Memory is the faculty of the brain by which information is encoded and retrieved when needed. Memory is vital to experiences, it is the retention of information over time for the purpose of influencing future action. If we could not remember past events, we could not learn or develop language, relationships, or personal identity. Memory is understood as an informational processing system with explicit and implicit functioning, made up of a sensory processor, short-term memory, long-term memory; this can be related to the neuron. The sensory processor allows information from the outside world to be sensed in the form of chemical and physical stimuli and attended to various levels of focus and intent. Working memory serves as an encoding and retrieval processor. Information in the form of stimuli is encoded in accordance with explicit or implicit functions by the working memory processor; the working memory retrieves information from stored material. The function of long-term memory is to store data through various categorical models or systems.
Explicit and implicit functions of memory are known as declarative and non-declarative systems. These systems lack thereof. Declarative, or explicit, memory is the conscious recollection of data. Under declarative memory resides episodic memory. Semantic memory refers to memory, encoded with specific meaning, while episodic memory refers to information, encoded along a spatial and temporal plane. Declarative memory is the primary process thought of when referencing memory. Non-declarative, or implicit, memory is the unconscious recollection of information. An example of a non-declarative process would be the unconscious learning or retrieval of information by way of procedural memory, or a priming phenomenon. Priming is the process of subliminally arousing specific responses from memory and shows that not all memory is consciously activated, whereas procedural memory is the slow and gradual learning of skills that occurs without conscious attention to learning. Memory is not a perfect processor, is affected by many factors.
The ways by which information is encoded and retrieved can all be corrupted. The amount of attention given new stimuli can diminish the amount of information that becomes encoded for storage; the storage process can become corrupted by physical damage to areas of the brain that are associated with memory storage, such as the hippocampus. The retrieval of information from long-term memory can be disrupted because of decay within long-term memory. Normal functioning, decay over time, brain damage all affect the accuracy and capacity of the memory. Memory loss is described as forgetfulness or amnesia. Sensory memory holds sensory information less than one second; the ability to look at an item and remember what it looked like with just a split second of observation, or memorization, is the example of sensory memory. It is an automatic response. With short presentations, participants report that they seem to "see" more than they can report; the first experiments exploring this form of sensory memory were conducted by George Sperling using the "partial report paradigm".
Subjects were presented with a grid of 12 letters, arranged into three rows of four. After a brief presentation, subjects were played either a high, medium or low tone, cuing them which of the rows to report. Based on these partial report experiments, Sperling was able to show that the capacity of sensory memory was 12 items, but that it degraded quickly; because this form of memory degrades so participants would see the display but be unable to report all of the items before they decayed. This type of memory cannot be prolonged via rehearsal. Three types of sensory memories exist. Iconic memory is a fast decaying store of visual information. Echoic memory is a fast decaying store of auditory information, another type of sensory memory that stores sounds that have been perceived for short durations. Haptic memory is a type of sensory memory. Short-term memory is known as working memory. Short-term memory allows recall for a period of several seconds to a minute without rehearsal, its capacity is very limited: George A. Miller, when working at Bell Laboratories, conducted experiments showing that the store of short-term memory was 7±2 items.
Modern estimates of the capacity of short-term memory are lower of the order of 4–5 items. For example, in recalling a ten-digit telephone number, a person could chunk the digits into three groups: first, the area code a three-digit chunk and lastly a four-digit chunk; this method of remembering telephone numbers is far more effective than attempting to remember a string of 10 digits. This may be reflected in some countries in the tendency to display telephone numbers as several chunks of two to four numbers. Short-term memory is believed to rely on an acoustic code for storing information, to a lesser extent a visual code. Conrad found that test subjects had more difficulty recalling collections of letters that were acoustically similar (e.g. E
Successive approximation ADC
A successive approximation ADC is a type of analog-to-digital converter that converts a continuous analog waveform into a discrete digital representation via a binary search through all possible quantization levels before converging upon a digital output for each conversion. Key DAC = digital-to-analog converter EOC = end of conversion SAR = successive approximation register S/H = sample and hold circuit Vin = input voltage Vref = reference voltage The successive approximation analog-to-digital converter circuit consists of four chief subcircuits: A sample and hold circuit to acquire the input voltage. An analog voltage comparator that compares Vin to the output of the internal DAC and outputs the result of the comparison to the successive approximation register. A successive approximation register subcircuit designed to supply an approximate digital code of Vin to the internal DAC. An internal reference DAC that, for comparison with VREF, supplies the comparator with an analog voltage equal to the digital code output of the SARin.
