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How do we calculate effective resistance of a NMOS, operating in linear region across drain and source?

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    \$\begingroup\$ I recall the formula Re = 1/GM with GM = K * W/L * Ve, where K = MU*Cox, and Ve = Vgs - Vt; this was long channel physics mode; \$\endgroup\$ – analogsystemsrf Jul 3 '19 at 1:34
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answer

\$1/R_{ds}=g_m=\Delta I_{ds}/ \Delta V_{ds}\$ @ Vgs

While RdsOn is often rated in data sheets for ~ 2.5 to 3 x Vgs(th) aka Vt the threshold conduction at some std current like Ids=xxx uA with Vgs=Vds.

Thus gm reduces as Vgs reduces towards Vt yet if Load , Rd >> Rds then Vds is near 0. So maximum voltage gain is when Rd is near Rds which changes with Vgs and you know that for AC V gain = -Vds/Vgs= -gm*Rd.

Y Question

What is Vgs where the maximum small signal voltage gain is maximum?

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