See Also

Digital-to-analog converter

In electronics Electronics

The field of electronics comprises the study and use of systems that operate by controlling the flow of ... 

, a digital-to-analog converter is a device for converting a digital code to an analog signal . Digital-to-analog converters are the interface between the abstract digital world and the analog real life. Simple switches, a network of resistor Resistor

|- align = "center" | |width = "25"| ... 

s, current Current

Current may refer to: * Current affairs [i] ... 

 sources or capacitors may implement this conversion. An analog-to-digital converter  performs the reverse operation. A DAC usually only deals with pulse-code modulation Pulse-code modulation

Pulse-code modulation [i] is a digital [i] representation of an analog signal [i] where the ... 

 -encoded signals. The job of converting various compressed forms of signals into PCM is left to codecs.

Discussions

  Discussion Features

   Ask a question about 'Digital-to-analog converter'

   Start a new discussion about 'Digital-to-analog converter'

   Answer questions about 'Digital-to-analog converter'

   'Digital-to-analog converter' discussion forum


Encyclopedia

In electronics Electronics

The field of electronics comprises the study and use of systems that operate by controlling the flow of ... 

, a digital-to-analog converter is a device for converting a digital code to an analog signal . Digital-to-analog converters are the interface between the abstract digital world and the analog real life. Simple switches, a network of resistor Resistor

|- align = "center"
|
|width = "25"|
... 

s, current Current

Current may refer to:
  • Current affairs [i]

... 

 sources or capacitors may implement this conversion.

An analog-to-digital converter  performs the reverse operation.

A DAC usually only deals with pulse-code modulation Pulse-code modulation

Pulse-code modulation [i] is a digital [i] representation of an analog signal [i] where the ... 

 -encoded signals. The job of converting various compressed forms of signals into PCM is left to codecs.

Basic ideal operation




The DAC fundamentally converts finite-precision numbers into a physical quantity, usually an electrical voltage. Normally the output voltage is a linear function Linear function

A linear function can refer to two slightly different concepts.... 

 of the input number. Usually these numbers are updated at uniform sampling intervals and can be thought of as numbers obtained from a sampling process. These numbers are written to the DAC, sometimes along 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 held in time at the current value until the next input number is latched resulting in a piecewise constant Step function

In mathematics [i], a function [i] on the real number [i]s is called a step function if it can ... 

 output. This is equivalently a zero-order hold Zero-order hold

The Zero-order hold is a mathematical model of the practical reconstruction of sampled signals done by c... 

 operation and has an effect on the frequency response of the reconstructed signal.



The fact that practical DACs do not output a sequence of dirac impulses Dirac delta function

The Dirac delta or Dirac's delta, often referred to as the unit impulse function and introduced by... 

  but instead output a sequence of piecewise constant values or rectangular pulses Rectangular function

The rectangular function is defined as,
... 

, means that there is an inherent effect of the zero-order hold Zero-order hold

The Zero-order hold is a mathematical model of the practical reconstruction of sampled signals done by c... 

 on the effective frequency response of the DAC resulting in a mild roll-off of gain at the higher frequencies . This zero-order hold effect is a consequence of the hold action of the DAC and is not due to the sample and hold that might precede a conventional analog to digital converter as is often misunderstood.

Applications


Audio


Most modern audio signals are stored in digital form and in order to be heard through speakers they must be converted into an analog signal. DACs are therefore found in CD player Compact disc player

A compact disc player or CD player is an electronic device to play audio from compact disc [i]s. ... 

s, digital music player Digital audio player

A digital audio player is a device that stores, organizes and plays digital music file [i] ... 

s, and PC sound card Sound card

A sound card is a computer [i] expansion card [i] that can input and output sound [i] under control of c ... 

s.

Specialist stand-alone DACs can also be found in high-end hi-fi systems. These normally take the digital output of a CD player Compact disc player

A compact disc player or CD player is an electronic device to play audio from compact disc [i]s. ... 

  and convert the signal into a line-level output that can then be fed into a pre-amplifier Preamplifier

A preamplifier is an electronic amplifier [i] which precedes another amplifier to prepare an electronic ... 

 stage. Some of these can also be made to interface with computers using a USB Universal Serial Bus

Universal Serial Bus is a serial [i] bus [i] standard to interface [i] ... 

 interface.

Video


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 2003, analog monitors are more common than digital, but this may change as flat panel displays become more widespread. The DAC is usually integrated with some memory Computer storage

Computer storage, computer memory, and often casually memory refer to computer [i] component ... 

 , which contains conversion tables for gamma correction Gamma correction

Gamma correction, gamma nonlinearity, gamma encoding, or often simply gamma, is the na... 

, 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.

DAC types


The most common types of electronic DACs are:

  • the Pulse Width Modulator Pulse-width modulation

    Pulse-width modulation of a signal [i] or power [i]source involves the modulation [i] ... 

