Effective number of bits (ENOB) is a measure of the

dynamic range Dynamic range (abbreviated DR, DNR, or DYR) is the ratio between the largest and smallest values that a certain quantity can assume. It is often used in the context of signals, like sound and light. It is measured either as a ratio or as a base-1 ...

of an

analog-to-digital converter In electronics, an analog-to-digital converter (ADC, A/D, or A-to-D) is a system that converts an analog signal, such as a sound picked up by a microphone or light entering a digital camera, into a digital signal. An ADC may also provide ...

(ADC),

digital-to-analog converter In electronics, a digital-to-analog converter (DAC, D/A, D2A, or D-to-A) is a system that converts a digital signal into an analog signal. An analog-to-digital converter (ADC) performs the reverse function. There are several DAC architec ...

, or their associated circuitry. The resolution of an ADC is specified by the number of

bit The bit is the most basic unit of information in computing and digital communications. The name is a portmanteau of binary digit. The bit represents a logical state with one of two possible values. These values are most commonly represente ...

s used to represent the analog value. Ideally, a 12-bit ADC will have an effective number of bits of almost 12. However, real signals have noise, and real circuits are imperfect and introduce additional

noise Noise is unwanted sound considered unpleasant, loud or disruptive to hearing. From a physics standpoint, there is no distinction between noise and desired sound, as both are vibrations through a medium, such as air or water. The difference arise ...

and

distortion In signal processing, distortion is the alteration of the original shape (or other characteristic) of a signal. In communications and electronics it means the alteration of the waveform of an information-bearing signal, such as an audio signal ...

. Those imperfections reduce the number of bits of accuracy in the ADC. The ENOB describes the effective resolution of the system in bits. An ADC may have a 12-bit resolution but the effective number of bits, when used in a system, may be 9.5. ENOB is also used as a quality measure for other blocks such as sample-and-hold amplifiers. Thus analog blocks may be included in signal-chain calculations. The total ENOB of a chain of blocks is usually less than the ENOB of the worst block. The frequency band of a signal converter where ENOB is still guaranteed is called the effective resolution bandwidth and is limited by dynamic quantization problems. For example, an ADC has some aperture uncertainty. The instant a real ADC samples its input varies from sample to sample. Because the input signal is changing, that time variation translates to an output variation. For example, an ADC may sample 1 ns late. If the input signal is a 1 V sinewave at 1,000,000 radians/second (roughly 160 kHz), the input voltage may be changing by as much as 1 MV/s. A sampling time error of 1 ns would cause a sampling error of about 1 mV (an error in the 10th bit). If the frequency were 100 times faster (about 16 MHz), then the maximum error would be 100 times greater: about 100 mV on a 1 V signal (an error in the third or fourth bit).

Definition

An often used definition for ENOB is, Equation 1. :

\mathrm = \frac,

where * ENOB is given in bits *

SINAD Signal-to-noise and distortion ratio (SINAD) is a measure of the quality of a signal from a communications device, often defined as : \mathrm = \frac, where P is the average power of the signal, noise and distortion components. SINAD is usually ex ...

(signal, noise, and distortion) is a power ratio indicating the quality of the signal in dB. * the 6.02 term in the divisor converts

decibels The decibel (symbol: dB) is a relative unit of measurement equal to one tenth of a bel (B). It expresses the ratio of two values of a Power, root-power, and field quantities, power or root-power quantity on a logarithmic scale. Two signals whose ...

(a log₁₀ representation) to bits (a log₂ representation),

6.02 \approx 20 \log_2

. * the 1.76 term comes from quantization error in an ideal ADC. 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.

Notes

References

* * *

External links

Video tutorial on ENOB
from Texas Instruments
The Effective Number of Bits (ENOB)
(PDF) April 2011

Rohde & Schwarz Rohde & Schwarz GmbH & Co KG (, ) is an international electronics group specializing in the fields of electronic test equipment, broadcast & media, cybersecurity, radiomonitoring and radiolocation, and radiocommunication. The company provides ...

- This application note explains how to measure the oscilloscope ENOB. {{DEFAULTSORT:Enob Digital signal processing Noise (electronics) Measurement