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| [[File:WM WM8775SEDS-AB.jpg|thumb|right|250px|4-channel stereo multiplexed analog-to-digital converter WM8775SEDS made by [[Wolfson Microelectronics]] placed on an [[Sound Blaster X-Fi|X-Fi Fatal1ty Pro]] [[sound card]].]]
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| An '''analog-to-digital converter''' (abbreviated '''ADC''', '''A/D''' or '''A to D''') is a device that converts a continuous physical quantity (usually voltage) to a digital number that represents the quantity's amplitude.
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| The conversion involves [[Quantization (signal processing)|quantization]] of the input, so it necessarily introduces a small amount of error. Instead of doing a single conversion, an ADC often performs the conversions ("[[Sampling (signal processing)|samples]]" the input) periodically. The result is a sequence of digital values that have converted a continuous-time and continuous-amplitude [[analog signal]] to a [[discrete-time]] and discrete-amplitude [[digital signal]].
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| An ADC is defined by its bandwidth (the range of frequencies it can measure) and its signal to noise ratio (how accurately it can measure a signal relative to the noise it introduces). The actual bandwidth of an ADC is characterized primarily by its [[sampling rate]], and to a lesser extent by how it handles errors such as [[aliasing]]. The [[dynamic range]] of an ADC is influenced by many factors, including the resolution (the number of output levels it can [[quantize]] a signal to), linearity and accuracy (how well the quantization levels match the true analog signal) and [[jitter]] (small timing errors that introduce additional noise). The dynamic range of an ADC is often summarized in terms of its [[effective number of bits]] (ENOB), 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 chosen to match the bandwidth and required signal to noise ratio of the signal to be quantized. If an ADC operates at a sampling rate greater than twice the bandwidth of the signal, then [[Nyquist–Shannon sampling theorem|perfect reconstruction]] is possible given an ideal ADC and neglecting quantization error. The presence of quantization error limits the dynamic range of even an ideal ADC, however, if the dynamic range of the ADC exceeds that of the input signal, its effects may be neglected resulting in an essentially perfect digital representation of the input signal.
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| An ADC may also provide an isolated measurement such as an [[electronics|electronic]] device that converts an input analog [[voltage]] or [[Electric current|current]] to a digital number proportional to the magnitude of the voltage or current. However, some non-electronic or only partially electronic devices, such as [[rotary encoder]]s, can also be considered ADCs. The digital output may use different coding schemes. Typically the digital output will be a [[two's complement]] binary number that is proportional to the input, but there are other possibilities. An encoder, for example, might output a [[Gray code]].
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| The inverse operation is performed by a [[digital-to-analog converter]] (DAC).
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| ==Concepts==
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| ===Resolution===
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| [[File:ADC voltage resolution.svg|250px|thumb|'''Fig. 1.''' An 8-level ADC coding scheme.]]
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| 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 [[Analog-to-digital converter#Oversampling|oversampling]]. The values are usually stored electronically in [[Binary numeral system|binary]] form, so the resolution is usually expressed in [[bit]]s. In consequence, the number of discrete values available, or "levels", 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, since 2<sup>8</sup> = 256. The values can represent the ranges from 0 to 255 (i.e. unsigned integer) or from −128 to 127 (i.e. signed integer), depending on the application.
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| Resolution can also be defined electrically, and expressed in [[volt]]s. The minimum change in voltage required to guarantee a change in the output code level is called the [[least significant bit]] (LSB) 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 discrete values:
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| :<math>Q = \dfrac{E_ \mathrm {FSR}}{{2^M}-1},</math>
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| where ''M'' is the ADC's resolution in bits and ''E''<sub>FSR</sub> is the full scale voltage range (also called 'span'). ''E''<sub>FSR</sub> is given by
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| :<math>E_ \mathrm {FSR} = V_ \mathrm {RefHi} - V_ \mathrm {RefLow}, \,</math>
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| where ''V''<sub>RefHi</sub> and ''V''<sub>RefLow</sub> are the upper and lower extremes, respectively, of the voltages that can be coded.
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| Normally, the number of voltage intervals is given by
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| :<math>N = 2^M - 1, \,</math>
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| where ''M'' is the ADC's resolution in bits.<ref>{{cite web|url=http://iamechatronics.com/notes/general-engineering/279-digitization-of-analog-quantities |title=Digitization of Analog Quantities |publisher=Iamechatronics.com |date= |accessdate=2012-06-11}}</ref>
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| That is, one voltage interval is assigned in between two consecutive code levels.
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| Example:
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| * Coding scheme as in figure 1 (assume input signal x(t) = Acos(t), A = 5V)
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| * [[Full scale]] measurement range = -5 to 5 volts
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| * ADC resolution is 8 bits: 2<sup>8</sup> – 1 = 256 – 1 = 255 quantization levels (codes)
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| * ADC voltage resolution, ''Q'' = (5 V − (−5) V) / 255 = 10 V / 255 ≈ 0.039 V ≈ 39 mV.
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| In practice, the useful resolution of a converter is limited by the best [[signal-to-noise ratio]] (SNR) that can be achieved for a digitized signal. An ADC can resolve a signal to only a certain number of bits of resolution, called the effective number of bits (ENOB). One effective bit of resolution changes the [[signal-to-noise ratio]] of the digitized signal by 6 dB, if the resolution is limited by the ADC. If a [[preamplifier]] has been used prior to A/D conversion, the noise introduced by the amplifier can be an important contributing factor towards the overall SNR.
