The digital-analog converter, abbreviated DAC, is used when digital signals or individual values need to be converted to analog signals. The DAC is thus also called D/A converter or digital-to-analog converter. Digital-analog converters are basic components for nearly all devices of digital entertainment electronics, like CD players, and communication technology, like in mobile telephones. Often, the DAC is implemented as an integrated circuit.
Function of the DAC
The digital-analog converter creates a stepped signal from a continuous value pool. However, it cannot re-create a continuous signal. It is not possible to undo the one-time stepping of 1 LSB. However, with a series of variable values, the stepping can be smoothed by the required filtering.
A digital signal is understood as a value-discrete and time-discrete signal. The DAC converts the quantized information, which exists as binary information, into a signal. This is then supplied continuously to a device operating on an analog technology basis.
For the conversion into a digital signal, i.e. a time-continuous, but value-discrete signal, the signal value is held in an input register until the next scan point. When points with different signal values follow close on each other, various curves are possible for the resulting analog, thus also value-continuous signal because of the scan points.
The spectrum can show distortions because of the quantized steps of the digital-analog converter. Accordingly, a lowering and distortion of the amplitudes can occur even in the desired frequency range. These linear distortions are normally compensated on the digital side by additional filters. In this way, the raising of the higher frequency components below one half of the scanning frequency increases inversely to the Sinc function curve.
When the cutoff frequency of the filter is notably higher than the signal frequency, the curve of the output signal approaches the stepped curve. The stepped curve indicates quantization noise.
The digital signal sent to the digital-analog converter is dimensionless. Thus it must be multiplied with the specified value Ur. With this, there are two main possibilities. With a fixed reference value as the first possibility, the digital input signal is mapped in a fixed output area. The peak value of the output signal is specified by the reference. The second possibility is the variable reference value. The digital-analog converter can be set within its signal range by an electrical signal. This process is called an attenuator circuit. The signal is possible as a 2- or 4-quadrant multiplication.
With an ideal DAC, there is a linear relation between output and input quantity. Other codings like for example two’s complements or BCD codes also exist.
However, digital-analog converters also exist with non-linear quantizing characteristics , like for example according to the logarithmicµ-law- and A-lawprocedure for telephone networks.
In addition to the quantization error, further deviations must be taken into consideration. The errors of the characteristics between real and ideal conversion include nonlinearity errors, zero point errors (offset), and amplification errors (gain errors). The last is often stated as a fraction of the actual value. On the other hand, the zero point error together with the nonlinearity error and the quantization error is listed as a fraction of the final value or a multiple of an LSB.
Errors also may occur in the stepping, for example with non-uniform height of a step or with a step of a higher value. With individual steps, it is possible that they may have different heights. When the input quantity rises step by step, a decrease in the value of the output quantity may occur, depending on the realization procedure. This happens especially when there is carry-over of several binary digits. Then the digital-analog converter is no longer monotonous.
Furthermore, time fluctuations in the clock influence the structure of the output signal.
In regard to the realization procedure, differentiation is made between the direct procedure and the parallel procedure. With the former one, the output signal is generated depending on the number of steps by the same number of resistors in a voltage divider. With this, each resistor is weighted the same. The associated step is selected with the digital value via a multiplexer. The procedure is guaranteed to be monotonous. It is offered with a resolution of 8 bits with 272 switches and 256 resistors.
With the parallel procedure, the binary digits count, as the output signal is generated by the same number of resistors. With this, each resistor is weighted according to the significance of the associated digit.
The R2R network each time halves the electric current in a chain of current dividers.
The number of required switches is equal to the number of bits used for representation of the digital values. Depending on the value of the associated binary digit, 1 or 0, the differently weighted currents are directed away unused or are switched to a bus line. The sum of all connected currents is converted to a voltage by means of an operation amplifier. A good compromise between effort and conversion duration is offered by the parallel procedure, and it is used frequently.
