# Digital to Analog Converter or DAC

Op amp is extensively used as main building block of **digital to analog convertor**. **Digital to analog convertor** is an electronics device in form of IC, which converts digital signal to its equivalent analog signal. The **DAC** can be realized in many ways. One of the popular **digital to analog convertor** circuit is **binary weighted ladder**.This is basically a summing amplifier designed with suitable resistances, as shown below.

Now, applying Kirchhoff Current Law at node 1 of the above circuit, we get,
Before going through the above circuit of **digital to analog convertor**, Let us put some suitable values of different resistors connected in the circuit.
Such as, R_{f} = 10KΩ, R_{1} = 10KΩ, R_{2} = 20KΩ, R_{3} = 40KΩ and R_{4}= 80KΩ.

Putting these values in equation (i) we get,
Now, let us also apply voltage at input terminals either 0 or 1 volt. Putting , 0 volt at all inputs,(i.e. v_{1} = 0, v_{2} = 0, v_{3} = 0 and v_{4} = 0) we get,

So, for digital input 0000, we get analog output 0 volt. Putting, 1V at last input only,(i.e. v_{1}=0, v_{2}=0, v_{3}=0 and v_{4}=1V), we get,
Similarly, for v_{1} = 0, v_{2} = 0, v_{3} = 1, v_{4} = 0

For, v_{1} = 0, v_{2} = 0, v_{3} = 1, v_{4} = 1
In this way the inputs and corresponding outputs can be represented in a table as shown below.

Binary Input [v_{1} v_{2} v_{3} v_{4}] | Decimal Value | Output(-v_{0}) |

0000 | 0 | 0 |

0001 | 1 | 0.125 |

0010 | 2 | 0.25 |

0011 | 3 | 0.375 |

0100 | 4 | 0.5 |

0101 | 5 | 0.625 |

0110 | 6 | 0.75 |

0111 | 7 | 0.875 |

1000 | 8 | 1.0 |

1001 | 9 | 1.125 |

1010 | 10 | 1.25 |

1011 | 11 | 1.375 |

1100 | 12 | 1.5 |

1101 | 13 | 1.625 |

1110 | 14 | 1.75 |

1111 | 15 | 1.875 |

**DAC**. A four bit

**DAC**can be represented as shown below.