Digital-to-analog converter

Overview

Electronics

Electronics is the branch of science, engineering and technology that deals with electrical circuits involving active electrical components such as vacuum tubes, transistors, diodes and integrated circuits, and associated passive interconnection technologies...

, a

**digital-to-analog converter**(

**DAC**or

**D-to-A**) is a device that converts a digital (usually binary) code to an analog signal

Analog signal

An analog or analogue signal is any continuous signal for which the time varying feature of the signal is a representation of some other time varying quantity, i.e., analogous to another time varying signal. It differs from a digital signal in terms of small fluctuations in the signal which are...

(current, voltage

Voltage

Voltage, otherwise known as electrical potential difference or electric tension is the difference in electric potential between two points — or the difference in electric potential energy per unit charge between two points...

, or electric charge

Electric charge

Electric charge is a physical property of matter that causes it to experience a force when near other electrically charged matter. Electric charge comes in two types, called positive and negative. Two positively charged substances, or objects, experience a mutual repulsive force, as do two...

). An analog-to-digital converter

Analog-to-digital converter

An analog-to-digital converter is a device that converts a continuous quantity to a discrete time digital representation. An ADC may also provide an isolated measurement...

(ADC) performs the reverse operation. Signals are easily stored and transmitted in digital

Digital

A digital system is a data technology that uses discrete values. By contrast, non-digital systems use a continuous range of values to represent information...

form, but a DAC is needed for the signal to be recognized by human senses or other non-digital systems.

A common use of digital-to-analog converters is generation of audio signals from digital information in music players.

Unanswered Questions

Discussions

Encyclopedia

In electronics

, a

(current, voltage

, or electric charge

). An analog-to-digital converter

(ADC) performs the reverse operation. Signals are easily stored and transmitted in digital

form, but a DAC is needed for the signal to be recognized by human senses or other non-digital systems.

A common use of digital-to-analog converters is generation of audio signals from digital information in music players. Digital video signals are converted to analog in televisions and cell phones to display colors and shades. Digital-to-analog conversion can degrade a signal, so conversion details are normally chosen so that the errors are negligible.

Due to cost and the need for matched components, DACs are almost exclusively manufactured on integrated circuits (ICs). There are many DAC architectures

which have different advantages and disadvantages. The suitability of a particular DAC for an application is determined by a variety of measurements including speed and resolution.

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.

A typical DAC converts the abstract numbers into a concrete sequence of impulse

s that are then processed by a reconstruction filter

using some form of interpolation

to fill in data between the impulses. Other DAC methods (e.g., methods based on delta-sigma modulation

) produce a pulse-density modulated

signal that can then be filtered in a similar way 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 added to the reconstructed signal.

These numbers are written to the DAC, typically with a clock signal

that causes each number to be latched 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

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 zero-order hold

in sample data textbooks) or rectangular pulses causes multiple harmonics above the Nyquist frequency

. Usually, these are removed with a low pass filter acting as a reconstruction filter in applications that require it.

s 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 card

s.

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 card

s.

In VoIP (Voice over IP) applications, the source must first be digitized for transmission, so it undergoes conversion via an Analog-to-Digital Converter

, and is then reconstructed into analog using a DAC on the receiving party's end.

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 display

s 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

.

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

electromechanical digital-to-analog converter linkage in the IBM Selectric typewriter.

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

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 / mu-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)

Electronics

Electronics is the branch of science, engineering and technology that deals with electrical circuits involving active electrical components such as vacuum tubes, transistors, diodes and integrated circuits, and associated passive interconnection technologies...

, a

**digital-to-analog converter**(**DAC**or**D-to-A**) is a device that converts a digital (usually binary) code to an analog signalAnalog signal

An analog or analogue signal is any continuous signal for which the time varying feature of the signal is a representation of some other time varying quantity, i.e., analogous to another time varying signal. It differs from a digital signal in terms of small fluctuations in the signal which are...

(current, voltage

Voltage

Voltage, otherwise known as electrical potential difference or electric tension is the difference in electric potential between two points — or the difference in electric potential energy per unit charge between two points...

, or electric charge

Electric charge

Electric charge is a physical property of matter that causes it to experience a force when near other electrically charged matter. Electric charge comes in two types, called positive and negative. Two positively charged substances, or objects, experience a mutual repulsive force, as do two...

