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{{Short description|Device that converts a digital signal into an analog signal}}
⚫ {{refimprove|date=August 2016}}
{{For|digital television converter boxes|digital television adapter}} {{about|conversion of digital signals to analog signals|digital television converter boxes|digital television adapter}}
{{Redirect|D2A|the D2A dive bomber|Aichi D1A}} {{Redirect|D2A|the D2A dive bomber|Aichi D1A}}
{{redirect|d-a-c|other uses|DAC (disambiguation)}}
{{Multiple issues|
⚫ {{refimprove|date=August 2016}}
{{prose|date=November 2019}}
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{{Use American English|date=January 2020}}


] CS4382 digital-to-analog converter as used in a ].]] ] CS4382 digital-to-analog converter as used in a ].]]
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In ], a '''digital-to-analog converter''' ('''DAC''', '''D/A''', '''D2A''', or '''D-to-A''') is a system that converts a ] into an ]. An ] (ADC) performs the reverse function. In ], a '''digital-to-analog converter''' ('''DAC''', '''D/A''', '''D2A''', or '''D-to-A''') is a system that converts a ] into an ]. An ] (ADC) performs the reverse function.


There are several DAC ]; the suitability of a DAC for a particular application is determined by ] including: ], maximum ] and others. Digital-to-analog conversion can degrade a signal, so a DAC should be specified that has insignificant errors in terms of the application. Due to the complexity and the need for precisely matched ], all but the most specialized DACs are implemented as ] (ICs). There are several DAC ]; the suitability of a DAC for a particular application is determined by ] including: ], maximum ] and others. Digital-to-analog conversion can degrade a signal, so a DAC should be specified that has insignificant errors in terms of the application.


DACs are commonly used in ] to convert digital data streams into analog audio signals. They are also used in ]s and ]s to convert digital video data into analog video signals which connect to the screen drivers to display monochrome or color images. These two applications use DACs at opposite ends of the frequency/resolution trade-off. The audio DAC is a low-frequency, high-resolution type while the video DAC is a high-frequency low- to medium-resolution type. Discrete DACs would typically be extremely high speed low resolution power hungry types, as used in military ] systems. Very high speed test equipment, especially sampling ]s, may also use discrete DACs. DACs are commonly used in ] to convert digital data streams into analog ]s. They are also used in ]s and ]s to convert digital video data into ]. These two applications use DACs at opposite ends of the frequency/resolution trade-off. The audio DAC is a low-frequency, high-resolution type while the video DAC is a high-frequency low- to medium-resolution type.


Due to the complexity and the need for precisely matched ], all but the most specialized DACs are implemented as ] (ICs). These typically take the form of ] (MOS) ] chips that integrate both ] and ].
⚫ ==Overview==
⚫ ]
⚫ A DAC converts an ] finite-precision number (usually a ] ]) into a physical quantity (e.g., a ] or a ]). In particular, DACs are often used to convert finite-precision ] data to a continually varying physical ].


Discrete DACs (circuits constructed from multiple discrete ] instead of a packaged IC) would typically be extremely high-speed low-resolution power-hungry types, as used in military ] systems. Very high-speed test equipment, especially sampling ]s, may also use discrete DACs.
An ''ideal'' DAC converts the abstract numbers into a conceptual sequence of ]s that are then processed by a ] using some form of ] to fill in data between the impulses. A conventional ''practical'' DAC converts the numbers into a ] made up of a sequence of ]s that is modeled with the ]. Other DAC methods (such as those based on ]) produce a ] output that can be similarly filtered to produce a smoothly varying signal.


⚫ ==Overview==
As per the ], a DAC can reconstruct the original signal from the sampled data provided that its bandwidth meets certain requirements (e.g., a ] signal with ] less than the ]). Digital sampling introduces ] that manifests as low-level noise added to the reconstructed signal.
⚫ ]

⚫ A DAC converts an ] finite-precision number (usually a ] ]) into a physical quantity (e.g., a ] or a ]). In particular, DACs are often used to convert finite-precision ] data to a continually varying physical ].
]. In a practical DAC, a filter or the finite bandwidth of the device smooths out the step response into a continuous curve.]]

Instead of impulses, a conventional ''practical'' DAC updates the analog voltage at uniform ], which is then interpolated via a ] to continuously varied levels.

These numbers are written to the DAC, typically with a ] that causes each number to be ]ed in sequence, at which time the DAC output voltage changes rapidly from the previous value to the value represented by the currently latched number. The effect of this is that the output voltage is ''held'' in time at the current value until the next input number is latched, resulting in a ] or staircase-shaped output. This is equivalent to a ] operation and has an effect on the frequency response of the reconstructed signal.

The fact that DACs output a sequence of piecewise constant values (known as ] in sample data textbooks) or ] causes multiple harmonics above the ]. Usually, these are removed with a ] acting as a reconstruction filter in applications that require it.


Provided that a signal's bandwidth meets the requirements of the ] (i.e., a ] signal with ] less than the ]) and was sampled with infinite resolution, the original signal can theoretically be reconstructed from the sampled data. However, an ADC's filtering can't ''entirely'' eliminate all frequencies above the Nyquist frequency, which will ] into the baseband frequency range. And the ADC's digital sampling process introduces some ] (rounding error), which manifests as low-level noise. These errors can be kept within the requirements of the targeted application (e.g. under the limited ] for audio applications).
Other DAC methods (e.g., methods based on ]) produce a ] signal that can then be filtered in a similar way to produce a smoothly varying signal.


