Digital to Analog Converters (D/A)

john August 10, 2017 12 Comments

A D/A Converter is used when the binary output from a digital system is to be converted into its equivalent analog voltage or current.

The binary output will be a sequence of 1’s and 0’s. Thus they ma be difficult to follow. But, a D/A converter help the user to interpret easily.

Basically, a D/A converter have an op-amp. It can be classified into 2 types. They are

1. Digital to Analog Converter using Binary-Weighted Resistors

A D/A converter using binary-weighted resistors is shown in the figure below. In the circuit, the op-amp is connected in the inverting mode. The op-amp can also be connected in the non-inverting mode. The circuit diagram represents a 4-digit converter. Thus, the number of binary inputs is four.

Digital-to-Analog Converter Circuit - Binary-Weighted Resistors Method

Digital-to-Analog Converter Circuit – Binary-Weighted Resistors Method

We know that, a 4-bit converter will have 24 = 16 combinations of output. Thus, a corresponding 16 outputs of analog will also be present for the binary inputs.

 

Four switches from b0 to b3 are available to simulate the binary inputs: in practice, a 4-bit binary counter such as a 7493 can also be used.

Working

The circuit is basically working as a current to voltage converter.

  • b0 is closed

It will be connected directly  to the +5V.

Thus, voltage across R = 5V

Current through R = 5V/10kohm = 0.5mA

Current through feedback resistor, Rf = 0.5mA (Since, Input bias current, IB is negligible)

Thus, output voltage = -(1kohm)*(0.5mA) = -0.5V

  • b1 is closed, b0 is open

R/2 will be connected to the positive supply of the +5V.

Current through R will become twice the value of current (1mA) to flow through Rf.

Thus, output voltage also doubles.

  • b0 and b1 are closed

Current through Rf = 1.5mA

Output voltage = -(1kohm)*(1.5mA) = -1.5V

Thus, according to the position (ON/OFF) of the switches (bo-b3), the corresponding “binary-weighted” currents will be obtained in the input resistor. The current through Rf will be the sum of these currents. This overall current is then converted to its proportional output voltage. Naturally, the output will be maximum if the switches (b0-b3) are closed

V0 = -Rf *([b0/R][b1/(R/2)][b2/(R/4)][b3/(R/8)]) – where each of the inputs b3, b2, b1, and b0 may either be HIGH (+5V) or LOW (0V).

The graph with the analog outputs versus possible combinations of inputs is shown below.

Digital-to-Analog Converter Circuit - Binary-Weighted Resistors Method Graph

Digital-to-Analog Converter Circuit – Binary-Weighted Resistors Method Graph

The output is a negative going staircase waveform with 15 steps of -).5V each. In practice, due to the variations in the logic HIGH voltage levels, all the steps will not have the same size. The value of the feedback resistor Rf changes the size of the steps. Thus, a desired size for a step can be obtained by connecting the appropriate feedback resistor. The only condition to look out for is that the maximum output voltage should not exceed the saturation levels of the op-amp. Metal-film resistors are more preferred for obtaining accurate outputs.

 

Disadvantages

If the number of inputs (>4) or combinations (>16) is more, the binary-weighted resistors may not be readily available. This is why; R and 2R method is more preferred as it requires only two sets of precision resistance values.

2. Digital to Analog Converter with R and 2R Resistors

A D/A converter with R and 2R resistors is shown in the figure below. As in the binary-weighted resistors method, the binary inputs are simulated by the switches (b0-b3), and the output is proportional to the binary inputs. Binary inputs can be either in the HIGH (+5V) or LOW (0V) state. Let b3 be the most significant bit and thus is connected to the +5V and all the other switchs are connected to the ground.

Digital to Analog Converter with R and 2R Resistors

Digital to Analog Converter with R and 2R Resistors

Thus, according to Thevenin’s equivalent resistance, RTH,

 

RTH = [{[(2RII2R + R)} II2R] + R}II2R] + R = 2R = 20kOhms.

The resultant circuit is shown below.

Digital to Analog Converter with R and 2R Resistors - Resultant Circuit

Digital to Analog Converter with R and 2R Resistors – Resultant Circuit

Graph is given below.

Digital to Analog Converter with R and 2R Resistors - Graph

Digital to Analog Converter with R and 2R Resistors – Graph

In the figure shown above, the negative input is at virtual ground, therefore the current through RTH=0.

Current through 2R connected to +5V = 5V/20kohm = 0.25 mA

The current will be the same as that in Rf.

Vo = -(20kohm)*(0.25mA) = -5V

Output voltage equation is given below.

V0 = -Rf (b3/2R+b2/4R+b1/8R+b0/16R)

Comments
  • klemens
    November 7, 2016

    any one to help out with full details on the components within the DAC circuit diagram and a view of layout

  • excellent thanks

  • POOJA
    April 15, 2014

    can we use 741 in place of 351??
    plz reply..

    • Seetharaman
      April 16, 2014

      You can use TL071, which is an FET input opamp of equivalent characteristic to LF351.

    • Ambika
      April 19, 2015

      yes, of course….741 is also acceptable..

  • POOJA
    April 12, 2014

    Hi… Your post helped me to understand the concept of DAC.

  • November 16, 2013

    it require the types of of electronic switch used in dac

  • June 15, 2013

    Hello there! Good post! Please inform us when I will see a follow up!

  • k.vijaykumar
    October 23, 2012

    give more informatiom about R/2R dac

  • October 10, 2012

    very informative

  • June 23, 2011

    electrical electronic is the best thing ever happen to the world.

  • haitham hashim
    June 22, 2011

    Of the best and most practical information

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