ADC Quantization Noise Calculator
Calculate theoretical SNR (signal-to-noise ratio from quantization only), LSB size, RMS quantization noise voltage, and noise spectral density for an N-bit ADC. Includes oversampling SNR gain.
How to Use
- Enter ADC resolution in bits (typically 8–24).
- Enter the full-scale voltage range (unipolar = V<sub>ref</sub>; bipolar = 2·V<sub>ref</sub>).
- Optionally enter sampling rate and oversampling ratio (OSR) for noise density calculation.
- Results: theoretical SNR in dB, LSB size, RMS quantization noise, noise spectral density, and oversampling gain.
Show Work
Formulas
History of Quantization Theory
Bernard Widrow\'s 1956 MIT doctoral thesis "A Study of Rough Amplitude Quantization by Means of Nyquist Sampling Theory" formalized the statistical treatment of quantization noise, establishing that for "busy" signals the error behaves as white noise uniformly distributed over ±½ LSB. The famous 6.02·N + 1.76 dB formula falls directly out of this analysis — it\'s the ratio of signal RMS to quantization noise RMS expressed in dB.
Oversampling and decimation as a resolution-enhancement technique was formalized by Inose and Yasuda in 1962, who built the first Σ-Δ (sigma-delta) modulator. Their 1-bit noise-shaping converter at high oversampling ratios produced effective resolution far beyond any flash or SAR ADC of the era. Commercial Σ-Δ ADCs from Analog Devices (AD1700 series) and Burr-Brown in the 1980s made 18–24-bit resolution practical for instrumentation and audio.
Modern ADCs routinely approach the theoretical SNR limit. Precision Σ-Δ parts like the LTC2508-32 (32-bit) achieve 145+ dB SNR — less than 10 dB below the theoretical ideal of 148 dB for 24-bit. The gap is primarily thermal noise and reference drift; further improvements require chopped references, low-noise bias circuits, and active temperature compensation.
About This Calculator
Enter ADC resolution, full-scale voltage, and optionally sample rate and oversampling ratio. The tool computes theoretical SNR (quantization-only), LSB size, RMS quantization noise voltage, and noise spectral density. If an OSR is provided, it adds the oversampling SNR gain.
These are theoretical limits. Real ADCs fall 1–3 dB short due to reference noise, clock jitter, and nonlinearity. Actual SNR and ENOB appear in datasheets as \"Typical SINAD\" specs at rated input frequency — usually under idealized conditions (nearly full-scale sine, optimal input bandwidth). For worst-case performance, check SNR vs. input amplitude and temperature plots. Everything runs client-side.
Frequently Asked Questions
Where does 6.02·N + 1.76 come from?
Quantization noise has a uniform distribution over ±½ LSB, giving RMS value LSB/√12. A full-scale sine wave has RMS value (2<sup>N</sup>·LSB)/(2√2). The SNR is 20·log(signal/noise) = 20·log(2<sup>N</sup> · √12 / (2√2)) = 20·log(2<sup>N</sup>·√(3/2)) = 6.02·N + 1.76 dB. Every added bit increases SNR by 6.02 dB.
What does oversampling do to SNR?
Oversampling spreads the quantization noise over a wider frequency range; after digital low-pass filtering at the signal band, only a fraction of the noise remains. SNR improves by 10·log(OSR) — 4× OSR → +6 dB → +1 effective bit, 16× → +12 dB → +2 bits, etc.
Difference between SNR and SNDR?
SNR includes only noise (white quantization noise in theory). SINAD (or SNDR) includes noise + distortion — real-world harmonic distortion from nonlinearities. Datasheets quote both. ENOB is derived from SINAD: ENOB = (SINAD − 1.76) / 6.02.
What's noise spectral density?
Quantization noise power (LSB²/12) spread across the Nyquist bandwidth (f<sub>s</sub>/2). NSD = (LSB²/12) / (f<sub>s</sub>/2) with units V²/Hz. Useful for comparing ADC noise to analog input noise, or estimating the noise in a specific signal bandwidth.
Why is quantization noise treated as white?
For "busy" signals (spanning many LSBs, changing sample-to-sample), the error is effectively random and uniformly distributed over ±½ LSB. For slow or near-DC signals, quantization error is correlated — periodic pattern noise, not white. That\'s why dithering (adding small noise) helps randomize it for low-level signal fidelity.
Common Use Cases
Audio ADC Selection
24-bit ADC: theoretical SNR = 146 dB. Real ADCs achieve 110–120 dB (ENOB ~19) due to thermal noise and reference drift. Still plenty for any audio use.
MCU Built-in ADC
ESP32 12-bit ADC: theoretical SNR = 74 dB, typical measured SNR 70 dB (ENOB ~11). Adequate for temperature and battery monitoring.
Seismic / Geophysical Monitoring
24-bit Σ-Δ at 500 Hz OSR gains 27 dB beyond 6.02·N+1.76, reaching 170+ dB effective SNR at sub-Hz signal bandwidths.
Oscilloscope ADC
8-bit flash ADC at 1 Gsps: SNR = 50 dB (ENOB ~8). Trade off resolution for speed; acceptable for waveform display.
Instrumentation DMM
22-bit integrating ADC in a 6½-digit multimeter: theoretical 134 dB SNR; measured ~120 dB limited by input amp and reference noise.
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