difference time-domain method.

The path loss in other frequency bands (medium wave (MW), shortwave (SW or HF), microwave (SHF)) is predicted with similar methods, though the concrete algorithms and formulas may be very different from those for VHF/UHF. Reliable prediction of the path loss in the SW/HF band is particularly difficult, and its accuracy is comparable to weather predictions.

Easy approximations for calculating the path loss over distances significantly shorter than the distance to the radio horizon:

 * In free space the path loss increases with 20 dB per decade (one decade is when the distance between the transmitter and the receiver increases ten times) or 6 dB per octave (one octave is when the distance between the transmitter and the receiver doubles). This can be used as a very rough first-order approximation for (microwave) communication links;
 * For signals in the UHF/VHF band propagating over the surface of the Earth the path loss increases with roughly 35–40 dB per decade (10–12 dB per octave). This can be used in cellular networks as a first guess.

Examples
In cellular networks, such as UMTS and GSM, which operate in the UHF band, the value of the path loss in built-up areas can reach 110–140 dB for the first kilometer of the link between the base transceiver station (BTS) and the mobile. The path loss for the first ten kilometers may be 150–190 dB (Note: These values are very approximate and are given here only as an illustration of the range in which the numbers used to express the path loss values can eventually be, these are not definitive or binding figures—the path loss may be very different for the same distance along two different paths and it can be different even along the same path if measured at different times.)

In the radio wave environment for mobile services the mobile antenna is close to the ground. Line-of-sight propagation (LOS) models are highly modified. The signal path from the BTS antenna normally elevated above the roof tops is refracted down into the local physical environment (hills, trees, houses) and the LOS signal seldom reaches the antenna. The environment will produce several deflections of the direct signal onto the antenna, where typically 2–5 deflected signal components will be vectorially added.

These refraction and deflection processes cause loss of signal strength, which changes when the mobile antenna moves (Rayleigh fading), causing instantaneous variations of up to 20 dB. The network is therefore designed to provide an excess of signal strength compared to LOS of 8–25 dB depending on the nature of the physical environment, and another 10 dB to overcome the fading due to movement.

title: Path loss


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Path profile

In telecommunication, a path profile is a graphic representation of the physical features of a propagation path in the vertical plane containing both endpoints of the path, showing the surface of the Earth and including trees, buildings, and other features that may obstruct the radio signal.

Profiles are drawn either with an effective Earth radius simulated by a parabolic arc--in which case the ray paths are drawn as straight lines--or with a "flat Earth"-- in which case the ray paths are drawn as parabolic arcs.

title: Path profile


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Path quality analysis

Path quality analysis: In a communications path, an analysis that (a) includes the overall evaluation of the component quality measures, the individual link quality measures, and the aggregate path quality measures, and (b) is performed by evaluating communications parameters, such as bit error ratio, signal-plus-noise-plus-distortion to noise-plus-distortion ratio, and spectral distortion.

title: Path quality analysis


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Payload

Payload is the object or the entity which is being carried by an aircraft or launch vehicle. Sometimes payload also refers to the carrying capacity of an aircraft or launch vehicle, usually measured in terms of weight. Depending on the nature of the flight or mission, the payload of a vehicle may include cargo, passengers, flight crew, munitions, scientific instruments or experiments, or other equipment. Extra fuel, when optionally carried, is also considered part of the payload.

In a commercial context (i.e., an airline or air freight carrier), payload may refer only to revenue-generating cargo or paying passengers. A payload of ordnance carried by a combat aircraft is sometimes alternatively referred to as the aircraft's warload.

For a rocket, the payload can be a satellite, space probe, or spacecraft carrying humans, animals, or cargo. For a ballistic missile, the payload is one or more warheads and related systems; their total weight is referred to as the throw-weight.

The fraction of payload to the total liftoff weight of the air or spacecraft is known as the "payload fraction". When the weight of the payload and fuel are considered together, it is known as the "useful load fraction". In spacecraft, "mass fraction" is normally used, which is the ratio of payload to everything else, including the rocket structure.

Relationship of range and payload
There is a natural trade-off between the payload and the range of an aircraft. A payload range diagram (also known as the "elbow chart") illustrates the trade-off.

The top horizontal line represents the maximum payload. It is limited structurally by maximum zero-fuel weight (MZFW) of the aircraft. Maximum payload is the difference between maximum zero-fuel weight and operational empty weight (OEW). Moving left-to-right along the line shows the constant maximum payload as the range increases. More fuel needs to be added for more range.

The vertical line represents the range at which the combined weight of the aircraft, maximum payload and needed fuel reaches the maximum take-off weight (MTOW) of the aircraft. If the range is increased beyond that point, payload has to be sacrificed for fuel.

The maximum take-off weight is limited by a combination of the maximum net power of the engines and the lift/drag ratio of the wings. The diagonal line after the range-at-maximum-payload point shows how reducing the payload allows increasing the fuel (and range) when taking off with the maximum take-off weight.

The second kink in the curve represents the point at which the maximum fuel capacity is reached. Flying further than that point means that the payload has to be reduced further, for an even lesser increase in range. The absolute range is thus the range at which an aircraft can fly with maximum possible fuel without carrying any payload.

Examples
Examples of payload capacity:
 * de Havilland Mosquito B Mk.IV Series 2: 920 kg
 * Boeing B-17 Flying Fortress: 1,800 kg (typical long range missions), 3,600 kg or more (short range missions)
 * Petlyakov Pe-8 4,990 kg (internal)
 * B-52H Stratofortress: 31,500 kg
 * Antonov An-225 Mriya: 250,000 kg
 * Saturn V:
 * Payload to Low Earth Orbit 140,000 kg
 * Payload to Lunar orbit 47,000 kg
 * Space Shuttle:
 * Payload to Low Earth Orbit (Not counting the 110,000 kg serviced orbiter) 27,000 kg (53,700 lb)
 * Payload to geostationary transfer orbit (Not counting the 110,000 kg serviced orbiter) 3,810 kg (8,390 lb)
 * Trident (missile): 2800 kg throw weight
 * Automated Transfer Vehicle
 * Payload: 7,667 kg 8 racks with 2 x 0.314 m3 and 2 x 0.414 m3
 * Envelope: each 1.146 m3 in front of 4 of these 8 racks
 * Cargo mass: Dry cargo: 1,500 - 5,500 kg
 * Water: 0 – 840 kg
 * Gas (Nitrogen, Oxygen, air, 2 gases/flight): 0 – 100 kg
 * ISS Refueling propellant: 0 – 860 kg (306 kg of fuel, 554 kg of oxidizer)
 * ISS re-boost and attitude control propellant: 0 - 4,700 kg
 * Total cargo upload capacity: 7,667 kg

Structural capacity
For aircraft, the weight of fuel in wing tanks does not contribute as significantly to the bending moment of the wing as does weight in the fuselage. So even when the airplane has been loaded with its maximum payload that the wings can support, it can still carry a significant amount of fuel.

