From Wikipedia, the free encyclopedia
In electronics, a
digital-to-analog converter (DAC
or D-to-A) is a device for converting a digital
(usually binary) code to an analog signal (current, voltage or electric charge).
An analog-to-digital converter
(ADC) performs the reverse operation.
Basic
ideal operation
Ideally sampled signal. Signal of a typical interpolating DAC
output
A DAC converts an abstract finite-precision number
(usually a fixed-point binary number) into a
concrete
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 impulses 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.
By the Nyquist–Shannon sampling
theorem, sampled data can be reconstructed perfectly provided
that its bandwidth meets certain requirements (e.g., a baseband signal with bandwidth less than the
Nyquist
frequency). However, even with an ideal reconstruction filter,
digital sampling introduces quantization error that makes
perfect reconstruction practically impossible. Increasing the
digital resolution
(i.e., increasing the number of bits
used in each sample) or introducing sampling dither can reduce this error.
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 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.
Piecewise constant signal typical of a zero-order
(non-interpolating) DAC output.
The fact that practical DACs output a sequence of piecewise
constant values or rectangular pulses would cause
multiple harmonics above the nyquist frequency. These are typically
removed with a low pass filter acting as a reconstruction
filter.
However, this filter means that there is an inherent effect of
the zero-order
hold on the effective frequency response of the DAC resulting
in a mild roll-off of gain
at the higher frequencies (often a 3.9224 dB loss at the Nyquist
frequency) and depending on the filter, phase distortion. Not
all DACs have a zero order response however. This high-frequency
roll-off is the output characteristic of the DAC, and is not an
inherent property of the sampled data.
Applications
Audio
Top-loading CD player and external digital-to-analog
converter.
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 stand-alone DACs can also be found in high-end hi-fi systems.
These normally take the digital output of a CD player (or dedicated
transport) and convert the signal
into a line-level output that can then be fed into
a pre-amplifier stage.
Similar digital-to-analog converters can be found in digital
speakers such as USB speakers, and in sound cards.
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 2007, analog inputs are more commonly used than
digital, but this may change as flat panel displays with DVI and/or HDMI connections become 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.
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, and is now becoming common in high-fidelity
audio.
- 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 non-linearity
(the actual 1-bit DAC), and negative feedback loop, in a
technique called delta-sigma modulation. This
results in an effective high-pass filter acting on the quantization (signal
processing) noise, thus steering this noise out of the low
frequencies of interest into the high frequencies of little
interest, which is called noise shaping (very high
frequencies because of the oversampling). The quantization noise at
these high frequencies are removed or greatly attenuated by use of
an analog low-pass filter at the output (sometimes a simple RC low-pass circuit 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 either 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 modulation shows that a 1-bit DAC with a simple
first-order integrator
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 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 (such as MASH) are used to achieve higher degrees of
noise-shaping with a stable topology.
- the binary weighted DAC, which contains one resistor or current source
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 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 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 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 (ENOB) 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 Nyquist–Shannon sampling
theorem, a signal must be sampled at over twice the frequency 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 is 48 kHz—many work at only this frequency, offering
the use of other sample rates only through (often poor) internal resampling.
- 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.
- 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 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.
Other measurements, such as phase distortion and sampling period
instability, can also be very important for some applications.
DAC figures
of merit
- Static performance:
- Differential non-linearity (DNL) shows how much two adjacent
code analog values deviate from the ideal 1LSB step ^{[1]}
- Integral non-linearity (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 (1LSB 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 noise. This
limits performance to less than 20~21 bits even in 24-bit
DACs.
- Frequency domain performance
- Spurious-free dynamic range (SFDR) indicates in dB the ratio
between the powers of the converted main signal and the greatest
undesired spur
- Signal to noise and distortion 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 distortion
(THD) is the sum of the powers of all HDi
- If the maximum DNL error is less than 1 LSB, then D/A converter
is guaranteed to be monotonic.
However many monotonic converters may hav a maximum DNL greater
than 1 LSB.
- Time domain performance:
- Glitch energy
- Response uncertainty
- Time non-linearity (TNL)
See also
References
Further
reading
- Kester, Walt, The Data Conversion
Handbook, ISBN
0-7506-7841-0, http://www.analog.com/library/analogDialogue/archives/39-06/data_conversion_handbook.html
- 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.
External
links