DAC Scaling

Map digital codes to analog outputs and quantify rounding error.

Formulas

D = 2ᴺ or 2ᴺ − 1; Vdac = code × Vref / D

Vout = G × Vdac + Voffset; output step = G × Vref / D

Required code = clamp(round[(Vdesired − Voffset) / output step], 0, 2ᴺ − 1)

Quantization error = achieved output at required code − Vdesired

Model & assumptions

Ideal unipolar voltage DAC plus positive external gain. Amplifier supply limits, settling, offset error, and INL are excluded.

Ideal LSB uses a 2ᴺ denominator; endpoint mode reaches Vref at the highest code. Choose the convention from the actual datasheet.

Example with default inputs

Final analog output

3.3 V

DAC pin output

1.65 V

Required DAC code

3,103 counts

Achievable desired output

4.99995 V

Output voltage per step

1.61133 mV

Quantization / clipping error

-48.8281 µV

Maximum analog output

6.59839 V