Payload constraints
Launch and transport system differ not only on the payload that can be carried but also in the stresses and other factors placed on the payload. The payload must not only be lifted to its target, it must also arrive safely, whether elsewhere on the surface of the Earth or a specific orbit. To ensure this the payload, such as a warhead or satellite, is designed to withstand certain amounts of various types of "punishment" on the way to its destination. Most rocket payloads are fitted within a payload fairing to protect them against dynamic pressure of high-velocity travel through the atmosphere, and to improve the overall aerodynamics of the launch vehicle. Most aircraft payloads are carried within the fuselage for similar reasons. Outsize cargo may require a fuselage with unusual proportions, such as the Super Guppy.

The various constraints placed on the launch system can be roughly categorized into those that cause physical damage to the payload and those that can damage its electronic or chemical makeup. Examples of physical damage include extreme accelerations over short time scales caused by atmospheric buffeting or oscillations, extreme accelerations over longer time scales caused by rocket thrust and gravity, and sudden changes in the magnitude or direction of the acceleration caused by how quick engines are throttled and shut down, etc. Electrical, chemical, or biological payloads can be damaged by extreme temperatures (hot or cold), rapid changes in temperature or pressure, contact with fast moving air streams causing ionization, and radiation exposure from cosmic rays, the van Allen belt, or solar wind.

title: Payload


text:
Pseudo bit error ratio

Pseudo bit error ratio (PBER) in adaptive high-frequency (HF) radio, is a bit error ratio derived by a majority decoder that processes redundant transmissions.

Note: In adaptive HF radio automatic link establishment, PBER is determined by the extent of error correction, such as by using the fraction of non-unanimous votes in the 2-of-3 majority decoder.

title: Pseudo bit error ratio


text:
Greater Poland Voivodeship

Greater Poland Voivodeship (Województwo wielkopolskie ) is a voivodeship, or province, in west-central Poland. The province is named after the region called Greater Poland or Wielkopolska. The modern province includes most of this historic region, except for some western and northern parts.

Greater Poland Voivodeship is second in area and third in population among Poland's sixteen voivodeships, with an area of 29826 km2 and a population of close to 3.5 million. Its capital city is Poznań; other important cities include Kalisz, Konin, Piła, Ostrów Wielkopolski, Gniezno (an early capital of Poland) and Leszno. It is bordered by seven other voivodeships: West Pomeranian to the northwest, Pomeranian to the north, Kuyavian-Pomeranian to the north-east, Łódź to the south-east, Opole to the south, Lower Silesian to the southwest and Lubusz to the west.

History
Greater Poland, sometimes called the "cradle of Poland," formed the heart of the 10th-century early Polish state. Poznań and Gniezno were early centers of royal power, but following the region's devastation by pagan rebellion in the 1030s, and an invasion by Bretislaus I of Bohemia in 1038, the capital was moved by Casimir the Restorer from Gniezno to Kraków. The two cities are seats of Poland's oldest diocese (Poznań, est. in 968) and archdiocese (Gniezno, est. in 1000), playing a crucial role in the Christianization of Poland.

In the testament of Bolesław III Wrymouth, which initiated the period of fragmentation of Poland (1138–1320), the western part of Greater Poland (including Poznań) was granted to Mieszko III the Old. The eastern part, with Gniezno and Kalisz, was part of the Duchy of Kraków, granted to Władysław II the Exile. However, for most of the period the two parts were under a single ruler, and were known as the Duchy of Greater Poland (although at times there were separately ruled duchies of Poznań, Gniezno, Kalisz and Ujście). It was one of the leading and fastest developing regions of Poland, with municipal rights modeled after Poznań and Kalisz becoming the basis of municipal form of government for several towns in the region, as two of five local Polish variants of medieval town rights. The region came under the control of Władysław I the Elbow-High in 1314, and thus became part of the reunited Poland of which Władysław was crowned king in 1320.

In the reunited kingdom, and later in the Polish–Lithuanian Commonwealth, the country came to be divided into administrative units called voivodeships. In the case of the Greater Poland region these were Poznań Voivodeship and Kalisz Voivodeship. The Commonwealth also had larger subdivisions known as prowincja, one of which was named Greater Poland. However, this prowincja covered a larger area than the Greater Poland region itself, also taking in Kuyavia, Masovia and Royal Prussia. (This division of Crown Poland into two entities called Greater and Lesser Poland had its roots in the Statutes of Casimir the Great of 1346–1362, where the laws of "Greater Poland" – the northern part of the country – were codified in the Piotrków statute, with those of "Lesser Poland" in the separate Wiślica statute.)

In 1768, a new Gniezno Voivodeship was formed out of the northern part of Kalisz Voivodeship. However more far-reaching changes would come with the Partitions of Poland. In the first partition (1772), northern parts of Greater Poland along the Noteć (German Netze) were taken over by Prussia, becoming the Netze District. In the second partition (1793) the whole of Greater Poland was absorbed by Prussia, becoming part of the province of South Prussia. It remained so in spite of the first Greater Poland Uprising (1794), part of the unsuccessful Kościuszko Uprising directed chiefly against the Russian Empire.

More successful was the Greater Poland Uprising of 1806, which led to the region's becoming part of the Napoleonic Duchy of Warsaw (forming the Poznań Department and parts of the Kalisz and Bydgoszcz Departments). However, following the Congress of Vienna in 1815, Greater Poland was again partitioned, with the western part (including Poznań) going to Prussia. The eastern part joined the Russian-controlled Kingdom of Poland, where it formed the Kalisz Voivodeship until 1837, then the Kalisz Governorate (merged into the Warsaw Governorate between 1844 and 1867).

Within the Prussian empire, western Greater Poland became the Grand Duchy of Posen (Poznań), which theoretically held some autonomy. Following an unrealized uprising in 1846, and the more substantial but still unsuccessful uprising of 1848 (during the Spring of Nations), the Grand Duchy was replaced by the Province of Posen. The authorities made efforts to Germanize the region, particularly after the founding of Germany in 1871, and from 1886 onwards the Prussian Settlement Commission was active in increasing German land ownership in formerly Polish areas.

Following the end of World War I, the Greater Poland Uprising (1918–1919) ensured that most of the region became part of the newly independent Polish state, forming most of Poznań Voivodeship (1921–1939). Northern and some western parts of Greater Poland remained in Germany, where they formed much of the province of Posen-West Prussia (1922–1938), whose capital was Schneidemühl (Piła).

Following the German invasion of 1939, Greater Poland was incorporated into Nazi Germany, becoming the province called Reichsgau Posen, later Reichsgau Wartheland (Warthe being the German name for the Warta river). The Polish population was oppressed, with many former officials and others considered potential enemies by the Nazis being imprisoned or executed, including at the notorious Fort VII concentration camp in Poznań. The Polish population was also subjected to expulsions, kidnapping of children and forced labour. Germany also operated the Stalag XXI-A, Stalag XXI-C, Stalag XXI-D and other prisoner-of-war camps for Polish, French, British, Moroccan, Algerian, Dutch, Belgian, Serbian, Italian, American, Norwegian, and Soviet POWs. Poznań was declared a stronghold city (Festung) in the closing stages of the war, being taken by the Red Army in the Battle of Poznań, which ended on 22 February 1945.