). An analog-to-digital converter

Analog-to-digital converter

An analog-to-digital converter is a device that converts a continuous quantity to a discrete time digital representation. An ADC may also provide an isolated measurement...

(ADC) performs the reverse operation. Signals are easily stored and transmitted in digital

Digital

A digital system is a data technology that uses discrete values. By contrast, non-digital systems use a continuous range of values to represent information...

form, but a DAC is needed for the signal to be recognized by human senses or other non-digital systems.

A common use of digital-to-analog converters is generation of audio signals from digital information in music players. Digital video signals are converted to analog in televisions and cell phones to display colors and shades. Digital-to-analog conversion can degrade a signal, so conversion details are normally chosen so that the errors are negligible.

Due to cost and the need for matched components, DACs are almost exclusively manufactured on integrated circuits (ICs). There are many DAC architectures

Hardware architecture

In engineering, hardware architecture refers to the identification of a system's physical components and their interrelationships. This description, often called a hardware design model, allows hardware designers to understand how their components fit into a system architecture and provides...

which have different advantages and disadvantages. The suitability of a particular DAC for an application is determined by a variety of measurements including speed and resolution.

## Overview

A DAC converts an abstractAbstract object

An abstract object is an object which does not exist at any particular time or place, but rather exists as a type of thing . In philosophy, an important distinction is whether an object is considered abstract or concrete. Abstract objects are sometimes called abstracta An abstract object is an...

finite-precision number (usually a fixed-point

Fixed-point arithmetic

In computing, a fixed-point number representation is a real data type for a number that has a fixed number of digits after the radix point...

binary number) into a physical quantity (e.g., a voltage

Voltage

Voltage, otherwise known as electrical potential difference or electric tension is the difference in electric potential between two points — or the difference in electric potential energy per unit charge between two points...

or a pressure

Pressure

Pressure is the force per unit area applied in a direction perpendicular to the surface of an object. Gauge pressure is the pressure relative to the local atmospheric or ambient pressure.- Definition :...

). In particular, DACs are often used to convert finite-precision time series

Time series

In statistics, signal processing, econometrics and mathematical finance, a time series is a sequence of data points, measured typically at successive times spaced at uniform time intervals. Examples of time series are the daily closing value of the Dow Jones index or the annual flow volume of the...

data to a continually varying physical signal.

A typical DAC converts the abstract numbers into a concrete sequence of impulse

Dirac delta function

The Dirac delta function, or δ function, is a generalized function depending on a real parameter such that it is zero for all values of the parameter except when the parameter is zero, and its integral over the parameter from −∞ to ∞ is equal to one. It was introduced by theoretical...

s that are then processed by a reconstruction filter

Reconstruction filter

In a mixed-signal system , a reconstruction filter is used to construct a smooth analogue signal from a digital input, as in the case of a digital to analogue converter or other sampled data output device....

using some form of interpolation

Interpolation

In the mathematical field of numerical analysis, interpolation is a method of constructing new data points within the range of a discrete set of known data points....

to fill in data between the impulses. Other DAC methods (e.g., methods based on delta-sigma modulation

Delta-sigma modulation

Delta-sigma modulation is a method for encoding high-resolution or analog signals into lower-resolution digital signals. The conversion is done using error feedback, where the difference between the two signals is measured and used to improve the conversion...

) produce a pulse-density modulated

Pulse-density modulation

Pulse-density modulation, or PDM, is a form of modulation used to represent an analog signal with digital data. In a PDM signal, specific amplitude values are not encoded into pulses of different size as they would be in PCM. Instead, it is the relative density of the pulses that corresponds to...

signal that can then be filtered in a similar way 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

Baseband

In telecommunications and signal processing, baseband is an adjective that describes signals and systems whose range of frequencies is measured from close to 0 hertz to a cut-off frequency, a maximum bandwidth or highest signal frequency; it is sometimes used as a noun for a band of frequencies...

signal with bandwidth less than the Nyquist frequency

Nyquist frequency

The Nyquist frequency, named after the Swedish-American engineer Harry Nyquist or the Nyquist–Shannon sampling theorem, is half the sampling frequency of a discrete signal processing system...

). Digital sampling introduces quantization error

Quantization error

In analog-to-digital conversion, the difference between the actual analog value and quantized digital value is called quantization error or quantization distortion. This error is either due to rounding or truncation...

that manifests as low-level noise added to the reconstructed signal.