The successive approximation register is initialized so that the most significant bit is equal to a digital 1. This code is fed into the DAC, which supplies the analog equivalent of this digital code into the comparator circuit for comparison with the sampled input voltage. If this analog voltage exceeds Vin the comparator causes the SAR to reset this bit; the next bit is set to 1 and the same test is done, continuing this binary search until every bit in the SAR has been tested. The resulting code is the digital approximation of the sampled input voltage and is output by the SAR at the end of the conversion. Mathematically, let Vin = xVref, so x in is the normalized input voltage; the objective is to digitize x to an accuracy of 1/2n. The algorithm proceeds as follows: Initial approximation x0 = 0. Ith approximation xi = xi−1 − s/2i.where, s is the signum-function. It follows using mathematical induction; as shown in the above algorithm, a SAR ADC requires: An input voltage source Vin. A reference voltage source Vref to normalize the input.
A DAC to convert the ith approximation xi to a voltage. A comparator to perform the function s by comparing the DAC's voltage with the input voltage. A register to store the output of the comparator and apply xi−1 − s/2i. Example: The ten steps to converting an analog input to 10 bit digital, using successive approximation, are shown here for all voltages from 5 V to 0 V in 0.1 V iterations. Since the reference voltage is 5 V, when the input voltage is 5 V all bits are set; as the voltage is decreased to 4.9 V, only some of the least significant bits are cleared. The MSB will remain set until the input is one half the reference voltage, 2.5 V. The binary weights assigned to each bit, starting with the MSB, are 2.5, 1.25, 0.625, 0.3125, 0.15625, 0.078125, 0.0390625, 0.01953125, 0.009765625, 0.0048828125. All of these add up to 4.9951171875, meaning binary 1111111111, or one LSB less than 5. When the analog input is being compared to the internal DAC output, it is being compared to each of these binary weights, starting with the 2.5 V and either keeping it or clearing it as a result.
By adding the next weight to the previous result, comparing again, repeating until all the bits and their weights have been compared to the input, the end result, a binary number representing the analog input, is found. One of the most common implementations of the successive approximation ADC, the charge-redistribution successive approximation ADC, uses a charge scaling DAC; the charge scaling DAC consists of an array of individually switched binary-weighted capacitors. The amount of charge upon each capacitor in the array is used to perform the aforementioned binary search in conjunction with a comparator internal to the DAC and the successive approximation register. First, the capacitor array is discharged to the offset voltage of the comparator, VOS; this step provides automatic offset cancellation. Next, all of the capacitors within the array are switched to the input signal, vIN; the capacitors now have a charge equal to their respective capacitance times the input voltage minus the offset voltage upon each of them.
In the third step, the capacitors are switched so that this charge is applied across the comparator's input, creating a comparator input voltage equal to −vIN. The actual conversion process proceeds. First, the MSB capacitor is switched to VREF, which corresponds to the full-scale range of the ADC. Due to the binary-weighting of the array the MSB capacitor forms a 1:1 charge divider with the rest of the array. Thus, the input voltage to the comparator is now −vIN plus VREF/2. Subsequently, if vIN is greater than VREF/2 the comparator outputs a digital 1 as the MSB, otherwise it outputs a digital 0 as the MSB; each capacitor is tested in the same manner until the comparator input voltage converges to the offset voltage, or at least as close as possible given the resolution of the DAC. When implemented as an analog circuit – where the value of each successive bit is not 2N – a successive approximation approach might not output the ideal value because the binary search algorithm incorrectly removes what it believes to be half of the values the unknown input cannot be.
