Understanding the R/2R Ladder Digital‑to‑Analog Converter

The R/2R ladder DAC is a popular alternative to the traditional binary‑weighted (R/2ⁿR) converter, offering a simpler resistor set‑up without sacrificing performance.

R/2R vs. R/2ⁿR DAC

Traditional binary‑weighted designs require a unique resistor value for each bit—often eight different resistors for an 8‑bit converter. This diversity increases BOM complexity and assembly effort.

Although you could group identical resistors in series to mimic the required values, this merely shifts the complexity from variety to quantity, making the circuit bulkier and harder to manage.

What Is an R/2R Ladder DAC?

By arranging only two resistor types (R and 2R) in a ladder pattern, the circuit achieves the same binary weighting while keeping the component count manageable. The schematic below illustrates this ladder network:

Understanding the R/2R Ladder Digital‑to‑Analog Converter

Although the math is a bit more involved than with simple weighted resistors, you can analyze the ladder using Thevenin equivalents or simulate it in SPICE. The resulting output voltages for each 3‑bit input are listed in the table below:

Binary	Output Voltage
000	0.00 V
001	-1.25 V
010	-2.50 V
011	-3.75 V
100	-5.00 V
101	-6.25 V
110	-7.50 V
111	-8.75 V

Related Worksheet:

Digital‑to‑Analog Conversion Worksheet

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