# How Digital to Analogue Converters (DAC) works?

It is very important question in digital electronics that **How Digital to Analogue Converters (DAC) works?** In our real world most of signals are analogue continues in nature. But if we want to process it further we need to convert these analogue signals in digital signals and after process again we have to convert it in analogue form using **Digital to Analogue Converters.**

The input of a** Digital to Analogue Converters** (D/A) is an *n-*bit binary signal, available in parallel form. Normally, digital signals are available at the output of latches or registers and the voltages correspond to logic 0 and logic 1. We should know that the logic levels (0 or 1) do not have precisely fixed voltages. Therefore, these voltages are applied directly to the converter for digital-to-analogue computation, but they are used to operate digitally controlled switches. The switch is operated to one of the two positions depending upon the digital signal logic levels (logic 0 or logic 1) which connects precisely fixed voltages or voltage references V(1) or V(0) to the converter input, corresponding to logic 1 and logic 0 respectively.

The analogue output voltage Vo of an *n*-bit straight binary D/A converter can be related to the digital input by the equation

Vo = K (2^{n}^{-1 }. *b ^{n}*

^{–1 }+ 2

^{n}^{–2 }.

*b*

^{n}^{–2}+ 2

^{n}^{–3}.

*b*

^{n}^{–3 }+ ………+ 2

^{2}.

*b*

^{2}+ 2.

*b*

^{1}+

*b*

^{0}).

Where K = proportionality factor equivalent to step size in voltage,

*b ^{n }*= 1, if the

*n*

^{th }bit of the digital input is 1,

= 0, if the *n*^{th} bit of the digital input is 0.

There are two types of commonly used D/A converters as mentioned below.

- Weighted-resistor D/A converter, and
- R-2R ladder D/A converter.

Some specification of **Digital to Analogue Converters we should know when we use it those are **resolution, accuracy, conversion speed, dynamic range, nonlinearity (NL) and differential nonlinearity (DNL) and monotonocity .

*Resolution*

The *resolution *of a D/A converter is the number of states (2n) into which the full-scale range is divided or resolved. Here, n is the number of bits in the input digital word. The higher the number of bits, the better is the resolution. An eight-bit D/A converter have 255 resolvable levels. It is said to have a percentage resolution of (1/255)×100=0.39% or simply an eight-bit resolution.

*Accuracy*

The *accuracy *of a D/A converter is the difference between the actual analogue output and the ideal expected output when a given digital input is applied. Sources of error include the *gain error *(or full-scale error), the *offset error *(or zero-scale error), *nonlinearity errors *and a drift of all these factors.

*Conversion Speed or Settling Time*

The *conversion speed *of a D/A converter is expressed in terms of its settling time. The *settling time *is the time period that has elapsed for the analogue output to reach its final value within a specified error band after a digital input code change has been effected. General-purpose D/A converters have a settling time of several microseconds, while some of the high-speed D/A converters have a settling time of a few nanoseconds. The settling time specification for D/A converter type number AD 9768 from Analogue Devices USA, for instance, is 5 ns.

*Dynamic Range*

This is the ratio of the largest output to the smallest output, excluding zero, expressed in dB. For linear D/A converters it is 20×log2n, which is approximately equal to 6n_ For companding-type D/A converters, discussed in Section 12.3, it is typically 66 or 72 dB.

*Nonlinearity and Differential Nonlinearity*

*Nonlinearity *(NL) is the maximum deviation of analogue output voltage from a straight line drawn between the end points, expressed as a percentage of the full-scale range or in terms of LSBs.

*Differential nonlinearity *(DNL) is the worst-case deviation of any adjacent analogue outputs from the ideal one-LSB step size.

*Monotonocity*

In an ideal D/A converter, the analogue output should increase by an identical step size for every one-LSB increment in the digital input word. When the input of such a converter is fed from the output of a counter, the converter output will be a perfect staircase waveform. In such cases, the converter is said to be exhibiting perfect monotonocity. A D/A converter is considered as monotonic if its analogue output either increases or remains the same but does not decrease as the digital input code advances in one-LSB steps. If the DNL error of the converter is less than or equal to twice its worst-case nonlinearity error, it guarantees monotonocity.