A R-2R ladder circuit as the binary current divider that is finest application in digital to analog conversion. This video shows how to analyze the R-2R ladder circuit. In this video, the circuit has three nodes. First, this video shows analysis of the resistance on third node. Since the 2R is connected in parallel with 2R, they will give the R resistance on this node. Then the Resistance on third node is connected in series connection with the resistor on second node, so we have parallel connection between 2R and 2R on second node. It will give R resistance on second node. Lastly, the resistor on first node is connected to resistance on second node in series connection, so the the resistance on first node also R. Here is the video:
Now, the current analysis i1, i2 adn i3. The Ireference is going to node one. Since the resistance on node one is same, the Iref is splited into two on the same current, i1 and i1. So i1 is half of the iref. The i2 is half of the i1 and the i3 a half of i2. The i1, i2 and i3 are determined by following equation:
From this analysis, we can conclude this R-2R circuit produces the current or signal that decreased in a binary. We can also extend R-2R to the larger number node.