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| ====Quantization error====
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| {{Main|Quantization error}}
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| Quantization error is the noise introduced by [[quantization (signal processing)|quantization]] in an ideal ADC. It is a rounding error between the analog input voltage to the ADC and the output digitized value. The noise is non-linear and signal-dependent.
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| In an ideal analog-to-digital converter, where the quantization error is uniformly distributed between −1/2 LSB and +1/2 LSB, and the signal has a uniform distribution covering all quantization levels, the [[Signal-to-quantization-noise ratio]] (SQNR) can be calculated from
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| :<math>\mathrm{SQNR} = 20 \log_{10}(2^Q) \approx 6.02 \cdot Q\ \mathrm{dB} \,\!</math> <ref>{{cite book|last=Lathi|first=B.P.|title=Modern Digital and Analog Communication Systems (3rd edition)|year=1998|publisher=Oxford University Press}}</ref> | |
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| Where Q is the number of quantization bits. For example, a [[16-bit]] ADC has a maximum signal-to-noise ratio of 6.02 × 16 = 96.3 dB, and therefore the quantization error is 96.3 dB below the maximum level. Quantization error is distributed from DC to the [[Nyquist frequency]], consequently if part of the ADC's bandwidth is not used (as in [[oversampling]]), some of the quantization error will fall out of band, effectively improving the SQNR. In an [[oversampling|oversampled]] system, [[noise shaping]] can be used to further increase SQNR by forcing more quantization error out of the band.
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| ====Dither====
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| {{Main|dither}}
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| In ADCs, performance can usually be improved using [[dither]]. This is a very small amount of random noise ([[white noise]]), which is added to the input before conversion.
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| Its effect is to cause the state of the LSB to randomly oscillate between 0 and 1 in the presence of very low levels of input, rather than sticking at a fixed value. Rather than the signal simply getting cut off altogether at this low level (which is only being quantized to a resolution of 1 bit), it extends the effective range of signals that the ADC can convert, at the expense of a slight increase in noise – effectively the quantization error is diffused across a series of noise values which is far less objectionable than a hard cutoff. The result is an accurate representation of the signal over time. A suitable filter at the output of the system can thus recover this small signal variation.
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| An audio signal of very low level (with respect to the bit depth of the ADC) sampled without dither sounds extremely distorted and unpleasant. Without dither the low level may cause the least significant bit to "stick" at 0 or 1. With dithering, the true level of the audio may be calculated by averaging the actual quantized sample with a series of other samples [the dither] that are recorded over time.
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| A virtually identical process, also called dither or [[dithering]], is often used when quantizing photographic images to a fewer number of bits per pixel—the image becomes noisier but to the eye looks far more realistic than the quantized image, which otherwise becomes [[colour banding|banded]]. This analogous process may help to visualize the effect of dither on an analogue audio signal that is converted to digital.
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| Dithering is also used in integrating systems such as [[electricity meter]]s. Since the values are added together, the dithering produces results that are more exact than the LSB of the analog-to-digital converter.
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| Note that dither can only increase the resolution of a sampler, it cannot improve the linearity, and thus accuracy does not necessarily improve.
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| ===Accuracy===
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| An ADC has several sources of errors. [[Quantization (signal processing)|Quantization]] error and (assuming the ADC is intended to be linear) non-[[linearity]] are intrinsic to any analog-to-digital conversion.
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| These errors are measured in a unit called the [[least significant bit]] (LSB). In the above example of an eight-bit ADC, an error of one LSB is 1/256 of the full signal range, or about 0.4%.
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| ====Non-linearity====
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| All ADCs suffer from non-linearity errors caused by their physical imperfections, causing their output to deviate from a linear function (or some other function, in the case of a deliberately non-linear ADC) of their input. These errors can sometimes be mitigated by [[calibration]], or prevented by testing.
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| Important parameters for linearity are [[Integral nonlinearity|integral non-linearity]] (INL) and [[Differential nonlinearity|differential non-linearity]] (DNL). These non-linearities reduce the dynamic range of the signals that can be digitized by the ADC, also reducing the effective resolution of the ADC.
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| ===Jitter===<!--[[Sampling (signal processing)]] links here-->
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| When digitizing a sine wave <math>x(t)=A \sin{(2 \pi f_0 t)}</math>, the use of a non-ideal sampling clock will result in some uncertainty in when samples are recorded. Provided that the actual sampling time ''uncertainty'' due to the ''clock [[jitter]]'' is <math>\Delta t</math>, the error caused by this phenomenon can be estimated as <math>E_{ap} \le |x'(t) \Delta t| \le 2A \pi f_0 \Delta t</math>. This will result in additional recorded noise that will reduce the [[ENOB]] below that predicted by [[quantization error]] alone.
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| The error is zero for DC, small at low frequencies, but significant when high frequencies have high amplitudes. This effect can be ignored if it is drowned out by the ''quantizing error''. Jitter requirements can be calculated using the following formula: <math>\Delta t < \frac{1}{2^q \pi f_0}</math>, where q is the number of ADC bits.