==Applications== ==Applications==
] ]
DACs and ADCs are part of an ] that has contributed greatly to the ]. To illustrate, consider a typical long-distance telephone call. The caller's voice is converted into an analog electrical signal by a ], then the analog signal is converted to a digital stream by an ADC. The digital stream is then divided into ]s where it may be sent along with other ], not necessarily audio. The packets are then received at the destination, but each packet may take a completely different route and may not even arrive at the destination in the correct time order. The digital voice data is then extracted from the packets and assembled into a digital data stream. A DAC converts this back into an analog electrical signal, which drives an ], which in turn drives a ], which finally produces sound. DACs and ADCs are part of an ] that has contributed greatly to the ]. To illustrate, consider a typical long-distance telephone call. The caller's voice is converted into an analog electrical signal by a ], then the analog signal is converted to a digital stream by an ADC. The digital stream is then divided into ]s where it may be sent along with other ], not necessarily audio. The packets are then received at the destination, but each packet may take a completely different route and may not even arrive at the destination in the correct time order. The digital voice data is then extracted from the packets and assembled into a digital data stream. A DAC converts this back into an analog electrical signal, which drives an ], which in turn drives a ], which finally produces sound.


===Audio=== ===Audio===
⚫ ] (top) and external digital-to-analog converter (bottom) from the same company.]]
⚫ Most modern audio signals are stored in digital form (for example ]s and ]) and in order to be heard through speakers they must be converted into an analog signal. DACs are therefore found in ]s, ]s, and PC ]s.
] as an add-on for CD players, having only about 12 cm width, intended to improve the sound of older or less expensive players.]]


⚫ Most modern audio signals are stored in digital form (for example ]s and ]s), and in order to be heard through speakers, they must be converted into an analog signal. DACs are therefore found in ]s, ]s, and PC ]s.
⚫ Specialist standalone DACs can also be found in high-end ] systems. These normally take the digital output of a compatible ] or dedicated ] (which is basically a CD player with no internal DAC) and convert the signal into an analog ] output that can then be fed into an ] to drive speakers.


⚫ Specialist standalone DACs can also be found in high-end ] systems. These normally take the digital output of a compatible CD player or dedicated ] (which is basically a CD player with no internal DAC) and convert the signal into an analog ] output that can then be fed into an ] to drive speakers.
⚫ Similar digital-to-analog converters can be found in ] such as ] speakers, and in ]s.


⚫ Similar digital-to-analog converters can be found in ] such as ] speakers, and in ]s.
⚫ In ] (Voice over IP) applications, the source must first be digitized for transmission, so it undergoes conversion via an ], and is then reconstructed into analog using a DAC on the receiving party's end.


⚫ In ] applications, the source must first be digitized for transmission, so it undergoes conversion via an ADC and is then reconstructed into analog using a DAC on the receiving party's end.
⚫ ]


===Video=== ===Video===
⚫ Video sampling tends to work on a completely different scale altogether thanks to the highly nonlinear response both of cathode ray tubes (for which the vast majority of digital video foundation work was targeted) and the human eye, using a "gamma curve" to provide an appearance of evenly distributed brightness steps across the display's full dynamic range - hence the need to use ]s in computer video applications with deep enough color resolution to make engineering a hardcoded value into the DAC for each output level of each channel impractical (e.g. an Atari ST or Sega Genesis would require 24 such values; a 24-bit video card would need 768...). Given this inherent distortion, it is not unusual for a television or video projector to truthfully claim a linear contrast ratio (difference between darkest and brightest output levels) of 1000:1 or greater, equivalent to 10 bits of audio precision even though it may only accept signals with 8-bit precision and use an LCD panel that only represents 6 or 7 bits per channel.


⚫ Video signals from a digital source, such as a computer, must be converted to analog form if they are to be displayed on an analog monitor. As of 2007, analog inputs were more commonly used than digital, but this changed as ]s with ] and/or ] connections became more widespread.{{Citation needed|date=October 2011}} A video DAC is, however, incorporated in any digital video player with analog outputs. The DAC is usually integrated with some ] (]), which contains conversion tables for ], contrast and brightness, to make a device called a ].
⚫ Video sampling tends to work on a completely different scale altogether thanks to the highly nonlinear response both of cathode ray tubes (for which the vast majority of digital video foundation work was targeted) and the human eye, using a "gamma curve" to provide an appearance of evenly distributed brightness steps across the display's full dynamic range - hence the need to use ]s in computer video applications with deep enough colour resolution to make engineering a hardcoded value into the DAC for each output level of each channel impractical (e.g. an Atari ST or Sega Genesis would require 24 such values; a 24-bit video card would need 768...). Given this inherent distortion, it is not unusual for a television or video projector to truthfully claim a linear contrast ratio (difference between darkest and brightest output levels) of 1000:1 or greater, equivalent to 10 bits of audio precision even though it may only accept signals with 8-bit precision and use an LCD panel that only represents 6 or 7 bits per channel.

⚫ Video signals from a digital source, such as a computer, must be converted to analog form if they are to be displayed on an analog monitor. As of 2007, analog inputs were more commonly used than digital, but this changed as ]s with ] and/or ] connections became more widespread.{{Citation needed|date=October 2011}} A video DAC is, however, incorporated in any digital video player with analog outputs. The DAC is usually integrated with some ] (]), which contains conversion tables for ], contrast and brightness, to make a device called a ].


=== Digital potentiometer ===
A device that is distantly related to the DAC is the ], used to control an analog signal digitally. A device that is distantly related to the DAC is the ], used to control an analog signal digitally.


