Please help! Op Amp question

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

  1. dacrazyazn

    Thread Starter Member

    Mar 30, 2009
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    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.
     
  2. t_n_k

    AAC Fanatic!

    Mar 6, 2009
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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
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    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...
     
  4. t_n_k

    AAC Fanatic!

    Mar 6, 2009
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    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
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    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
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    You should be able to go from here ...
     
  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
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    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!
     
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