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| <center>
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| {| class="wikitable"
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| |-
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| ! rowspan="2" | Output size <br />(bits) || colspan="7" | Signal Frequency
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| |-
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| ! 1 Hz||1 kHz || 10 kHz || 1 MHz || 10 MHz || 100 MHz || 1 GHz
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| |- style="text-align:right;"
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| || 8 || style="text-align:right;"| 1,243 µs || style="text-align:right;"| 1.24 µs || style="text-align:right;"| 124 ns || style="text-align:right;"| 1.24 ns || style="text-align:right;"| 124 ps || style="text-align:right;"| 12.4 ps || style="text-align:right;"| 1.24 ps
| |
| |- style="text-align:right;"
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| || 10 || style="text-align:right;"| 311 µs || style="text-align:right;"| 311 ns || style="text-align:right;"| 31.1 ns || style="text-align:right;"| 311 ps || style="text-align:right;"| 31.1 ps || style="text-align:right;"| 3.11 ps || style="text-align:right;"| 0.31 ps
| |
| |- style="text-align:right;"
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| || 12 || style="text-align:right;"| 77.7 µs || style="text-align:right;"| 77.7 ns || style="text-align:right;"| 7.77 ns || style="text-align:right;"| 77.7 ps || style="text-align:right;"| 7.77 ps || style="text-align:right;"| 0.78 ps || style="text-align:right;"| 0.08 ps
| |
| |- style="text-align:right;"
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| || 14 || style="text-align:right;"| 19.4 µs || style="text-align:right;"| 19.4 ns || style="text-align:right;"| 1.94 ns || style="text-align:right;"| 19.4 ps || style="text-align:right;"| 1.94 ps || style="text-align:right;"| 0.19 ps || style="text-align:right;"| 0.02 ps
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| |-
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| | style="text-align:right;"| 16 || style="text-align:right;"| 4.86 µs || style="text-align:right;"| 4.86 ns || style="text-align:right;"| 486 ps || style="text-align:right;"| 4.86 ps || style="text-align:right;"| 0.49 ps || style="text-align:right;"| 0.05 ps || style="text-align:center;"| –
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| |-
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| | style="text-align:right;"| 18 || style="text-align:right;"| 1.21 ns || style="text-align:right;"| 121 ps || style="text-align:right;"| 6.32 ps || style="text-align:right;"| 1.21 ps || style="text-align:right;"| 0.12 ps || style="text-align:center;"| – || style="text-align:center;"| –
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| |-
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| | style="text-align:right;"| 20 || style="text-align:right;"| 304 ps || style="text-align:right;"| 30.4 ps || style="text-align:right;"| 1.58 ps || style="text-align:right;"| 0.16 ps || style="text-align:center;"| – || style="text-align:center;"| – || style="text-align:center;"| –
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| |-
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| |}
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| </center> | |
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| Clock jitter is caused by [[phase noise]].<ref>[http://www.maxim-ic.com/appnotes.cfm/an_pk/800/ Maxim App 800: "Design a Low-Jitter Clock for High-Speed Data Converters"]. maxim-ic.com (July 17, 2002).</ref><ref>{{cite web
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| | title = Jitter effects on Analog to Digital and Digital to Analog Converters
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| | url = http://www.thewelltemperedcomputer.com/Lib/Troisi.pdf
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| | accessdate = 19 August 2012}}</ref>
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| The resolution of ADCs with a digitization bandwidth between 1 MHz and 1 GHz is limited by jitter.<ref>{{cite journal|doi=10.1016/j.csi.2005.12.005|title=The effects of aperture jitter and clock jitter in wideband ADCs|author=Löhning, Michael and Fettweis, Gerhard |year=2007|journal=Computer Standards & Interfaces archive|volume =29 |issue =1|pages =11–18}}</ref>
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| When sampling audio signals at 44.1 kHz, the [[anti-aliasing filter]] should have eliminated all frequencies above 22 kHz.
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| The input frequency (in this case, < 22 kHz kHz), not the ADC clock frequency, is the determining factor with respect to jitter performance.<ref>Redmayne, Derek and Steer, Alison (8 December 2008)
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| [http://www.eetimes.com/design/automotive-design/4010074/Understanding-the-effect-of-clock-jitter-on-high-speed-ADCs-Part-1-of-2- Understanding the effect of clock jitter on high-speed ADCs]. eetimes.com
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| </ref>
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| ===Sampling rate===
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| {{Main|Sampling_(signal_processing)}}
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| {{Main|Sampling rate}}
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| The analog signal is [[continuous function|continuous]] in [[time]] and it is necessary to convert this to a flow of digital values. It is therefore required to define the rate at which new digital values are sampled from the analog signal. The rate of new values is called the ''sampling rate'' or ''[[sampling frequency]]'' of the converter.
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| A continuously varying bandlimited signal can be sampled (that is, the signal values at intervals of time T, the sampling time, are measured and stored) and then the original signal can be ''exactly'' reproduced from the discrete-time values by an [[interpolation]] formula. The accuracy is limited by quantization error. However, this faithful reproduction is only possible if the sampling rate is higher than twice the highest frequency of the signal. This is essentially what is embodied in the [[Shannon-Nyquist sampling theorem]].
