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Equation 3 · Part 1 · How Edge AI Electronics and Sensor Systems Actually Work

Symbol Δ^2

Δ2/12\Delta^2/12
Δ2\Delta^2

What this part means

Δ^2 is squared: multiply the underlying quantity by itself. The square is a mathematical operation, not a second independent variable.

Its job in the formula

Δ^2 is squared: multiply the underlying quantity by itself. The square is a mathematical operation, not a second independent variable.

The passage around this formula

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 Δ\Delta = VFSV_{FS}/2^{N} , and that rounding itself injects noise, with power approximately Δ2\Delta^2/12 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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Learn the underlying idea

An exponent tells how a base is used in multiplication. In x³, x is the base and 3 is the exponent: x³ = x × x × x.

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Sources cited in the surrounding passage

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