Digital-to-analog converter

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 charges). Digital-to-Analog Converters are the interface between the abstract digital world and the analog real life. Simple switches, a network of resistors, current sources or capacitors may implement this conversion.

An analog to digital converter or ADC performs the reverse operation.

Applications

Audio

An analog signal from a microphone or other sound source can be converted to digital form for storage in a computer, where it can be edited if necessary and then reconstructed for playback. In a personal computer, the conversion is usually done in a sound card, but there are some USB devices that do this conversion externally to improve the sound quality.

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 (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 analogue signal digitally.

DAC types

The most common types of electronic DACs are:

• the Pulse Width Modulator, the simplest DAC type. A stable current (electricity) 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 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 for the quantization (signal processing) noise, thus pushing this noise out of the pass-band. Most very high resolution DACs (greater than 16 bits) 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 and enable further suppression of quantization noise.

• 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 R2R Ladder DAC, which is a binary weighted DAC that creates each value with a repeating structure of 2 resistor values, R and R times two. This improves DAC precision due to the ease of producing many equal matched values of resistors or current sources, but lowers conversion speed due to parasitic capacitance.

• the Segmented DAC, which contains an equal resistor or current source segment for each possible value of DAC output. An 8-bit binary Segmented DAC would have 256 segments and a 16 bit binary Segmented DAC would have 65536 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.

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 Shannon-Nyquist sampling theorem, a signal must be sampled at over twice the bandwidth of the desired signal. For instance, to reproduce signals in all the audible spectrum, which includes frequencies of up to 20 kHz, it is necesary 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 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 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:
  • DNL (Differential Non-Linearity) shows how much two adjacent code analog values deviate from the ideal 1LSB step
  • INL (Integrated Non-Linearity) shows how much the DAC transfer characteristic deviates from an ideal one
  • Gain
  • Offset

• 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

• Time domain performance
  • Glitch Energy
  • Response Uncertainty
  • TNL (Time Non-Linearity)

See also

• Modem

External links

• R-2R Ladder DAC explained with circuit diagrams.