ENOB

In electrical engineering ENOB is an abbreviation for the "Effective Number of Bits" of a DAC or ADC. This concept is best explained by use of an example.

Example

The following are measurements of a 3-bit unipolar D/A convertor with reference voltage "V"_ref = 8 V:
*(-0.01, 1.03, 2.02, 2.96, 3.95, 5.02, 6.00, 7.08) VThe offset error in this case is -0.01 V or -0.01 LSB as 1 V = 1 LSB in this example. The gain error is $frac\{7.08+0.01\}\{1\}-frac\{7\}\{1\}\; =\; 0.09\; LSB$.

Correcting the offset and gain error, we obtain the following list of measurements:
*(0, 1.03, 2.00, 2.93, 3.91, 4.96, 5.93, 7) LSBThis allows the INL and DNL to be calculated:
* INL = (0, 0.03, 0, -0.07, -0.09, -0.04, -0.07, 0) LSB
* DNL = (0.03, -0.03, -0.07, -0.02, 0.05, -0.03, 0.07, 0) LSB

The absolute and relative accuracy can now be calculated. In this case, the effective number of bits (ENOB) absolute accuracy is calculated using the largest absolute deviation $D$, in this case 0.08 V:

$D\; =\; frac\{V\_\{ref\{2^\{ENOB\; Rightarrow\; ENOB\_\{abs\}\; =\; 6.64\; mathrm\{bits\}$

The effective number of bits relative accuracy is calculated using the largest relative (INL) deviation $d$, in this case 0.09 V.

$d\; =\; frac\{V\_\{ref\{2^\{ENOB\; Rightarrow\; ENOB\_\{rel\}\; =\; 6.47\; mathrm\{bits\}$

Note that the effective number of bits can be larger or smaller than the actual number of bits. When the ENOB is smaller than the ANOB, this means that some of the least significant bits of the result are inaccurate.

Definition

An often used definition for ENOB is$ENOB\; =\; frac\{SNR-1.76\}\{6.02\}$, where all values are given in dB, and SNR is the ratio of the wanted signal (the "fundamental") to the sum of all distortion and noise products, after the DC term is removed.

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

References

* cite book
last = Gielen
first = Georges
title = Analog Building Blocks for Signal Processing
publisher = KULeuven-ESAT-MICAS
location = Leuven
year = 2006

ee also

*Signal-to-noise ratio
*Digital-to-analog converter