# Digital-analog converter - Part 1

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.

### Conversion

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.

### Reference Value

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.

### Quantizing Characteristic

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.

### Deviations

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.

### Realization Procedure

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.

### Counting Procedure

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.