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Suppose we have an NMOS transistor that has gm=2mSg_m=2 mS and rd=5kΩr_d = 5 \mathrm{k} \Omega for a Q point of VGSQ=2V,IDQ=4mA,V_{GSQ} =2 V, I_{DQ}=4 mA, and VDSQ=10V.V_ {DSQ}= 10 V. Sketch the drain characteristics to scale for a small region around the Q point, say, for vGS=1.8,v_{GS}=1.8, 2.0, and 2.2 V and for 9.0<vDS<11.0V.9.0<v_{DS}<11.0 V.

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The drain characteristics for given NMOS transistor in range for 9<vDS<119<v_{DS}<11 has slope of:

1rd=ΔiDΔvDSvGS=2 V=0.0002\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 vGSv_{GS}, the change in drain current for the same vDSv_{DS} is:

gm=ΔiDΔvGSVDSQ=2103g_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:

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

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

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

for 9<vDS<119<v_{DS}<11 The drain characteristics is shown in graph below

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