Question 7.18: A student writes the drain flicker noise current of a MOS de...

A student writes the drain flicker noise current of a MOS device as \left[K /\left(W L C_{o x} f\right)\right] g_m^2=\left[K /\left(W L C_{o x} f\right)\right] \left(\sqrt{2 \mu_n C_{o x}(W / L) I_D}\right)^2=2 K \mu_n I_D /\left(L^2 f\right) , concluding that the flicker noise current is independent of W. Explain the flaw in this argument.

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A fair comparison must keep both the overdrive and I_D constant as W changes. (If we allow V_{GS} − V_{T H} to change, then the drain voltage headroom also changes.). Thus, we can express the drain flicker noise current as \left[K /\left(W L C_{o x} f\right)\right]\left(4 I_D^2\right) /\left(V_{G S}-V_{T H}\right)^2 , which reveals that the noise current decreases as W L increases.

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