Discussion in 'Homework Help' started by dacrazyazn, Mar 30, 2009.

1. ### dacrazyazn Thread Starter Member

Mar 30, 2009
22
0
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.

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2. ### t_n_k AAC Fanatic!

Mar 6, 2009
5,448
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Hi,

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

3. ### dacrazyazn Thread Starter Member

Mar 30, 2009
22
0
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.

4. ### t_n_k AAC Fanatic!

Mar 6, 2009
5,448
783
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.

5. ### dacrazyazn Thread Starter Member

Mar 30, 2009
22
0
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!

6. ### t_n_k AAC Fanatic!

Mar 6, 2009
5,448
783
You should be able to go from here ...

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7. ### Ron H AAC Fanatic!

Apr 14, 2005
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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.

8. ### dacrazyazn Thread Starter Member

Mar 30, 2009
22
0
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!