After the war, Greater Poland was fully within the Polish People's Republic, as Poznań Voivodeship. With the reforms of 1975 this was divided into smaller provinces (the voivodeships of Kalisz, Konin, Leszno and Piła, and a smaller Poznań Voivodeship). The present-day Greater Poland Voivodeship, again with Poznań as its capital, was created on 1 January 1999 out of the former Poznań, Kalisz, Konin, Piła and Leszno Voivodeships, pursuant to the Polish local government reforms adopted in 1998.

Cities and towns
The voivodeship contains 7 cities and 106 towns. These are listed below in descending order of population (according to official figures for 2019 ): • Cities (governed by a city mayor or prezydent miasta):

• # Poznań (535,802)

• # Kalisz (100,482)

• # Piła (71,846)

• # Konin (71,427)

• # Ostrów Wielkopolski (71,947)

• # Gniezno (68,323)

• # Leszno (63,774)

• Towns:

• # Luboń (31,891)

• # Września (30,688)

• # Swarzędz (30,343)

• # Śrem (29,566)

• # Krotoszyn (28,845)

• # Turek (26,955)

• # Jarocin (26,155)

• # Wągrowiec (25,675)

• # Kościan (23,880)

• # Środa Wielkopolska (23,368)

• # Koło (21,838)

• # Gostyń (20,235)

• # Rawicz (20,225)

• # Szamotuły (18,752)

• # Chodzież (18,602)

• # Złotów (18,498)

• # Oborniki (18,104)

• # Pleszew (17,297)

• # Trzcianka (17,159)

• # Grodzisk Wielkopolski (14,644)

• # Nowy Tomyśl (14,574)

• # Ostrzeszów (14,137)

• # Kępno (14,101)

• # Mosina (14,060)

• # Słupca (13,712)

• # Wolsztyn (13,107)

• # Wronki (11,173)

• # Rogoźno (11,128)

• # Czarnków (10,675)

• # Międzychód (10,574)

• # Murowana Goślina (10,387)

• # Puszczykowo (9,695)

• # Kostrzyn (9,674)

• # Opalenica (9,587)

• # Pobiedziska (9,259)

• # Jastrowie (8,597)

• # Pniewy (8,047)

• # Kórnik (7,894)

• # Witkowo (7,828)

• # Trzemeszno (7,661)

• # Zbąszyń (7,264)

• # Koźmin Wielkopolski (6,499)

• # Kłodawa (6,446)

• # Krzyż Wielkopolski (6,220)

• # Buk (6,036)

• # Sieraków (6,031)

• # Stęszew (5,946)

• # Wieleń (5,870)

• # Śmigiel (5,688)

• # Czempiń (5,297)

• # Wyrzysk (5,146)

• # Odolanów (5,135)

• # Nowe Skalmierzyce (4,751)

• # Zduny (4,512)

• # Golina (4,495)

• # Skoki (4,407)

• # Krobia (4,325)

• # Szamocin (4,223)

• # Kleczew (4,159)

• # Okonek (3,869)

• # Nekla (3,791)

• # Ujście (3,695)

• # Opatówek (3,673)

• # Krajenka (3,647)

• # Rakoniewice (3,594)

• # Miłosław (3,576)

• # Sompolno (3,539)

• # Gołańcz (3,310)

• # Tuliszków (3,266)

• # Kobylin (3,249)

• # Miejska Górka (3,232)

• # Ślesin (3,153)

• # Dobrzyca (3,130)

• # Pyzdry (3,127)

• # Margonin (2,988)

• # Zagórów (2,985)

• # Lwówek (2,964)

• # Łobżenica (2,951)

• # Bojanowo (2,906)

• # Rydzyna (2,895)

• # Kaczory

• # Sulmierzyce (2,880)

• # Poniec (2,859)

• # Książ Wielkopolski (2,715)

• # Czerniejewo (2,666)

• # Kłecko (2,632)

• # Wysoka (2,628)

• # Borek Wielkopolski (2,508)

• # Obrzycko (2,382)

• # Rychwał (2,372)

• # Osieczna (2,352)

• # Mieścisko

• # Żerków (2,121)

• # Raszków (2,108)

• # Pogorzela (2,095)

• # Dąbie (1,999)

• # Jutrosin (1,984)

• # Grabów nad Prosną (1,939)

• # Ostroróg (1,908)

• # Koźminek

• # Mikstat (1,837)

• # Chocz (1,790)

• # Wielichowo (1,755)

• # Krzywiń (1,706)

• # Przedecz (1,667)

• # Dolsk (1,558)

• # Stawiszyn (1,520)

• # Jaraczewo (1,412)

• # Rychtal

• # Dobra (1,390)

• # Miasteczko Krajeńskie

Topography
The relief of Greater Poland, geological conditions and soil have been shaped by two glaciations:
 * The Baltic glaciation in the lowlands of northern and central Europe where there are now numerous lakes of the Pomeranian Lake District, a feature especially common in and around Poznań and Gniezno.
 * The Mid-glaciation in the southern part of the province, where there is less terrain diversity and a lack of major lakes.

The highest elevation is Greater Kobyla Mountain (284 m) in the Ostrzeszowski Hills, the lowest area is located in the valley of the Warta River at the mouth of its tributary the Noteć (21 m) in the north-western part of the region. Agriculturally fertile soils account for around 60% of the province's area, while 20%, the rest of the non-forested or urban areas, is mostly wetland soil (muck-peat and alluvial soils).

An area of approximately 800000 ha is covered by forests, this represents around 25.8% of the total surface area of the region. In the lake districts of the northern and central parts of the province there are about 800 lakes; 58% of which cover an area of at least 10 ha and 8%, with an area exceeding 100 ha. The largest reservoir is the natural Greater Powidzkie Lake (1036 ha) in the Gniezno Lake District.

Wielkopolska Region lies within the basin of the Oder River, 88% of the province's surface water drains into the Warta river basin, and the remaining 12% is drained by a multitude of other river systems, including the Barycz, Ladislaus Trench and Obrzycy waterways. The quality of river waters is generally poor, but their condition is gradually improving and should soon be classed as 'clean'.

Geology
The main mineral energy resources in Greater Poland are lignite, natural gas, oil and peat.

Brown coal deposits are currently mined in the Konin area, and form the basis for the province's power industry (the Pątnów-Adams-Konin coal-fired power stations account for more than 10% of the national electricity production). The region also has significant quantities of peat deposits; it is calculated that there are ca. 886000 ha of land covered with an average thickness of 1.5 m of peat. An abundance of raw materials used in the production of numerous medicines was recently discovered in the muds of Błażejewo, Oderbank and Mechnacz. In addition, very large deposits of brown coal have been discovered in the vicinity of Kościan, these however are not currently being extracted and probably never will be extracted, due to the expense that would be incurred in adapting the site to build a coal mine and the need to resettle thousands of people.

Rock salt is mined intensively at a salt mine in Kłodawa (this mine alone accounts for about 20% of domestic production).

