Can soomebody help me for this question of Microelectornics

This is from Miscroelectronics Circuits by Sedra Smith
6th Edition

The question is 5-26

plz help me to solve it

hey,moonnightingale
here's my answer , I hope it can be helpful.
As the nmos is in the "Saturation Region" and the current source is a dc source, it means:
Id=0.5 * Un * Cox * (w/L) * (Vgs-Vth)^2 * (1+λVds)
and here ,Vgs=Vds :
Id=0.5 * Un * Cox * (w/L) * (Vds-Vth)^2 * (1+λVds)

the right part of the equation has only one unknown, Vds.

for convenience ,before Sketching the curve for Vds versus Id, I first think about the curve for Id versus Vds.

so Id is a function of Vds.
it's very easy to notice that the function has the value of zero when vds = vth.
derive the first derivative and second derivative for the function above.
in order to make it simple ,I substitute some numbers into the function.
I suppose vth=0.7, λ=0.1.
from the first derivative , I know the extreme value of the function happens when vds=0.65 < 0.7.
this means the function is always increasing when vds>vth.
from the second derivative , I know the function is concave upward when Vds>vth.

so...the graph for Id vesus Vds (when vds>vth) can be easily sketched .

and ....finally you can get the graph you need by rotating the graph.


if you want to know more Details about Curve Sketching, refer to Section 4.5 of James Stewart 's "Calculus."

regards.
alex,