Time-to-digital Converter
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Time-to-digital Converter
In electronic instrumentation and signal processing, a time-to-digital converter (TDC) is a device for recognizing events and providing a digital representation of the time they occurred. For example, a TDC might output the time of arrival for each incoming pulse. Some applications wish to measure the time interval between two events rather than some notion of an absolute time. In electronics time-to-digital converters (TDCs) or time digitizers are devices commonly used to measure a time interval and convert it into digital (binary) output. In some cases interpolating TDCs are also called time counters (TCs). TDCs are used to determine the time interval between two signal pulses (known as start and stop pulse). Measurement is started and stopped when the rising or falling edge of a signal pulse crosses a set threshold. This pattern is seen in many physical experiments, like time-of-flight and lifetime measurements in atomic and high energy physics, experiments that involve laser ...
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Electronics
The field of electronics is a branch of physics and electrical engineering that deals with the emission, behaviour and effects of electrons using electronic devices. Electronics uses active devices to control electron flow by amplification and rectification, which distinguishes it from classical electrical engineering, which only uses passive effects such as resistance, capacitance and inductance to control electric current flow. Electronics has hugely influenced the development of modern society. The central driving force behind the entire electronics industry is the semiconductor industry sector, which has annual sales of over $481 billion as of 2018. The largest industry sector is e-commerce, which generated over $29 trillion in 2017. History and development Electronics has hugely influenced the development of modern society. The identification of the electron in 1897, along with the subsequent invention of the vacuum tube which could amplify and rectify small ...
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Crystal Oscillator
A crystal oscillator is an electronic oscillator circuit that uses a piezoelectric crystal as a frequency-selective element. The oscillator frequency is often used to keep track of time, as in quartz wristwatches, to provide a stable clock signal for digital integrated circuits, and to stabilize frequencies for radio transmitters and receivers. The most common type of piezoelectric resonator used is a quartz crystal, so oscillator circuits incorporating them became known as crystal oscillators. However, other piezoelectricity materials including polycrystalline ceramics are used in similar circuits. A crystal oscillator relies on the slight change in shape of a quartz crystal under an electric field, a property known as inverse piezoelectricity. A voltage applied to the electrodes on the crystal causes it to change shape; when the voltage is removed, the crystal generates a small voltage as it elastically returns to its original shape. The quartz oscillates at a stable ...
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Fractional Part
The fractional part or decimal part of a non‐negative real number x is the excess beyond that number's integer part. If the latter is defined as the largest integer not greater than , called floor of or \lfloor x\rfloor, its fractional part can be written as: :\operatorname (x)=x - \lfloor x \rfloor,\; x > 0. For a positive number written in a conventional positional numeral system (such as binary or decimal), its fractional part hence corresponds to the digits appearing after the radix point. The result is a real number in the half-open interval x, -\lfloor , x, \rfloor , or by the Weisstein,_Eric_W._"Fractional_Part."_From_MathWorld--A_Wolfram_Web_Resource
/ref> :\operatorname_(x)=\begin x_-_\lfloor_x_\rfloor_&_x_\ge_ ...
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Probabilities
Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty."Kendall's Advanced Theory of Statistics, Volume 1: Distribution Theory", Alan Stuart and Keith Ord, 6th Ed, (2009), .William Feller, ''An Introduction to Probability Theory and Its Applications'', (Vol 1), 3rd Ed, (1968), Wiley, . The higher the probability of an event, the more likely it is that the event will occur. A simple example is the tossing of a fair (unbiased) coin. Since the coin is fair, the two outcomes ("heads" and "tails") are both equally probable; the probability of "heads" equals the probability of "tails"; and since no other outcomes are possible, the probability of either "heads" or "tails" is 1/2 (which could also be written as 0.5 or 50%). These conce ...
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Quantization Error
Quantization, in mathematics and digital signal processing, is the process of mapping input values from a large set (often a continuous set) to output values in a (countable) smaller set, often with a finite number of elements. Rounding and truncation are typical examples of quantization processes. Quantization is involved to some degree in nearly all digital signal processing, as the process of representing a signal in digital form ordinarily involves rounding. Quantization also forms the core of essentially all lossy compression algorithms. The difference between an input value and its quantized value (such as round-off error) is referred to as quantization error. A device or algorithmic function that performs quantization is called a quantizer. An analog-to-digital converter is an example of a quantizer. Example For example, rounding a real number x to the nearest integer value forms a very basic type of quantizer – a ''uniform'' one. A typical (''mid-tread'') uni ...
