the R-2R ladder

The R-2R ladder is the clever fix for the binary-weighted DAC's impossible resistor spread. Instead of resistors that range from R to thousands of R, it uses only TWO values — a resistor R and a resistor twice as big, 2R — repeated in a simple ladder pattern. Yet it still produces perfect binary weighting, each bit worth half the last. It is the workhorse structure inside most real DACs precisely because making just two well-matched values is easy.

The trick is how the ladder repeatedly halves a current. At each rung, the network ahead looks like the same resistance, so the current splits in two: half goes down to the output, half carries on to the next rung, where it splits again. Bit by bit the available current is halved — full weight, half, quarter, eighth — exactly the binary weights you want. Each bit's switch steers its 2R leg either toward the output (a 1) or to ground (a 0). The beauty is that only the ratio R to 2R must be accurate, and resistors that sit side by side on the same chip match that 2:1 ratio extremely well and drift together with temperature.

Why this matters: because only two values and their matching matter, R-2R ladders scale gracefully to 12, 16, even more bits, where binary-weighted designs cannot. They are compact, easy to trim, and stable. The honest limits: the switches themselves have a little resistance that adds error if not handled, and at the highest resolutions you still need laser-trimmed or calibrated resistors. But for turning a number into a voltage cleanly and cheaply, the R-2R ladder is the standard answer.