Effective number of bits (ENOB) is a measure of the real
dynamic range
Dynamics (from Greek δυναμικός ''dynamikos'' "powerful", from δύναμις ''dynamis'' " power") or dynamic may refer to:
Physics and engineering
* Dynamics (mechanics), the study of forces and their effect on motion
Brands and ent ...
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 (signal processing), digi ...
(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.
DACs are commonly used in musi ...
(DAC), or associated circuitry. Although the resolution of a converter may be specified by the number of
bit
The bit is the most basic unit of information in computing and digital communication. 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 represented as ...
s used to represent the analog value, real circuits however are imperfect and introduce additional
noise
Noise is sound, chiefly unwanted, unintentional, or harmful sound considered unpleasant, loud, or disruptive to mental or hearing faculties. From a physics standpoint, there is no distinction between noise and desired sound, as both are vibrat ...
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. The ENOB describes the effective resolution of a real converter in terms of the number of bits an ideal converter with the same resolution would have.
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.
Definition
An often used definition for ENOB is
[, Equation 1.]
:
where
* ENOB is given in bits
*
SINAD
Signal-to-noise and distortion ratio (SNDR) is a term used for a set of measures of the quality of a signal from a communications device. These include SINAD and SINADR.
SINAD
The signal-to-noise and distortion ratio (SINAD) is a measure of the ...
(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 or root-power quantity on a logarithmic scale. Two signals whose levels differ by one decibel have a ...
(a log
10 representation) to bits (a log
2 representation),
[.]
* the 1.76 term comes from quantization error in an ideal ADC.
This definition compares the SINAD of an ideal converter of ENOB bits with the SINAD of the converter being tested. The ENOB may be fractional. So while an ADC may use 12 bits, its ENOB may only be 9.5, corresponding to a hypothetical ideal converter with 9.5 bits.
Effective resolution bandwidth
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 at which a real ADC takes a sample of its input varies from sample to sample. Because the input signal changes, 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 change 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).
Notes
References
*
*
*
External links
Video tutorial on ENOBfrom Texas Instruments
The Effective Number of Bits (ENOB)(PDF) April 2011
Rohde & Schwarz - This application note explains how to measure the oscilloscope ENOB.
{{DEFAULTSORT:Enob
Digital signal processing
Noise (electronics)
Measurement