## Practical operation

Instead of impulses, usually the sequence of numbers update the analogue voltage at uniform sampling intervals.These numbers are written to the DAC, typically with a clock signal

Clock signal

In electronics and especially synchronous digital circuits, a clock signal is a particular type of signal that oscillates between a high and a low state and is utilized like a metronome to coordinate actions of circuits...

that causes each number to be latched 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 piecewise constant or 'staircase' shaped output. This is equivalent to a zero-order holdZero-order hold

The zero-order hold is a mathematical model of the practical signal reconstruction done by a conventional digital-to-analog converter . That is, it describes the effect of converting a discrete-time signal to a continuous-time signal by holding each sample value for one sample interval...

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 zero-order hold

Zero-order hold

The zero-order hold is a mathematical model of the practical signal reconstruction done by a conventional digital-to-analog converter . That is, it describes the effect of converting a discrete-time signal to a continuous-time signal by holding each sample value for one sample interval...

in sample data textbooks) or rectangular pulses causes multiple harmonics above the Nyquist frequency

Nyquist frequency

The Nyquist frequency, named after the Swedish-American engineer Harry Nyquist or the Nyquist–Shannon sampling theorem, is half the sampling frequency of a discrete signal processing system...

. Usually, these are removed with a low pass filter acting as a reconstruction filter in applications that require it.

### Audio

Most modern audio signals are stored in digital form (for example MP3MP3

MPEG-1 or MPEG-2 Audio Layer III, more commonly referred to as MP3, is a patented digital audio encoding format using a form of lossy data compression...

s and CDs

Compact Disc

The Compact Disc is an optical disc used to store digital data. It was originally developed to store and playback sound recordings exclusively, but later expanded to encompass data storage , write-once audio and data storage , rewritable media , Video Compact Discs , Super Video Compact Discs ,...

) 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 card

Sound card

A sound card is an internal computer expansion card that facilitates the input and output of audio signals to and from a computer under control of computer programs. The term sound card is also applied to external audio interfaces that use software to generate sound, as opposed to using hardware...

s.

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

Transport (recording)

A transport is a device that handles a particular physical storage medium itself, and extracts or records the information to and from the medium, to an outboard set of processing electronics that the transport is connected to.A transport houses no electronics itself for encoding and decoding the...

(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

Amplifier

Generally, an amplifier or simply amp, is a device for increasing the power of a signal.In popular use, the term usually describes an electronic amplifier, in which the input "signal" is usually a voltage or a current. In audio applications, amplifiers drive the loudspeakers used in PA systems to...

to drive speakers.

Similar digital-to-analog converters can be found in digital speakers

Digital speakers

Digital speakers are a form of loudspeaker technology. Not to be confused with modern digital formats and processing, they are a mature technology, having been experimented with extensively by Bell Labs as far back as the 1920s.-Principle of operation:...

such as USB

Universal Serial Bus

USB is an industry standard developed in the mid-1990s that defines the cables, connectors and protocols used in a bus for connection, communication and power supply between computers and electronic devices....

speakers, and in sound card

Sound card

A sound card is an internal computer expansion card that facilitates the input and output of audio signals to and from a computer under control of computer programs. The term sound card is also applied to external audio interfaces that use software to generate sound, as opposed to using hardware...

s.

In VoIP (Voice over IP) applications, the source must first be digitized for transmission, so it undergoes conversion via an Analog-to-Digital Converter

Analog-to-digital converter

An analog-to-digital converter is a device that converts a continuous quantity to a discrete time digital representation. An ADC may also provide an isolated measurement...

, 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 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 display

Flat panel display

Flat panel displays encompass a growing number of electronic visual display technologies. They are far lighter and thinner than traditional television sets and video displays that use cathode ray tubes , and are usually less than thick...

s with DVI

Digital Visual Interface

The Digital Visual Interface is a video interface standard covering the transmission of video between a source device and a display device. The DVI standard has achieved widespread acceptance in the PC industry, both in desktop PCs and monitors...

and/or HDMI

High-Definition Multimedia Interface

HDMI is a compact audio/video interface for transmitting uncompressed digital data. It is a digital alternative to consumer analog standards, such as radio frequency coaxial cable, composite video, S-Video, SCART, component video, D-Terminal, or VGA...

