hey guys, this is my first post here and i really appreciate the time you put out to help me.. heres the problem.

"the OpAmp differentiator, with R=10kΩ and C=100pF has the input Vs(t)=2[sin(ωt)]u(t)V. Determine the frequency at which the OpAmp saturates at +15v or -15v.

 

Hi,

Have you made an attempt at a solution? If so please provide a copy of your work so far.

 

i have tried to get it started... so far i got.

KCL around the neg end of the OpAmp (node A).
(the lower left hand side resistor, i called R1 and the other one i called R2)

i2-iC-i1=iN (i2 correspond with R2 same with 1 and C)
i2=(Vo-Va)/R2
iC=C*d(Va)/dt
i1=Va/R1

now i thought since the opamp needs to be ideal*?* i set iN=0 as well as Va=0

This brought me to the problem. because if Va equals to zero, then i would have zero for i1 and iC.

i dont know for sure if i am going about this correctly, i was trying to follow an example from the book and modify the work to fit this solution. Please help...

 

In fact the Op-Amp configuration requires the voltage Va(t) at node A to equal Vs(t) - rather than zero as you have suggested. Assuming the current into Op-Amp at node A is zero is fine.

You should be able to solve your equations given these conditions.

 

alright so i tried to solve it completely... and i got.

Va(t)=Vs(t)
Vs=2sin(ωt)u(t)V

-Vs/R1 + (Vo-Vs)/R2 - C*d(Vs)/dt = 0
(-2Vs + Vo)/R - C*d(Vs)/dt = 0 (since R1 and R2 are the same)
∫(-2Vs + Vo)/R*dt=∫C*d(Vs) (separated the two and multiplied by dt)
Vo/R*t - 4/R∫sin(ωt)*dt=CVs
Vo/R*t - (4/ωR)*cos(ωt)=2Csin(ωt)

and im stuck here. can someone also explained what the u(t) in Vs is for? Thanks!

 

You should be able to go from here ...

 

You should be able to go from here ...

I Got the answer by using the gain equation:

Av=Zf/Zs + 1

I plugged my answer for ω into your equation for Vo and got 15V peak, verifying both approaches.

 

Thank you soo much guys! i found my problem... i was looking at the WRONG DIAGRAM for the WRONG PROBLEM in the book. >.< ive done this a lot of times. but def it was outside of what we were learning. Thank you to Ron and T_N_K you guys are awesome. this is a great community btw! i've gotten so much just reading the "textbook" on this site! Thanks again!