Depending on the difference between actual and ideal performance, the maximum error can exceed several LSBs as the error between the actual and ideal 2N becomes large for one or more bits. Since we don't know the actua
Liquid crystals are a state of matter which has properties between those of conventional liquids and those of solid crystals. For instance, a liquid crystal may flow like a liquid, but its molecules may be oriented in a crystal-like way. There are many different types of liquid-crystal phases, which can be distinguished by their different optical properties; the contrasting areas in the textures correspond to domains where the liquid-crystal molecules are oriented in different directions. Within a domain, the molecules are well ordered. LC materials may not always be in a liquid-crystal phase. Liquid crystals can be divided into thermotropic and metallotropic phases. Thermotropic and lyotropic liquid crystals consist of organic molecules, although a few minerals are known. Thermotropic LCs exhibit a phase transition into the liquid-crystal phase. Lyotropic LCs exhibit phase transitions as a function of both temperature and concentration of the liquid-crystal molecules in a solvent. Metallotropic LCs are composed of both inorganic molecules.
Examples of liquid crystals can be found both in the natural world and in technological applications. Most contemporary electronic displays use liquid crystals. Lyotropic liquid-crystalline phases are abundant in living systems but can be found in the mineral world. For example, many proteins and cell membranes are liquid crystals. Other well-known examples of liquid crystals are solutions of soap and various related detergents, as well as the tobacco mosaic virus, some clays. In 1888, Austrian botanical physiologist Friedrich Reinitzer, working at the Karl-Ferdinands-Universität, examined the physico-chemical properties of various derivatives of cholesterol which now belong to the class of materials known as cholesteric liquid crystals. Other researchers had observed distinct color effects when cooling cholesterol derivatives just above the freezing point, but had not associated it with a new phenomenon. Reinitzer perceived that color changes in a derivative cholesteryl benzoate were not the most peculiar feature.
He found that cholesteryl benzoate does not melt in the same manner as other compounds, but has two melting points. At 145.5 °C it melts into a cloudy liquid, at 178.5 °C it melts again and the cloudy liquid becomes clear. The phenomenon is reversible. Seeking help from a physicist, on March 14, 1888, he wrote to Otto Lehmann, at that time a Privatdozent in Aachen, they exchanged samples. Lehmann examined the intermediate cloudy fluid, reported seeing crystallites. Reinitzer's Viennese colleague von Zepharovich indicated that the intermediate "fluid" was crystalline; the exchange of letters with Lehmann ended on April 24, with many questions unanswered. Reinitzer presented his results, with credits to Lehmann and von Zepharovich, at a meeting of the Vienna Chemical Society on May 3, 1888. By that time, Reinitzer had discovered and described three important features of cholesteric liquid crystals: the existence of two melting points, the reflection of circularly polarized light, the ability to rotate the polarization direction of light.
After his accidental discovery, Reinitzer did not pursue studying liquid crystals further. The research was continued by Lehmann, who realized that he had encountered a new phenomenon and was in a position to investigate it: In his postdoctoral years he had acquired expertise in crystallography and microscopy. Lehmann started a systematic study, first of cholesteryl benzoate, of related compounds which exhibited the double-melting phenomenon, he was able to make observations in polarized light, his microscope was equipped with a hot stage enabling high temperature observations. The intermediate cloudy phase sustained flow, but other features the signature under a microscope, convinced Lehmann that he was dealing with a solid. By the end of August 1889 he had published his results in the Zeitschrift für Physikalische Chemie. Lehmann's work was continued and expanded by the German chemist Daniel Vorländer, who from the beginning of 20th century until his retirement in 1935, had synthesized most of the liquid crystals known.
However, liquid crystals were not popular among scientists and the material remained a pure scientific curiosity for about 80 years. After World War II work on the synthesis of liquid crystals was restarted at university research laboratories in Europe. George William Gray, a prominent researcher of liquid crystals, began investigating these materials in England in the late 1940s, his group synthesized many new materials that exhibited the liquid crystalline state and developed a better understanding of how to design molecules that exhibit the state. His book Molecular Structure and the Properties of Liquid Crystals became a guidebook on the subject. One of the first U. S. chemists to study liquid crystals was Glenn H. Brown, starting in 1953 at the University of Cincinnati and at Kent State University. In 1965, he organized the first international conference on liquid crystals, in Kent, with about 100 of the world's top liquid crystal scientists in attendance; this conference marked the beginning of a worldwide effort to perform research in this field, which soon led to the development of practical applications for these unique materials.