Throughout the province there are significant deposits of aggregates, gypsum, ceramic materials, and lacustrine chalk. In Kościan the largest and most modern, a natural gas production site is in operation. It supplies raw material for Kościańska Zieme, and Zielona Gora CHP. It is estimated that at the rate local gas reserves are being exploited, the reserves in Kościan will be enough for about 20 years of operation, thus practically allowing for local independence against the effects of gas crises.

Climate
Wielkopolska is influenced by oceanic air masses that affect the mildness of the climate. The farther east one travels the more distinctly continental the climate becomes. The area is situated in the Silesian Greater Poland agro-climatic region where the average annual temperature is about 8.2 °C, and in the north drops to around 7.6 °C. It is slightly warmer in the south and west where the average temperature is usually about 8.5 °C. The number of days with snow can reach up to 57 days in and around the Kalisz district.

The growing season is one of the longest in Poland. On the province's southern plains this season constitutes around 228 days, while north of Gniezno and Szamotuły this gradually declines to 216 days.

Precipitation ranges from 500 to 550 mm. Despite this the region is still faced with a deficit in rainfall, particularly in the eastern part of the province (around Słupcy, Kazimierz Biskupi, Kleczew) where sometimes experience only 450 mm of rainfall per year, this threatens steppization of the region. Throughout the province there is typically a prevailing westerly wind.

Transportation
Greater Poland is a major transport hub within Poland; a great deal of traffic from Russia and other states of the former Soviet Union passes through Poznań and Konin to reach Germany and other EU member states. To the south runs the international route from Gdańsk via Poznań and Leszno to Prague and then to the south of Europe. There is also a major highway in the province, the A2 motorway, which when completed will run from the western border of Poland with Germany, through Poznań to Warsaw and then via Belarus to Moscow.

The main railway hubs located in Greater Poland are Poznań, Piła and Ostrów Wielkopolski. PKP Intercity operate a number of trains a day between Warsaw and Berlin which provide a fast connection for the two cities also to Poznań. This route was the first in Poland, adapted for use by the European high-speed transportation system. The Poznań Główny railway station is the second busiest railway station in Poland. In the near future the government expects to construct a high-speed rail line in the shape of a Y connecting Kalisz and Poznań from Łódź, Warsaw and Wrocław.

Poznań is the port of arrival for most international travellers as it plays host to Ławica International Airport, which has recently seen the second-highest passenger growth rate in the country.

Economy
The Gross domestic product (GDP) of the province was 40.4 billion € in 2018, accounting for 8.1% of Polish economic output. GDP per capita adjusted for purchasing power was 19,700 € or 65% of the EU27 average in the same year. The GDP per employee was 72% of the EU average.

Politics
The Greater Poland voivodeship's government is headed by the province's voivode (governor) who is appointed by the Polish Prime Minister. The voivode is then assisted in performing his duties by the voivodeship's marshal, who is the appointed speaker for the voivodeship's executive and is elected by the sejmik (provincial assembly). The current voivode of Greater Poland is Łukasz Mikołajczyk, whilst the present marshal is Marek Woźniak.

The Sejmik of Greater Poland consists of 39 members.

Administrative division
Greater Poland Voivodeship is divided into 35 counties (powiats): 4 city counties and 31 land counties. These are further divided into 226 gminas.

The counties are listed in the following table (ordering within categories is by decreasing population).

Protected areas
Protected areas in Greater Poland Voivodeship include two National Parks and 12 Landscape Parks. These are listed below.
 * Drawno National Park (partly in Lubusz and West Pomeranian Voivodeships)
 * Greater Poland National Park
 * Barycz Valley Landscape Park (partly in Lower Silesian Voivodeship)
 * Chłapowski Landscape Park
 * Lednica Landscape Park
 * Powidz Landscape Park
 * Promno Landscape Park
 * Przemęt Landscape Park (partly in Lubusz Voivodeship)
 * Pszczew Landscape Park (partly in Lubusz Voivodeship)
 * Puszcza Zielonka Landscape Park
 * Rogalin Landscape Park
 * Sieraków Landscape Park
 * Warta Landscape Park
 * Żerków-Czeszewo Landscape Park

Sights
Greater Poland Voivodeship boasts 11 Historic Monuments of Poland:
 * Gorzeński Palace and park complex in Dobrzyca
 * Renaissance Basilica on the Holy Mountain, Głogówko
 * Royal Gniezno Cathedral
 * Manor and park complex in Koszuty
 * Kórnik Castle and park complex with the All Saints' Church in Kórnik
 * Ląd Abbey
 * Benedictine Monastery with the Romanesque-Gothic-Baroque Church of the Nativity of the Virgin Mary in Lubiń
 * Ostrów Lednicki
 * Poznań Old Town with the Ostrów Tumski, and the adjacent Park Cytadela and Fort Winiary
 * Baroque Raczyński Palace and park complex in Rogalin
 * Rydzyna Old Town with the Baroque Rydzyna Castle

The province is rich in historic architecture ranging from Romanesque and Gothic to Renaissance, Baroque and Art Nouveau. Numerous towns possess preserved historic market squares and town halls. The voivodeship is abundant in palaces, including in Antonin (often visited by Fryderyk Chopin), Czempiń, Kobylniki, Kołaczkowo (former home of Nobel Prize-winning novelist Władysław Reymont), Objezierze (visited by writers Adam Mickiewicz and Józef Ignacy Kraszewski) and Śmiełów (former place of stay of Adam Mickiewicz).

There are numerous World War II memorials in the province, including memorials at the sites of Nazi massacres of Poles, and museums at the sites of the former Chełmno extermination camp, Fort VII concentration camp in Poznań, and prison camp in Luboń.

Poland's largest church, the Basilica of Our Lady of Licheń, is located in the voivodeship.

There is an underground touristic route in the Kłodawa Salt Mine, considered the world's deepest underground tourist route.

The oldest preserved European signpost beyond the boundaries of the former Roman Empire is located in Konin.

Cuisine
In addition to traditional nationwide Polish cuisine, Greater Poland Voivodeship is known for its variety of regional and local traditional foods and drinks, which include especially various meat products (incl. various types of kiełbasa), cheeses, honeys, beverages and various dishes and meals, officially protected by the Ministry of Agriculture and Rural Development of Poland. Among the most known local snacks are the St. Martin's croissant from Poznań and Kalisz andruts.

Notable centers of traditional meat production include Grodzisk Wielkopolski, Krotoszyn, Kruszewnia, Nowy Tomyśl, Ostrzeszów, Rawicz, Trzcianka and Złotniki, whereas centers of traditional cheese and quark production include Wągrowiec, Gniezno, Kępno, Oborniki, Witkowo, Witoldzin and Września.

Grodzisk Wielkopolski is the place of origin of the Grodziskie beer style. Other traditional Polish beers, officially protected by the Ministry of Agriculture and Rural Development of Poland, are produced in Bojanowo, Czarnków and Miłosław.

Sports
Football and speedway enjoy the largest following in the province, with top football clubs being Lech Poznań and Warta Poznań, and Poland's most accomplished speedway team being Unia Leszno.