===Mechanical=== ===Mechanical===
] ]


A one-bit mechanical actuator assumes two positions: one when on, another when off. The motion of several one-bit actuators can be combined and weighted with a ] mechanism to produce finer steps. The ] typewriter uses such as system. When a typewriter key is pressed, it moves a metal bar (interposer) down that has several lugs. The lugs are the information bits. When a key is pressed, its interposer is moved by the motor. If a lug is present at one position, it will move the corresponding selector bail (bar); if the lug is not present, the selector bail stays where it is. The discrete motions of the bails are combined by a whiffle tree, and the output controls the rotation and tilt of the Selectric's typeball.<ref>Joachim Duebbers, </ref> A one-bit mechanical actuator assumes two positions: one when on, another when off. The motion of several one-bit actuators can be combined and weighted with a ] mechanism to produce finer steps. The ] typewriter uses such a system.<ref>{{cite web |author=Brian Brumfield |url=https://www.youtube.com/watch?v=uTjxwVfx8GA | archive-url=https://web.archive.org/web/20151229033401/https://www.youtube.com/watch?v=uTjxwVfx8GA| archive-date=2015-12-29 | url-status=dead|title=Selectric Repair 10-3A Input: Keyboard |date=Sep 2, 2014 |via=YouTube |df=ymd-all}}</ref>

=== Communications ===
DACs are widely used in modern communication systems enabling the generation of digitally-defined transmission signals. High-speed DACs are used for ] and ultra-high-speed DACs are employed in ] systems.