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| Since a practical ADC cannot make an instantaneous conversion, the input value must necessarily be held constant during the time that the converter performs a conversion (called the ''conversion time''). An input circuit called a [[sample and hold]] performs this task—in most cases by using a [[capacitor]] to store the analog voltage at the input, and using an electronic switch or gate to disconnect the capacitor from the input. Many ADC [[integrated circuit]]s include the sample and hold subsystem internally.
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| ====Aliasing====
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| {{Main|Aliasing}}
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| {{Main|undersampling}}
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| An ADC works by sampling the value of the input at discrete intervals in time. Provided that the input is sampled above the [[Nyquist rate]], defined as twice the highest frequency of interest, then all frequencies in the signal can be reconstructed. If frequencies above half the Nyquist rate are sampled, they are incorrectly detected as lower frequencies, a process referred to as aliasing. Aliasing occurs because instantaneously sampling a function at two or fewer times per cycle results in missed cycles, and therefore the appearance of an incorrectly lower frequency. For example, a 2 kHz sine wave being sampled at 1.5 kHz would be reconstructed as a 500 Hz sine wave.
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| To avoid aliasing, the input to an ADC must be low-pass [[electronic filter|filtered]] to remove frequencies above half the sampling rate. This filter is called an ''[[anti-aliasing filter]]'', and is essential for a practical ADC system that is applied to analog signals with higher frequency content. In applications where protection against aliasing is essential, oversampling may be used to greatly reduce or even eliminate it.
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| Although aliasing in most systems is unwanted, it should also be noted that it can be exploited to provide simultaneous down-mixing of a band-limited high frequency signal (see [[undersampling]] and [[frequency mixer]]). The alias is effectively the lower [[heterodyne]] of the signal frequency and sampling frequency.<ref>{{cite web|title=RF-Sampling and GSPS ADCs - Breakthrough ADCs Revolutionize Radio Architectures|url=http://www.ti.com/lit/sg/snwt001/snwt001.pdf|publisher=Texas Instruments|accessdate=4 November 2013}}</ref>
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| ====Oversampling====
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| {{Main|Oversampling}}
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| Signals are often sampled at the minimum rate required, for economy, with the result that the quantization noise introduced is [[white noise]] spread over the whole pass band of the converter. If a signal is sampled at a rate much higher than the [[Nyquist frequency]] and then [[Digital filter|digitally filtered]] to limit it to the signal bandwidth there are the following advantages:
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| * digital filters can have better properties (sharper [[rolloff]], phase) than analogue filters, so a sharper anti-aliasing filter can be realised and then the signal can be downsampled giving a better result
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| * a 20-bit ADC can be made to act as a 24-bit ADC with 256× oversampling
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| * the [[signal-to-noise ratio]] due to [[quantization noise]] will be higher than if the whole available band had been used. With this technique, it is possible to obtain an effective resolution larger than that provided by the converter alone
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| * The improvement in SNR is 3 dB (equivalent to 0.5 bits) per octave of oversampling which is not sufficient for many applications. Therefore, oversampling is usually coupled with noise shaping (see sigma-delta modulators). With noise shaping, the improvement is 6L+3 dB per octave where L is the order of loop filter used for noise shaping. e.g. – a 2nd order loop filter will provide an improvement of 15 dB/octave.
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| Oversampling is typically used in audio frequency ADCs where the required sampling rate (typically 44.1 or 48 kHz) is very low compared to the clock speed of typical transistor circuits (>1 MHz). In this case, by using the extra bandwidth to distribute quantization error onto out of band frequencies, the accuracy of the ADC can be greatly increased at no cost. Furthermore, as any aliased signals are also typically out of band, aliasing can often be completely eliminated using very low cost filters.
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| ===Relative speed and precision===
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| The speed of an ADC varies by type. The Wilkinson ADC is limited by the clock rate which is processable by current digital circuits. Currently,{{when|date=August 2012}} frequencies up to 300 MHz are possible.<ref>310 Msps ADC by Linear Technology, http://www.linear.com/product/LTC2158-14.</ref> For a successive-approximation ADC, the conversion time scales with the logarithm of the resolution, e.g. the number of bits. Thus for high resolution, it is possible that the successive-approximation ADC is faster than the Wilkinson. However, the time consuming steps in the Wilkinson are digital, while those in the successive-approximation are analog. Since analog is inherently slower than digital, as the resolution increases, the time required also increases. Thus there are competing processes at work. Flash ADCs are certainly the fastest type of the three. The conversion is basically performed in a single parallel step. For an 8-bit unit, conversion takes place in a few tens of nanoseconds.
