Effective number of bits

Effective number of bits (ENOB) is a measure of the dynamic performance of an analog-to-digital converter (ADC) and its associated circuitry. The resolution of an ADC is specified by the number of bits used to represent the analog value, in principle giving 2^N signal levels for an N-bit signal. However, all real ADC circuits introduce noise and distortion. ENOB specifies the resolution of an ideal ADC circuit that would have the same resolution as the circuit under consideration.

ENOB is also used as a quality measure for other blocks such as sample-and-hold amplifiers. This way, analog blocks can be easily included in signal-chain calculations as the total ENOB of a chain of blocks is usually below the ENOB of the worst block.

Definition

An often used definition for ENOB is^[1]

$\mathrm{ENOB} = \frac{\mathrm{SINAD}-1.76}{6.02}$,

where all values are given in dB and:

• SINAD is the ratio indicating the quality of the signal.
• The 6.02 term in the divisor converts decibels (a log₁₀ representation) to bits (a log₂ representation).^{[note 1]}
• The 1.76 term comes from quantization error in an ideal ADC.^{[note 2]}

This definition compares the SINAD of an ideal ADC or DAC with a word length of ENOB bits with the SINAD of the ADC or DAC being tested.

See also

• Signal-to-noise ratio

Notes

1. $6.02 \approx 20 \log_{10}2$
2. $1.76 \approx 10 \log_{10}\left( 3/2 \right)$^[2]

References

1. Kester 2009, p. 5, Equation 1.
2. Eq. 2.8 in "Design of multi-bit delta-sigma A/D converters", Yves Geerts, Michiel Steyaert, Willy M. C. Sansen, 2002.

• Gielen, Georges (2006). Analog Building Blocks for Signal Processing. Leuven: KULeuven-ESAT-MICAS.
• Kester, Walt (2009), Understand SINAD, ENOB, SNR, THD, THD + N, and SFDR so You Don't Get Lost in the Noise Floor (PDF), Tutorial, Analog Devices, MT-003
• Maxim (December 17, 2001), Glossary of Frequently Used High-Speed Data Converter Terms, Application Note, Maxim, 740

External links

• Video tutorial on ENOB from Texas Instruments
• The Effective Number of Bits (ENOB) - This application note explains how to measure the oscilloscope ENOB.