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Probability Distribution
In probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment. It is a mathematical description of a random phenomenon in terms of its sample space and the probabilities of events (subsets of the sample space). For instance, if is used to denote the outcome of a coin toss ("the experiment"), then the probability distribution of would take the value 0.5 (1 in 2 or 1/2) for , and 0.5 for (assuming that the coin is fair). Examples of random phenomena include the weather conditions at some future date, the height of a randomly selected person, the fraction of male students in a school, the results of a survey to be conducted, etc. Introduction A probability distribution is a mathematical description of the probabilities of events, subsets of the sample space. The sample space, often denoted by \Omega, is the set of all possible outcomes of a random phe ...
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Clock Signal
In electronics and especially synchronous digital circuits, a clock signal (historically also known as ''logic beat'') oscillates between a high and a low state and is used like a metronome to coordinate actions of digital circuits. A clock signal is produced by a clock generator. Although more complex arrangements are used, the most common clock signal is in the form of a square wave with a 50% duty cycle, usually with a fixed, constant frequency. Circuits using the clock signal for synchronization may become active at either the rising edge, falling edge, or, in the case of double data rate, both in the rising and in the falling edges of the clock cycle. Digital circuits Most integrated circuits (ICs) of sufficient complexity use a clock signal in order to synchronize different parts of the circuit, cycling at a rate slower than the worst-case internal propagation delays. In some cases, more than one clock cycle is required to perform a predictable action. As ICs become mo ...
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Vernier Scale
A vernier scale, named after Pierre Vernier, is a visual aid to take an accurate measurement reading between two graduation markings on a linear scale by using mechanical interpolation, thereby increasing resolution and reducing measurement uncertainty by using vernier acuity to reduce human estimation error. It may be found on many types of instrument measuring linear or angular quantities, but in particular on a vernier caliper which measures internal or external diameter of hollow cylinders. The vernier is a subsidiary scale replacing a single measured-value pointer, and has for instance ten divisions equal in distance to nine divisions on the main scale. The interpolated reading is obtained by observing which of the vernier scale graduations is coincident with a graduation on the main scale, which is easier to perceive than visual estimation between two points. Such an arrangement can go to a higher resolution by using a higher scale ratio, known as the vernier constant. A ...
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Analog-to-digital Converter
In electronics, an analog-to-digital converter (ADC, A/D, or A-to-D) 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 also provide an isolated measurement such as an electronic device that converts an analog input voltage or current to a digital number representing the magnitude of the voltage or current. Typically the digital output is a two's complement binary number that is proportional to the input, but there are other possibilities. There are several ADC architectures. Due to the complexity and the need for precisely matched components, all but the most specialized ADCs are implemented as integrated circuits (ICs). These typically take the form of metal–oxide–semiconductor (MOS) mixed-signal integrated circuit chips that integrate both analog and digital circuits. A digital-to-analog converter (DAC) performs the reverse function; it converts a digital signa ...
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Distributed Amplifier
Distributed amplifiers are circuit designs that incorporate transmission line theory into traditional amplifier design to obtain a larger gain-bandwidth product than is realizable by conventional circuits. History The design of the distributed amplifiers was first formulated by William S. Percival in 1936. In that year Percival proposed a design by which the transconductances of individual vacuum tubes could be added linearly without lumping their element capacitances at the input and output, thus arriving at a circuit that achieved a gain-bandwidth product greater than that of an individual tube. Percival's design did not gain widespread awareness however, until a publication on the subject was authored by Ginzton, Hewlett, Jasberg, and Noe in 1948. It is to this later paper that the term ''distributed amplifier'' can actually be traced. Traditionally, DA design architectures were realized using vacuum tube technology. Current technology More recently, III-V semicondu ...
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CMOS
Complementary metal–oxide–semiconductor (CMOS, pronounced "sea-moss", ) is a type of metal–oxide–semiconductor field-effect transistor (MOSFET) fabrication process that uses complementary and symmetrical pairs of p-type and n-type MOSFETs for logic functions. CMOS technology is used for constructing integrated circuit (IC) chips, including microprocessors, microcontrollers, memory chips (including CMOS BIOS), and other digital logic circuits. CMOS technology is also used for analog circuits such as image sensors (CMOS sensors), data converters, RF circuits (RF CMOS), and highly integrated transceivers for many types of communication. The CMOS process was originally conceived by Frank Wanlass at Fairchild Semiconductor and presented by Wanlass and Chih-Tang Sah at the International Solid-State Circuits Conference in 1963. Wanlass later filed US patent 3,356,858 for CMOS circuitry and it was granted in 1967. commercialized the technology with the trademark "COS-MO ...
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