With the counting procedure of the digital-analog converted, the output signal is created again with the same number of time steps as permitted by the steps. The ON-time of an individual switch is specified with the digital value, where a periodic repetition of the duty cycle exists in the pulse width modulation. The arithmetic mean of a voltage switched on or off in this way forms the final output signal.
Areas of Application
Digital-analog converters are installed in music players and PC sound cards for playback of digital signals on CDs or MP3 files via speakers.
In order to be able to display digital signals on a (PC) monitor, they must be converted by circuits connected to the work memory (RAMDAC).
Generation of transmission signals in mobile communication devices requires very fast conversion of digital to analog signals.
Digital-analog converters are also used for control of many technical devices with electromechanical or electrochemical actors and as digital potentiometers or multipliers, for example for volume control on TVs.
Function of a Digital-analog Converter
A digital-analog converter is not a reversed analog-digital converter. A once quantized time- and value-discrete digital signal can never again be converted back into the original analog signal.
The reason for this is that an analog signal is time- and value-continuous, so that the amplitude can be measured at any time of the signal. On the other hand, a digital signal is reduced to specific scanning points: Accordingly, statements concerning the condition of the signal can be made at the respective point in time, but not about the condition of the signal between the individual scanning points.
An input register keeps the value at output of the signal from one scanning point to the next. This creates various courses of an analog, i.e. time- and value-continuous signal. As only the digital scanning points are available for the process of the digital-analog converter, different courses can result. Undesirable frequencies in the high range can be eliminated with anti-aliasing filters applied to the analog signal.
Quantization steps, i.e. the division of the signal into scanning points, also cause distortion of the signal. This is caused by the phenomenon of enveloping quantity curves, the so-called sampling or cardinal curves, the Sinc function. As the deviations caused by this are often rather in the low frequency ranges, they can be reduced or eliminated with the aid of low-pass filters. Depending on the type of signal, a quantization step can include one or more scanning points.
However, when the distortion is below the filter range, the well-known quantization noise is caused.
Specific causes for measuring value errors
In addition to the zero point error, the amplification error, and the non-linearity error, some further specific causes for a deviation from ideal and reality can be named for the digital-analog converter:
When the input values increase step by step, a reduction of the output values may occur depending on the implementation method being used. These are called step errors. The probability for occurrence of this error increases with the number of binary digits.
Time fluctuations, so-called jitter, have a considerable influence onto the output signal.
Classification of digital-analog converters according to the implementation method
A voltage divider has exactly 1 resistor for each quantization step. All resistors are weighted equally and are allocated to their quantization step by means of a so-called 1-of-n switch.
Although this method can be realized fastest, the effort increases strongly with increasing signal resolution. A known example is the 8-bit converter with its 256 resistors and 272 switches.
A digital signal logically is composed of binary digits. The number of resistors with the parallel method corresponds to the number of binary digits of the signal. With this, the individual resistors are weighted according to the significance of their associated binary digit. Each bit in the representation of the digital signal requires a switch. The different-value currents are switched to a bus line or directed away, depending on whether they are 0 or 1. All connected currents are converted to voltage by means of an operational amplifier.
With this implementation of the digital-analog converter, the signal is generated with the aid of time steps. Here, the total number of time steps corresponds to the number of quantization steps. Only a single switch is used, which is switched on or off by the digital signal, and this specifies the scanning frequency. Accordingly, the final signal is the arithmetic means of the voltage switched on and off in this way.
As the process requires counting of the time steps as well as forming of the front, this means it is time-consuming, but can be realized rather easily and cost-effectively. It is often used as an integrated circuit for microprocessors.
Classification of Digital-analog converters by wiring
Another type of classification is the way how the digital signal is directed into the digital-analog converter. This is done either parallel, with one bit per connection line, or serial, with only one data line. In this case, the input signal in most cases is an electrical voltage with standardized representation. An additional control line is used to verify the validity of the supplied data.
The output of the analog signal can also be used for classification of digital-analog converters. Thus, the signal can be provided either as current (voltage-output DAC) or as voltage (current-output DAC). In most cases, an amplifier circuit is required after processing for processing of the converted signal.