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). Cirrus Logic ( is a fabless semiconductor supplier specializing in analog mixed-signal and DSP chips Sound Blaster X-Fi is a PCI or PCI-E Sound card series from Creative Technology. Electronics refers to the flow of charge (moving Electrons through Nonmetal conductors (mainly Semiconductors, whereas electrical An analog or analogue signal is any continuous signal for which the time varying feature (variable of the signal is a representation of some other Electric current is the flow (movement of Electric charge. The SI unit of electric current is the Ampere. Electrical tension (or voltage after its SI unit, the Volt) is the difference of electrical potential between two points of an electrical Electric charge is a fundamental conserved property of some Subatomic particles which determines their Electromagnetic interaction.
An analog-to-digital converter (ADC) performs the reverse operation. An analog-to-digital converter (abbreviated ADC, A/D or A to D) is an electronic integrated circuit which converts continuous signals to
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Basic ideal operation
The DAC fundamentally converts finite-precision numbers (usually fixed-point binary numbers) into a continuously varying physical quantity, usually an analogue electrical voltage. The binary numeral system, or base-2 number system, is a Numeral system that represents numeric values using two symbols usually 0 and 1.
In an ideal DAC, the numbers are output as a sequence of impulses, that are then filtered by a reconstruction filter. The Dirac delta or Dirac's delta is a mathematical construct introduced by the British theoretical physicist Paul Dirac. In a mixed-signal system ( analog and digital) a reconstruction filter (or anti-imaging filter) is used to construct a smooth analogue signal from the output This would, in principle, reproduce a sampled signal precisely up to the Nyquist frequency, although in practice a perfect reconstruction filter cannot be practically constructed as it has infinite phase delay; and there are errors due to quantisation.
Practical operation
Instead of impulses, usually the sequence of numbers update the analogue voltage at uniform sampling intervals. Sampling theorem The Nyquist–Shannon sampling theorem states that perfect reconstruction
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. In Electronics and especially synchronous Digital circuits a clock signal is a signal used to coordinate the actions of two or more circuits In Electronics, a latch is a kind of Bistable Multivibrator, an Electronic circuit which has two stable states and thereby can store 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. In Mathematics, a function on the Real numbers is called a step function (or staircase function) if it can be written as a finite This is equivalent to a zero-order hold operation and has an effect on the frequency response of the reconstructed signal. The zero-order hold (ZOH is a mathematical model of the practical Signal reconstruction done by a conventional Digital-to-analog converter (DAC
The fact that practical DACs output a sequence of piecewise constant values or rectangular pulses would cause multiple harmonics above the nyquist frequency. The rectangular function (also known as the rectangle function, rect function, unit pulse, or the normalized Boxcar function) These are typically removed with a low pass filter acting as a reconstruction filter. A low-pass filter is a filter that passes low- Frequency signals but Attenuates (reduces the Amplitude of signals with frequencies
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. The zero-order hold (ZOH is a mathematical model of the practical Signal reconstruction done by a conventional Digital-to-analog converter (DAC 9224 dB loss at the Nyquist frequency) and depending on the filter, phase distortion. The Nyquist frequency, named after the Swedish-American engineer Harry Nyquist or the Nyquist–Shannon sampling theorem, is half the Sampling frequency This high-frequency roll-off is the output characteristic of the DAC, and is not an inherent property of the sampled data.
Applications
Audio
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. MPEG-1 Audio Layer 3, more commonly referred to as MP3, is a Digital audio encoding format using a form of Lossy data compression A Compact Disc (also known as a CD) is an Optical disc used to store digital data, originally developed for storing digital audio DACs are therefore found in CD players, digital music players, and PC sound cards. A Compact Disc player (often written as compact disc player) or CD player, is an electronic device which plays audio Compact Discs CD players are often A digital audio player, more commonly referred to as an MP3 player, is a Consumer electronics device that stores organizes and plays audio files Some A sound card (also known as an audio card is a Computer Expansion card that facilitates the input and output of audio signals to/from a computer under
Specialist stand-alone DACs can also be found in high-end hi-fi systems. High fidelity or hi-fi reproduction is a term used by home stereo listeners and home audio enthusiasts ( Audiophiles to refer to high-quality reproduction 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. A Compact Disc player (often written as compact disc player) or CD player, is an electronic device which plays audio Compact Discs CD players are often A transport is a device that handles a particular physical storage medium (such as Magnetic tape, Audio CD, CD-R, or other type of recordable media itself Line level is a term used to denote the strength of an audio signal used to transmit analog sound information between audio components such as CD and DVD A preamplifier (preamp or control amp in some parts of the world is an Electronic amplifier which precedes another amplifier to prepare an electronic Some of these can also be made to interface with computers using a USB 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 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. Year 2007 ( MMVII) was a Common year starting on Monday of the Gregorian calendar in the 21st century. Flat panel displays encompass a growing number of technologies enabling video displays that are lighter and much thinner than traditional television and video displays that use Cathode The High-Definition Multimedia Interface ( HDMI) is a compact audio/video connector interface for transmitting uncompressed digital streams 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. Computer data storage, often called storage or memory, refers to Computer components devices and recording media that retain digital Gamma correction, gamma nonlinearity, gamma encoding, or often simply gamma, is the name of a nonlinear operation used to code and decode luminance Random Access Memory Digital-to-Analog Converter (RAMDAC is a combination of three fast DACs with a small SRAM used in computer graphics Display adapters
A device that is distantly related to the DAC is the digitally controlled potentiometer, used to control an analog signal digitally. A potentiometer is a three-terminal Resistor with a sliding contact that forms an adjustable Voltage divider.
