ADC · DAC Resolution & SNR
From the resolution in bits, the reference voltage and the sample rate, it derives the size of one LSB, the ideal full-scale SNR, the dynamic range and the Nyquist frequency. Enter a measured SNR or SINAD to get the effective number of bits (ENOB). Demonstrative tool.
ADC/DAC resolution & SNR tool
1 · Converter parameters
Ideal SNR and dynamic range hold for a full-scale sine with quantization noise only (ideal converter). The ENOB needs a SINAD measured on the real device; an SNR yields noise-equivalent bits instead.
Results
- 1 LSB size
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- 1 LSB [µV]
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- Ideal SNR (full-scale)
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- Dynamic range
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- Nyquist frequency
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- ENOB (from measured SINAD)
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enter a measured SINAD to compute the ENOB
How it works
What are quantization and the LSB?
An N-bit converter splits the full-scale range Vref into 2ᴺ equal steps: the smallest is the LSB = Vref/2ᴺ, the smallest resolvable voltage change. Each extra bit halves the LSB — from 12 to 16 bits it shrinks 16× — so high resolution demands clean references and a low noise floor.
An N-bit converter splits the full-scale input range Vref into 2ᴺ equal steps. The smallest step is the Least Significant Bit (LSB): the smallest voltage change the converter can resolve, and it sets the quantization "grid step".
Each extra bit halves the LSB: at the same Vref, going from 12 to 16 bits shrinks the LSB by 16×. That is why high resolution demands clean references and a low noise floor — otherwise the last bits drown in noise.
Where does 6.02·N + 1.76 come from?
Rounding to the quantization grid introduces an error, modelled as uniform noise over ±½ LSB with power LSB²/12. Compared with a full-scale sine’s power, in dB it gives the ideal SNR = 6.02·N + 1.76 dB. The 6.02 = 20·log₁₀(2) term is the gain per bit; the +1.76 dB comes from the sine/noise shape ratio. It is an unbeatable theoretical ceiling.
Rounding a continuous signal to the quantization grid introduces an error. Modelled as white noise uniform over ±½ LSB, its power is LSB²/12 (the variance of a uniform distribution). A full-scale sine has power (Vref/2)²/2. The ratio of the two powers, in dB, gives the ideal SNR:
The 6.02 = 20·log₁₀(2) term is the SNR gain per added bit; the +1.76 dB = 10·log₁₀(1.5) comes from the shape ratio between the sine and the uniform noise. It is a theoretical ceiling: no real converter beats it.
For an ideal converter, limited only by quantization noise, the dynamic range numerically equals this full-scale SNR. In real devices distortion and spurs make the two diverge.
What are ENOB and SINAD?
A real converter does not reach its theoretical SNR: thermal noise, clock jitter, non-linearity and distortion erode it. The ENOB comes from the SINAD, not from the SNR: SINAD puts both noise and distortion in the denominator, SNR only noise. ENOB = (SINAD − 1.76)/6.02. A “16-bit” ADC with a 90 dB SINAD has ENOB ≈ 14.7 bits: that is the figure of merit to compare converters with, not the nominal resolution.
A real converter does not reach its theoretical SNR: thermal noise, clock jitter, non-linearity and distortion erode it. By measuring the SINAD (Signal-to-Noise-And-Distortion, which also includes harmonics) you invert the formula and obtain the effective number of bits, ENOB:
A "16-bit" ADC with a 90 dB SINAD has an ENOB of about 14.7 bits: the last bits carry no information, they are noise. ENOB is the figure of merit to use when comparing converters — more than the nominal resolution.
What are Nyquist and aliasing?
Sampling at rate fs, only components below half of fs — the Nyquist frequency (f_Nyq = fs/2) — can be represented unambiguously. Anything, signal or noise, above Nyquist folds back into the useful band as an alias, indistinguishable from a legitimate component: that is why an anti-aliasing filter always precedes an ADC.
Sampling at rate fs, only components below half of fs can be represented unambiguously: the Nyquist frequency. Anything (signal or noise) above Nyquist "folds back" into the useful band as an alias, indistinguishable from a legitimate component.
That is why an anti-aliasing filter always precedes an ADC, attenuating everything above Nyquist before sampling. Background and formulas in the tool wiki.