CALCULATORS / SIGNALS, SAMPLING AND DATA

Ideal ADC quantization-noise estimate calculator

Ideal uniform ADC quantization noise; full-scale uncorrelated error assumption.

signals-quantization-noise.napkin / editable

SCENARIO COMPARISON

Compare the numbers.

This source describes an analytical model. Its quantities and checks are the view.

Scenario	stepV	noiseRmsmV	idealSineSnrDb
	0.000805664	0.232575	74.0081
	0.000644531	0.18606	74.0081

All calculated quantities are listed with the inputs. Switch to Source to inspect the equations.

SCENARIOS / CALCULATED VALUESSAME SOURCE

Change an input to see the consequences.

quantization noise budget0.23 mV✓ passes

BASELINE INPUTS

fullScale3.3 Vbits12

CALCULATED

step0.00080566 V

noiseRms0.23258 mV

idealSineSnrDb74.008

Edits change the baseline source.

THE SOURCE

Edits below update the same model.

# Ideal ADC quantization-noise estimate
# Scope: Ideal uniform ADC quantization noise; full-scale uncorrelated error assumption.
# Status: illustrative worked example; engineering review pending.
# Inputs are example values. Checks are editable example requirements, not standards.

fullScale = 3.3 V
bits = 12

step := fullScale/2^bits [V]
noiseRms := step/sqrt(12) [mV]
idealSineSnrDb := 6.0206*bits+1.7609

check quantization noise budget: noiseRms <= 0.3 mV

scenario alternative: fullScale = 2.64 V

Calculated from your source · not saved

Baseline · Baseline

quantization noise budget0.23 mV ✓ passes

alternative · alternative

quantization noise budget0.19 mV ✓ passes

Illustrative first-order example. Checks are editable requirements, not design standards. The broader topic may require additional equations, data, and validation.

Formula and units

This example uses the following equations. Input names and units match the editable source above.

step: step = fullScale/2^bits [V]
noise rms: noiseRms = step/sqrt(12) [mV]
ideal sine snr db: idealSineSnrDb = 6.0206*bits+1.7609

Original worked example

These are the baseline values in the downloadable source. Edits above let you test your own values.

Given

full scale: 3.3 V
bits: 12

Calculated

step: 0.000805664 V
noise rms: 0.232575 mV
ideal sine snr db: 74.0081

Assumptions and limits

Ideal uniform ADC quantization noise; full-scale uncorrelated error assumption.

The requirement checks use the limits written in this example. Passing a check does not establish that the model covers every load, material behavior, or operating condition in a real design.

Download this .napkin example ↓

Take it further with your agent

Napkin keeps the inputs, equations, checks and assumptions together in one study. Your agent sets it up; you change the numbers.

Try with Claude ↗

codex 'Use Napkin (https://napkin.engineering/mcp, or the local Napkin plugin) to build a study: Ideal ADC quantization-noise estimate. Inputs: bit depth; range; signal model; bandwidth. Outputs: conditional quantization-noise and ideal SNR. Model scope: Sampled-data models with stated bandwidth and noise assumptions. Read napkin_capabilities and the current snapshot. Ask me for the values that matter, label assumptions with units, author .napkin source, validate it and apply it with napkin_source using the current revision, then open the study. Add checks for the limits I supply. Keep unsupported analyses explicit.'

Claude needs the Napkin connector; Codex needs the Napkin plugin. Set up your agent ↗

The broader study

The topic brief below describes the broader scope. The worked example above states the particular calculation it implements.

Inputs: bit depth, range, signal model, bandwidth
Outputs: conditional quantization-noise and ideal SNR
Modes: calculate, compare, sweep
Drawing: Signal, samples and spectrum

EXECUTABLE WORKED EXAMPLE · FIRST-ORDER MODEL · CHECK THE SCOPE & ASSUMPTIONS