# Example of DAC problem

Linear Integrated Circuit Applications
2020-11-20 01:16:26
# Example of DAC problem

In the previous chapter, we discussed the two types of DACs. This chapter deals with an example of a problem based on the DAC Ladder R-2R.

## Example

Let's find the value of the analog output voltage of the DAC Ladder R-2R for a binary input, $ b_ {2} b_ {1} b_ {0} $ = 100.

### Circuit diagram and its simplification

The ** circuit diagram ** of a 3 bit R-2R Ladder DAC in binary input, $ b_ {2} b_ {1} b_ {0} $ = 100 applied to it is shown in the following figure -

In the above circuit, there are series combinations and parallel of resistances for the left of ** point A ** with respect to the ground. Thus, we can replace this whole network of resistors with a single resistor having a resistance of $ 2R Omega $.

The ** simplified diagram ** is shown in the following figure -

We can replace the part of the network which is connected to the left of point B with respect to the earth in utilizing an equivalent circuit of Thevenin. The ** modified electrical diagram ** is shown in the following figure -

In the circuit above, there is a series combination of two resistors. Replace this combination with a single resistor. The final ** electrical diagram ** after simplification is shown in the following figure -

Now the circuit diagram above looks like an ** inverting amplifier **. It has an input voltage of $ - frac {V_ {R}} {2} $ volts, an input resistor of $ 2R Omega $ and a return resistor of $ 2R Omega $.

The ** output voltage ** of the above circuit will be -

$$ V_ {0} = - frac {2R} {2R} left (- frac {V_ {R}} {2} right) $$

$$ V_ {0} = frac {V_ {R}} {2} $$

Therefore, the ** output voltage ** of the 3-bit R-2R Ladder DAC is $ frac {V_ {R}} {2} $ volts for a binary input, $ b_ {2} b_ {1} b_ {0} $ = 100.