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| There is, as expected, somewhat of a tradeoff between speed and precision. Flash ADCs have drifts and uncertainties associated with the comparator levels. This results in poor linearity. For successive-approximation ADCs, poor linearity is also present, but less so than for flash ADCs. Here, non-linearity arises from accumulating errors from the subtraction processes. Wilkinson ADCs have the highest linearity of the three. These have the best differential non-linearity. The other types require channel smoothing to achieve the level of the Wilkinson.<ref>{{Harvtxt|Knoll|1989|pp=664–665}}</ref><ref>{{Harvtxt|Nicholson|1974|pp=313–315}}</ref>
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| ===The sliding scale principle===
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| The sliding scale or randomizing method can be employed to greatly improve the linearity of any type of ADC, but especially flash and successive approximation types. For any ADC the mapping from input voltage to digital output value is not exactly a [[floor function|floor]] or [[ceiling function]] as it should be. Under normal conditions, a pulse of a particular amplitude is always converted to a digital value. The problem lies in that the ranges of analog values for the digitized values are not all of the same width, and the [[differential linearity]] decreases proportionally with the divergence from the average width. The sliding scale principle uses an averaging effect to overcome this phenomenon. A random, but known analog voltage is added to the sampled input voltage. It is then converted to digital form, and the equivalent digital amount is subtracted, thus restoring it to its original value. The advantage is that the conversion has taken place at a random point. The statistical distribution of the final levels is decided by a weighted average over a region of the range of the ADC. This in turn desensitizes it to the width of any specific level.<ref>{{Harvtxt|Knoll|1989|pp=665–666}}</ref><ref>{{Harvtxt|Nicholson|1974|pp=315–316}}</ref>
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| ==ADC types==
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| These are the most common ways of implementing an electronic ADC:
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| * A '''direct-conversion ADC''' or '''[[flash ADC]]''' has a bank of [[comparator]]s sampling the input signal in parallel, each firing for their decoded voltage range. The comparator bank feeds a [[logic circuit]] that generates a code for each voltage range. Direct conversion is very fast, capable of [[gigahertz]] sampling rates, but usually has only 8 bits of resolution or fewer, since the number of comparators needed, 2<sup>N</sup> – 1, doubles with each additional bit, requiring a large, expensive circuit. ADCs of this type have a large [[Die (integrated circuit)|die]] size, a high input [[capacitance]], high power dissipation, and are prone to produce [[glitch]]es at the output (by outputting an out-of-sequence code). Scaling to newer submicrometre technologies does not help as the device mismatch is the dominant design limitation. They are often used for [[video]], wideband communications or other fast signals in [[optical storage]].
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| * A '''[[Successive Approximation ADC|successive-approximation ADC]]''' uses a comparator to successively narrow a range that contains the input voltage. At each successive step, the converter compares the input voltage to the output of an internal [[digital to analog converter]] which might represent the midpoint of a selected voltage range. At each step in this process, the approximation is stored in a successive approximation register (SAR). For example, consider an input voltage of 6.3 V and the initial range is 0 to 16 V. For the first step, the input 6.3 V is compared to 8 V (the midpoint of the 0–16 V range). The comparator reports that the input voltage is less than 8 V, so the SAR is updated to narrow the range to 0–8 V. For the second step, the input voltage is compared to 4 V (midpoint of 0–8). The comparator reports the input voltage is above 4 V, so the SAR is updated to reflect the input voltage is in the range 4–8 V. For the third step, the input voltage is compared with 6 V (halfway between 4 V and 8 V); the comparator reports the input voltage is greater than 6 volts, and search range becomes 6–8 V. The steps are continued until the desired resolution is reached.
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| * A '''ramp-compare ADC''' produces a [[Sawtooth wave|saw-tooth signal]] that ramps up or down then quickly returns to zero. When the ramp starts, a timer starts counting. When the ramp voltage matches the input, a comparator fires, and the timer's value is recorded. Timed ramp converters require the least number of [[transistor]]s. The ramp time is sensitive to temperature because the circuit generating the ramp is often just some simple [[electronic oscillator|oscillator]]. There are two solutions: use a clocked counter driving a [[Digital-to-analog converter|DAC]] and then use the comparator to preserve the counter's value, or calibrate the timed ramp. A special advantage of the ramp-compare system is that comparing a second signal just requires another comparator, and another register to store the voltage value. A very simple (non-linear) ramp-converter can be implemented with a microcontroller and one resistor and capacitor.<ref>[http://www.atmel.com/dyn/resources/prod_documents/doc0942.pdf Atmel Application Note AVR400: Low Cost A/D Converter]. atmel.com</ref> Vice versa, a filled capacitor can be taken from an [[operational amplifier applications#Integrator|integrator]], time-to-amplitude converter, [[phase detector]], [[sample and hold]] circuit, or [[peak and hold]] circuit and discharged. This has the advantage that a slow [[comparator]] cannot be disturbed by fast input changes.
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| * The '''Wilkinson ADC''' was designed by [[Denys Wilkinson|D. H. Wilkinson]] in 1950. The Wilkinson ADC is based on the comparison of an input voltage with that produced by a charging capacitor. The capacitor is allowed to charge until its voltage is equal to the amplitude of the input pulse (a comparator determines when this condition has been reached). Then, the capacitor is allowed to discharge linearly, which produces a ramp voltage. At the point when the capacitor begins to discharge, a gate pulse is initiated. The gate pulse remains on until the capacitor is completely discharged. Thus the duration of the gate pulse is directly proportional to the amplitude of the input pulse. This gate pulse operates a linear gate which receives pulses from a high-frequency oscillator clock. While the gate is open, a discrete number of clock pulses pass through the linear gate and are counted by the address register. The time the linear gate is open is proportional to the amplitude of the input pulse, thus the number of clock pulses recorded in the address register is proportional also. Alternatively, the charging of the capacitor could be monitored, rather than the discharge.<ref>{{Harvtxt|Knoll|1989|pp=663–664}}</ref><ref>{{Harvtxt|Nicholson|1974|pp=309–310}}</ref>
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| * An '''[[integrating ADC]]''' (also '''dual-slope''' or '''multi-slope''' ADC) applies the unknown input voltage to the input of an [[operational amplifier applications#Integrator|integrator]] and allows the voltage to ramp for a fixed time period (the run-up period). Then a known reference voltage of opposite polarity is applied to the integrator and is allowed to ramp until the integrator output returns to zero (the run-down period). The input voltage is computed as a function of the reference voltage, the constant run-up time period, and the measured run-down time period. The run-down time measurement is usually made in units of the converter's clock, so longer integration times allow for higher resolutions. Likewise, the speed of the converter can be improved by sacrificing resolution. Converters of this type (or variations on the concept) are used in most digital [[Voltmeter#Digital voltmeter|voltmeters]] for their linearity and flexibility.