==Types== ==Types==
The most common types of electronic DACs are:<ref>http://www.analog.com/media/en/training-seminars/design-handbooks/Data-Conversion-Handbook/Chapter3.pdf</ref> The most common types of electronic DACs are:<ref name="ADDCH">{{cite web |url=http://www.analog.com/media/en/training-seminars/design-handbooks/Data-Conversion-Handbook/Chapter3.pdf |title=Data Converter Architectures |work=Analog-Digital Conversion |publisher=] |access-date=2017-08-30 |df=ymd-all |ref={{sfnref|"Data Converter Architectures"}}|url-status=live |archive-url=https://web.archive.org/web/20170830032212/http://www.analog.com/media/en/training-seminars/design-handbooks/Data-Conversion-Handbook/Chapter3.pdf |archive-date=2017-08-30}}</ref>
* The ], the simplest DAC type. A stable ] or ] is switched into a low-pass ] with a duration determined by the digital input code. This technique is often used for electric motor speed control, but has many other applications as well. * The ] where a stable ] or ] is switched into a low-pass ] with a duration determined by the digital input code. This technique is often used for ] and dimming ]s.
* Oversampling DACs or interpolating DACs such as those employing ], use a pulse density conversion technique with ]. Audio delta-sigma DACs are sold with 384&nbsp;kHz sampling rate and quoted 24-bit resolution, though quality is lower due to inherent noise (see {{Slink|2=Figures of merit|nopage=y}}). Some consumer electronics use a type of oversampling DAC referred to as a ].
* Oversampling DACs or interpolating DACs such as the delta-sigma DAC, use a pulse density conversion technique. The ] technique allows for the use of a lower resolution DAC internally. A simple ] is often chosen because the oversampled result is inherently linear. The DAC is driven with a ] signal, created with the use of a ], ] (the actual 1-bit DAC), and ] loop, in a technique called ]. This results in an effective ] acting on the ] noise, thus steering this noise out of the low frequencies of interest into the megahertz frequencies of little interest, which is called ]. The quantization noise at these high frequencies is removed or greatly attenuated by use of an analog low-pass filter at the output (sometimes a simple ] is sufficient). Most very high resolution DACs (greater than 16 bits) are of this type due to its high ] and low cost. Higher oversampling rates can relax the specifications of the output low-pass filter and enable further suppression of quantization noise. Speeds of greater than 100 thousand samples per second (for example, 192&nbsp;kHz) and resolutions of 24 bits are attainable with delta-sigma DACs. A short comparison with pulse-width modulation shows that a 1-bit DAC with a simple first-order ] would have to run at 3&nbsp;THz (which is physically unrealizable) to achieve 24 meaningful bits of resolution, requiring a higher-order low-pass filter in the noise-shaping loop. A single integrator is a low-pass filter with a ] inversely proportional to frequency and using one such integrator in the noise-shaping loop is a first order delta-sigma modulator. Multiple higher order topologies (such as ]) are used to achieve higher degrees of noise-shaping with a ].
* The binary-weighted DAC, which contains individual electrical components for each bit of the DAC connected to a summing point. These precise voltages or currents sum to the correct output value. This is one of the fastest conversion methods but suffers from poor accuracy because of the high precision required for each individual voltage or current. Such high-precision components are expensive, so this type of converter is usually limited to 8-bit resolution or less.{{Citation needed|date=February 2012}} * The binary-weighted DAC, which contains individual electrical components for each bit of the DAC connected to a summing point, typically an ]. Each input in the summing has powers-of-two weighting with the most current or voltage at the ]. This is one of the fastest conversion methods but suffers from poor accuracy because of the high precision required for each individual voltage or current.<ref>{{Cite web |url=https://www.electronics-tutorial.net/analog-integrated-circuits/data-converters/binary-weighted-resistor-dac/index.html |title=Binary Weighted Resistor DAC |website=Electronics Tutorial |language=en-US |access-date=2018-09-25 |df=ymd-all}}</ref>
** Switched ] DAC contains a parallel resistor network. Individual resistors are enabled or bypassed in the network based on the digital input. ** Switched ] DAC contains a parallel resistor network. Individual resistors are enabled or bypassed in the network based on the digital input.
** Switched ] DAC, from which different current sources are selected based on the digital input. ** Switched ] DAC, from which different current sources are selected based on the digital input. ]
** Switched ] DAC contains a parallel capacitor network. Individual capacitors are connected or disconnected with switches based on the input. ** Switched ] DAC contains a parallel capacitor network. Individual capacitors are connected or disconnected with switches based on the input.
* The ] DAC which is a binary-weighted DAC that uses a repeating cascaded structure of resistor values R and 2R. This improves the precision due to the relative ease of producing equal valued-matched resistors (or current sources). ** The ] DAC which is a binary-weighted DAC that uses a repeating cascaded structure of resistor values R and 2R. This improves the precision due to the relative ease of producing equal valued-matched resistors.
* The Successive-Approximation or Cyclic DAC,<ref>http://www.analog.com/media/en/training-seminars/design-handbooks/Data-Conversion-Handbook/Chapter3.pdf p.&nbsp;3.29</ref> which successively constructs the output during each cycle. Individual bits of the digital input are processed each cycle until the entire input is accounted for. * The successive approximation or cyclic DAC,{{sfn|"Data Converter Architectures"|p=3.29}} which successively constructs the output during each cycle. Individual bits of the digital input are processed each cycle until the entire input is accounted for.
* The ] DAC, which contains an equal resistor or current-source segment for each possible value of DAC output. An 8-bit thermometer DAC would have 255 segments, and a 16-bit thermometer DAC would have 65,535 segments. This is perhaps the fastest and highest precision DAC architecture but at the expense of high cost. Conversion speeds of >1 billion samples per second have been reached with this type of DAC. * The ] DAC, which contains an equal resistor or current-source segment for each possible value of DAC output. An 8-bit thermometer DAC would have 255 segments, and a 16-bit thermometer DAC would have 65,535 segments. This is a fast and highest precision DAC architecture but at the expense of requiring many components which, for practical implementations, fabrication requires high-density ].<ref>{{Citation |url=https://www.analog.com/media/en/training-seminars/tutorials/MT-014.pdf |archive-url=https://web.archive.org/web/20150503154823/http://www.analog.com/media/en/training-seminars/tutorials/MT-014.pdf |archive-date=2015-05-03 |url-status=live |author=Walt Kester |title=Basic DAC Architectures I: String DACs and Thermometer (Fully Decoded) DACs |publisher=]}}</ref>
* Hybrid DACs, which use a combination of the above techniques in a single converter. Most DAC integrated circuits are of this type due to the difficulty of getting low cost, high speed and high precision in one device. * Hybrid DACs, which use a combination of the above techniques in a single converter. Most DAC integrated circuits are of this type due to the difficulty of getting low cost, high speed and high precision in one device.
** The segmented DAC, which combines the thermometer-coded principle for the most significant bits and the binary-weighted principle for the least significant bits. In this way, a compromise is obtained between precision (by the use of the thermometer-coded principle) and number of resistors or current sources (by the use of the binary-weighted principle). The full binary-weighted design means 0% segmentation, the full thermometer-coded design means 100% segmentation. ** The segmented DAC, which combines the thermometer-coded principle for the most significant bits and the binary-weighted principle for the least significant bits. In this way, a compromise is obtained between precision (by the use of the thermometer-coded principle) and number of resistors or current sources (by the use of the binary-weighted principle). The full binary-weighted design means 0% segmentation, the full thermometer-coded design means 100% segmentation.
* Most DACs, shown earlier in this list, rely on a constant reference voltage to create their output value. Alternatively, a ''multiplying DAC''<ref>{{cite web |url=http://www.analog.com/static/imported-files/overviews/AnalogMultiplyingDACs.pdf |title=Multiplying DACs, flexible building blocks |format=PDF |year=2010 |publisher=Analog Devices inc. |accessdate=29 March 2012}}</ref> takes a variable input voltage for their conversion. This puts additional design constraints on the bandwidth of the conversion circuit. * Most DACs shown in this list rely on a constant reference voltage or current to create their output value. Alternatively, a ''multiplying DAC''<ref>{{cite web |url=https://www.analog.com/media/en/news-marketing-collateral/solutions-bulletins-brochures/AnalogMultiplyingDACs.pdf |archive-url=https://web.archive.org/web/20110516075112/http://www.analog.com/static/imported-files/overviews/AnalogMultiplyingDACs.pdf |archive-date=2011-05-16 |url-status=live |title=Multiplying DACs: Flexible Building Blocks |year=2010 |publisher=] |access-date=29 March 2012 |df=ymd-all}}</ref> takes a variable input voltage or current as a conversion reference. This puts additional design constraints on the bandwidth of the conversion circuit.
* Modern high-speed DACs have an interleaved architecture, in which multiple DAC cores are used in parallel. Their output signals are combined in the analog domain to enhance the performance of the combined DAC.<ref>{{Cite book|title=Interleaving Concepts for Digital-to-Analog Converters: Algorithms, Models, Simulations and Experiments|last=Schmidt|first=Christian|date=2020|publisher=Springer Fachmedien Wiesbaden|isbn=9783658272630|location=Wiesbaden|language=en|doi=10.1007/978-3-658-27264-7|s2cid=199586286}}</ref> The combination of the signals can be performed either in the time domain or in the frequency domain.