Liquid crystal materials became a focus of research in the development of flat panel electronic displays beginning in 1962 at RCA Laboratories. When physical che
An operational amplifier is a DC-coupled high-gain electronic voltage amplifier with a differential input and a single-ended output. In this configuration, an op-amp produces an output potential, hundreds of thousands of times larger than the potential difference between its input terminals. Operational amplifiers had their origins in analog computers, where they were used to perform mathematical operations in many linear, non-linear, frequency-dependent circuits; the popularity of the op-amp as a building block in analog circuits is due to its versatility. By using negative feedback, the characteristics of an op-amp circuit, its gain and output impedance, bandwidth etc. are determined by external components and have little dependence on temperature coefficients or engineering tolerance in the op-amp itself. Op-amps are among the most used electronic devices today, being used in a vast array of consumer and scientific devices. Many standard IC op-amps cost only a few cents in moderate production volume.
Op-amps may be used as elements of more complex integrated circuits. The op-amp is one type of differential amplifier. Other types of differential amplifier include the differential amplifier, the instrumentation amplifier, the isolation amplifier, negative-feedback amplifier; the amplifier's differential inputs consist of a non-inverting input with voltage V+ and an inverting input with voltage V−. The output voltage of the op-amp Vout is given by the equation V out = A OL, where AOL is the open-loop gain of the amplifier; the magnitude of AOL is very large, therefore a quite small difference between V+ and V− drives the amplifier output nearly to the supply voltage. Situations in which the output voltage is equal to or greater than the supply voltage are referred to as saturation of the amplifier; the magnitude of AOL is not well controlled by the manufacturing process, so it is impractical to use an open-loop amplifier as a stand-alone differential amplifier. Without negative feedback, with positive feedback for regeneration, an op-amp acts as a comparator.
If the inverting input is held at ground directly or by a resistor Rg, the input voltage Vin applied to the non-inverting input is positive, the output will be maximum positive. Since there is no feedback from the output to either input, this is an open-loop circuit acting as a comparator. If predictable operation is desired, negative feedback is used, by applying a portion of the output voltage to the inverting input; the closed-loop feedback reduces the gain of the circuit. When negative feedback is used, the circuit's overall gain and response becomes determined by the feedback network, rather than by the op-amp characteristics. If the feedback network is made of components with values small relative to the op amp's input impedance, the value of the op-amp's open-loop response AOL does not affect the circuit's performance; the response of the op-amp circuit with its input and feedback circuits to an input is characterized mathematically by a transfer function. The transfer functions are important in most applications such as in analog computers.
High input impedance at the input terminals and low output impedance at the output terminal are useful features of an op-amp. In the non-inverting amplifier on the right, the presence of negative feedback via the voltage divider Rf, Rg determines the closed-loop gain ACL = Vout / Vin. Equilibrium will be established when Vout is just sufficient to "reach around and pull" the inverting input to the same voltage as Vin; the voltage gain of the entire circuit is thus 1 + Rf/Rg. As a simple example, if Vin = 1 V and Rf = Rg, Vout will be 2 V the amount required to keep V− at 1 V; because of the feedback provided by the Rf, Rg network, this is a closed-loop circuit. Another way to analyze this circuit proceeds by making the following assumptions: When an op-amp operates in linear mode, the difference in voltage between the non-inverting pin and the inverting pin is negligibly small; the input impedance between and pins is much larger than other resistances in the circuit. The input signal Vin appears at both and pins, resulting in a current i through Rg equal to Vin/Rg: i = V in R g.
