This article has multiple issues. Please help improve it or discuss these issues on the talk page . (Learn how and when to remove these template messages)
(Learn how and when to remove this template message) |

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.

- Overview
- Applications
- Audio
- Video
- Mechanical
- Communications
- Types
- Performance
- Figures of merit
- See also
- References
- Further reading
- External links

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 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.

Due to the complexity and the need for precisely matched components, all but the most specialized DACs are implemented as integrated circuits (ICs). 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.

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.

An *ideal* DAC converts the abstract numbers into a conceptual sequence of impulses that are then processed by a reconstruction filter using some form of interpolation to fill in data between the impulses. A conventional *practical* DAC converts the numbers into a piecewise constant function made up of a sequence of rectangular functions that is modeled with the zero-order hold. Other DAC methods (such as those based on delta-sigma modulation) produce a pulse-density modulated output that can be similarly filtered to produce a smoothly varying signal.

As per the Nyquist–Shannon sampling theorem, a DAC can reconstruct the original signal from the sampled data provided that its bandwidth meets certain requirements (e.g., a baseband signal with bandwidth less than the Nyquist frequency). Digital sampling introduces quantization error that manifests as low-level noise in the reconstructed signal.

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 loudspeaker, which finally produces sound.

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 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 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 flat panel displays with DVI and/or HDMI connections became more widespread.^{[ citation needed ]} 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.

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

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.^{ [1] }

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

The most common types of electronic DACs are:^{ [2] }

- 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. Speeds of greater than 100 thousand samples per second (for example, 192 kHz) and resolutions of 24 bits are attainable with delta-sigma DACs.
- 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 values with most current or voltage at the most-significant bit. 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.
^{ [3] }This type of converter is usually limited to 8-bit resolution or less.^{[ citation needed ]}- 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.
- 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,
^{ [4] }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.
^{ [5] } - 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*^{ [6] }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.
^{ [7] }The combination of the signals can be performed either in the time domain or in the frequency domain.

The most important characteristics of a DAC are:^{[ citation needed ]}

- 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
^{1}) levels while an 8-bit DAC is designed for 256 (2^{8}) 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.
^{[ citation needed ]} - 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 accompany 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 quantisation distortion of loud signals for better performance of quiet signals.

- Static performance:
- Differential nonlinearity (DNL) shows how much two adjacent code analog values deviate from the ideal 1 LSB step.
^{ [8] } - 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).
^{ [8] } - Gain error
^{ [8] } - Offset error
^{ [8] } - 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 limits performance to less than 20~21 bits even in 24-bit DACs.

- Differential nonlinearity (DNL) shows how much two adjacent code analog values deviate from the ideal 1 LSB step.
- 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.
^{ [8] } - 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
^{ [8] } - 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
^{ [8] } - 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.
^{ [8] }

- Spurious-free dynamic range (SFDR) indicates in dB the ratio between the powers of the converted main signal and the greatest undesired spur.
- Time domain performance:
- Glitch impulse area (glitch energy)
^{ [8] }

- Glitch impulse area (glitch energy)

In electronics, an **analog-to-digital converter** is a system that converts an analog signal, such as a sound picked up by a microphone or light entering a digital camera, into a digital signal. An ADC may also provide an isolated measurement such as an electronic device that converts an input analog voltage or current to a digital number representing the magnitude of the voltage or current. Typically the digital output is a two's complement binary number that is proportional to the input, but there are other possibilities.

In signal processing, **sampling** is the reduction of a continuous-time signal to a discrete-time signal. A common example is the conversion of a sound wave to a sequence of samples.

A **numerically-controlled oscillator** (**NCO**) is a digital signal generator which creates a synchronous, discrete-time, discrete-valued representation of a waveform, usually sinusoidal. NCOs are often used in conjunction with a digital-to-analog converter (DAC) at the output to create a direct digital synthesizer (DDS).

