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Question

Suppose we have an NMOS transistor that has $g_m=2 mS$ and $r_d = 5 \mathrm{k} \Omega$ for a Q point of $V_{GSQ} =2 V, I_{DQ}=4 mA,$ and $V_ {DSQ}= 10 V.$ Sketch the drain characteristics to scale for a small region around the Q point, say, for $v_{GS}=1.8,$ 2.0, and 2.2 V and for $9.0

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The drain characteristics for given NMOS transistor in range for $9 has slope of:

$\frac{1}{r_d}=\frac{\Delta i_D}{\Delta v_{DS}}|_{v_{GS}=2\ \text{V}}=0.0002$

It means that for a change in drain-to-source voltage for a volt, drain current will change for 0.2 mA. For a change in value of $v_{GS}$, the change in drain current for the same $v_{DS}$ is:

$g_m=\frac{\Delta i_D}{\Delta v_{GS}}|_{V_{DSQ}}=2\cdot 10^{-3}$

It means that for a change in gate-to-source voltage for a volt, drain current will change for 2 mA. The curves are described by following equations:

$i_D\ \text{[mA]}=0.2v_{DS}\ \text{[V]}+1.8$

$i_D\ \text{[mA]}=0.2v_{DS}\ \text{[V]}+2$

$i_D\ \text{[mA]}=0.2v_{DS}\ \text{[V]}+2.2$

for $9 The drain characteristics is shown in graph below

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