In electronics, a digital-to-analog converter is a function that converts digital data into
an analog signal. An analog-to-digital converter performs the reverse function. Unlike analog
signals, digital data can be transmitted, manipulated, and stored without degradation,
albeit with more complex equipment. But a DAC is needed to convert the digital signal
to analog to drive an earphone or loudspeaker amplifier in order to produce sound.
DACs and their inverse, 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 packets where it may be mixed with other digital data, not necessarily audio.
The digital packets are then sent to 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 into an analog electrical signal, which drives an audio amplifier, which in
turn drives a loudspeaker, which finally produces sound.
There are several DAC architectures; the suitability of a DAC for a particular application is determined
by six main parameters: physical size, power consumption, resolution, speed, accuracy,
cost. Due to the complexity and the need for precisely matched components, all but the
most specialist DACs are implemented as integrated circuits. Digital-to-analog conversion can
degrade a signal, so a DAC should be specified that 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 speed/resolution trade-off. The audio DAC is a low speed high
resolution type while the video DAC is a high speed low to medium resolution type. Discrete
DACs 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
A DAC converts an abstract finite-precision number into a physical quantity. 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 impulses that are then processed by a reconstruction filter
using some form of interpolation to fill in data between the impulses. Other DAC methods
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. Digital sampling introduces quantization error that manifests
as low-level noise added to the reconstructed signal.
Practical operation
Instead of impulses, usually the sequence of numbers update the analog voltage at uniform
sampling intervals, which are then often interpolated via a reconstruction filter to continuously
varied levels. 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 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 hold operation
and has an effect on the frequency response of the reconstructed signal.
The fact that DACs output a sequence of piecewise constant values 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.
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 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 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 VoIP 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 Video sampling tends to work on a completely
different scale altogether thanks to the highly nonlinear response both of cathode ray tubes
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. Given this inherent
distortion, it is not unusual for a television or video projector to truthfully claim a linear
contrast ratio 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, 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. Mechanical
An unusual application of digital-to-analog conversion was the whiffletree electromechanical
digital-to-analog converter linkage in the IBM Selectric typewriter.
DAC types The most common types of electronic DACs are:
The pulse-width modulator, the simplest DAC type. 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, 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 oversampling technique
allows for the use of a lower resolution DAC internally. A simple 1-bit DAC is often chosen
because the oversampled result is inherently linear. The DAC is driven with a pulse-density
modulated signal, created with the use of a low-pass filter, step nonlinearity, and
negative feedback loop, in a technique called delta-sigma modulation. This results in an
effective high-pass filter acting on the quantization noise, thus steering this noise out of the
low frequencies of interest into the megahertz frequencies of little interest, which is called
noise shaping. The quantization noise at these high frequencies is removed or greatly attenuated
by use of an analog low-pass filter at the output. Most very high resolution DACs 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 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 integrator would have to run at 3 THz 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 frequency response
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 are used to achieve
higher degrees of noise-shaping with a stable topology.
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.Switched
resistor DAC contains of 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. However, wide converters perform slowly due
to increasingly large RC-constants for each added R-2R link.
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 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 and number of resistors or current sources. 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 takes a variable input voltage for their
conversion. This puts additional design constraints on the bandwidth of the conversion circuit.
DAC performance DACs are very important to system performance.
The most important characteristics of these devices 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 base two logarithm 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. Resolution determines color depth in video applications and audio bit depth
in audio applications. Maximum sampling rate
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 theorem defines a relationship between
the sampling frequency and 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 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 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. This is
a very important DAC characteristic for dynamic and small signal DAC applications.
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 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. Non-linear PCM encodings 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
DAC figures of merit Static performance:
Differential nonlinearity shows how much two adjacent code analog values deviate from the
ideal 1 LSB step. Integral nonlinearity 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 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 of white noise. This
limits performance to less than 20~21 bits even in 24-bit DACs.
Frequency domain performance Spurious-free dynamic range indicates in dB
the ratio between the powers of the converted main signal and the greatest undesired spur.
Signal-to-noise and distortion ratio 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 indicates the power of the i-th harmonic of the converted main
signal Total harmonic distortion is the sum of the
powers of all HDi If the maximum DNL error 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
Response uncertainty Time nonlinearity
See also Integral linearity
I²S Modem
RAMDAC References
Further reading
External links ADC and DAC Glossary