Since the establishment of the province, several international sports competitions were co-hosted by the province, including the EuroBasket 2009 and UEFA Euro 2012.

Szczypiorno, Kalisz is considered the cradle of Polish handball.

Curiosities

 * In the 16th-17th centuries, there were sizeable Scottish communities in Poznań and Łobżenica, and smaller ones in Borek Wielkopolski, Gostyń, Skoki and Szamotuły.

title: Greater Poland Voivodeship


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Penetration

Penetration may refer to:

Science and technology

 * Passage through a partition or wall by a wire, cable, or other electrically conductive object
 * Penetration (firestop), an opening in a wall or floor assembly required to have a fire-resistance rating, for the purpose of accommodating the passage of a mechanical, electrical, or structural penetrant
 * Penetration (weapons), the ability to pierce the target's armor or other protection
 * Penetration depth of light or any electromagnetic radiation in a physical medium
 * Penetrating trauma, injury that occurs when an object pierces the skin and enters a tissue of the body
 * In roofing, pipes, conduits, and HVAC supports passing through the room
 * An unauthorized act of bypassing access control

Arts and media

 * Penetration (band), a punk rock band
 * "Penetration", a song on Iggy and the Stooges' album Raw Power
 * "Penetration", a song on Pedro the Lion's album Control
 * "Penetration", a song by The Pyramids
 * Body of Lies (film), a film formerly known as Penetration

Other uses

 * Penetration (warfare), the breaching of, and moving past, a defensive military line
 * Market penetration or brand penetration, the degree to which a product or service is known and/or used
 * Sexual penetration, or sexual intercourse
 * in some jurisdictions, a criminal charge related to various sexual offences
 * In basketball, the ability of a player to drive through the opposition's defense
 * In magic, an illusion in which one object appears to pass through another

title: Penetration


text:
Performance measurement period

In telecommunication, performance measurement period is the period during which performance parameters are measured.

A performance measurement period is determined by required confidence limits and may vary as a function of the observed parameter values. User time is divided into consecutive performance measurement periods to enable measurement of user information transfer reliability.

title: Performance measurement period


text:
Periscope antenna

In telecommunication, a periscope antenna is an antenna configuration in which the transmitting antenna is oriented to produce a vertical radiation pattern, and a flat or off-axis parabolic reflector, mounted above the transmitting antenna, is used to direct the beam in a horizontal path toward the receiving antenna.

A periscope antenna facilitates increased terrain clearance without long transmission lines, while permitting the active equipment to be located at or near ground level for ease of maintenance.

title: Periscope antenna


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Personal mobility

In Universal Personal Telecommunications (UPT), personal mobility is the ability of a user to access telecommunication services at any UPT terminal on the basis of a personal identifier, and the capability of the network to provide those services in accord with the user's service profile.

Personal mobility involves the network's capability to locate the terminal associated with the user for the purposes of addressing, routing, and charging the user for calls. "Access" is intended to convey the concepts of both originating and terminating services. Management of the service profile by the user is not part of personal mobility. The personal mobility aspects of personal communications are based on the UPT number.

title: Personal mobility


text:
Phantom circuit

In telecommunication and electrical engineering, a phantom circuit is an electrical circuit derived from suitably arranged wires with one or more conductive paths being a circuit in itself and at the same time acting as one conductor of another circuit.

Phantom group

A phantom group is composed of three circuits that are derived from two single-channel circuits to form a phantom circuit. Here the phantom circuit is a third circuit derived from two suitably arranged pairs of wires, called side circuits, with each pair of wires being a circuit in itself and at the same time acting as one conductor of the third circuit. The "side circuits" within phantom circuits can be coupled to their respective voltage drops by center-tapped transformers, usually called "repeating coils". The center taps are on the line side of the side circuits. Current from the phantom circuit is split evenly by the center taps. This cancels crosstalk from the phantom circuit to the side circuits. Phantom working increased the number of circuits on long-distance routes in the early 20th century without putting up more wires. Phantoming declined with the adoption of carrier systems.

It is theoretically possible to create a phantom circuit from two other phantom circuits and so on up in a pyramid with a maximum 2n-1 circuits being derived from n original circuits. However, more than one level of phantoming is usually impractical. Isolation between the phantom circuit and the side circuits relies on accurate balance of the line and transformers. Imperfect balance results in crosstalk between the phantom and side circuits and this effect accumulates as each level of phantoms is added. Even small levels of crosstalk are unacceptable on analogue telecommunications circuits since speech crosstalk is still intelligible down to quite low levels.

Phantom microphone powering
Condenser microphones have impedance converter (current amplifier) circuitry that requires powering; in addition, the capsule of any non-electret, non-RF condenser microphone requires a polarizing voltage to be applied. Since the mid- to late 1960s most balanced, professional condenser microphones for recording and broadcast have used phantom powering. It can be provided by outboard AC or battery supplies, but nowadays is most often built into the mixing console, recorder or microphone preamplifier to which the microphones are connected.

By far the most common circuit uses +48 V DC fed through a matched pair of 6.8 kΩ resistors for each input channel. This arrangement has been standardized by the IEC and ISO, along with a less-commonly-used arrangement with +12 V DC and 680 Ω feed resistors.

As a practical matter, phantom powering allows the same two-conductor shielded cables to be used for both dynamic microphones and condenser microphones, while being harmless to balanced microphones that aren't designed to consume it, since the circuit balance prevents any substantial DC from flowing through the output circuit of those microphones.

DC phantom
Simple DC signalling can be achieved on a telecommunications line in a similar way to phantom powering of microphones. A switch connected to the transformer centre-tap at one end of the line can operate a similarly connected relay at the other end. The return path is through the ground connection. This arrangement can be used for remotely controlling equipment.

Carrier circuit phantoms
From the 1950s to around the 1980s, using phantoms on star-quad trunk carrier circuits was a popular method of deriving a high quality broadcast audio circuit. The multiplexed FDM telecommunications carrier system usually did not use the baseband of the cable because it was inconvenient to separate low frequencies with filters. On the other hand, a one-way audio phantom could be formed from the two pairs (go and return signals) making up the star-quad cable.

Unloaded phantom
Unloaded phantom is a phantom configuration of loaded lines (a circuit fitted with loading coils). The idea here is not to create additional circuits. Rather, the purpose is to cancel or greatly reduce the effect of the loading coils fitted to a line. The reason for doing this is that loaded lines have a definite cut-off frequency and it may be desired to equalise the line to a frequency which is higher than this, for example to make a circuit suitable for use by a broadcaster. Ideally, the loading would be removed or reduced for a permanent connection, but this is not feasible for temporary arrangements such as a requirement for outside broadcast. Instead, two circuits in a phantom configuration can be used to greatly reduce the inductance being inserted by the loading coils, and hence the loading effect.

It works because the loading coils used on balanced lines have two windings, one for each leg of the circuit. They are both wound on a common core and the windings are so arranged that the magnetic flux induced by both of them is in the same direction. Both windings induce an emf in each other as well as their own self-induction. This effect greatly increases the inductance of the coil and hence its loading effectiveness. By contrast, when the circuit is in the phantom configuration the currents in the two wires of each pair are in the same direction and the magnetic flux is being cancelled. This has precisely the opposite effect and the inductance is greatly reduced.