Since Kirchhoff's current law states that the same current must leave a node as enter it, since the impedance into the pin is near infinity, we can assume all of the same current i flow
Simian Mobile Disco
Simian Mobile Disco are an English electronic music duo and production team, formed in 2003 by James Ford and Jas Shaw of the band Simian. Musically, they are known for their analogue production. Ford is known for his production work. Simian Mobile Disco formed as a DJ duo, on the side of their early four-piece band Simian, they released a number of early tastemaker singles, such as "The Mighty Atom / Boatrace / Upside Down" on I'm a Cliché and "The Count", on Kitsuné, but gained more fame for their remixes of artists such as Muse, The Go! Team and others. In 2006, Kitsuné released the duo's underground hit "Hustler", which features guest vocals from New York singer Char Johnson; the band's debut album, Attack Decay Sustain Release was released on 18 June 2007 on Wichita Recordings. Among the tracks included on it are "Sleep Deprivation", "Hustler", "Tits and Acid", "I Believe", "Hot Dog" and lead single "It's the Beat", which features Ninja from UK indie band The Go! Team on vocals; the album contains five new tracks, the European version includes a bonus disc.
The album was preceded by mix compilations in April for the "Bugged Out" series. SMD supported Klaxons at the Brixton Academy on 5 December 2007, The Chemical Brothers at the Birmingham National Indoor Arena on 7 December 2007, at Aintree Pavilion on 9 December 2007 and Brighton Centre on 12 December 2007. SMD made a mix for Mixmag. While working on their second studio album, they released a collection of remixed SMD originals entitled Sample and Hold, which contains eleven tracks and was released in the UK on 28 July 2008. In January 2009, they announced on their Myspace page that a new album would be released in 2009, they released a new track, "Synthesise", on 12 February, through a music video that "features live visual accompaniment" for the track. Two days a new song was broadcast on BBC Radio 1 named "10,000 Horses Can't Be Wrong", soon followed by the release on 6 March of the official music video on their YouTube channel, their second studio album Temporary Pleasure was announced on 6 May, featuring many guests including Gruff Rhys of Super Furry Animals, Alexis Taylor of Hot Chip, Beth Ditto of Gossip, Chris Keating of Yeasayer.
On New Year's Eve 2009 Simian Mobile Disco headlined "Get Loaded in the Dark" at the Brixton Academy, alongside Annie Mac, Chase & Status and Sub Focus. During the introduction of their Essential Mix made for Radio 1, broadcast on 9 January 2010, they gave hints on what would be a "techno-based album" expected for in 2010. Since the duo has established what will be a quarterly residency to JDH and Dave P's Fixed nights, in NYC. In March 2010 the duo announced their new club-night project, curated by the duo and accompanied by what they say to be "a brand new imprint" titled Delicacies; the first single on Delicacies was set to be released in late May, both physically and digitally. The first two tracks are entitled "Aspic" and "Nerve Salad". Simian Mobile Disco announced that every track will "take the name of an exotic, bizarre, delicacy from around the world". Simian Mobile Disco played the Together Winter Music Festival at the Alexandra Palace in London on 26 November 2011. In February 2012, Simian Mobile Disco announced the follow-up to Delicacies, released on 14 May 2012.
"Seraphim" was released as the album's lead single on 9 April. On 2 October 2012 they released their fourth EP A Form of Change, whose four tracks included on the release were taken from Unpatterns recording sessions. In March 2014, it was announced that on 26 April 2014, Simian Mobile Disco would be recording for a new album, Whorl, at an intimate show in Pioneertown, CA; the two band members performed using one sequencer each. The recorded tracks were polished in their studio for the eventual album release. After wrapping touring and support for Whorl, the duo took a short hiatus in 2015. Ford produced albums for Florence and the Machine, Mumford & Sons and The Last Shadow Puppets, while Shaw built a new studio and released a series of solo EPs; the duo announced in 2016 that they would release four singles, totalling eight new tracks, during the year born out of jam sessions in the new studio. As of July, two of these singles have been released; the singles see the duo abandoning the tradition of naming their traditional techno tracks after exotic cuisine, "for the simple reason that we've pretty much run out of weird and wonderful food stuffs to steal names from.
