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R-2R ladder DAC (4-bit)

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Objective

Convert a 4-bit digital code to an analog voltage with an R-2R resistor ladder: Vout = Vref · code / 16.

Procedure

Run with D3 = 1, D2 = 0, D1 = 1, D0 = 0.
Change the four bit batteries between 0 V and 5 V and compute the expected output.

Theory

Each bit contributes Vref·2^i/16 at the output node because of the ladder's binary attenuation. For code 1010 (decimal 10) and Vref = 5 V: Vout = 5 · 10/16 = 3.125 V.

Questions to answer

How many resistor values are needed for an N-bit R-2R DAC?

Components used

4 × Battery / DC source, 8 × Resistor 220 ohm 1/4W

About the model

Ideal wires; component models as listed in the catalogue (no parasitics, no temperature drift). Built without a breadboard so the schematic stays readable.