==Performance== ==Performance==
⚫ The most important characteristics of a DAC are:{{cn|date=August 2016}}

⚫ ;Resolution: The number of possible output levels the DAC is designed to reproduce. This is usually stated as the number of ]s it uses, which is the ] of the number of levels. For instance a 1-bit DAC is designed to reproduce 2 (2<sup>1</sup>) levels while an 8-bit DAC is designed for 256 (2<sup>8</sup>) levels. Resolution is related to the ] which is a measurement of the actual resolution attained by the DAC. Resolution determines ] in video applications and ] in audio applications.
⚫ DACs are very important to system performance. The most important characteristics of these devices are:{{cn|date=August 2016}}
⚫ ;Maximum ]: The maximum speed at which the DACs circuitry can operate and still produce correct output. The ] defines a relationship between this and the ] of the sampled signal.
⚫ ;Resolution: The number of possible output levels the DAC is designed to reproduce. This is usually stated as the number of ]s it uses, which is the base two ] of the number of levels. For instance a 1 bit DAC is designed to reproduce 2 (2<sup>1</sup>) levels while an 8 bit DAC is designed for 256 (2<sup>8</sup>) levels. Resolution is related to the ] which is a measurement of the actual resolution attained by the DAC. Resolution determines ] in video applications and ] in audio applications.
⚫ ;]: The ability of a DAC's analog output to move only in the direction that the digital input moves (i.e., if the input increases, the output doesn't dip before asserting the correct output.) This characteristic is very important for DACs used as a low-frequency signal source or as a digitally programmable trim element.{{cn|reason=Not a common specification IME. Bad behavior in this respect will be amply demonstrated as distortion.|date=August 2019}}
⚫ ;Maximum ]: A measurement of the maximum speed at which the DACs circuitry can operate and still produce the correct output. As stated above, the ] defines a relationship between this and the ] of the sampled signal.
⚫ ;] and noise (THD+N): A measurement of the distortion and noise introduced to the signal by the DAC. It is expressed as a percentage of the total power of unwanted ] and noise that accompanies the desired signal.
⚫ ;]: The ability of a DAC's analog output to move only in the direction that the digital input moves (i.e., if the input increases, the output doesn't dip before asserting the correct output.) This characteristic is very important for DACs used as a low frequency signal source or as a digitally programmable trim element.
⚫ ;] and noise (THD+N): A measurement of the distortion and noise introduced to the signal by the DAC. It is expressed as a percentage of the total power of unwanted ] ] and noise that accompany the desired signal. This is a very important DAC characteristic for dynamic and small signal DAC applications.
;]: A measurement of the difference between the largest and smallest signals the DAC can reproduce expressed in ]s. This is usually related to resolution and ]. ;]: A measurement of the difference between the largest and smallest signals the DAC can reproduce expressed in ]s. This is usually related to resolution and ].


Other measurements, such as ] and ], can also be very important for some applications, some of which (e.g. wireless data transmission, composite video) may even ''rely'' on accurate production of phase-adjusted signals. Other measurements, such as ] and ], can also be very important for some applications, some of which (e.g. wireless data transmission, composite video) may even ''rely'' on accurate production of phase-adjusted signals.


⚫ Non-linear PCM encodings (A-law / μ-law, ADPCM, NICAM) attempt to improve their effective dynamic ranges by using logarithmic step sizes between the output signal strengths represented by each data bit. This trades greater quantization distortion of loud signals for better performance of quiet signals.
Linear PCM audio sampling usually works on the basis of each bit of resolution being equivalent to 6 decibels of amplitude (a 2x increase in volume or precision).

⚫ Non-linear PCM encodings (A-law / μ-law, ADPCM, NICAM) attempt to improve their effective dynamic ranges by a variety of methods - logarithmic step sizes between the output signal strengths represented by each data bit (trading greater quantisation distortion of loud signals for better performance of quiet signals)


==Figures of merit== ==Figures of merit==

* Static performance: * Static performance:
** ] (DNL) shows how much two adjacent code analog values deviate from the ideal 1&nbsp;LSB step.<ref></ref> ** ] (DNL) shows how much two adjacent code analog values deviate from the ideal 1&nbsp;LSB step.<ref name="maxim">{{cite web |url=http://www.maxim-ic.com/appnotes.cfm/appnote_number/641/ |title=ADC and DAC Glossary |publisher=Maxim |df=ymd-all |url-status=live |archive-url=https://web.archive.org/web/20070308223113/http://www.maxim-ic.com/appnotes.cfm/appnote_number/641 |archive-date=2007-03-08}}</ref>
** ] (INL) shows how much the DAC transfer characteristic deviates from an ideal one. That is, the ideal characteristic is usually a straight line; INL shows how much the actual voltage at a given code value differs from that line, in LSBs (1&nbsp;LSB steps). ** ] (INL) shows how much the DAC transfer characteristic deviates from an ideal one. That is, the ideal characteristic is usually a straight line; INL shows how much the actual voltage at a given code value differs from that line, in LSBs (1&nbsp;LSB steps).<ref name="maxim"/>
** Gain ** Gain error<ref name="maxim"/>
** Offset ** Offset error<ref name="maxim"/>
** Noise is ultimately limited by the ] generated by passive components such as resistors. For audio applications and in room temperatures, such noise is usually a little less than 1 ] (microvolt) of ]. This limits performance to less than 20~21 bits even in 24-bit DACs. ** Noise is ultimately limited by the ] generated by passive components such as resistors. For audio applications and in room temperatures, such noise is usually a little less than 1{{nbsp}}] (microvolt) of ]. This practically limits resolution to less than 20~21 bits, even in 24-bit DACs.
* Frequency domain performance * Frequency domain performance
** ] (SFDR) indicates in dB the ratio between the powers of the converted main signal and the greatest undesired spur. ** ] (SFDR) indicates in dB the ratio between the powers of the converted main signal and the greatest undesired spur.<ref name="maxim"/>
** Signal-to-noise and distortion ratio (SNDR) indicates in dB the ratio between the powers of the converted main signal and the sum of the noise and the generated harmonic spurs ** Signal-to-noise and distortion (]) indicates in dB the ratio between the powers of the converted main signal and the sum of the noise and the generated harmonic spurs<ref name="maxim"/>
** i-th harmonic distortion (HDi) indicates the power of the i-th harmonic of the converted main signal ** i-th harmonic distortion (HDi) indicates the power of the i-th harmonic of the converted main signal
** ] (THD) is the sum of the powers of all HDi ** ] (THD) is the sum of the powers of all the harmonics of the input signal<ref name="maxim"/>
** If the maximum DNL error is less than 1 LSB, then the {{nowrap|D/A}} converter is guaranteed to be monotonic. However, many monotonic converters may have a maximum DNL greater than 1 LSB. ** If the maximum DNL is less than 1 LSB, then the {{nowrap|D/A}} converter is guaranteed to be monotonic. However, many monotonic converters may have a maximum DNL greater than 1 LSB.<ref name="maxim"/>
* Time domain performance: * Time domain performance:
** Glitch impulse area (glitch energy) ** Glitch impulse area (glitch energy)<ref name="maxim"/><!--]-->
** Response uncertainty
** Time nonlinearity (TNL)


