Digital-to-analog converter

A digital -to-analog converter (DAC, engl. Digital -to- analog converter (DAC) ), and digital -to-analog converters or D / A converter referred to, is used to convert digital signals into analog signals or single values ​​. DACs are elementary components of almost all devices of the digital consumer electronics (eg CD player) and communications technology (eg mobile phones ). In general, the DAC of an integrated circuit (IC) is performed.

• 2.1 Zero error, gain error and nonlinearity error
• 2.2 Error in the staging
• 2.3 Temporal and aperture error

• 3.1 Direct method
• 3.2 Parallel Process
• 3.3 counting method / 1 - bit converter
• 3.4 Delta-Sigma-Verfahren/1-Bit- to N - bit converter
• 3.5 Hybrid converter

• 4.1 Digital control
• 4.2 Analog Output and Output

• 5.1 audio
• 5.2 Video
• 5.3 Engineering Controls
• 5.4 Digital Potentiometer and multiplier
• 5.5 Communications Engineering

Function

An analog -to-digital converter generates a stepped signal of a continuous range of values ​​. A digital to analog converter may generate a continuous signal is not out of the stepped signal. The once occurred gradation in steps of 1 LSB ( least significant bit) is not to be undone. In a sequence of variable values, the grading is, however, cut off by a necessary filtering.

A digital signal is a time-discrete and value- discrete signal, as shown adjacent display. The digital -to-analog converter converts the quantized information available as a binary information in a signal which may be continuously provided to an analog technical operating equipment.

Steps of implementation

For a reaction in a continuous-time ( but still worth discrete ) signal, the signal value is held until the next sample point in an input register. When individual measurement points and slowly varying sizes at the output results in a course as in the second image entered as horizontal lines.

In a rapid sequence of points with different signal values ​​varied profiles are possible because of the sampling points for the resulting analog (also worth continuous ) signal. The dotted line in the second image follows the samples, but does not resemble the original signal. It contains higher frequency components, which must be prevented by anti -aliasing filter on the analog side usually. The storage of the sample points is dominated in this case by the filter.

In the next picture of the absolute values ​​of the frequency spectrum of a DAC is shown without anti -aliasing filter, which outputs a sine wave with the frequency f. This sine wave occurs repeatedly in harmonics. Here fc is the sampling frequency. All signal components with a frequency above half the sampling frequency to the filter to suppress.

By quantizing the spectrum distortions, which are caused by the red - dashed lines drawn and enveloping amount during the sinc function. Thus, it is also less than half the sampling frequency, ie in the desired frequency range, to a distortion and reduction of amplitudes. These linear distortions are usually offset by additional filter on the digital side, drawn in blue dots in the image. This higher frequency components below half the sampling frequency are inversely raised more for sinc function curve.

Is the signal frequency significantly lower than the cutoff frequency of the filter, the curve of the output signal approximates the stepped profile. The graduation is noticeable as quantization noise.

Reference value

Since the DAC supplied digital signal is dimensionless, it must be multiplied by a predetermined value Ur. There are two ways in principle.

• Fixed reference value (eg internally generated reference voltage): The digital input signal is mapped into a fixed output range, the reference specifies the peak value of the output signal.
• Variable reference value: The DA converter is in its signal range by an externally applied electrical signal adjustable ( attenuator ). This is for a 2 - Possible or 4-quadrant multiplication. Especially designed for this purpose ICs are called multiplying DAC (german Multiplying DAC).

Quantization

In an ideal digital - to-analog converter preferably is a linear relationship between input and output. There are

And besides other encodings, such as two's complement, BCD code can be used.

There are also DA converter with nonlinear quantization eg after logarithmic A-law and μ - law method for telephone networks.

Deviations

In addition to quantization are further errors observed.

Zero error, gain error and nonlinearity error

As deviations of the characteristics between the real and the ideal converter following errors are defined (see picture):

• Zero error (offset)
• Gain error ( engl. Gain Error)
• Nonlinearity error

The gain error is often expressed as a fraction of the current value, the zero-point error with the quantization and the non-linearity error of the final value as a fraction or a multiple of the LSB.

Error in the grading

Individual steps can vary high.

At step by step increasing input size, it can happen depending on the realization method that decreases a value of the output, especially if there is a carry over several binary digits, for example 0111 1111 after 1000 to 0000. In this case, the converter is not monotonic.

Temporal and aperture error

Temporal variations in the clock (jitter) affecting the structure of the output signal. Details of the maximum allowable jitter see under the same heading in the article ADU.

Realization process

Direct method

Here the output signal is generated by as many resistors in a voltage divider as there are steps; each resistor is equal weighted. With the digital value of the assigned level is selected via a 1- of-n switch ( multiplexer ). This method is fast and guaranteed monotonic with increasing resolution but comparatively expensive. An example of the method is an 8- bit converter 256 and resistors 272 switches.

Parallel process

Here, the output signal is generated by as many resistors as there are binary; each resistor is weighted so as to correspond to the valence of the associated body.

Easy to manufacture and in the implementation of the R2R network, each halving of an electric current makes in a chain of current dividers (only possible with Dualkode ).