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| * A '''delta-encoded ADC''' or '''counter-ramp''' has an up-down [[counter]] that feeds a [[digital to analog converter]] (DAC). The input signal and the DAC both go to a comparator. The comparator controls the counter. The circuit uses negative [[feedback]] from the comparator to adjust the counter until the DAC's output is close enough to the input signal. The number is read from the counter. Delta converters have very wide ranges and high resolution, but the conversion time is dependent on the input signal level, though it will always have a guaranteed worst-case. Delta converters are often very good choices to read real-world signals. Most signals from physical systems do not change abruptly. Some converters combine the delta and successive approximation approaches; this works especially well when high frequencies are known to be small in magnitude.
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| * A '''pipeline ADC''' (also called '''subranging quantizer''') uses two or more steps of subranging. First, a coarse conversion is done. In a second step, the difference to the input signal is determined with a [[digital to analog converter]] (DAC). This difference is then converted finer, and the results are combined in a last step. This can be considered a refinement of the successive-approximation ADC wherein the feedback reference signal consists of the interim conversion of a whole range of bits (for example, four bits) rather than just the next-most-significant bit. By combining the merits of the successive approximation and flash ADCs this type is fast, has a high resolution, and only requires a small die size.
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| * A '''sigma-delta ADC''' (also known as a '''delta-sigma ADC''') oversamples the desired signal by a large factor and filters the desired signal band. Generally, a smaller number of bits than required are converted using a Flash ADC after the filter. The resulting signal, along with the error generated by the discrete levels of the Flash, is fed back and subtracted from the input to the filter. This negative feedback has the effect of [[noise shaping]] the error due to the Flash so that it does not appear in the desired signal frequencies. A digital filter (decimation filter) follows the ADC which reduces the sampling rate, filters off unwanted noise signal and increases the resolution of the output ([[sigma-delta modulation]], also called [[delta-sigma modulation]]).
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| * A '''time-interleaved ADC''' uses M parallel ADCs where each ADC samples data every M:th cycle of the effective sample clock. The result is that the sample rate is increased M times compared to what each individual ADC can manage. In practice, the individual differences between the M ADCs degrade the overall performance reducing the SFDR.<ref>{{cite journal|last=Vogel|first=Christian|title=The Impact of Combined Channel Mismatch Effects in Time-interleaved ADCs|journal=IEEE Transactions on Instrumentation and Measurement|year=2005|volume=55|issue=1|pages=415–427|doi=10.1109/TIM.2004.834046}}</ref> However, technologies exist to correct for these time-interleaving mismatch errors.
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| * An '''ADC with intermediate FM stage''' <!--(is there a better name?)--> first uses a voltage-to-frequency converter to convert the desired signal into an oscillating signal with a frequency proportional to the voltage of the desired signal, and then uses a [[frequency counter]] to convert that frequency into a digital count proportional to the desired signal voltage. Longer integration times allow for higher resolutions. Likewise, the speed of the converter can be improved by sacrificing resolution. The two parts of the ADC may be widely separated, with the frequency signal passed through an [[opto-isolator]] or transmitted wirelessly. Some such ADCs use sine wave or square wave [[frequency modulation]]; others use [[pulse-frequency modulation]]. Such ADCs were once the most popular way to show a digital display of the status of a remote analog sensor.<ref>
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| [http://www.analog.com/static/imported-files/tutorials/MT-028.pdf Analog Devices MT-028 Tutorial: "Voltage-to-Frequency Converters"] by Walt Kester and James Bryant 2009,
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| apparently adapted from Kester, Walter Allan (2005) [http://books.google.com/books?id=0aeBS6SgtR4C&pg=RA2-PA274 ''Data conversion handbook''], Newnes, p. 274, ISBN 0750678410.</ref><ref>
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| [http://ww1.microchip.com/downloads/en/AppNotes/00795a.pdf Microchip AN795 "Voltage to Frequency / Frequency to Voltage Converter"] p. 4: "13-bit A/D converter"
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| </ref><ref>Carr, Joseph J. (1996) [http://books.google.com/books?id=1yBTAAAAMAAJ ''Elements of electronic instrumentation and measurement''], Prentice Hall, p. 402, ISBN 0133416860.</ref><ref>[http://www.globalspec.com/reference/3127/Voltage-to-Frequency-Analog-to-Digital-Converters "Voltage-to-Frequency Analog-to-Digital Converters"]. globalspec.com</ref><ref>Pease, Robert A. (1991) [http://books.google.com/books?id=3kY4-HYLqh0C&pg=PA130 ''Troubleshooting Analog Circuits''], Newnes, p. 130, ISBN 0750694998.</ref>
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| There can be other ADCs that use a combination of electronics and other [[Technology|technologies]]:
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| * A '''[[Time stretch analog-to-digital converter|time-stretch analog-to-digital converter (TS-ADC)]]''' digitizes a very wide bandwidth analog signal, that cannot be digitized by a conventional electronic ADC, by time-stretching the signal prior to digitization. It commonly uses a [[Photonics|photonic]] [[preprocessor]] [[Front-end and back-end|frontend]] to time-stretch the signal, which effectively slows the signal down in time and compresses its bandwidth. As a result, an electronic [[Front-end and back-end|backend]] ADC, that would have been too slow to capture the original signal, can now capture this slowed down signal. For continuous capture of the signal, the frontend also divides the signal into multiple segments in addition to time-stretching. Each segment is individually digitized by a separate electronic ADC. Finally, a [[digital signal processor]] rearranges the samples and removes any distortions added by the frontend to yield the binary data that is the digital representation of the original analog signal.