This configuration is most commonly used on the two pairs of a star-quad cable. It is not so successful with other pairs of wires. The difference in the path of the two pairs can easily destroy the balance and results in crosstalk and interference.

This configuration can also be called "bunched pairs". However, "bunched pairs" can also refer to the straightforward connection of two lines in parallel which is not a phantom circuit and will not reduce the loading.

Sources and references

 * AT&T: 'Principles of Electricity Applied to Telephone and Telegraph Work', 1953 (PDF-File, 39MB)
 * AT&T: 'Principles of Electricity Applied to Telephone and Telegraph Work', 1953 (PDF-File, 39MB)

title: Phantom circuit


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Phased array

In antenna theory, a phased array usually means an electronically scanned array, a computer-controlled array of antennas which creates a beam of radio waves that can be electronically steered to point in different directions without moving the antennas. The general theory of an electromagnetic phased array also finds applications in ultrasonic and medical imaging application (phased array ultrasonics) and in optics optical phased array.

In a simple array antenna, the radio frequency current from the transmitter is fed to multiple individual antenna elements with the proper phase relationship so that the radio waves from the separate elements combine (superpose) to form beams, to increase power radiated in desired directions and suppress radiation in undesired directions. In a phased array, the power from the transmitter is fed to the radiating elements through devices called phase shifters, controlled by a computer system, which can alter the phase or signal delay electronically, thus steering the beam of radio waves to a different direction. Since the size of an antenna array must extend many wavelengths to achieve the high gain needed for narrow beamwidth, phased arrays are mainly practical at the high frequency end of the radio spectrum, in the UHF and microwave bands, in which the operating wavelengths are conveniently small.

Phased arrays were originally conceived for use in military radar systems, to steer a beam of radio waves quickly across the sky to detect planes and missiles. These systems are now widely used and have spread to civilian applications such as 5G MIMO for cell phones. The phased array principle is also used in acoustics, and phased arrays of acoustic transducers are used in medical ultrasound imaging scanners (phased array ultrasonics), oil and gas prospecting (reflection seismology), and military sonar systems.

The term "phased array" is also used to a lesser extent for unsteered array antennas in which the phase of the feed power and thus the radiation pattern of the antenna array is fixed. For example, AM broadcast radio antennas consisting of multiple mast radiators fed so as to create a specific radiation pattern are also called "phased arrays".

Types
Phased arrays take multiple forms. However, the four most common are the passive electronically scanned array (PESA), active electronically scanned array (AESA), hybrid beam forming phased array, and digital beam forming (DBF) array.

A passive phased array or passive electronically scanned array (PESA) is a phased array in which the antenna elements are connected to a single transmitter and/or receiver, as shown in the first animation at top. PESAs are the most common type of phased array. Generally speaking, a PESA uses one receiver/exciter for the entire array.

An active phased array or active electronically scanned array (AESA) is a phased array in which each antenna element has an analog transmitter/receiver (T/R) module which creates the phase shifting required to electronically steer the antenna beam. Active arrays are a more advanced, second-generation phased-array technology that are used in military applications; unlike PESAs they can radiate several beams of radio waves at multiple frequencies in different directions simultaneously. However, the number of simultaneous beams is limited by practical reasons of electronic packaging of the beam formers to approximately three simultaneous beams for an AESA. Each beam former has a receiver/exciter connected to it.

A hybrid beam forming phased array can be thought of as a combination of an AESA and a digital beam forming phased array. It uses subarrays that are active phased arrays (for instance, a subarray may be 64, 128 or 256 elements and the number of elements depends upon system requirements). The subarrays are combined to form the full array. Each subarray has its own digital receiver/exciter. This approach allows clusters of simultaneous beams to be created.

A digital beam forming (DBF) phased array has a digital receiver/exciter at each element in the array. The signal at each element is digitized by the receiver/exciter. This means that antenna beams can be formed digitally in a field programmable gate array (FPGA) or the array computer. This approach allows for multiple simultaneous antenna beams to be formed.

A conformal antenna is a phased array in which the individual antennas, instead of being arranged in a flat plane, are mounted on a curved surface. The phase shifters compensate for the different path lengths of the waves due to the antenna elements' varying position on the surface, allowing the array to radiate a plane wave. Conformal antennas are used in aircraft and missiles, to integrate the antenna into the curving surface of the aircraft to reduce aerodynamic drag.

History

Phased array transmission was originally shown in 1905 by Nobel laureate Karl Ferdinand Braun who demonstrated enhanced transmission of radio waves in one direction. During World War II, Nobel laureate Luis Alvarez used phased array transmission in a rapidly steerable radar system for "ground-controlled approach", a system to aid in the landing of aircraft. At the same time, the GEMA in Germany built the Mammut 1. It was later adapted for radio astronomy leading to Nobel Prizes for Physics for Antony Hewish and Martin Ryle after several large phased arrays were developed at the University of Cambridge Interplanetary Scintillation Array. This design is also used for radar, and is generalized in interferometric radio antennas.

In 1966, most phased-array radars use ferrite phase shifters or traveling-wave tubes to dynamically adjust the phase. The AN/SPS-33 -- installed on the nuclear-powered ships Long Beach and Enterprise around 1961 -- was claimed to be the only operational 3-D phased array in the world in 1966. The AN/SPG-59 was designed to generate multiple tracking beams from the transmitting array and simultaneously program independent receiving arrays. The first civilian 3D phased array was built in 1960 at the National Aviation Facilities Experimental Center; but was abandoned in 1961.

In 2004, Caltech researchers demonstrated the first integrated silicon-based phased array receiver at 24 GHz with 8 elements. This was followed by their demonstration of a CMOS 24 GHz phased array transmitter in 2005 and a fully integrated 77 GHz phased array transceiver with integrated antennas in 2006 by the Caltech team. In 2007, DARPA researchers announced a 16-element phased-array radar antenna which was also integrated with all the necessary circuits on a single silicon chip and operated at 30–50 GHz.

The relative amplitudes of—and constructive and destructive interference effects among—the signals radiated by the individual antennas determine the effective radiation pattern of the array. A phased array may be used to point a fixed radiation pattern, or to scan rapidly in azimuth or elevation. Simultaneous electrical scanning in both azimuth and elevation was first demonstrated in a phased array antenna at Hughes Aircraft Company, California in 1957.

Broadcasting
In broadcast engineering, the term 'phased array' has a meaning different from its normal meaning, it means an ordinary array antenna, an array of multiple mast radiators designed to radiate a directional radiation pattern, as opposed to a single mast which radiates an omnidirectional pattern. Broadcast phased arrays have fixed radiation patterns and are not 'steered' during operation as are other phased arrays.