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

Computer storage

Computer data storage, often called storage or memory, refers to computer components and recording media that retain digital data. Data storage is one of the core functions and fundamental components of computers....

(RAM

Random-access memory

Random access memory is a form of computer data storage. Today, it takes the form of integrated circuits that allow stored data to be accessed in any order with a worst case performance of constant time. Strictly speaking, modern types of DRAM are therefore not random access, as data is read in...

), which contains conversion tables for gamma correction

Gamma correction

Gamma correction, gamma nonlinearity, gamma encoding, or often simply gamma, is the name of a nonlinear operation used to code and decode luminance or tristimulus values in video or still image systems...

, contrast and brightness, to make a device called a RAMDAC

RAMDAC

Random Access Memory Digital-to-Analog Converter is a combination of three fast DACs with a small SRAM used in computer graphics display adapters to store the color palette and to generate the analog signals to drive a color monitor...

.

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

### Mechanical

An unusual application of digital-to-analog conversion was the whiffletreeWhippletree (mechanism)

A whippletree or whiffletree is a mechanism to distribute force evenly through linkages. The mechanism may also be referred to as an equalizer, leader bar or double tree. It consists of a bar pivoted at or near the centre, with force applied from one direction to the pivot, and from the other...

electromechanical digital-to-analog converter linkage in the IBM Selectric typewriter.

## DAC types

The most common types of electronic DACs are:- The pulse-width modulatorPulse-width modulationPulse-width modulation , or pulse-duration modulation , is a commonly used technique for controlling power to inertial electrical devices, made practical by modern electronic power switches....

, the simplest DAC type. A stable current or voltageVoltage

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, but has many other applications as well. - Oversampling DACs or interpolating DACs such as the delta-sigma DAC, use a pulse density conversion technique. The oversamplingOversamplingIn signal processing, oversampling is the process of sampling a signal with a sampling frequency significantly higher than twice the bandwidth or highest frequency of the signal being sampled...

technique allows for the use of a lower resolution DAC internally. A simple 1-bit DAC1-bit DACA Bitstream or 1-bit DAC is a consumer electronics marketing term describing an oversampling digital-to-analog converter with an actual 1-bit DAC in a delta-sigma loop operating at multiples of the sampling frequency...

is often chosen because the oversampled result is inherently linear. The DAC is driven with a pulse-density modulatedPulse-density modulationPulse-density modulation, or PDM, is a form of modulation used to represent an analog signal with digital data. In a PDM signal, specific amplitude values are not encoded into pulses of different size as they would be in PCM. Instead, it is the relative density of the pulses that corresponds to...

signal, created with the use of a low-pass filterLow-pass filterA low-pass filter is an electronic filter that passes low-frequency signals but attenuates signals with frequencies higher than the cutoff frequency. The actual amount of attenuation for each frequency varies from filter to filter. It is sometimes called a high-cut filter, or treble cut filter...

, step nonlinearitySign functionIn mathematics, the sign function is an odd mathematical function that extracts the sign of a real number. To avoid confusion with the sine function, this function is often called the signum function ....

(the actual 1-bit DAC), and negative feedbackNegative feedbackNegative feedback occurs when the output of a system acts to oppose changes to the input of the system, with the result that the changes are attenuated. If the overall feedback of the system is negative, then the system will tend to be stable.- Overview :...

loop, in a technique called delta-sigma modulationDelta-sigma modulationDelta-sigma modulation is a method for encoding high-resolution or analog signals into lower-resolution digital signals. The conversion is done using error feedback, where the difference between the two signals is measured and used to improve the conversion...

. This results in an effective high-pass filterHigh-pass filterA high-pass filter is a device that passes high frequencies and attenuates frequencies lower than its cutoff frequency. A high-pass filter is usually modeled as a linear time-invariant system...

acting on the quantization (signal processing)Quantization (signal processing)Quantization, in mathematics and digital signal processing, is the process of mapping a large set of input values to a smaller set – such as rounding values to some unit of precision. A device or algorithmic function that performs quantization is called a quantizer. The error introduced by...

noise, thus steering this noise out of the low frequencies of interest into the megahertz frequencies of little interest, which is called noise shapingNoise shapingNoise 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...

