DAC Resolution Calculator Formula

Understand the math behind the dac resolution calculator. Each variable explained with a worked example.

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Formulas Used

Step Size (LSB)

step_size_mv = v_ref / pow(2, bits) * 1000

Output Voltage

v_output = digital_code * v_ref / pow(2, bits)

Maximum Output

v_max = (pow(2, bits) - 1) * v_ref / pow(2, bits)

Variables

VariableDescriptionDefault
bitsDAC Bits(bits)10
v_refReference Voltage(V)5
digital_codeDigital Input Code512

How It Works

DAC Resolution

Formulas

Step Size = V_ref / 2^N

V_out = Code x V_ref / 2^N

V_max = (2^N - 1) x V_ref / 2^N

The DAC converts a digital number into an analog voltage. Each increment of the digital code changes the output by one LSB.

Worked Example

10-bit DAC with 5 V reference, digital code = 512.

bits = 10v_ref = 5digital_code = 512
  1. 01Step size = 5 / 1024 = 4.883 mV
  2. 02V_out = 512 x 5 / 1024 = 2.500 V
  3. 03V_max = 1023 x 5 / 1024 = 4.995 V

Frequently Asked Questions

Why can the DAC not reach full Vref?

The maximum code is 2^N - 1, so V_max = Vref x (2^N-1)/2^N, which is one LSB below Vref.

What is glitch energy?

A brief output spike during code transitions caused by internal switch timing. It matters in high-speed and audio applications.

R-2R vs resistor string DAC?

R-2R ladder is compact and monotonic. Resistor string (thermometer) has guaranteed monotonicity and better DNL but more components.

Ready to run the numbers?

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