SNR ⇄ ENOB
Convert between signal-to-noise ratio and effective number of bits.
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The engineering
ENOB is the honest resolution: take the measured SINAD of the whole signal chain and ask how many ideal bits it equals. A '24-bit' module with 105 dB SINAD is a 17.1-bit instrument — the datasheet's marketing bits and the physics bits differ by the analog front end.
Measure SINAD with a near-full-scale sine; every dB you lose to noise and distortion costs a sixth of a bit.
Where this math comes from
The formula inverts Bennett's 1948 quantization-noise result: if an ideal N-bit converter gives 6.02N + 1.76 dB, then a measured ratio defines an effective N. The convention was formalized as converters became instruments, in IEEE Std 1057 (1994) and 1241 (2000) — the documents that ended datasheet bit inflation, mostly.
ENOB is now the single number that lets you compare a Σ-Δ audio part against a SAR DAQ chip honestly.
- 1948W. R. BennettQuantization noise law — the forward direction.
- 1994IEEE Std 1057Digitizer testing standardized; ENOB defined operationally.
- 2000IEEE Std 1241ADC test methods make ENOB the honest-resolution metric.
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