Instead, a semi-random automated process has been used to create the track names". In September, a new album Welcome To Sideways was announced for release in November 2016; the nine-track album, featuring "Staring At All This Handle", "Remember In Reverse" along with seven brand new tracks, will come with a bonus mixed version. Like their previous Delicacies album from 2010, the tracks are more club-focused than the experimental style found on Whorl. Ford commented: "We realize that from an outsider point of view, it can seem like we change quite radically with every album we do but from our point of view it always feels like a smooth transition. People who have stuck with us this long, appreciate the fact that we aren’t trying to repeat ourselves with every album, will enjoy another slight turn sideways."The album was promoted with a series of live shows and an appearance on BBC Radio 1's Essential Mix in early 2017. Towards the end of the year the duo began a monthly residency on NTS Radio.
In December 2017, Simian Mobile Disco signed a music publishing deal with Warner/Chappell Music. The
Electronics comprises the physics, engineering and applications that deal with the emission and control of electrons in vacuum and matter. The identification of the electron in 1897, along with the invention of the vacuum tube, which could amplify and rectify small electrical signals, inaugurated the field of electronics and the electron age. Electronics deals with electrical circuits that involve active electrical components such as vacuum tubes, diodes, integrated circuits and sensors, associated passive electrical components, interconnection technologies. Electronic devices contain circuitry consisting or of active semiconductors supplemented with passive elements; the nonlinear behaviour of active components and their ability to control electron flows makes amplification of weak signals possible. Electronics is used in information processing, telecommunication, signal processing; the ability of electronic devices to act as switches makes digital information-processing possible. Interconnection technologies such as circuit boards, electronics packaging technology, other varied forms of communication infrastructure complete circuit functionality and transform the mixed electronic components into a regular working system, called an electronic system.
An electronic system may be a component of a standalone device. Electrical and electromechanical science and technology deals with the generation, switching and conversion of electrical energy to and from other energy forms; this distinction started around 1906 with the invention by Lee De Forest of the triode, which made electrical amplification of weak radio signals and audio signals possible with a non-mechanical device. Until 1950 this field was called "radio technology" because its principal application was the design and theory of radio transmitters and vacuum tubes; as of 2018 most electronic devices use semiconductor components to perform electron control. The study of semiconductor devices and related technology is considered a branch of solid-state physics, whereas the design and construction of electronic circuits to solve practical problems come under electronics engineering; this article focuses on engineering aspects of electronics. Digital electronics Analogue electronics Microelectronics Circuit design Integrated circuits Power electronics Optoelectronics Semiconductor devices Embedded systems An electronic component is any physical entity in an electronic system used to affect the electrons or their associated fields in a manner consistent with the intended function of the electronic system.
Components are intended to be connected together by being soldered to a printed circuit board, to create an electronic circuit with a particular function. Components may be packaged singly, or in more complex groups as integrated circuits; some common electronic components are capacitors, resistors, transistors, etc. Components are categorized as active or passive. Vacuum tubes were among the earliest electronic components, they were solely responsible for the electronics revolution of the first half of the twentieth century. They allowed for vastly more complicated systems and gave us radio, phonographs, long-distance telephony and much more, they played a leading role in the field of microwave and high power transmission as well as television receivers until the middle of the 1980s. Since that time, solid-state devices have all but taken over. Vacuum tubes are still used in some specialist applications such as high power RF amplifiers, cathode ray tubes, specialist audio equipment, guitar amplifiers and some microwave devices.
In April 1955, the IBM 608 was the first IBM product to use transistor circuits without any vacuum tubes and is believed to be the first all-transistorized calculator to be manufactured for the commercial market. The 608 contained more than 3,000 germanium transistors. Thomas J. Watson Jr. ordered all future IBM products to use transistors in their design. From that time on transistors were exclusively used for computer logic and peripherals. Circuits and components can be divided into two groups: digital. A particular device may consist of circuitry that has a mix of the two types. Most analog electronic appliances, such as radio receivers, are constructed from combinations of a few types of basic circuits. Analog circuits use a continuous range of voltage or current as opposed to discrete levels as in digital circuits; the number of different analog circuits so far devised is huge because a'circuit' can be defined as anything from a single component, to systems containing thousands of components.
