Editing Analog-to-digital converter (section)

===Resolution===
[[File:ADC voltage resolution.svg|250px|thumb|'''Fig. 1.''' An 8-level ADC coding scheme]]
The resolution of the converter indicates the number of different, i.e. discrete, values it can produce over the allowed range of analog input values. Thus a particular resolution determines the magnitude of the quantization error and therefore determines the maximum possible [[signal-to-noise ratio]] for an ideal ADC without the use of [[oversampling]].  The input samples are usually stored electronically in [[Binary numeral system|binary]] form within the ADC, so the resolution is usually expressed as the [[audio bit depth]]. In consequence, the number of discrete values available is usually 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 (2<sup>8</sup>&nbsp;=&nbsp;256). The values can represent the ranges from 0 to 255 (i.e. as unsigned integers) or from −128 to 127 (i.e. as signed integer), depending on the application.

Resolution can also be defined electrically, and expressed in [[volt]]s. The 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 intervals:

:<math>R = \dfrac{E_\mathrm {FSR}}{2^M - 1},</math>

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

:<math>E_ \mathrm {FSR} = V_\mathrm {RefHi} - V_ \mathrm {RefLow}, \,</math>

where ''V''<sub>RefHi</sub> and ''V''<sub>RefLow</sub> are the upper and lower extremes, respectively, of the voltages that can be coded.

Normally, the number of voltage intervals is given by

:<math>N = 2^M -1, \,</math>

where ''M'' is the ADC's resolution in bits.<ref>{{cite web|url=http://www.ti.com/lit/an/sbaa051a/sbaa051a.pdf |archive-url=https://ghostarchive.org/archive/20221009/http://www.ti.com/lit/an/sbaa051a/sbaa051a.pdf |archive-date=2022-10-09 |url-status=live |title=Principles of Data Acquisition and Conversion |publisher=Texas Instruments |date=April 2015 |access-date=2016-10-18}}</ref>

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: 2<sup>3</sup> = 8 quantization levels (codes)
* ADC voltage resolution, ''Q'' = 1&nbsp;V / ( 2<sup>3</sup> - 1 ) = 0.143&nbsp;V (intervals)

In many cases, the useful resolution of a converter is limited by the [[signal-to-noise ratio]] (SNR) and other errors in the overall system expressed as an ENOB.

[[File:Frequency spectrum of a sinusoid and its quantization noise floor.gif|thumb|300px|Comparison of quantizing a sinusoid to 64 levels (6 bits) and 256 levels (8 bits).  The additive noise created by 6-bit quantization is 12&nbsp;dB greater than the noise created by 8-bit quantization.  When the spectral distribution is flat, as in this example, the 12&nbsp;dB difference manifests as a measurable difference in the noise floors.]]

====Quantization error====
[[File:Conversion AD DA.png|thumb|Analog to digital conversion as shown with fig. 1 and fig. 2]]

Quantization error is introduced by the [[quantization (signal processing)|quantization]] inherent in an ideal ADC. It is a rounding error between the analog input voltage to the ADC and the output digitized value. The error is nonlinear and signal-dependent. In an ideal ADC, where the quantization error is uniformly distributed between −{{Fraction|1|2}} LSB and +{{Fraction|1|2}} LSB, and the signal has a uniform distribution covering all quantization levels, the [[signal-to-quantization-noise ratio]] (SQNR) is given by

:<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|year=1998|publisher=Oxford University Press|edition=3rd}}</ref>

where Q is the number of quantization bits.  For example, for a [[audio bit depth|16-bit]] ADC, the quantization error is 96.3&nbsp;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 is the case with [[oversampling]], some of the quantization error will occur [[out-of-band]], effectively improving the SQNR for the bandwidth in use.  In an oversampled system, [[noise shaping]] can be used to further increase SQNR by forcing more quantization error out of band.

====Dither====
{{Main|dither}}

In ADCs, performance can usually be improved using [[dither]]. This is a very small amount of random noise (e.g. [[white noise]]), which is added to the input before conversion. Its effect is to randomize the state of the LSB based on the signal. Rather than the signal simply getting cut off altogether at low levels, it extends the effective range of signals that the ADC can convert, at the expense of a slight increase in noise. Dither can only increase the resolution of a sampler. It cannot improve the linearity, and thus accuracy does not necessarily improve.

Quantization distortion in an audio signal of very low level with respect to the bit depth of the ADC is correlated with the signal and sounds distorted and unpleasant. With dithering, the distortion is transformed into noise. The undistorted signal may be recovered accurately by averaging over time. 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.

Dither is often applied 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 analog audio signal that is converted to digital.