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How to solve for v_o of this weighted summer circuit?

  1. Jun 4, 2013 #1

    dla

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    1. The problem statement, all variables and given/known data
    I am trying to derive the expression for v_o for this weighted summer circuit. I've attached the circuit diagram.

    2. Relevant equations



    3. The attempt at a solution

    I get that the first op-amp output is just the total current x R_a, and then you take that output and find the current of R_b + current of v_3/R_3 and v_4/R_4 and multply all that by R_c to get the v_o, this is what I got

    [itex]\huge
    v_{o} = \frac{v_{1} R_{a}}{R_{1}}\frac{R_{c}}{R_{b}} +\frac{v_{2} R_{a}}{R_{2}}\frac{R_{c}}{R_{b}} + \frac{v_{3} R_{c}} {R_{3}} +\frac{v_{4} R_{c}} {R_{4}}[/itex]

    However the answer says that the last two terms are negative, how come?

    [itex]\huge v_{o} = \frac{v_{1} R_{a}}{R_{1}}\frac{R_{c}}{R_{b}} +\frac{v_{2} R_{a}}{R_{2}}\frac{R_{c}}{R_{b}} -\frac{v_{3} R_{c}} {R_{3}} -\frac{v_{4} R_{c}} {R_{4}}[/itex]
     

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    Last edited: Jun 4, 2013
  2. jcsd
  3. Jun 4, 2013 #2

    NascentOxygen

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    Staff: Mentor

    output = -1x(total current x R_a)

    The input goes to each OP_AMP's inverting input
     
  4. Jun 4, 2013 #3

    dla

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    Thank you! I get it.
     
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