# Multi Op Amp Analysis

I am asked this for homework:

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.

• Hint: If negative feedback is working as it should, you will end up with V_a = v_1 and V_b = v_2. – The Photon Sep 18 '13 at 20:35
• Your node equations cannot be correct as they add voltage and currents together. A node equations is a KCL equation which involves only currents. – Alfred Centauri Sep 18 '13 at 21:47
• Yes, pay attention to your units. Volts cannot equal Volts + Amps. – dext0rb Sep 18 '13 at 22:12

Thus, for example, for the first op-amp, both inputs have a voltage of $v_1$. So, how to proceed?
$\dfrac{v_1 - V_{REF}}{R_2} + \dfrac{v_1 - v_x}{R_1} + \dfrac{v_1 - v_2}{R_F} = 0$