==See also== ==See also==
*{{anl|I²S}}
*]
*]
*]
*]


==References== ==References==
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== Further reading == == Further reading ==
{{Refbegin}}
* {{Citation * {{Citation
| title = The Data Conversion Handbook | title = The Data Conversion Handbook
Line 122: Line 115:
| first = Walt | first = Walt
| isbn = 0-7506-7841-0 | isbn = 0-7506-7841-0
| url = http://www.analog.com/library/analogDialogue/archives/39-06/data_conversion_handbook.html | url = https://www.analog.com/en/resources/technical-books/data-conversion-handbook.html
| year = 2005
⚫ }}
| publisher = Newnes
}}
* S. Norsworthy, Richard Schreier, Gabor C. Temes, ''Delta-Sigma Data Converters''. {{ISBN|0-7803-1045-4}}. * S. Norsworthy, Richard Schreier, Gabor C. Temes, ''Delta-Sigma Data Converters''. {{ISBN|0-7803-1045-4}}.
* Mingliang Liu, ''Demystifying Switched-Capacitor Circuits''. {{ISBN|0-7506-7907-7}}. * Mingliang Liu, ''Demystifying Switched-Capacitor Circuits''. {{ISBN|0-7506-7907-7}}.
Line 131: Line 126:
* A Anand Kumar, ''Fundamentals of Digital Circuits''. {{ISBN|81-203-1745-9}}, {{ISBN|978-81-203-1745-1}}. * A Anand Kumar, ''Fundamentals of Digital Circuits''. {{ISBN|81-203-1745-9}}, {{ISBN|978-81-203-1745-1}}.
* Ndjountche Tertulien, "CMOS Analog Integrated Circuits: High-Speed and Power-Efficient Design". {{ISBN|978-1-4398-5491-4}}. * Ndjountche Tertulien, "CMOS Analog Integrated Circuits: High-Speed and Power-Efficient Design". {{ISBN|978-1-4398-5491-4}}.
{{Refend}}


== External links == == External links ==
* * {{cite web |url=http://www.maxim-ic.com/appnotes.cfm/an_pk/641/CMP/WP-36 |title=ADC and DAC Glossary |archive-url=https://web.archive.org/web/20091213023149/http://www.maxim-ic.com/appnotes.cfm/an_pk/641/CMP/WP-36 |archive-date=2009-12-13 |url-status=dead}}
*
* with circuit diagrams.
* Outlines HD, IMD and NPR measurements, also includes a derivation of quantization noise


{{Authority control}} {{Authority control}}
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Latest revision as of 06:46, 6 December 2024

Device that converts a digital signal into an analog signal This article is about conversion of digital signals to analog signals. For digital television converter boxes, see digital television adapter. "D2A" redirects here. For the D2A dive bomber, see Aichi D1A. "d-a-c" redirects here. For other uses, see DAC (disambiguation).
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8-channel Cirrus Logic CS4382 digital-to-analog converter as used in a sound card.

In electronics, a digital-to-analog converter (DAC, D/A, D2A, or D-to-A) is a system that converts a digital signal into an analog signal. An analog-to-digital converter (ADC) performs the reverse function.

There are several DAC architectures; the suitability of a DAC for a particular application is determined by figures of merit including: resolution, maximum sampling frequency and others. Digital-to-analog conversion can degrade a signal, so a DAC should be specified that has insignificant errors in terms of the application.

DACs are commonly used in music players to convert digital data streams into analog audio signals. They are also used in televisions and mobile phones to convert digital video data into analog video signals. These two applications use DACs at opposite ends of the frequency/resolution trade-off. The audio DAC is a low-frequency, high-resolution type while the video DAC is a high-frequency low- to medium-resolution type.

Due to the complexity and the need for precisely matched components, all but the most specialized DACs 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.

Discrete DACs (circuits constructed from multiple discrete electronic components instead of a packaged IC) would typically be extremely high-speed low-resolution power-hungry types, as used in military radar systems. Very high-speed test equipment, especially sampling oscilloscopes, may also use discrete DACs.

Overview

Sampled signal.

A DAC converts an abstract finite-precision number (usually a fixed-point binary number) into a physical quantity (e.g., a voltage or a pressure). In particular, DACs are often used to convert finite-precision time series data to a continually varying physical signal.

