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op amp exercise

Hi, in this exercise I need to find the values of Ra and Rb so that Vo is equal to Vx and Vy times an x value. I know how to find a equation with Rb, but I don’t know how to get an equation that contains Ra. More specifically, I don’t know how Ra affects the circuit. Could someone explain me how Ra have an impact in the circuit and how that impact is represented in an equation?

The exercise actually comes with an answer: Vo = (2Rb*Vs)/10k - (Rb/10k)(Vx + Vy)

I know Ra isn’t in the equation, but there are also several sets of values for Rb AND Ra that are needed to get that given “x” amplification in Vo. I really don’t get it.

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    \$\begingroup\$ Are your opamps assumed to be ideal? Because for ideal opamps, Ra has no effect... \$\endgroup\$
    – brhans
    Commented Apr 18, 2018 at 13:53
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    \$\begingroup\$ I'm afraid you're stuck for legitimate reasons. Either you misinterpreted the exercise instructions, or the professor made a mistake, or he just purposely set up a trap. \$\endgroup\$
    – dim
    Commented Apr 18, 2018 at 13:59

1 Answer 1

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The "Logic Diagram" has several logical error in context with the question.

  • Ra has no effect on the VoA,VoB ( within practical limits < 10M typ. ). There is no input current assumed and thus no voltage drop.

  • Rb always controls gain as well in other fixed parts.

    - As a differential amplifier Vo has zero gain for Vx-Vy and thus Ra and Rb has no affect on either if it is a differential input.

  • Regardless is no input current is assumed or there is, Vx and Vy must have a current path to 0V (gnd symbol) No matter how large ( 1M 100M ...) in order to be within the CM range of finite Supply range. If however Vx uses Gnd as the return path instead of Vy, then this satisfies the requirement until disconnected. i.e. Vx and Vy need to be biased in the middle of the CM range. e.g. 10M~100M.

  • Vs and OA-C are not input bias offset voltage balanced, so Vs shud go into 5k then Rb for common mode feedback.

Conclusion

  • the design does not work.

  • differential outputs are summed and thus cancel with no ouput.

  • (to teach you to think)

    • never assume the assumptions OR schematic are valid , unless it can be verified by experience of trusted sources... —- even your own transcribed errors.
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    \$\begingroup\$ "As a differential amplifier Vo has zero gain for Vx-Vy and thus Ra and Rb has no affect on either if it is a differential input." However, the circuit shown is NOT a differential amplifier. The third op amp is operating as a summer rather than a diff amp. - So, the gain as described does not depend on Ra, but it does depend on Rb. \$\endgroup\$
    – WhatRoughBeast
    Commented Oct 17, 2019 at 19:40
  • \$\begingroup\$ You said the same as me but in few words. Ty I clarified a tad \$\endgroup\$
    – D.A.S.
    Commented Oct 17, 2019 at 19:43

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