    , the simplest DAC type. A stable current Current

    Current may refer to:
  • Current affairs [i]

... 

 or voltage Voltage

Voltage is the difference of electrical potential [i] between two points of an electrical network [i] ... 

 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 is now becoming common in high-fidelity audio.

  • Oversampling DACs such as the Delta-Sigma DAC, a pulse density conversion technique. The oversampling technique allows for the use of a lower resolution DAC internally. A simple 1-bit DAC is often chosen as it is inherently linear. The DAC is driven with a pulse density modulated signal, created through negative feedback. The negative feedback will act as a high-pass filter High-pass filter

    A high-pass filter is a filter [i] that passes high frequencies [i] well, bu ... 

     for the quantization  noise, thus pushing this noise out of the pass-band. Most very high resolution DACs are of this type due to its high linearity and low cost. Speeds of greater than 100 thousand samples per second and resolutions of 24 bits are attainable with Delta-Sigma DACs. Simple first order Delta-Sigma modulators or higher order topologies such as MASH - Multi stage noise SHaping can be used to generate the pulse density signal. Higher oversampling rates relax the specifications of the output Low-pass filter Low-pass filter

    A low-pass filter is a filter [i] that passes low frequencies [i] well, but ... 

     and enable further suppression of quantization noise.


  • the Binary Weighted DAC, which contains one resistor Resistor

    |- align = "center"

|
|width = "25"|
... 

 or current source Current source

A current source is an electrical or electronic device that delivers or absorbs electric current.... 

 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 Ladder Resistor Ladder

    A Resistor Ladder, or R-2R Ladder is the most simple and inexpensive way to perform digital [i] to analog [i]... 

     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 . However, wide converters performs 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.


  • 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 and number of resistors or current sources . The full binary weighted design means 0% segmentation, the full thermometer coded design means 100% segmentation.


  • 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.

DAC performance


DACs are at the beginning of the analog signal chain, which makes them 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 bits it uses, which is the base two logarithm Logarithm

    The logarithm is the mathematical [i] operation that is the inverse [i] of ... 

     of the number of levels. For instance a 1 bit DAC is designed to reproduce 2 levels while an 8 bit DAC is designed for 256 levels. Resolution is related to the Effective Number of Bits which is a measurement of the actual resolution attained by the DAC.


  • Maximum sampling frequency: 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 Shannon-Nyquist sampling theorem Nyquist–Shannon sampling theorem

    The NyquistShannon sampling theorem is a fundamental result in the field of information theory [i], in p... 

    , a signal must be sampled at over twice the bandwidth Bandwidth

    Bandwidth is a measure of frequency [i] range and is typically measured in hertz [i].

... 

 of the desired signal. For instance, to reproduce signals in all the audible spectrum, which includes frequencies of up to 20 kHz, it is necessary to use DACs that operate at over 40 kHz. The CD standard samples audio at 44.1 kHz, thus DACs of this frequency are often used. A common frequency in cheap computer sound cards Sound card

A sound card is a computer [i] expansion card [i] that can input and output sound [i] under control of c ... 

 is 48 kHz - many work at only this frequency, offering the use of other sample rates only through internal resampling.

  • monotonicity: This refers to the ability of DACs analog output to increase with an increase in digital code or the converse. This characteristic is very important for DACs used as a low frequency signal source or as a digitally programmable trim element.


  • THD+N: 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 harmonic distortion Distortion

    A distortion is the alteration of the original shape of an object, image, sound, waveform or other form... 

     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 Decibels. This is usually related to DAC resolution and noise floor Noise floor

    In signal theory [i], the noise floor is the measure of the signal created from the sum of all the noise [i] ... 

    .


Other measurements, such as Phase distortion and Sampling Period Instability, can also be very important for some applications.

DAC Figures of Merit


  • Static performance:
    • DNL shows how much two adjacent code analog values deviate from the ideal 1LSB step
    • 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 .
    • Gain
    • Offset


  • Frequency domain performance
    • SFDR indicates in dB the ratio between the powers of the converted main signal and the greatest undesired spur
    • 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
    • HDi indicates the power of the i-th harmonic of the converted main signal
    • THD is the sum of the powers of all HDi


  • Time domain performance
    • Glitch Energy
    • Response Uncertainty
    • TNL

See also


  • Modem Modem

    A modem is a device [i] that modulates [i] an analog carrier [i] ... 



Links and books


  • See an Audio Note valve DAC kit with USB interface being built.
  • with circuit diagrams.
  • explains how INL and DNL are calculated.


  • S. Norsworthy, Richard Schreier, Gabor C. Temes, Delta-Sigma Data Converters. ISBN 0-7803-1045-4.
  • Mingliang Liu, Demystifying Switched-Capacitor Circuits. ISBN 0-750-67907-7.
  • Behzad Razavi, Principles of Data Conversion System Design. ISBN 0-780-31093-4.
  • Phillip E. Allen, Douglas R. Holberg, CMOS Analog Circuit Design. ISBN 0-195-11644-5.



Categories: