This is the type of resistive network used for the D to A conversion.

Figure shows the basic R-2R ladder network. It consists of resistors of only two values, R and 2R. This will simplify the network and also the selection of network components. The R-2R network is the heart of R-2R ladder type DAC and the one shown in Figure is a 4 bit R-2R network.

It is possible to have a 2 bit, 3 bit, 5 bit or n bit R-2R ladder.

di d2 d3 d4 is a 4 bit digital input word with d1 as the most significant bit (MSB) and d4 as the least significant bit (LSB). voThe analog Output voltage which is proportional to the digital input.

Analysis of R-2R Network:

The R-2R network can be analyzed by using the Thevenin's theorem. While analyzing, we will obtain the output voltage corresponding to each digital input and then add them to get the final value of Voltage .It is the principle of superposition and we can apply it to this network because this is a linear network.

Step 1: Calculate the output due to MSB only (di )

• The digital input d1 d2 d3 d4 = 1000. Let the corresponding output be vo= v01.
• Assume that logic 1 corresponds to a voltage VR,and logic 0 corresponds to 0 volts
• The network corresponding to d1 d, d3 d4 = 1000 is shown in Figure.

$v_{01}= v_{oc}= \dfrac{2R}{2R+2R}\times{}V_R = \dfrac{V_R}{2}$

• The output voltage corresponding to MSB bit d1 is$\dfrac{V_R}{2}$

Step 2 : output voltage only due to bit d2 :

• The digital input d1 d2 d3 d4 = 0100.