# R - 2R Ladder Digital to Analog Converter

Real-world signals are continuous or analog in nature. In any digital system, we process only digital data. The result or output of the digital system is a digital signal. For controlling the real-world situation, the digital data has to be converted into analog form. For example, for controlling the speed of the motor, the signal must be an analog signal.

Digital to analog converters or DAC converts the n-bits digital signal into analog signals. There are lots of techniques for conversion of the digital signal into the analog signal. One of them is R-2R DAC.

R-2R ladder Digital to Analog converter is the most widely used circuit for converting the digital signal into the analog signal. For implementing R-2R DAC we require only two different values of resistors, one is R and other is 2R.

For n-bit R-2R DAC, we require 2n resistors. (n+1) resistors of value 2R and (n-1) resistors of value R. Circuit diagram for 4-bit R-2R DA converter is shown below:

Here D0 is LSB and D3 is MSB. Let us assume that the voltage is '+V' for logic '1' and '0V' for logic '0'.

We can use superposition theorem to calculate the output voltage of the circuit.

If D3 is 1 and other all digits are 0 then, the output voltage is equal to +V/2. If D2 is 1 and other all digits are 0 then, the output voltage is equal to +V/4. If D1 is 1 and other all digits are 0 then, the output voltage is equal to +V/8. If D3 is 1 and other all digits are 0 then, the output voltage is equal to +V/16.

If all the digits are 1 then, the output voltage is given by:

$$V_{out}={V\over 2}+{V\over 4}+{V\over 8}+{V\over 16}$$

For n-bit DAC, the output voltage for the kth bit is given by:

$$V_{out}={V \over 2^{n-k}}$$

1. It doesn't require any precise resistor.
2. It requires only two values of resistors.

1. The data conversion speed is low.

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