A **spectrum analyzer** measures the magnitude of an input signal versus frequency within the full frequency range of the instrument. The primary use is to measure the power of the spectrum of known and unknown signals. The input signal that most common spectrum analyzers measure is electrical; however, spectral compositions of other signals, such as acoustic pressure waves and optical light waves, can be considered through the use of an appropriate transducer. Spectrum analyzers for other types of signals also exist, such as optical spectrum analyzers which use direct optical techniques such as a monochromator to make measurements.

**Quantization**, in mathematics and digital signal processing, is the process of mapping input values from a large set to output values in a (countable) smaller set, often with a finite number of elements. Rounding and truncation are typical examples of quantization processes. Quantization is involved to some degree in nearly all digital signal processing, as the process of representing a signal in digital form ordinarily involves rounding. Quantization also forms the core of essentially all lossy compression algorithms.

**Noise shaping** is a technique typically used in digital audio, image, and video processing, usually in combination with dithering, as part of the process of quantization or bit-depth reduction of a digital signal. Its purpose is to increase the apparent signal-to-noise ratio of the resultant signal. It does this by altering the spectral shape of the error that is introduced by dithering and quantization; such that the noise power is at a lower level in frequency bands at which noise is considered to be less desirable and at a correspondingly higher level in bands where it is considered to be more desirable. A popular noise shaping algorithm used in image processing is known as ‘Floyd Steinberg dithering’; and many noise shaping algorithms used in audio processing are based on an ‘Absolute threshold of hearing’ model.

In signal processing, **oversampling** is the process of sampling a signal at a sampling frequency significantly higher than the Nyquist rate. Theoretically, a bandwidth-limited signal can be perfectly reconstructed if sampled at the Nyquist rate or above it. The Nyquist rate is defined as twice the bandwidth of the signal. Oversampling is capable of improving resolution and signal-to-noise ratio, and can be helpful in avoiding aliasing and phase distortion by relaxing anti-aliasing filter performance requirements.

**Analogue electronics** are electronic systems with a continuously variable signal, in contrast to digital electronics where signals usually take only two levels. The term "analogue" describes the proportional relationship between a signal and a voltage or current that represents the signal. The word analogue is derived from the Greek word ανάλογος (analogos) meaning "proportional".

**Delta-sigma** modulation is a method for encoding analog signals into digital signals as found in an analog-to-digital converter (ADC). It is also used to convert high bit-count, low-frequency digital signals into lower bit-count, higher-frequency digital signals as part of the process to convert digital signals into analog as part of a digital-to-analog converter (DAC).

A **resistor ladder** is an electrical circuit made from repeating units of resistors. Two configurations are discussed below, a string resistor ladder and an R–2R ladder.

A **flash ADC** is a type of analog-to-digital converter that uses a linear voltage ladder with a comparator at each "rung" of the ladder to compare the input voltage to successive reference voltages. Often these reference ladders are constructed of many resistors; however, modern implementations show that capacitive voltage division is also possible. The output of these comparators is generally fed into a digital encoder, which converts the inputs into a binary value.

A **switched capacitor** (**SC**) is an electronic circuit element implementing a filter. It works by moving charges into and out of capacitors when switches are opened and closed. Usually, non-overlapping signals are used to control the switches, so that not all switches are closed simultaneously. Filters implemented with these elements are termed "switched-capacitor filters", and depend only on the ratios between capacitances. This makes them much more suitable for use within integrated circuits, where accurately specified resistors and capacitors are not economical to construct.

A **successive approximation ADC** is a type of analog-to-digital converter that converts a continuous analog waveform into a discrete digital representation via a binary search through all possible quantization levels before finally converging upon a digital output for each conversion.

In digital audio using pulse-code modulation (PCM), **bit depth** is the number of bits of information in each sample, and it directly corresponds to the **resolution** of each sample. Examples of bit depth include Compact Disc Digital Audio, which uses 16 bits per sample, and DVD-Audio and Blu-ray Disc which can support up to 24 bits per sample.

