Tricky Circuit

A four-bit R–2R DAC

Turn four bits into a voltage

DAC means Digital to Analog Converter: it turns a number into a voltage. An R–2R ladder combines resistors of resistance R and twice R. A bit is 0 or 1. LSB (Least Significant Bit) has weight 1; MSB (Most Significant Bit) has weight 8 here. Four bits select 16 voltage levels.

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EXPERIMENT BENCH

Change the circuit settings, predict the readings, then check a challenge. These are learning models, with the assumptions explained in each lesson.

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How it works

Ideal four-bit voltage ladder with a buffer, a circuit that follows voltage without loading the ladder. The output is unloaded. Reference Vref is 1–5 V. Resistor errors, switch glitches, settling time and output-current limits are omitted.

b0 to b3 are input bits with weights 1, 2, 4 and 8. Code is their weighted sum. Vout is output voltage; Vref is reference voltage. One LSB step is Vref/16. Code 15 is one step below Vref, not equal to it.

Difficulty

  1. Build · Observe

    Power on at Vref = 5 V. Set only b3 = 1, code 8, to obtain 2.5 V.

    Need a hint?

    Vref=5 V; b3=1; b2=b1=b0=0 → 2.5 V

  2. Explore · Experiment

    Keep Vref = 5 V. Set b2 = b0 = 1 and the other bits to 0, code 5, for 1.5625 V.

    Need a hint?

    Vref=5 V; b2=b0=1; b3=b1=0 → 1.5625 V

  3. Solve it · Solve

    At Vref = 5 V set all four bits to 1, code 15. Reach 4.6875 V and explain the missing last step.

    Need a hint?

    Vref=5 V; b3=b2=b1=b0=1 → 4.6875 V

Extra reading and circuit recipes

A four-bit R–2R DAC

A digital controller stores numbers, while an analog circuit responds to voltage. A resistor ladder is a bridge between them: switches choose fractions of a reference and the output adds those fractions.

code = b0 + 2b1 + 4b2 + 8b3; Vout = Vref × code/16; ΔV = Vref/16

At 5 V, one step is 0.3125 V. The highest code is 15 steps, or 4.6875 V. This small staircase has no values between its steps unless another circuit changes the output.

A useful connection

The ladder needs only two resistor values. Accurate ratios matter more than choosing a magical absolute resistance.

A surprising detail

Adding a bit doubles the number of codes and halves the ideal voltage step at the same reference.

A useful trap to avoid

Sixteen codes run from 0 to 15. Dividing by 15 would make this model’s transfer equation wrong.

At code 8, Vref changes from 5 V to 2 V. Vout becomes…

  1. 1 V
  2. 2 V
  3. 2.5 V
Read more

Code 8 selects half the reference: 2 × 8/16 = 1 V.

Half the reference

Use only the most significant bit.

Code 8 produces 2.5 V at a 5 V reference.

A tiny first step

Use only the least significant bit.

Code 1 produces 0.3125 V at a 5 V reference.

Try another change

Compare code 7 (0111) with code 8 (1000). Many bits change, but the ideal voltage rises by only one step. Real switches can briefly produce a glitch, which this model omits.

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