Provided that a signal's bandwidth meets the requirements of the Nyquist–Shannon sampling theorem (i.e., a baseband signal with bandwidth less than the Nyquist frequency) and was sampled with infinite resolution, the original signal can theoretically be reconstructed from the sampled data. However, an ADC's filtering can't entirely eliminate all frequencies above the Nyquist frequency, which will alias into the baseband frequency range. And the ADC's digital sampling process introduces some quantization error (rounding error), which manifests as low-level noise. These errors can be kept within the requirements of the targeted application (e.g. under the limited dynamic range of human hearing for audio applications).

Applications

A simplified functional diagram of an 8-bit DAC

DACs and ADCs are part of an enabling technology that has contributed greatly to the digital revolution. To illustrate, consider a typical long-distance telephone call. The caller's voice is converted into an analog electrical signal by a microphone, then the analog signal is converted to a digital stream by an ADC. The digital stream is then divided into network packets where it may be sent along with other digital data, not necessarily audio. The packets are then received at the destination, but each packet may take a completely different route and may not even arrive at the destination in the correct time order. The digital voice data is then extracted from the packets and assembled into a digital data stream. A DAC converts this back into an analog electrical signal, which drives an audio amplifier, which in turn drives a speaker, which finally produces sound.

Audio

Top-loading CD player (top) and external digital-to-analog converter (bottom) from the same company.
A 1990s external DAC from Audio Alchemy as an add-on for CD players, having only about 12 cm width, intended to improve the sound of older or less expensive players.

Most modern audio signals are stored in digital form (for example MP3s and CDs), and in order to be heard through speakers, they must be converted into an analog signal. DACs are therefore found in CD players, digital music players, and PC sound cards.

Specialist standalone DACs can also be found in high-end hi-fi systems. These normally take the digital output of a compatible CD player or dedicated transport (which is basically a CD player with no internal DAC) and convert the signal into an analog line-level output that can then be fed into an amplifier to drive speakers.

Similar digital-to-analog converters can be found in digital speakers such as USB speakers, and in sound cards.

In voice over IP applications, the source must first be digitized for transmission, so it undergoes conversion via an ADC and is then reconstructed into analog using a DAC on the receiving party's end.

Video

Video sampling tends to work on a completely different scale altogether thanks to the highly nonlinear response both of cathode ray tubes (for which the vast majority of digital video foundation work was targeted) and the human eye, using a "gamma curve" to provide an appearance of evenly distributed brightness steps across the display's full dynamic range - hence the need to use RAMDACs in computer video applications with deep enough color resolution to make engineering a hardcoded value into the DAC for each output level of each channel impractical (e.g. an Atari ST or Sega Genesis would require 24 such values; a 24-bit video card would need 768...). Given this inherent distortion, it is not unusual for a television or video projector to truthfully claim a linear contrast ratio (difference between darkest and brightest output levels) of 1000:1 or greater, equivalent to 10 bits of audio precision even though it may only accept signals with 8-bit precision and use an LCD panel that only represents 6 or 7 bits per channel.

Video signals from a digital source, such as a computer, must be converted to analog form if they are to be displayed on an analog monitor. As of 2007, analog inputs were more commonly used than digital, but this changed as flat-panel displays with DVI and/or HDMI connections became more widespread. A video DAC is, however, incorporated in any digital video player with analog outputs. The DAC is usually integrated with some memory (RAM), which contains conversion tables for gamma correction, contrast and brightness, to make a device called a RAMDAC.

Digital potentiometer

A device that is distantly related to the DAC is the digitally controlled potentiometer, used to control an analog signal digitally.

Mechanical

IBM Selectric typewriter uses a mechanical digital-to-analog converter to control its typeball.

A one-bit mechanical actuator assumes two positions: one when on, another when off. The motion of several one-bit actuators can be combined and weighted with a whiffletree mechanism to produce finer steps. The IBM Selectric typewriter uses such a system.

Communications

DACs are widely used in modern communication systems enabling the generation of digitally-defined transmission signals. High-speed DACs are used for mobile communications and ultra-high-speed DACs are employed in optical communications systems.

Types

The most common types of electronic DACs are:

  • The pulse-width modulator where a stable current or voltage is switched into a low-pass analog filter with a duration determined by the digital input code. This technique is often used for electric motor speed control and dimming LED lamps.
  • Oversampling DACs or interpolating DACs such as those employing delta-sigma modulation, use a pulse density conversion technique with oversampling. Audio delta-sigma DACs are sold with 384 kHz sampling rate and quoted 24-bit resolution, though quality is lower due to inherent noise (see § Figures of merit). Some consumer electronics use a type of oversampling DAC referred to as a 1-bit DAC.
  • The binary-weighted DAC, which contains individual electrical components for each bit of the DAC connected to a summing point, typically an operational amplifier. Each input in the summing has powers-of-two weighting with the most current or voltage at the most-significant bit. This is one of the fastest conversion methods but suffers from poor accuracy because of the high precision required for each individual voltage or current.
    • Switched resistor DAC contains a parallel resistor network. Individual resistors are enabled or bypassed in the network based on the digital input.
    • Switched current source DAC, from which different current sources are selected based on the digital input.
      Current steering DAC - DAC1138KX
    • Switched capacitor DAC contains a parallel capacitor network. Individual capacitors are connected or disconnected with switches based on the input.
    • The R-2R ladder DAC which is a binary-weighted DAC that uses a repeating cascaded structure of resistor values R and 2R. This improves the precision due to the relative ease of producing equal valued-matched resistors.
  • The successive approximation or cyclic DAC, which successively constructs the output during each cycle. Individual bits of the digital input are processed each cycle until the entire input is accounted for.
  • The thermometer-coded DAC, which contains an equal resistor or current-source segment for each possible value of DAC output. An 8-bit thermometer DAC would have 255 segments, and a 16-bit thermometer DAC would have 65,535 segments. This is a fast and highest precision DAC architecture but at the expense of requiring many components which, for practical implementations, fabrication requires high-density IC processes.
  • Hybrid DACs, which use a combination of the above techniques in a single converter. Most DAC integrated circuits are of this type due to the difficulty of getting low cost, high speed and high precision in one device.
    • The segmented DAC, which combines the thermometer-coded principle for the most significant bits and the binary-weighted principle for the least significant bits. In this way, a compromise is obtained between precision (by the use of the thermometer-coded principle) and number of resistors or current sources (by the use of the binary-weighted principle). The full binary-weighted design means 0% segmentation, the full thermometer-coded design means 100% segmentation.
  • Most DACs shown in this list rely on a constant reference voltage or current to create their output value. Alternatively, a multiplying DAC takes a variable input voltage or current as a conversion reference. This puts additional design constraints on the bandwidth of the conversion circuit.
  • Modern high-speed DACs have an interleaved architecture, in which multiple DAC cores are used in parallel. Their output signals are combined in the analog domain to enhance the performance of the combined DAC. The combination of the signals can be performed either in the time domain or in the frequency domain.