DAC types
The most common types of electronic DACs are:
- the Pulse Width Modulator, the simplest DAC type. Pulse-width modulation (PWM of a signal or power source involves the Modulation of its Duty cycle, to either convey information over a A stable current or voltage is switched into a low pass analog filter with a duration determined by the digital input code. Electric current is the flow (movement of Electric charge. The SI unit of electric current is the Ampere. Electrical tension (or voltage after its SI unit, the Volt) is the difference of electrical potential between two points of an electrical An analogue filter handles analogue signals or continuous-time signals whether Electric potential, sound waves, or mechanical 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. In Signal processing, oversampling is the process of sampling a signal with a Sampling frequency significantly higher than twice the bandwidth 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 (the actual 1-bit DAC), and negative feedback loop, in a technique called delta-sigma modulation. Pulse-density modulation, or PDM, is a form of Modulation used to represent an Analog signal in the digital domain A low-pass filter is a filter that passes low- Frequency signals but Attenuates (reduces the Amplitude of signals with frequencies Negative Feedback feeds part of a System 's output inverted into the system's input generally with the result that fluctuations are attenuated The Delta-Sigma ( ΔΣ; or sigma-delta, ΣΔ) modulation is a method for encoding high resolution signals into lower resolution signals using Pulse-density 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). A high-pass filter is a filter that passes high frequencies well but attenuates (reduces the amplitude of frequencies lower than the Cutoff frequency In Digital signal processing, quantization is the process of approximating a continuous range of values (or a very large set of possible discrete values by a relatively-small Similar to Dither, noise shaping is a bit reduction technique used to minimize the impact of Quantization errors Noise shaping is used in many areas of Digital 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). A resistor–capacitor circuit (RC circuit, or RC filter or RC network, is an Electric circuit composed of resistors and capacitors driven by Most very high resolution DACs (greater than 16 bits) are of this type due to its high linearity and low cost. The word linear comes from the Latin word linearis, which means created by lines. 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, 192kHz) 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. Pulse-width modulation (PWM of a signal or power source involves the Modulation of its Duty cycle, to either convey information over a An integrator is a device to perform the mathematical operation known as integration, a fundamental operation in Calculus. 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. A low-pass filter is a filter that passes low- Frequency signals but Attenuates (reduces the Amplitude of signals with frequencies Frequency response is the measure of any system's spectrum response at the output to a signal of varying Frequency (but constant amplitude at its input Multiple higher order topologies (such as MASH) are used to achieve higher degrees of noise-shaping with a stable topology. The Delta-Sigma ( ΔΣ; or sigma-delta, ΣΔ) modulation is a method for encoding high resolution signals into lower resolution signals using Pulse-density Bibo redirects here For the Egyptian football player nicknamed Bibo see Mahmoud El-Khateeb.
- the Binary Weighted DAC, which contains one resistor or current source for each bit of the DAC connected to a summing point. |- align = "center"| |width = "25"| | |- align = "center"| || Potentiometer |- align = "center"| | | |- align = "center"| Resistor| | A current source is an electrical or electronic device that delivers or absorbs electric current 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. Two Resistor Ladder configurations are known a string resistor ladder and a R-2R ladder 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.
- 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.
