page_title: Analog-to-digital converter
section_title: Quantization error
hierarchical_section_title: Analog-to-digital converter / Explanation / Resolution / Quantization error
caption_attribution_description: By Megodenas - Schéma de conversion AD -&gt; DA d'un son Schema of Analog-Digital and Digital-Analog sound Conversion dun son analogique en numérique et numérique en analogique 3 étapes / 3 steps
context_page_description: In electronics, an analog-to-digital converter 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 an isolated measurement such as an electronic device that converts an input analog voltage or current to a digital number representing the magnitude of the voltage or current. Typically the digital output is a two's complement binary number that is proportional to the input, but there are other possibilities.
  There are several ADC architectures. Due to the complexity and the need for precisely matched components, all but the most specialized ADCs are implemented as integrated circuits. These typically take the form of metal–oxide–semiconductor mixed-signal integrated circuit chips that integrate both analog and digital circuits.
  A digital-to-analog converter performs the reverse function; it converts a digital signal into an analog signal.
context_section_description: Quantization error is introduced by the quantization inherent in an ideal ADC. It is a rounding error between the analog input voltage to the ADC and the output digitized value. The error is nonlinear and signal-dependent. In an ideal ADC, where the quantization error is uniformly distributed between −1/2 LSB and +1/2 LSB, and the signal has a uniform distribution covering all quantization levels, the Signal-to-quantization-noise ratio (SQNR) is given by
  where Q is the number of quantization bits.  For example, for a 16-bit ADC, the quantization error is 96.3 dB below the maximum level.
  Quantization error is distributed from DC to the Nyquist frequency. Consequently, if part of the ADC's bandwidth is not used, as is the case with oversampling, some of the quantization error will occur out-of-band, effectively improving the SQNR for the bandwidth in use.  In an oversampled system, noise shaping can be used to further increase SQNR by forcing more quantization error out of band.
caption: Analog to digital conversion as shown with fig. 1 and fig. 2.
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