Which book is this problem from?

Discussion in 'Homework Help' started by jimmeh, Dec 2, 2011.

  1. jimmeh

    Thread Starter New Member

    Dec 2, 2011
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    Hey,

    I just wanted to ask which book is this question from.

    Thanks
     
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  2. Gump

    Member

    Jun 7, 2010
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    I don't have a clue, but to help others narrow things down:

    1) When you say book are you meaning a printed book or one of AAC e-books/worksheets?
    2) Where did you get the figure from?
    3) What is the actual question, as that's just a schematic, the question could be anything.
     
  3. jimmeh

    Thread Starter New Member

    Dec 2, 2011
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    a) I mean Textbook.
    b) From the quiz given by my instructor.
    c)It wants you to find an expression for Vo the resistance values in variable terms.
     
  4. Vahe

    Member

    Mar 3, 2011
    75
    9
    You should be able to write an expression for Vo in terms of the resistances and the voltage sources Va and Vb. One approach is to take one voltage source at a time while turning the other off (short circuit). This is basically the application of superposition.

    --Vahe
     
  5. Vahe

    Member

    Mar 3, 2011
    75
    9
    Sorry, it looks like I tried to give you clue to solve the problem rather than answering your inquiry -- which was about the source of the figure. I am not sure what course you are taking to be able to have a guess. If you taking an electronics course, I would look at Sedra and Smith or something like that. If this is your first elementary circuits course you may want to look at Alexander/Sadiku, Nillson, Hayt/Kemmerly, etc.

    --Vahe
     
  6. Georacer

    Moderator

    Nov 25, 2009
    5,142
    1,266
    It looks like a Sedra/Smith image, but I can't find it in my copy. Maybe I'm not looking hard enough, or I have a different edition.
     
  7. praondevou

    AAC Fanatic!

    Jul 9, 2011
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    It's from "Electrical-Engineering-Principles-and-Applications 5th edition" from Allan R. Hambley, chapter 14, page 706, figure P14.21.

    [​IMG]
     
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  8. jimmeh

    Thread Starter New Member

    Dec 2, 2011
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    @praondevou


    Thank you so much man !!!!
     
  9. jimmeh

    Thread Starter New Member

    Dec 2, 2011
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    This is the solution but, I cant seem to reach it in any way..

    I did

    vp-va/ra + vp-vb/rb = o

    Tried to isolate vo.. but couldnt reach the right answer.

    Help Anyone?
     
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  10. praondevou

    AAC Fanatic!

    Jul 9, 2011
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    The origine of the left part of the formula you posted you will find on Wikipedia under "non-inverting amplifier".
    R1 and R2 determine the voltage gain of the amplifier.

    The other part of the formula is simply giving you the voltage at the non-inverting input (where Ra and Rb are tied together).

    Both values are then multiplied.

    Separate both parts and try to resolve for the voltage at the noninverting input first.
     
  11. Vahe

    Member

    Mar 3, 2011
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    You can use superposition to do this problem, the total output voltage v_o is due to v_A alone with v_B turned off (short circuit) plus due to v_B alone with v_A turned off. Start with v_A alone and v_B=0 (short circuit).

    Under this condition, R_A and R_B form a voltage divider to produce the voltage at the noninverting terminal

    <br />
V_+ = \frac{R_B}{R_A + R_B} v_A<br />

    Now, you can note that R_1 and R_2 form an noninverting amplifier with gain of  1 + R2/R1 from V_+ to v_o and therefore

    <br />
v_o = \left( 1+ \frac{R_2}{R_1} \right) V_+ = \left( 1+ \frac{R_2}{R_1} \right) \frac{R_B}{R_A + R_B} v_A<br />

    You can also find the relation between V_+ and v_o by noting that V_-=V_+ and I_-=0 and writing a KCL equation at the inverting terminal.

    Now consider v_B alone and v_A=0 (short circuit).

    Under this condition, R_A and R_B once again form a voltage divider to produce the voltage at the noninverting terminal (however in this case R_A is grounded instead of R_B)

    <br />
V_+ = \frac{R_A}{R_A + R_B} v_B<br />

    As in the previous case, R_1 and R_2 form an noninverting amplifier with gain of  1 + R2/R1 from V_+ to v_o and therefore

    <br />
v_o = \left( 1+ \frac{R_2}{R_1} \right) V_+ = \left( 1+ \frac{R_2}{R_1} \right) \frac{R_A}{R_A + R_B} v_B<br />

    The total output voltage is the sum of the individual output voltages computed above; therefore,

    <br />
 v_o = \left( 1+ \frac{R_2}{R_1} \right) \frac{R_B}{R_A + R_B} v_A + \left( 1+ \frac{R_2}{R_1} \right) \frac{R_A}{R_A + R_B} v_B = \left( 1+ \frac{R_2}{R_1} \right) \left( \frac{R_B}{R_A + R_B} v_A + \frac{R_A}{R_A + R_B} v_B \right)= \left( \frac{R_1+R_2}{R_1} \right) \left( \frac{R_B v_A + R_A v_B}{R_A + R_B} \right)<br />

    The last form matches the answer that you provided. Hope this explanation helps you out.

    Best regards,
    Vahe
     
    Last edited: Dec 3, 2011
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