. 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 RC low-pass circuitRC circuitA resistor–capacitor circuit ', or RC filter or RC network, is an electric circuit composed of resistors and capacitors driven by a voltage or current source...

is sufficient). Most very high resolution DACs (greater than 16 bits) are of this type due to its high linearity 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 kHz) and resolutions of 24 bits are attainable with delta-sigma DACs. A short comparison with pulse-width modulationPulse-width modulationPulse-width modulation , or pulse-duration modulation , is a commonly used technique for controlling power to inertial electrical devices, made practical by modern electronic power switches....

shows that a 1-bit DAC1-bit DACA Bitstream or 1-bit DAC is a consumer electronics marketing term describing an oversampling digital-to-analog converter with an actual 1-bit DAC in a delta-sigma loop operating at multiples of the sampling frequency...

with a simple first-order integratorIntegratorAn integrator is a device to perform the mathematical operation known as integration, a fundamental operation in calculus.The integration function is often part of engineering, physics, mechanical, chemical and scientific calculations....

would have to run at 3 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 filterLow-pass filterA low-pass filter is an electronic filter that passes low-frequency signals but attenuates signals with frequencies higher than the cutoff frequency. The actual amount of attenuation for each frequency varies from filter to filter. It is sometimes called a high-cut filter, or treble cut filter...

with a frequency responseFrequency responseFrequency response is the quantitative measure of the output spectrum of a system or device in response to a stimulus, and is used to characterize the dynamics of the system. It is a measure of magnitude and phase of the output as a function of frequency, in comparison to the input...

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 MASH) are used to achieve higher degrees of noise-shaping with a stable topologyBIBO stabilityIn electrical engineering, specifically signal processing and control theory, BIBO stability is a form of stability for linear signals and systems that take inputs. BIBO stands for Bounded-Input Bounded-Output...

. - The binary-weighted DAC, which contains one resistorResistorA linear resistor is a linear, passive two-terminal electrical component that implements electrical resistance as a circuit element.The current through a resistor is in direct proportion to the voltage across the resistor's terminals. Thus, the ratio of the voltage applied across a resistor's...

or current sourceCurrent sourceA current source is an electrical or electronic device that delivers or absorbs electric current. A current source is the dual of a voltage source. The term constant-current sink is sometimes used for sources fed from a negative voltage supply...

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 resistors and current sources are expensive, so this type of converter is usually limited to 8-bit resolution or less. - The R-2R ladderResistor LadderA resistor ladder is an electrical circuit made of repeating units of resistors. Two configurations are discussed below, a string resistor ladder and a 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 (or current sources). However, wide converters perform slowly due to increasingly large RC-constants for each added R-2R link. - 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 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.
- 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.

## DAC performance

DACs are very important to system performance. The most important characteristics of these devices are:-
**Resolution**: This is the number of possible output levels the DAC is designed to reproduce. This is usually stated as the number of bitBitA bit is the basic unit of information in computing and telecommunications; it is the amount of information stored by a digital device or other physical system that exists in one of two possible distinct states...

s it uses, which is the base two logarithmLogarithmThe logarithm of a number is the exponent by which another fixed value, the base, has to be raised to produce that number. For example, the logarithm of 1000 to base 10 is 3, because 1000 is 10 to the power 3: More generally, if x = by, then y is the logarithm of x to base b, and is written...

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 bitswhich is a measurement of the actual resolution attained by the DAC. Resolution determines color depthColor depthIn computer graphics, color depth or bit depth is the number of bits used to represent the color of a single pixel in a bitmapped image or video frame buffer. This concept is also known as bits per pixel , particularly when specified along with the number of bits used...

in video applications and audio bit depthAudio bit depthIn digital audio, bit depth describes the number of bits of information recorded for each sample. Bit depth directly corresponds to the resolution of each sample in a set of digital audio data...

in audio applications. -
**Maximum sampling rate**: This is a measurement of the maximum speed at which the DACs circuitry can operate and still produce the correct output. As stated in the Nyquist–Shannon sampling theoremSampling rateThe sampling rate, sample rate, or sampling frequency defines the number of samples per unit of time taken from a continuous signal to make a discrete signal. For time-domain signals, the unit for sampling rate is hertz , sometimes noted as Sa/s...Nyquist–Shannon sampling theoremThe Nyquist–Shannon sampling theorem, after Harry Nyquist and Claude Shannon, is a fundamental result in the field of information theory, in particular telecommunications and signal processing. Sampling is the process of converting a signal into a numeric sequence...