Phased arrays are used by many AM broadcast radio stations to enhance signal strength and therefore coverage in the city of license, while minimizing interference to other areas. Due to the differences between daytime and nighttime ionospheric propagation at mediumwave frequencies, it is common for AM broadcast stations to change between day (groundwave) and night (skywave) radiation patterns by switching the phase and power levels supplied to the individual antenna elements (mast radiators) daily at sunrise and sunset. For shortwave broadcasts many stations use arrays of horizontal dipoles. A common arrangement uses 16 dipoles in a 4×4 array. Usually this is in front of a wire grid reflector. The phasing is often switchable to allow beam steering in azimuth and sometimes elevation.

Radar
Phased arrays were invented for radar tracking of ballistic missiles, and because of their fast tracking abilities phased array radars are widely used in military applications. For example, because of the rapidity with which the beam can be steered, phased array radars allow a warship to use one radar system for surface detection and tracking (finding ships), air detection and tracking (finding aircraft and missiles) and missile uplink capabilities. Before using these systems, each surface-to-air missile in flight required a dedicated fire-control radar, which meant that radar-guided weapons could only engage a small number of simultaneous targets. Phased array systems can be used to control missiles during the mid-course phase of the missile's flight. During the terminal portion of the flight, continuous-wave fire control directors provide the final guidance to the target. Because the antenna pattern is electronically steered, phased array systems can direct radar beams fast enough to maintain a fire control quality track on many targets simultaneously while also controlling several in-flight missiles.

The AN/SPY-1 phased array radar, part of the Aegis Combat System deployed on modern U.S. cruisers and destroyers, "is able to perform search, track and missile guidance functions simultaneously with a capability of over 100 targets." Likewise, the Thales Herakles phased array multi-function radar used in service with France and Singapore has a track capacity of 200 targets and is able to achieve automatic target detection, confirmation and track initiation in a single scan, while simultaneously providing mid-course guidance updates to the MBDA Aster missiles launched from the ship. The German Navy and the Royal Dutch Navy have developed the Active Phased Array Radar System (APAR). The MIM-104 Patriot and other ground-based antiaircraft systems use phased array radar for similar benefits.

Phased arrays are used in naval sonar, in active (transmit and receive) and passive (receive only) and hull-mounted and towed array sonar.

Space probe communication
The MESSENGER spacecraft was a space probe mission to the planet Mercury (2011–2015 ). This was the first deep-space mission to use a phased-array antenna for communications. The radiating elements are circularly-polarized, slotted waveguides. The antenna, which uses the X band, used 26 radiative elements and can gracefully degrade.

Weather research usage
The National Severe Storms Laboratory has been using a SPY-1A phased array antenna, provided by the US Navy, for weather research at its Norman, Oklahoma facility since April 23, 2003. It is hoped that research will lead to a better understanding of thunderstorms and tornadoes, eventually leading to increased warning times and enhanced prediction of tornadoes. Current project participants include the National Severe Storms Laboratory and National Weather Service Radar Operations Center, Lockheed Martin, United States Navy, University of Oklahoma School of Meteorology, School of Electrical and Computer Engineering, and Atmospheric Radar Research Center, Oklahoma State Regents for Higher Education, the Federal Aviation Administration, and Basic Commerce and Industries. The project includes research and development, future technology transfer and potential deployment of the system throughout the United States. It is expected to take 10 to 15 years to complete and initial construction was approximately $25 million. A team from Japan's RIKEN Advanced Institute for Computational Science (AICS) has begun experimental work on using phased-array radar with a new algorithm for instant weather forecasts.

Optics
Within the visible or infrared spectrum of electromagnetic waves it is possible to construct optical phased arrays. They are used in wavelength multiplexers and filters for telecommunication purposes, laser beam steering, and holography. Synthetic array heterodyne detection is an efficient method for multiplexing an entire phased array onto a single element photodetector. The dynamic beam forming in an optical phased array transmitter can be used to electronically raster or vector scan images without using lenses or mechanically moving parts in a lensless projector. Optical phased array receivers have been demonstrated to be able to act as lensless cameras by selectively looking at different directions.

Satellite broadband internet transceivers
Starlink is a low Earth orbit satellite constellation that is under construction. It is designed to provide broadband internet connectivity to consumers; the user terminals of the system will use phased array antennas.

Radio-frequency identification (RFID)
By 2014, phased array antennas were integrated into RFID systems to increase the area of coverage of a single system by 100% to 76200 sqm while still using traditional passive UHF tags.

Human-machine interfaces (HMI)
A phased array of acoustic transducers, denominated airborne ultrasound tactile display (AUTD), was developed in 2008 at the University of Tokyo's Shinoda Lab to induce tactile feedback. This system was demonstrated to enable a user to interactively manipulate virtual holographic objects.

Radio astronomy
Phased Array Feeds (PAF) have recently been used at the focus of radio telescopes to provide many beams, giving the radio telescope a very wide field of view. Three examples are the ASKAP telescope in Australia, the Apertif upgrade to the Westerbork Synthesis Radio Telescope in The Netherlands, and the Florida Space Institute in the United States.

Array factor
The total directivity of a phased array will be a result of the gain of the individual array elements, and the directivity due their positioning in an array. This latter component is closely tied (but not equal to ) to the array factor. In a (rectangular) planar phased array, of dimensions $$M\times N$$, with inter-element spacing $$d_{x}$$ and $$d_{y}$$, respectively, the array factor can be calculated accordingly :$$AF=\sum_{n=1}^{N}I_{n1}\left[\sum_{m=1}^{M}I_{m1}\mathrm{e}^{j\left(m-1\right)\left(kd_{x}\sin\theta\cos\phi+\beta_{x}\right)}\right]\mathrm{e}^{j\left(n-1\right)\left(kd_{y}\sin\theta\sin\phi+\beta_{y}\right)}$$

Here, $$\theta$$ and $$\phi$$ are the directions which we are taking the array factor in, in the coordinate frame depicted to the right. The factors $$\beta_{x}$$ and $$\beta_{y}$$ are the progressive phase shift that is used to steer the beam electronically. The factors $$I_{n1}$$ and $$I_{m1}$$ are the excitation coefficients of the individual elements.

Beam steering is indicated in the same coordinate frame, however the direction of steering is indicated with $$\theta_{0}$$ and $$\phi_{0}$$, which is used in calculation of progressive phase:

$$\beta_{x}=-kd_{x}\sin\theta_{0}\cos\phi_{0}$$

$$\beta_{y}=-kd_{y}\sin\theta_{0}\sin\phi_{0}$$

In all above equations, the value $$k$$ describes the wavenumber of the frequency used in transmission.