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| == Commercial analog-to-digital converters ==
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| Commercial ADCs are usually implemented as [[integrated circuit]]s.
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| Most converters sample with 6 to 24 [[bit]]s of resolution, and produce fewer than 1 megasample per second. [[Johnson-Nyquist noise|Thermal noise]] generated by passive components such as resistors masks the measurement when higher resolution is desired. For audio applications and in room temperatures, such noise is usually a little less than {{nowrap|1 [[Volt|μV]]}} (microvolt) of [[white noise]]. If the MSB corresponds to a {{nowrap|[[Line level|standard 2 V]]}} of output signal, this translates to a noise-limited performance that is less than 20~21 bits, and obviates the need for any [[dither]]ing. As of February 2002, Mega- and giga-sample per second converters are available. Mega-sample converters are required in digital [[video camera]]s, [[video capture card]]s, and [[TV tuner card]]s to convert full-speed analog video to digital video files.
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| Commercial converters usually have ±0.5 to ±1.5 [[Least significant bit|LSB]] error in their output.
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| In many cases, the most expensive part of an integrated circuit is the pins, because they make the package larger, and each pin has to be connected to the integrated circuit's silicon. To save pins, it is common for slow ADCs to send their data one bit at a time over a [[serial bus|serial]] interface to the computer, with the next bit coming out when a clock signal changes state, say from 0 to 5 V. This saves quite a few pins on the ADC package, and in many cases, does not make the overall design any more complex (even [[microprocessor]]s which use [[memory-mapped I/O]] only need a few bits of a port to implement a [[serial bus]] to an ADC).
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| Commercial ADCs often have several inputs that feed the same converter, usually through an analog [[multiplexer]]. Different models of ADC may include [[sample and hold]] circuits, instrumentation [[amplifier]]s or [[high-voltage differential signalling|differential]] inputs, where the quantity measured is the difference between two voltages.
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| ==Applications==
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| ===Music recording===
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| Analog-to-digital converters are integral to current music reproduction technology. People produce much music on computers using an analog recording and therefore need analog-to-digital converters to create the [[pulse-code modulation]] (PCM) data streams that go onto [[compact disc]]s and digital music files.
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| The current crop of analog-to-digital converters utilized in music can sample at rates up to 192 [[kilohertz]]. Considerable literature exists on these matters, but commercial considerations often play a significant role. Most{{Citation needed|date=November 2008}} high-profile recording studios record in 24-bit/192-176.4 kHz pulse-code modulation (PCM) or in [[Direct Stream Digital]] (DSD) formats, and then downsample or decimate the signal for Red-Book CD production (44.1 kHz) or to 48 kHz for commonly used for radio and television broadcast applications.
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| ===Digital signal processing===
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| People must use ADCs to process, store, or transport virtually any analog signal in digital form. [[TV tuner card]]s, for example, use fast video analog-to-digital converters. Slow on-chip 8, 10, 12, or 16 bit analog-to-digital converters are common in [[microcontroller]]s. [[Digital storage oscilloscope]]s need very fast analog-to-digital converters, also crucial for [[software defined radio]] and their new applications.
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| ===Scientific instruments===
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| [[Digital imaging]] systems commonly use analog-to-digital converters in [[digitizing]] [[pixel]]s.
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| Some [[radar]] systems commonly use analog-to-digital converters to convert [[signal strength]] to digital values for subsequent [[signal processing]]. Many other in situ and remote sensing systems commonly use analogous technology.
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| The number of binary bits in the resulting digitized numeric values reflects the resolution, the number of unique discrete levels of [[quantization (signal processing)]]. The correspondence between the analog signal and the digital signal depends on the [[quantization error]]. The quantization process must occur at an adequate speed, a constraint that may limit the resolution of the digital signal.
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| Many [[sensor]]s produce an analog signal; [[temperature]], [[pressure]], [[pH]], [[Candela|light intensity]] etc. All these signals can be amplified and fed to an ADC to produce a digital number [[Proportionality (mathematics)|proportional]] to the input signal.
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| ==Electrical Symbol==
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| [[File:ADC Symbol.svg]]
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| ==Testing==
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| Testing an Analog to Digital Converter requires an analog input source, hardware to send control signals and capture digital data output. Some ADCs also require an accurate source of reference signal.
