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Mosfet numerical with capacitor

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SouravGuha7850

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Can anyone plz help me in solving these two numericals?I have to plot Vx and Ix wrt time.The initial voltages of C1 and C2 are 1V and 3V respectively.
 

Ah Razavi's old intuitive exercises. It's commonly discouraged to give direct answers to these problems and let the student use critical thinking. But if you'd like the easy way there's always a solutions manual somewhere in the internet. But before you go there try solving it with a few hints.

For (a)
(1) capacitor charging and discharging is based on Cdv/dt. so we can surmise that Ix=-Cdvx/dt (negative for discharging)
(2) use node equations. Ix=I1+Id
(3) since there's a current source present, C1 charges indefinitely (so keep in mind transition from saturation to triode and take note on continuity)
(4) for razavi I think Vt=0.7V so keep in mind on drain current equation when transitioning from saturation to triode.

for (b)
(1) same charging/discharging principle.
(2) you'll see that Vgs=2-Vc1 so at some point the device will turn off and values will theoretically remain constant with time.
(3) Here c1 is charged by the drain current so Id=Cdvc1/dt.

Cheers. Happy Solving!

- - - Updated - - -

Wait, C1 is 1V and C2 is 3V? then (b) will first reverse polarity. (i.e. drain and source will exchange)
 
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