defines a relationship between the sampling frequency and bandwidth of the sampled signal. -
**Monotonicity**: This refers to 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.Monotonic functionIn mathematics, a monotonic function is a function that preserves the given order. This concept first arose in calculus, and was later generalized to the more abstract setting of order theory.... -
**THD**: This is 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 harmonicTotal harmonic distortionThe total harmonic distortion, or THD, of a signal is a measurement of the harmonic distortion present and is defined as the ratio of the sum of the powers of all harmonic components to the power of the fundamental frequency...

+NHarmonicA harmonic of a wave is a component frequency of the signal that is an integer multiple of the fundamental frequency, i.e. if the fundamental frequency is f, the harmonics have frequencies 2f, 3f, 4f, . . . etc. The harmonics have the property that they are all periodic at the fundamental...

distortionDistortionA distortion is the alteration of the original shape of an object, image, sound, waveform or other form of information or representation. Distortion is usually unwanted, and often many methods are employed to minimize it in practice...

and noise that accompany the desired signal. This is a very important DAC characteristic for dynamic and small signal DAC applications. -
**Dynamic range**: This is a measurement of the difference between the largest and smallest signals the DAC can reproduce expressed in decibelDynamic rangeDynamic range, abbreviated DR or DNR, is the ratio between the largest and smallest possible values of a changeable quantity, such as in sound and light. It is measured as a ratio, or as a base-10 or base-2 logarithmic value.-Dynamic range and human perception:The human senses of sight and...DecibelThe decibel is a logarithmic unit that indicates the ratio of a physical quantity relative to a specified or implied reference level. A ratio in decibels is ten times the logarithm to base 10 of the ratio of two power quantities...

s. This is usually related to resolution and noise floorNoise floorIn signal theory, the noise floor is the measure of the signal created from the sum of all the noise sources and unwanted signals within a measurement system, where the noise is defined as any signal other than the one being monitored....

.

Other measurements, such as phase distortion

Phase distortion

In signal processing, phase distortion or phase-frequency distortion is distortion that occurs when a filter's phase response is not linear over the frequency range of interest, that is, the phase shift introduced by a circuit or device is not directly proportional to frequency, or the...

and jitter

Jitter

Jitter is the undesired deviation from true periodicity of an assumed periodic signal in electronics and telecommunications, often in relation to a reference clock source. Jitter may be observed in characteristics such as the frequency of successive pulses, the signal amplitude, or phase of...

, 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.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 / mu-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)

## DAC figures of merit

- Static performance:
- Differential nonlinearityDifferential nonlinearityDifferential 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 ; the accuracy of a DAC is mainly determined by this specification...

(DNL) shows how much two adjacent code analog values deviate from the ideal 1 LSB step. - Integral nonlinearityIntegral nonlinearityIntegral nonlinearity is a term describing the maximum deviation between the ideal output of a DAC and the actual output level...

(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
- Offset
- 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 noiseWhite noiseWhite noise is a random signal with a flat power spectral density. In other words, the signal contains equal power within a fixed bandwidth at any center frequency...

. This limits performance to less than 20~21 bits even in 24-bit DACs.

- Differential nonlinearity
- 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 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
- i-th harmonic distortion (HDi) indicates the power of the i-th harmonic of the converted main signal
- Total harmonic distortionTotal harmonic distortionThe total harmonic distortion, or THD, of a signal is a measurement of the harmonic distortion present and is defined as the ratio of the sum of the powers of all harmonic components to the power of the fundamental frequency...

(THD) is the sum of the powers of all HDi - If the maximum DNL error is less than 1 LSB, then the converter is guaranteed to be monotonic. However, many monotonic converters may have a maximum DNL greater than 1 LSB.

- Time domain performance:
- Glitch energy
- Response uncertainty
- Time nonlinearity (TNL)

## Further reading

- 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 RazaviBehzad RazaviBehzad Razavi is an Iranian-American professor and researcher of electrical and electronic engineering. Noted for his research in communications circuitry, Razavi is the director of the Communication Circuits Laboratory at the University of California Los Angeles. He is a Fellow and a...

,*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.