Quantization Noise Power

Compute ideal LSB step size, RMS quantization noise, noise power, and ideal SNR for uniform quantizers (ADC/DAC).

How to Use

  1. Select a workflow (Range + Bits, or LSB + Bits).
  2. Enter resolution (bits) and your full-scale range (peak-to-peak) or LSB size.
  3. Optionally enter sampling rate to view noise PSD and in-band noise.
  4. Open “Show Work” for formulas and step-by-step results.
Quantizer Readout
Ideal uniform quantization model (noise assumed uniformly distributed).
LSB (Δ)
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Noise RMS
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Noise Power
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Ideal SNR
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Note: —
Inputs & Settings
Ideal math. Tool stays deterministic and runs in your browser.
Common: 8, 10, 12, 14, 16, 24
Use Vpp for voltage-domain quantizers. dBFS option uses your reference amplitude below.
If provided, overrides range-based Δ in “LSB + Bits” mode.
Enables noise PSD (W/Hz) and in-band noise estimates (0…BW).
In-band noise assumes flat quantization noise PSD over 0…BW (BW ≤ Fs/2).
Used only for dBm/dBV/dBFS presentations; core math is unitless/voltage-domain.
Show Work (step-by-step)
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Work is shown in base terms (Δ, RMS, power). dB values are derived from selected references.

Reference Formulas (Ideal Uniform Quantization)

For an ideal uniform quantizer with step size Δ, quantization error is commonly modeled as uniformly distributed in [-Δ/2, +Δ/2] (when conditions for the model apply).

  • LSB step size: Δ = Vpp / 2^N (for an N-bit span across a peak-to-peak range)
  • Noise RMS (voltage-domain): e_rms = Δ / √12
  • Noise power (voltage-domain): P_n = e_rms^2 (or to watts using a load reference)
  • Ideal SNR for full-scale sine: SNR ≈ 6.02·N + 1.76 dB
  • White noise PSD (two-sided): S_e ≈ e_rms^2 / (Fs/2) (flat to Nyquist in the ideal model)
Real converters deviate due to nonlinearity, jitter, distortion, dither, filtering, and front-end noise.

FAQ

Is quantization noise always “white” and uniform?

Not always. The uniform/white model is an idealization that depends on signal conditions (e.g., adequate activity across codes, dither, and avoiding strong periodic correlation with the quantizer).

Why is there a 1.76 dB term in the ideal SNR equation?

It comes from comparing a full-scale sine’s RMS value to the RMS quantization noise of an ideal uniform quantizer.

What should I use for full-scale range?

Use the peak-to-peak input span that maps to the converter’s code range (after any gain/attenuation). For audio DAC/ADC discussions, full-scale is often expressed in dBFS relative to the maximum sine level.

Can this estimate noise in a bandwidth smaller than Nyquist?

Yes—if you enter sampling rate and bandwidth, the tool can estimate in-band noise by scaling the ideal flat PSD. This remains an approximation.

Tool Info

Last updated:

Updates may include unit support, improved references (dB), and edge-case handling.