ADC Effective Number of Bits (ENOB), SINAD & Ideal SNR (6.02N + 1.76)

Nominal bit count and measured ENOB describe different things

An ideal uniform N-bit quantizer with a full-scale sine input has an approximate quantization SNR of 6.02N + 1.76 dB when noise is evaluated over the full Nyquist band. The coefficients are rounded. This is a reference model, not an unconditional ceiling for every bandwidth, oversampling scheme or noise-shaped converter.

Measured SINAD includes noise and distortion. The conventional full-scale-sine conversion ENOB = (SINAD - 1.76)/6.02 expresses performance as an equivalent bit count under those test conditions. It is not a count of physically removed output bits or a complete DC accuracy specification. Input amplitude/frequency, sample rate, bandwidth and test setup matter.

Use a consistent full-scale reference when comparing measurements. Smaller input amplitudes can require a correction under the measurement definition. The example does not infer that correction or claim that all 12-bit converters deliver the same effective resolution.

Convert SINAD to an equivalent bit count

B3 is SINAD in dB. E2 retains the unrounded ENOB; 68.5 dB gives approximately 11.0864 bits. B2 does not enter this equation. A negative ENOB or an ENOB above nominal N is not silently clamped: inspect the measurement and reference assumptions rather than treating that number as a new hardware resolution.

=IF(NOT(ISNUMBER(B3)),"Enter numeric SINAD",(B3-1.76)/6.02)

Calculate the ideal reference SNR

B2 is the nominal integer bit count. This exercise accepts 1 through 32 bits as an implementation range, not a statement about every available ADC. E3 gives 74 dB for 12 bits and 98.08 dB for 16 bits using the rounded constants.

=IF(NOT(ISNUMBER(B2)),"Enter numeric bit count",IF(OR(B2<1,B2>32,B2<>INT(B2)),"Use integer bits from 1 to 32",6.02*B2+1.76))

Calculate nominal LSB size from the entire input span

B4 is the full-scale input span in volts, meaning upper input limit minus lower input limit. It is not automatically the reference voltage: the relationship depends on the converter input configuration. A range of -3.3 to +3.3 V has a span of 6.6 V.

E4 calculates span/2^N in millivolts. With 3.3 V span and 12 bits, it is 0.8056640625 mV. Doubling the span doubles the step; adding one nominal bit halves it. ENOB is not substituted for N in this nominal code-step calculation. Offset, gain and nonlinearity errors are not included.

=IF(COUNT(B2,B4)<>2,"Enter numeric bits and span",IF(OR(B2<1,B2>32,B2<>INT(B2)),"Use integer bits from 1 to 32",IF(B4<=0,"Span must be positive",1000*B4/2^B2)))

Further reading

• Microchip — ADC Effective Number of Bits
• Analog Devices — Defining and Testing Dynamic Parameters in High-Speed ADCs