These equations can be solved to predict the nulls, main lobe, and grating lobes of the array. Referring to the exponents in the array factor equation, we can say that major and grating lobes will occur at integer $$m,n=0,1,2,\dots$$ solutions to the following equations:

$$kd_{x}\sin\theta\cos\phi+\beta_{x}=\pm2m\pi$$

$$kd_{y}\sin\theta\sin\phi+\beta_{y}=\pm2n\pi$$

Worked example
It is common in engineering to provide phased array $$AF$$ values in decibels through $$AF_{dB}=10\log_{10}AF$$. Recalling the complex exponential in the array factor equation above, often, what is really meant by array factor is the magnitude of the summed phasor produced at the end of array factor calculation. With this, we can produce the following equation:$$AF_{dB}=10\log_{10}\Bigg\|\sum_{n=1}^{N}I_{1n}\left[\sum_{m=1}^{M}I_{m1}\mathrm{e}^{j\left(m-1\right)\left(kd_{x}\sin\theta\cos\phi+\beta_{x}\right)}\right]\mathrm{e}^{j\left(n-1\right)\left(kd_{y}\sin\theta\sin\phi+\beta_{y}\right)}\Bigg\|$$For the ease of visualization, we will analyze array factor given an input azimuth and elevation, which we will map to the array frame $$\theta$$ and $$\phi$$ through the following conversion:

$$\theta=\arccos\left(\cos\left(\theta_{az}\right)\sin\left(\theta_{el}\right)\right)$$

$$\phi=\arctan2\left(\sin\left(\theta_{el}\right),\sin\left(\theta_{az}\cos\left(\theta_{el}\right)\right)\right)$$

This represents a coordinate frame whose $$\mathbf{x}$$ axis is aligned with the array $$\mathbf{z}$$ axis, and whose $$\mathbf{y}$$ axis is aligned with the array $$\mathbf{x}$$ axis.

If we consider a $$16\times16$$ phased array, this process provides the following values for $$AF_{dB}$$, when steering to bore-sight ($$\theta_{0}=0^{\circ}$$,$$\phi_{0}=0^{\circ}$$): These values have been clipped to have a minimum $$AF$$ of -50 dB, however, in reality, null points in the array factor pattern will have values significantly smaller than this.

Different types of phased arrays
There are two main types of beamformers. These are time domain beamformers and frequency domain beamformers. From a theoretical point of view, both are in principle the same operation, with just a Fourier transform allowing conversion from one to the other type.

A graduated attenuation window is sometimes applied across the face of the array to improve side-lobe suppression performance, in addition to the phase shift.

Time domain beamformer works by introducing time delays. The basic operation is called "delay and sum". It delays the incoming signal from each array element by a certain amount of time, and then adds them together. A Butler matrix allows several beams to be formed simultaneously, or one beam to be scanned through an arc. The most common kind of time domain beam former is serpentine waveguide. Active phased array designs use individual delay lines that are switched on and off. Yttrium iron garnet phase shifters vary the phase delay using the strength of a magnetic field.

There are two different types of frequency domain beamformers.

The first type separates the different frequency components that are present in the received signal into multiple frequency bins (using either a Discrete Fourier transform (DFT) or a filterbank). When different delay and sum beamformers are applied to each frequency bin, the result is that the main lobe simultaneously points in multiple different directions at each of the different frequencies. This can be an advantage for communication links, and is used with the SPS-48 radar.

The other type of frequency domain beamformer makes use of Spatial Frequency. Discrete samples are taken from each of the individual array elements. The samples are processed using a DFT. The DFT introduces multiple different discrete phase shifts during processing. The outputs of the DFT are individual channels that correspond with evenly spaced beams formed simultaneously. A 1-dimensional DFT produces a fan of different beams. A 2-dimensional DFT produces beams with a pineapple configuration.

These techniques are used to create two kinds of phased array.
 * Dynamic – an array of variable phase shifters are used to move the beam
 * Fixed – the beam position is stationary with respect to the array face and the whole antenna is moved

There are two further sub-categories that modify the kind of dynamic array or fixed array.
 * Active – amplifiers or processors are in each phase shifter element
 * Passive – large central amplifier with attenuating phase shifters

Dynamic phased array
Each array element incorporates an adjustable phase shifter. These are collectively used to move the beam with respect to the array face.

Dynamic phased arrays require no physical movement to aim the beam. The beam is moved electronically. This can produce antenna motion fast enough to use a small pencil beam to simultaneously track multiple targets while searching for new targets using just one radar set, a capability known as track while search.

As an example, an antenna with a 2-degree beam with a pulse rate of 1 kHz will require approximately 8 seconds to cover an entire hemisphere consisting of 8,000 pointing positions. This configuration provides 12 opportunities to detect a 1000 m/s vehicle over a range of 100 km, which is suitable for military applications.

The position of mechanically steered antennas can be predicted, which can be used to create electronic countermeasures that interfere with radar operation. The flexibility resulting from phased array operation allows beams to be aimed at random locations, which eliminates this vulnerability. This is also desirable for military applications.

Fixed phased array
Fixed phased array antennas are typically used to create an antenna with a more desirable form factor than the conventional parabolic reflector or cassegrain reflector. Fixed phased arrays incorporate fixed phase shifters. For example, most commercial FM Radio and TV antenna towers use a collinear antenna array, which is a fixed phased array of dipole elements.

In radar applications, this kind of phased array is physically moved during the track and scan process. There are two configurations.
 * Multiple frequencies with a delay-line
 * Multiple adjacent beams

The SPS-48 radar uses multiple transmit frequencies with a serpentine delay line along the left side of the array to produce vertical fan of stacked beams. Each frequency experiences a different phase shift as it propagates down the serpentine delay line, which forms different beams. A filter bank is used to split apart the individual receive beams. The antenna is mechanically rotated.

Semi-active radar homing uses monopulse radar that relies on a fixed phased array to produce multiple adjacent beams that measure angle errors. This form factor is suitable for gimbal mounting in missile seekers.

Active phased array
Active electronically-scanned arrays (AESA) elements incorporate transmit amplification with phase shift in each antenna element (or group of elements). Each element also includes receive pre-amplification. The phase shifter setting is the same for transmit and receive.

Active phased arrays do not require phase reset after the end of the transmit pulse, which is compatible with Doppler radar and pulse-Doppler radar.

Passive phased array
Passive phased arrays typically use large amplifiers that produce all of the microwave transmit signal for the antenna. Phase shifters typically consist of waveguide elements controlled by magnetic field, voltage gradient, or equivalent technology.

The phase shift process used with passive phased arrays typically puts the receive beam and transmit beam into diagonally opposite quadrants. The sign of the phase shift must be inverted after the transmit pulse is finished and before the receive period begins to place the receive beam into the same location as the transmit beam. That requires a phase impulse that degrades sub-clutter visibility performance on Doppler radar and Pulse-Doppler radar. As an example, Yttrium iron garnet phase shifters must be changed after transmit pulse quench and before receiver processing starts to align transmit and receive beams. That impulse introduces FM noise that degrades clutter performance.

Passive phased array design is used in the AEGIS Combat System for direction-of-arrival estimation.

title: Phased array


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Phase distortion

In signal processing, phase distortion or phase-frequency distortion is distortion, that is, change in the shape of the waveform, that occurs when (a) a filter's phase response is not linear over the frequency range of interest, that is, the phase shift introduced by a circuit or device is not directly proportional to frequency, or (b) the zero-frequency intercept of the phase-frequency characteristic is not 0 or an integral multiple of 2π radians.

Audibility of phase distortion
Grossly changed phase relationships, without changing amplitudes, can be audible but the degree of audibility of the type of phase shifts expected from typical sound systems remains debated.

title: Phase distortion