**Effective number of bits** (**ENOB**) is a measure of the dynamic range of an analog-to-digital converter (ADC), digital-to-analog converter, or their associated circuitry. The resolution of an ADC is specified by the number of bits used to represent the analog value. Ideally, a 12-bit ADC will have an effective number of bits of almost 12. However, real signals have noise, and real circuits are imperfect and introduce additional noise and distortion. Those imperfections reduce the number of bits of accuracy in the ADC. The ENOB describes the effective resolution of the system in bits. An ADC may have 12-bit resolution, but the effective number of bits when used in a system may be 9.5.

**Precision Monolithics, Inc.** also known as **PMI**, was an American company based in Santa Clara, California, that developed and produced mixed signal and linear integrated circuits (ICs). It was a pioneer in the fields of digital-to-analog converters and operational amplifiers.

**Differential nonlinearity** is a term describing the deviation between two analog values corresponding to adjacent input digital values. It is an important specification for measuring error in a digital-to-analog converter (DAC); the accuracy of a DAC is mainly determined by this specification. Ideally, any two adjacent digital codes correspond to output analog voltages that are exactly one Least Significant Bit (LSB) apart. Differential non-linearity is a measure of the worst case deviation from the ideal 1 LSB step. For example, a DAC with a 1.5 LSB output change for a 1 LSB digital code change exhibits 1⁄2 LSB differential non-linearity. Differential non-linearity may be expressed in fractional bits or as a percentage of full scale. A differential non-linearity greater than 1 LSB may lead to a non-monotonic transfer function in a DAC. It is also known as a *missing code*.

**Spurious-free dynamic range** (**SFDR**) is the strength ratio of the fundamental signal to the strongest spurious signal in the output. It is also defined as a measure used to specify analog-to-digital and digital-to-analog converters and radio receivers.

An **integrating ADC** is a type of analog-to-digital converter that converts an unknown input voltage into a digital representation through the use of an integrator. In its basic implementation, the dual-slope converter, the unknown input voltage is applied to the input of the integrator and allowed to ramp for a fixed time 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 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.

The following outline is provided as an overview of and topical guide to electronics:

- ↑ Brian Brumfield (2014-09-02). "Selectric Repair 10-3A Input: Keyboard" – via YouTube.
- ↑ "Data Converter Architectures" (PDF).
*Analog-Digital Conversion*. Analog Devices. Archived (PDF) from the original on 2017-08-30. Retrieved 2017-08-30.CS1 maint: extra punctuation (link) - ↑ "Binary Weighted Resistor DAC".
*Electronics Tutorial*. Retrieved 2018-09-25. - ↑ "Data Converter Architectures", p. 3.29.
- ↑ Walt Kester,
*Basic DAC Architectures I: String DACs and Thermometer (Fully Decoded) DACs*(PDF), Analog Devices - ↑ "Multiplying DACs: Flexible Building Blocks" (PDF). Analog Devices. 2010. Retrieved 2012-03-29.
- ↑ 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. - 1 2 3 4 5 6 7 8 9 "ADC and DAC Glossary". Maxim. Archived from the original on 2007-03-08.

- Kester, Walt (2005),
*The Data Conversion Handbook*, ISBN 0-7506-7841-0 - 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. - Behzad Razavi,
*Principles of Data Conversion System Design*. ISBN 0-7803-1093-4. - Phillip E. Allen, Douglas R. Holberg,
*CMOS Analog Circuit Design*. ISBN 0-19-511644-5. - Robert F. Coughlin, Frederick F. Driscoll,
*Operational Amplifiers and Linear Integrated Circuits*. ISBN 0-13-014991-8. - 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.

This page is based on this Wikipedia article

Text is available under the CC BY-SA 4.0 license; additional terms may apply.

Images, videos and audio are available under their respective licenses.

Text is available under the CC BY-SA 4.0 license; additional terms may apply.

Images, videos and audio are available under their respective licenses.