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| The key parameters to test a SAR ADC are following:
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| # DC Offset Error
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| # DC Gain Error
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| # Signal to Noise Ratio (SNR)
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| # Total Harmonic Distortion (THD)
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| # Integral Non Linearity (INL)
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| # Differential Non Linearity (DNL)
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| # Spurious Free Dynamic Range
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| # Power Dissipation
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| ==See also==
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| * [[Audio converter]]
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| * [[Beta encoder]]
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| * [[Digital signal processing]]
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| * [[Integral linearity]]
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| * [[Modem]]
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| ==Notes==
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| {{reflist|30em}}
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| ==References==
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| * {{cite book
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| |last= Knoll|ref=harv
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| |first= Glenn F.
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| |title=Radiation Detection and Measurement
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| |edition= 2nd
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| |year= 1989
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| |publisher= John Wiley & Sons
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| |location= New York|isbn=0471815047}}
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| * {{cite book
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| |last= Nicholson|ref=harv
| |
| |first= P. W.
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| |title= Nuclear Electronics
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| |year= 1974|isbn=0471636975
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| |publisher= John Wiley & Sons
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| |location= New York
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| |pages= 315–316}}
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| ==Further reading==
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| * {{cite book
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| |first= Phillip E.
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| |last= Allen
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| |first2= Douglas R.
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| |last2= Holberg
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| |title= CMOS Analog Circuit Design
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| |isbn= 0-19-511644-5}}
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| * {{cite book
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| |first= Jacob
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| |last= Fraden
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| |title= Handbook of Modern Sensors: Physics, Designs, and Applications
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| |year= 2010
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| |publisher= Springer
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| |isbn= 978-1441964656}}
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| * {{cite book
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| |editor-last= Kester
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| |editor-first= Walt
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| |title= The Data Conversion Handbook
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| |year= 2005
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| |publisher= Elsevier: Newnes
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| |url= http://www.analog.com/library/analogDialogue/archives/39-06/data_conversion_handbook.html
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| |isbn= 0-7506-7841-0}}
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| * {{cite book
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| |last= Johns
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| |first= David
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| |last2= Martin
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| |first2= Ken
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| |title= Analog Integrated Circuit Design
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| |isbn= 0-471-14448-7}}
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| * {{cite book
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| |last= Liu
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| |first= Mingliang
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| |title= Demystifying Switched-Capacitor Circuits
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| |isbn= 0-7506-7907-7
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| }}
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| * {{cite book
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| |last= Norsworthy
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| |first= Steven R.
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| |last2= Schreier
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| |first2= Richard
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| |last3= Temes
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| |first3= Gabor C.
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| |title= Delta-Sigma Data Converters
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| |year= 1997
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| |publisher= IEEE Press
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| |isbn= 0-7803-1045-4}}
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| * {{cite book
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| |last= Razavi
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| |first= Behzad
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| |authorlink= Behzad Razavi
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| |title= Principles of Data Conversion System Design
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| |year= 1995
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| |publisher= IEEE Press
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| |location= New York, NY
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| |isbn= 0-7803-1093-4}}
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| * {{Cite journal
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| |last= Staller
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| |first= Len
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| |url= http://www.embedded.com/showArticle.jhtml?articleID=60403334
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| |title= Understanding analog to digital converter specifications
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| |date= February 24, 2005
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| |journal= Embedded Systems Design}}
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| * {{Cite journal
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| |last= Walden
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| |first= R. H.
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| |title= Analog-to-digital converter survey and analysis
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| |journal= IEEE Journal on Selected Areas in Communications
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| |volume= 17
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| |issue= 4
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| |pages= 539–550
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| |year= 1999
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| |doi= 10.1109/49.761034}}
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| ==External links==
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| {{wikibooks|Analog and Digital Conversion}}
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| * [http://ikalogic.com/tut_adc.php Counting Type ADC] A simple tutorial showing how to build your first ADC.
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| * [http://www.beis.de/Elektronik/DeltaSigma/DeltaSigma.html An Introduction to Delta Sigma Converters] A very nice overview of Delta-Sigma converter theory.
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| * [http://www.ieee.li/pdf/adc_evaluation_rf_expo_east_1987.pdf Digital Dynamic Analysis of A/D Conversion Systems through Evaluation Software based on FFT/DFT Analysis] RF Expo East, 1987
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| * [http://www.analog.com/library/analogDialogue/archives/39-06/architecture.html Which ADC Architecture Is Right for Your Application?] article by Walt Kester
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| * [http://www.maxim-ic.com/appnotes.cfm/an_pk/641/CMP/ELK-11 ADC and DAC Glossary] Defines commonly used technical terms.
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| * [http://www.robotplatform.com/knowledge/ADC/adc_tutorial.html Introduction to ADC in AVR] – Analog to digital conversion with Atmel microcontrollers
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| * [http://userver.ftw.at/~vogel/TIADC.html Signal processing and system aspects of time-interleaved ADCs.]
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| * [http://www.onmyphd.com/?p=analog.digital.converter Explanation of analog-digital converters with interactive principles of operations.]
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| {{DEFAULTSORT:Analog-To-Digital Converter}}
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| [[Category:Digital signal processing]]
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| [[Category:Electronic circuits]]
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