Are required as many switches as there are bits for representing the digital values ​​to be used. The differently weighted currents are switched according to the value (1 or 0 ) of the corresponding binary position on a manifold or derived unused. The sum of the connected streams - now usually integrated in the circuit - formed by an operational amplifier in a voltage. The parallel method offers a good compromise between cost and implementation time and is often used.

The counting method / 1 - bit converter

Here the output signal is generated by as many time steps as there are stages. With the digital value of the switch of a single switch and at periodic repetition in the duty cycle of a pulse width modulation are determined. The final output is of equal value as an on / off voltage. This simple and inexpensive -to-implement procedures required under the method presented here, the largest implementation time because the process is connected to a counting of time steps and averaging. This guaranteed monotonic operating DAU can be realized well as an integrated circuit and is especially common in the context of the clock signal in microprocessors. For the mean value formation is usually a simple low-pass can be used.

Delta-Sigma-Verfahren/1-Bit- to N - bit converter

Delta modulation, which offers certain similarities to the pulse width modulation is used in the delta -sigma modulation. Similar to the method of counting is reduced with one or more 1 -bit converters with additional continuous subtraction and integration of the output error and reaches a noise shaper, which shifts noise in the higher frequency ranges. There is a certain digital computational effort required for sample rate conversion and digital filtering. For good results, delta-sigma modulators higher order with high oversampling are used, such as 5th order and 64 times over-sampling. This method requires a high oversampling a small amount of filtering is well integrated, provides high accuracy and is using a 1-bit converter guaranteed monotonic. The main advantage over the method of counting is in principle caused by noise shaping, which allows for higher frequencies. This method is currently used increasingly not only in the audio, but also in the measurement technology.

Hybrid converter

This is not a standalone method, but it will be a combination of the above methods used. The precise delta-sigma method, for example, is combined with a simple, low-resolution parallel converter for the low-order bits in order to combine the advantages of both methods.

Wiring

Digital control

Another classification feature is the manner in which the digital value is supplied to the converter (interface)

• Parallel - each bit is a connecting cable or
• Serial - only one data line (see SPI or I ² C).

The input signals are electric voltages usually with a standardized representation of the two signal states, such as TTL, ECL, CMOS, LVDS.

To signal the validity of the pending data or configure the module further, additional control lines are needed. For serial controlled converters, the input register must be described in a number of clocks before the information is ready for implementation.

Analog output and output

The generated signal at the output as either

• Tension (english voltage output DAC) or
• Current ( current output DAC English )

Available. Almost always requires the unfavorable impedance and capacitance of the converter circuit further processing of the signal. An amplification circuit used for this purpose is determined by their limiting parameters the dynamic characteristics of the entire circuit (e.g., bandwidth) substantially with.

Areas of application

Audio

Audio signals are often stored in digital form (for example MP3s and CDs). To make them audible through speakers, a conversion to analog signals it delivers. DACs are therefore found in CD and digital music players, and PC sound cards. DACs are also available as individual units for mobile applications or as components in stereos.

Video

Digital generated video signals (eg, a computer) to be implemented on an analog monitor before being displayed. Here the DAU a memory ( RAM) is generally linked, are stored in the tables for gamma correction, contrast and brightness settings. Such a circuit is referred to as a RAMDAC.

Engineering Controls

In many technical devices, electromechanical or electrochemical actuators are controlled with digital calculated values ​​, their implementation is done by a DAC. Likewise DACs are used in battery chargers and digitally adjustable power supplies.

Digital potentiometers and multiplier

The DAC may also multiply a variable analog reference value to the digital input signal. One application is the digital potentiometer, which can be ( eg for volume control in audio amplifiers or televisions ) are controlled digitally as a variable resistor. Digital Potentiometer with EEPROM memory to remember the last set value even when the unit is disconnected from the mains voltage.

Communications Engineering

Extremely fast DA converter with integrated mixing and filtering capabilities (English Transmit DACs ) are used in communications technology, eg for the generation of transmit signals for mobile devices.

Important parameters

• Stabilization time ( settling time ) or processing speed ( update rate ) - A measure of the duration of implementation.
• Resolution (Resolution ) - width of the steps (even number of stages or the number of digits) that are used to display the input signal.
• Zero error - The converter characteristics ( excluding the grading) is moved. The analog value is different from the correct value by a constant amount.
• Sensitivity error, gain error - The converter characteristics ( excluding the grading) is rotated ( pitch error ). The analog value differs from the correct value by a constant percentage of the correct value.
• Integral nonlinearity - the error in that a a linear underlying converter characteristic curve ( without consideration of the gradation ), is non-rectilinear.
• Differential non-linearity - deviation of the height of the implementation stages with each other.
• Monotony - When increasing input size increases, the output variable or constant. No monotony when rising input variable, a return of the output is produced to a smaller value; possible in a differential non- linearity by more than 1 LSB.
• Quantization - Graphical representation of the relationship between the analog output values ​​and the digital input values ​​, eg following a linear or logarithmic function.
• Quantization - Due to the limited resolution induced deviation of the output signal from the functional ( steady ) course.
• Signal -to-noise ratio in dB
• Dynamic Parameters
• Intermodulation distortion in dB