Equation 2 · How Edge AI Electronics and Sensor Systems Actually Work
What does this equation mean?
Read the formula alongside the article passage below. Each part has a deeper page with its role in the equation, the supporting passage and nearby citations.
This equation states an equality: the expressions on both sides have the same value under the article’s assumptions. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.
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Symbol Δ
Δ is part of the quantity the equation computes from the expression on the right.
Symbol V_FS
S is an input to the expression that computes the quantity on the left.
Symbol N
N is an input to the expression that computes the quantity on the left.
=
The expressions on both sides represent the same quantity under the stated assumptions.
See an illustrated explanation →subscript
The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.
superscript
A raised number can be a power. When it is a label or bound, it selects a case or the upper limit of a sum; the formula’s structure distinguishes these uses.
See an illustrated explanation →How to interpret it
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What the article says around this equation
Once the signal is a clean, conditioned voltage, it has to become a digital code, and that conversion is not free either. An analog-to-digital converter maps a continuous voltage onto one of 2^N discrete codes spaced by a quantization step = /2^{N} , and that rounding itself injects noise, with power approximately /12 spread across the sampled bandwidth. The industry-standard way to describe and test this — offset error, gain error, integral and differential nonlinearity, effective number of bits — is defined by IEEE Standard 1241, which exists precisely so that a converter from one vendor can be compared against another using the same measured definitions rather than…
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Once the signal is a clean, conditioned voltage, it has to become a digital code, and that conversion is not free either. An analog-to-digital converter maps a continuous voltage onto one of 2^N discrete codes spaced by a quantization step = /2^{N} , and that rounding itself injects noise, with power approximately /12 spread across the sampled bandwidth. The industry-standard way to describe and test this — offset error, gain error, integral and differential nonlinearity, effective number of bits — is defined by IEEE Standard 1241, which exists precisely so that a converter from one vendor can be compared against another using the same measured definitions rather than incompatible datasheet marketing language [ 12 ] . Many sensor front ends sidestep some quantization noise using oversampling: sampling far faster than the signal actually requires spreads the fixed quantization noise over a wider bandwidth, so that filtering back down to the signal band recovers roughly 10 decibels of signal-to-noise ratio for a plain oversampled converter, where OSR is the oversampling ratio — and considerably more once the converter also shapes that noise rather than merely spreading it. A 2018 sigma-delta ADC built for a digital MEMS vibration gyroscope demonstrates the payoff directly: a switched-capacitor design achieving 107.6 dB of dynamic range and 100.2 dB signal-to-noise ratio across a 2 kHz measurement bandwidth, at 3.2 milliwatts, specifically by using oversampling with noise shaping rather than a faster, dumber converter [ 11 ] .
Sources cited in the surrounding passage
- [12] IEEE Standard for Terminology and Test Methods for Analog-to-Digital Converters ↗
- [11] A High-Dynamic-Range Switched-Capacitor Sigma-Delta ADC for Digital Micromechanical Vibration Gyroscopes ↗
These citations give research context. Read each source to check which claims it supports.
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