ENOB

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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.

1 Example
2 Definition
3 References
4 See also

[edit] 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) V

The 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) LSB

This 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.

[edit] 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.