Successive-approximation ADC: Difference between revisions

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When implemented as a real analog circuit, circuit inaccuracies and [[Noise (electronics)|noise]] may cause the binary search algorithm to incorrectly remove values it believes {{math|''V''<sub>in</sub>}} cannot be, so a successive-approximation ADC might not output the closest value. It is very important for the DAC to accurately produce all {{math|2<sup>''n''</sup>}} analog values for comparison against the unknown {{math|''V''<sub>in</sub>}} in order to produce a best match estimate. The maximal error can easily exceed several LSBs, especially as the error between the actual and ideal {{math|2<sup>''n''</sup>}} becomes large. Manufacturers may characterize the accuracy using an [[effective number of bits]] (ENOB) smaller than the actual number of output bits.
 
{{As of|2001}}, the component-matching limitations of the DAC generally limited the linearity to about 12&nbsp;bits in practical designs and mandated some form of trimming or calibration to achieve the necessary linearity for more than 12&nbsp;bits.<ref>{{Cite web |date=2001-10-02 |title=Understanding SAR ADCs: Their Architecture and Comparison with Other ADCs |url=https://www.analog.com/en/resources/technical-articles/successive-approximation-registers-sar-and-flash-adcs.html |url-status=live |archive-url=https://web.archive.org/web/20241118075147/https://www.analog.com/en/resources/technical-articles/successive-approximation-registers-sar-and-flash-adcs.html |archive-date=2024-11-18 |access-date=2025-01-03 |website=[[Analog Devices]]}}</ref> And since [[Johnson–Nyquist noise#Thermal noise on capacitors|kT/C noise]] is inversely proportional to capacitance, low noise demands a large input capacitance (which costs chip area and requires a more powerful drive buffer), which has motivated proposals around noise cancellation.<ref>{{Cite journal |last=Keerthy Kumar |first=Shashank |date=2023 |title=Design of a 13-Bit SAR ADC with kT/C noise cancellation technique |url=http://lup.lub.lu.se/student-papers/record/9142088 |journal=Master's Thesis published in [[Lund University]] Student Papers}}</ref> For comparison, for a {{math|1=''V''<sub>ref</sub>}} of 5&nbsp;V, the least significant bit of a 16-bit converter corresponds to 76&nbsp;µVμV, which is around the 64&nbsp;µμ[[Root mean square voltage|Vrms]] noise of a 1&nbsp;[[Picofarad|pF]] (large for on-chip) capacitor at [[room temperature]]. {{As of|2012}}, SAR ADCs are limited to 18&nbsp;bits, while [[delta-sigma]] ADCs (which can be 24&nbsp;bits) are better suited if more than 16&nbsp;bits are needed.<ref>{{Cite web |date=2012-05-07 |title=Understanding Noise, ENOB, and Effective Resolution in Analog-to-Digital Converters |url=https://www.analog.com/en/resources/technical-articles/noise-enob-and-effective-resoluition-in-analog-to-digital-converter-circuits--maxim-integrated.html |url-status=live |archive-url=https://web.archive.org/web/20240422221715/https://www.analog.com/en/resources/technical-articles/noise-enob-and-effective-resoluition-in-analog-to-digital-converter-circuits--maxim-integrated.html |archive-date=2024-04-22 |access-date=2024-12-28 |website=[[Analog Devices]]}}</ref> SAR ADCs are commonly found on [[microcontrollers]] because they are easy to integrate into a [[mixed-signal]] process, but suffer from inaccuracies from the internal reference voltage [[resistor ladder]] and [[Clock signal|clock]] and [[signal noise]] from the rest of the microcontroller, so external ADC chips may provide better accuracy.<ref>{{Cite web |last=Giovino |first=Bill |date=2018-11-21 |title=IoT Microcontrollers Have ADCs, but Know When to Choose and Apply an External ADC |url=https://www.digikey.com/en/articles/iot-microcontrollers-have-adcs-know-when-apply-an-external-adc |url-status=live |archive-url=https://web.archive.org/web/20240624010637/https://www.digikey.com/en/articles/iot-microcontrollers-have-adcs-know-when-apply-an-external-adc |archive-date=2024-06-24 |access-date=2025-01-03 |website=[[DigiKey]]}}</ref>
 
[[File:ADC animation 20.gif|thumb|alt=Successive approximation animation|Operation of successive-approximation ADC as input voltage falls from 5 to 0&nbsp;V. Iterations on the ''x'' axis, starting with the initial state at notch 1. Voltages on the ''y'' axis.|right]]