- 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 of the number of levels. A bit is a binary digit, taking a value of either 0 or 1 Binary digits are a basic unit of Information storage and communication In Mathematics, the logarithm of a number to a given base is the power or Exponent to which the base must be raised in order to produce For instance a 1 bit DAC is designed to reproduce 2 (21) levels while an 8 bit DAC is designed for 256 (28) levels. Resolution is related to the Effective Number of Bits (ENOB) which is a measurement of the actual resolution attained by the DAC. In Electrical engineering ENOB is an abbreviation for the Effective Number of Bits of a DAC or ADC.
- Maximum sampling frequency: This is a measurement of the maximum speed at which the DACs circuitry can operate and still produce the correct output. Sampling theorem The Nyquist–Shannon sampling theorem states that perfect reconstruction As stated in the Shannon-Nyquist sampling theorem, a signal must be sampled at over twice the frequency of the desired signal. The Nyquist–Shannon sampling theorem is a fundamental result in the field of Information theory, in particular Telecommunications and Signal processing Frequency is a measure of the number of occurrences of a repeating event per unit Time. 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. A sound card (also known as an audio card is a Computer Expansion card that facilitates the input and output of audio signals to/from a computer under Resampling is the digital process of changing the Sample rate or dimensions of digital imagery or audio by temporally or areally analysing and sampling the original data
- 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. The 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 It is expressed as a percentage of the total power of unwanted harmonic distortion and noise that accompany the desired signal. In Acoustics and Telecommunication, the harmonic of a Wave is a component Frequency of the signal that is an Integer A distortion is the alteration of the original shape (or other characteristic of an object image sound waveform or other form of information or representation 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. Dynamic range is a term used frequently in numerous fields to describe the Ratio between the smallest and largest possible values of a changeable quantity such as in Sound The decibel ( dB) is a logarithmic unit of measurement that expresses the magnitude of a physical quantity (usually power or intensity relative to This is usually related to DAC resolution and noise floor. In 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
Other measurements, such as Phase distortion and Sampling Period Instability, can also be very important for some applications. In signal processing phase distortion or phase-frequency distortion is Distortion that occurs when (a a filter's Phase response is not linear over the
DAC figures of merit
- Static performance:
- DNL (Differential Non-Linearity) shows how much two adjacent code analog values deviate from the ideal 1LSB step [1]
- INL (Integral Non-Linearity) 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. Johnson–Nyquist noise ( thermal noise, Johnson noise, or Nyquist noise) is the electronic noise generated by the thermal agitation For audio applications and in room temperatures, such noise is usually a little less than 1 μV (microVolt) of white noise. The volt (symbol V) is the SI derived unit of electric Potential difference or Electromotive force. White noise is a random signal (or process with a flat Power spectral density. This limits performance to less than 20~21 bits even in 24-bit DACs, and cannot be corrected unless one resorts to extremely low temperatures to create superconductivity: clearly an impractical proposition. Superconductivity is a phenomenon occurring in certain Materials generally at very low Temperatures characterized by exactly zero electrical resistance
- Frequency domain performance
- SFDR (Spurious Free Dynamic Range) indicates in dB the ratio between the powers of the converted main signal and the greatest undesired spur
- SNDR (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
- HDi (i-th Harmonic Distortion) indicates the power of the i-th harmonic of the converted main signal
- THD (Total harmonic distortion) is the sum of the powers of all HDi
- if the maximum DNL error is lessthan 1 LSB,then D/A converter is guaranteed to be monotonic. The 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
However many monotonic converters may have a maximum DNL greater than 1 LSB.
- Time domain performance
- Glitch Energy
- Response Uncertainty
- TNL (Time Non-Linearity)
See also
References
Links and books
- Controlling the X79000 FlexDAC with a Rotary Encoder
- Audio Hi-Fi DAC build See a high quality audio DAC being built. A digital television adapter, (DTA or digital-to-analog converter (box is a device that receives by means of an antenna, a Digital television (DTV transmission Modem (from mo dulator- dem odulator is a device that modulates an analog carrier signal to encode Digital information An analog-to-digital converter (abbreviated ADC, A/D or A to D) is an electronic integrated circuit which converts continuous signals to I2S, or Inter-IC Sound, or Integrated Interchip Sound, is an electrical Serial bus interface standard used for connecting digital audio devices
- R-2R Ladder DAC explained with circuit diagrams.
- Resistor/PWM Hybride DAC for hi-fi audio from cheap microcontrollers.
- INL/DNL Measurements for High-Speed ADCs explains how INL and DNL are calculated.
- How to build a Digital to Analog converter A cheap, simple, yet reliable home-made solution!
- Dynamic Evaluation of High-Speed, High Resolution D/A Converters Outlines HD, IMD and NPR measurements, also includes a derivation of quantization noise
- ADC and DAC Glossary
- 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.
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