Analog circuits are sometimes called linear circuits although many non-linear effects are used in analog circuits such as mixers, etc. Good examples of analog circuits include vacuum tube and transistor amplifiers, operational amplifiers and oscillators. One finds modern circuits that are analog; these days analog circuitry may use digital or microprocessor techniques to improve performance. This type of circuit is called "mixed signal" rather than analog or digital. Sometimes it may be difficult to differentiate between analog and digital circuits as they have elements of both linear and non-linear
In electronics, an analog-to-digital converter is a system that converts an analog signal, such as a sound picked up by a microphone or light entering a digital camera, into a digital signal. An ADC may provide an isolated measurement such as an electronic device that converts an input analog voltage or current to a digital number representing the magnitude of the voltage or current; the digital output is a two's complement binary number, proportional to the input, but there are other possibilities. There are several ADC architectures. Due to the complexity and the need for matched components, all but the most specialized ADCs are implemented as integrated circuits. A digital-to-analog converter performs the reverse function. An ADC converts a continuous-time and continuous-amplitude analog signal to a discrete-time and discrete-amplitude digital signal; the conversion involves quantization of the input, so it introduces a small amount of error or noise. Furthermore, instead of continuously performing the conversion, an ADC does the conversion periodically, sampling the input, limiting the allowable bandwidth of the input signal.
The performance of an ADC is characterized by its bandwidth and signal-to-noise ratio. The bandwidth of an ADC is characterized by its sampling rate; the SNR of an ADC is influenced by many factors, including the resolution and accuracy, aliasing and jitter. The SNR of an ADC is summarized in terms of its effective number of bits, the number of bits of each measure it returns that are on average not noise. An ideal ADC has an ENOB equal to its resolution. ADCs are required SNR of the signal to be digitized. If an ADC operates at a sampling rate greater than twice the bandwidth of the signal per the Nyquist–Shannon sampling theorem, perfect reconstruction is possible; the presence of quantization error limits the SNR of an ideal ADC. However, if the SNR of the ADC exceeds that of the input signal, its effects may be neglected resulting in an perfect digital representation of the analog input signal; the resolution of the converter indicates the number of discrete values it can produce over the range of analog values.
The resolution determines the magnitude of the quantization error and therefore determines the maximum possible average signal-to-noise ratio for an ideal ADC without the use of oversampling. The values are stored electronically in binary form, so the resolution is expressed as the audio bit depth. In consequence, the number of discrete values available is assumed to be a power of two. For example, an ADC with a resolution of 8 bits can encode an analog input to one in 256 different levels; the values can represent the ranges depending on the application. Resolution can be defined electrically, expressed in volts; the change in voltage required to guarantee a change in the output code level is called the least significant bit voltage. The resolution Q of the ADC is equal to the LSB voltage; the voltage resolution of an ADC is equal to its overall voltage measurement range divided by the number of intervals: Q = E F S R 2 M, where M is the ADC's resolution in bits and EFSR is the full scale voltage range.
EFSR is given by E F S R = V R e f H i − V R e f L o w, where VRefHi and VRefLow are the upper and lower extremes of the voltages that can be coded. The number of voltage intervals is given by N = 2 M, where M is the ADC's resolution in bits; that is, one voltage interval is assigned in between two consecutive code levels. Example: Coding scheme as in figure 1 Full scale measurement range = 0 to 1 volt ADC resolution is 3 bits: 23 = 8 quantization levels ADC voltage resolution, Q = 1 V / 8 = 0.125 V. In many cases, the useful resolution of a converter is limited by the signal-to-noise ratio and other errors in the overall system expressed as an ENOB. Quantization error is introduced by quantization in an ideal ADC, it is a rounding error between the analog input voltage to the output digitized value. The error is signal-dependent. In an ideal ADC, where the quantization error is uniformly distributed between −1/2 LSB and +1/2 LSB, the signal has a uniform distribution covering all quantization levels, the Signal-to-quantization-noise ratio is given by S Q N R = 20 log 10 ≈ 6.02 ⋅ Q d B Where Q is the number of quantization bits.
For example, for a 16-bit ADC, the quantization error is 96.3 dB below the maximum level. Quantization error is distributed from DC to the Nyquist frequency if part of the ADC's bandwidth is not used, as is the case