Question 29.5: Determine the tolerance of the MSB current source on a 10-bi......

CMOS Circuit Design, Layout, and Simulation [1366182]

Determine the tolerance of the MSB current source on a 10-bit binary-weighted current source array with a unit current source of 1 μA, which will result in a worst-case DNL that is less than ½ LSB.

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Since Eq. (29.30) defines the maximum $\left|\Delta I\right|$ needed to keep the DNL less than ½ LSB, we must first use this equation,

$\left|\Delta I\right|_{m a x,D N L}=\frac{0.5I}{2^{N}-1}=\frac{I}{2^{N+1}-2}$ (29.30)

|\Delta I|_{m a x,D N L}=\frac{1\times10^{-6}}{2^{11}-2}=0.4888\,\,\mathrm{nA}

For a 10-bit DAC, the MSB current source will have a value that is $2^9$ times larger than the unit current source, or 0.512 mA. Therefore, the range of values for which this array will have a DNL that is less than ½ LSB is

0.51199995\;\mathrm{mA}\leq I_{MSB}\leq0.5120004888\,\mathrm{mA}

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