Performance

The most important characteristics of a DAC are:

Resolution
The number of possible output levels the DAC is designed to reproduce. This is usually stated as the number of bits it uses, which is the binary logarithm of the number of levels. For instance a 1-bit DAC is designed to reproduce 2 (2) levels while an 8-bit DAC is designed for 256 (2) levels. Resolution is related to the effective number of bits which is a measurement of the actual resolution attained by the DAC. Resolution determines color depth in video applications and audio bit depth in audio applications.
Maximum sampling rate
The maximum speed at which the DACs circuitry can operate and still produce correct output. The Nyquist–Shannon sampling theorem defines a relationship between this and the bandwidth of the sampled signal.
Monotonicity
The ability of a DAC's analog output to move only in the direction that the digital input moves (i.e., if the input increases, the output doesn't dip before asserting the correct output.) This characteristic is very important for DACs used as a low-frequency signal source or as a digitally programmable trim element.
Total harmonic distortion and noise (THD+N)
A measurement of the distortion and noise introduced to the signal by the DAC. It is expressed as a percentage of the total power of unwanted harmonic distortion and noise that accompanies the desired signal.
Dynamic range
A measurement of the difference between the largest and smallest signals the DAC can reproduce expressed in decibels. This is usually related to resolution and noise floor.

Other measurements, such as phase distortion and jitter, can also be very important for some applications, some of which (e.g. wireless data transmission, composite video) may even rely on accurate production of phase-adjusted signals.

Non-linear PCM encodings (A-law / μ-law, ADPCM, NICAM) attempt to improve their effective dynamic ranges by using logarithmic step sizes between the output signal strengths represented by each data bit. This trades greater quantization distortion of loud signals for better performance of quiet signals.

Figures of merit

  • Static performance:
    • Differential nonlinearity (DNL) shows how much two adjacent code analog values deviate from the ideal 1 LSB step.
    • Integral nonlinearity (INL) shows how much the DAC transfer characteristic deviates from an ideal one. That is, the ideal characteristic is usually a straight line; INL shows how much the actual voltage at a given code value differs from that line, in LSBs (1 LSB steps).
    • Gain error
    • Offset error
    • Noise is ultimately limited by the thermal noise generated by passive components such as resistors. For audio applications and in room temperatures, such noise is usually a little less than 1 μV (microvolt) of white noise. This practically limits resolution to less than 20~21 bits, even in 24-bit DACs.
  • Frequency domain performance
    • Spurious-free dynamic range (SFDR) indicates in dB the ratio between the powers of the converted main signal and the greatest undesired spur.
    • Signal-to-noise and distortion (SINAD) indicates in dB the ratio between the powers of the converted main signal and the sum of the noise and the generated harmonic spurs
    • i-th harmonic distortion (HDi) indicates the power of the i-th harmonic of the converted main signal
    • Total harmonic distortion (THD) is the sum of the powers of all the harmonics of the input signal
    • If the maximum DNL is less than 1 LSB, then the D/A converter is guaranteed to be monotonic. However, many monotonic converters may have a maximum DNL greater than 1 LSB.
  • Time domain performance:
    • Glitch impulse area (glitch energy)

See also

  • I²S – A serial communication protocol for two-channel digital audio

References

  1. Brian Brumfield (2014-09-02). "Selectric Repair 10-3A Input: Keyboard". Archived from the original on 2015-12-29 – via YouTube.
  2. "Data Converter Architectures" (PDF). Analog-Digital Conversion. Analog Devices. Archived (PDF) from the original on 2017-08-30. Retrieved 2017-08-30.
  3. "Binary Weighted Resistor DAC". Electronics Tutorial. Retrieved 2018-09-25.
  4. "Data Converter Architectures", p. 3.29.
  5. Walt Kester, Basic DAC Architectures I: String DACs and Thermometer (Fully Decoded) DACs (PDF), Analog Devices, archived (PDF) from the original on 2015-05-03
  6. "Multiplying DACs: Flexible Building Blocks" (PDF). Analog Devices. 2010. Archived (PDF) from the original on 2011-05-16. Retrieved 2012-03-29.
  7. Schmidt, Christian (2020). Interleaving Concepts for Digital-to-Analog Converters: Algorithms, Models, Simulations and Experiments. Wiesbaden: Springer Fachmedien Wiesbaden. doi:10.1007/978-3-658-27264-7. ISBN 9783658272630. S2CID 199586286.
  8. ^ "ADC and DAC Glossary". Maxim. Archived from the original on 2007-03-08.

Further reading

External links

Categories: