The R−2R ladder circuit in Figure 2–50 is a binary current divider that finds applications in digital-to-analog signal conversion. The operation of this circuit can be explained using current division together with series and parallel equivalent resistance.

The equivalent resistance connected to ground at node 3 is 2Rk2R=R, which means that the equivalent resistance seen to the right of node 2 of R+R=2R. This in turn means that the total equivalent resistance connected to ground at node 2 is 2Rk2R=R and hence the equivalent resistance seen to the right of node 1 of R+R=2R. The net result is that the equivalent resistance seen to the right of each numbered node is 2R.
The reference current IREF entering node 1 divides equally between the two available 2R paths with the result that i1 = IREF=2, and the current into node 2 is also i1 = IREF=2. At node 2 this current again divides equally between the two 2R paths with the result that i2 = i1=2=IREF=4 and the current into node 3 is i2 = IREF=4. Finally, at node 3 this current divides equally once more so that i3 = i2=2=IREF=8. In sum, the currents in the 2R resistors connected to ground are all of the form ik = IREF=2k, where k is the node number to which the resistor is connected. Thus, the R−2R ladder circuit produces signals (currents in this case) that decrease in a binary fashion as we proceed down the ladder.
Clearly, the R−2R ladder can be extended to a larger number of nodes. Commercially available integrated circuit ladders have as many as eight-numbered nodes producing binary currents ranging from IREF=2 to IREF=256. The advantage of this circuit is that it produces this wide range of precisely related signals using only two values of resistance, namely R and 2R. This greatly simplifies the fabrication of the R−2R ladder in integrated circuit form.

Transcribed Image Text:

IREF FIGURE 2-50 2R R tw 2R 2 ww 2R 2R R (3) 2R ww 2R 13 2R riz fiz