I am asked this for homework:enter image description here

I am trying to do nodal analysis for part A of the question but am running into problems with number of unknowns versus number equations. Assuming I chose my nodes correctly I get:

$$V_a = V_1 + \frac{V_a}{R_2} + \frac{V_a-V_b}{R_F} + \frac{V_a-V_x}{R_1} $$ $$V_b = V_2 + \frac{V_b-V_x}{R_3} + \frac{V_b-V_a}{R_F} + \frac{V_b}{R_4} $$

I don't believe my node equations are correct but I believe that there is 3 unknowns (Va, Vb, and Vx | V1, V2, all resistors are known(?) ) and only two equations. I tried super position as well treating each stage as an inverting and noninverting with sources on and off.

Any help or guidance on how to approach this problem so that I can reduce it down into the given form would be appreciated .

Note: Vref does not equal ground.

  • 3
    \$\begingroup\$ Hint: If negative feedback is working as it should, you will end up with V_a = v_1 and V_b = v_2. \$\endgroup\$
    – The Photon
    Sep 18, 2013 at 20:35
  • 1
    \$\begingroup\$ Your node equations cannot be correct as they add voltage and currents together. A node equations is a KCL equation which involves only currents. \$\endgroup\$ Sep 18, 2013 at 21:47
  • \$\begingroup\$ Yes, pay attention to your units. Volts cannot equal Volts + Amps. \$\endgroup\$
    – dext0rb
    Sep 18, 2013 at 22:12

1 Answer 1


For op-amp problems, assuming negative feedback is present, the inverting and non-inverting inputs (ideally) have the same voltage.

Thus, for example, for the first op-amp, both inputs have a voltage of \$v_1\$. So, how to proceed?

The correct node equation for node A is:

\$\dfrac{v_1 - V_{REF}}{R_2} + \dfrac{v_1 - v_x}{R_1} + \dfrac{v_1 - v_2}{R_F} = 0\$

Can you take it from here?


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