A DAC converts an N-bit digital code into a proportional analog voltage. The naive approach — a binary-weighted resistor network with values R, 2R, 4R, 8R, ..., 2^(N-1)·R — falls apart fast. For a 12-bit DAC, you'd need resistors spanning a 4096:1 range, and they'd all need to match to within 1 part in 4096 (~0.025%). Silicon resistors can't hit that. The R-2R ladder solves this by using only two resistor values, R and 2R, and lets ratiometric matching do the work.

The structure: a repeating ladder where each "rung" has a switch that connects a 2R resistor either to ground or to the output node. The horizontal series resistors are all R, the vertical arms are all 2R. Every node in the ladder sees a Thevenin equivalent of 2R looking left and 2R looking right — so the impedance at every node is identical, and each bit position contributes exactly half the weight of the bit above it.

Why this is magical: the absolute value of R doesn't matter. What matters is that all your Rs match each other and all your 2Rs are exactly twice them. On silicon, you build the 2Rs as two Rs in series with identical geometry, orientation, and adjacent placement. Layout matching to 0.01% is routine even when the absolute resistance drifts 20% over process and temperature.

Concrete example: An 8-bit R-2R DAC with V_ref = 5V and R = 10kΩ. Digital code 10110100 (180 decimal) produces V_out = 5V × 180/256 = 3.516V. The switches route bits 7,5,4,2 to V_ref and bits 6,3,1,0 to ground. Each bit's contribution is halved by the ladder's binary attenuation as it propagates toward the output node.

Where you'll find them: Audio codecs, older 8-16 bit DACs in microcontrollers (PIC, AVR), oscilloscope calibration circuits, and — famously — the classic AD7541 12-bit DAC that lived in a million pieces of test equipment through the 80s and 90s. Modern high-resolution converters use sigma-delta or SAR architectures, but R-2R still dominates when you need moderate resolution with fast settling (nanoseconds, not microseconds) and no oversampling latency.

Rule of thumb: R-2R ladders scale well to about 14 bits before matching requirements become impractical. Beyond that, either segment the DAC (use R-2R for LSBs and thermometer coding for MSBs) or switch to a fundamentally different architecture. INL and DNL are dominated by the matching of the MSB switches — the top few bits get all the attention during layout.