Output Voltage of Instrumentation Amplifier Configuration

I'm trying to find the output voltage using the superposition theorem for this circuit configuration when RG is connected.

I'm working with ideal op amps. As far as I understand the circuit, when VB is grounded, AO2 is in non inverting configuration so Vo would be $$\left(1+\frac{R_4}{R_3+R_4} \parallel R_G\right) \times V_a$$ but I'm not sure.

When VA is grounded I don't know if there's a current through RG.

If somebody can help I would appreciate.

I've already explained my thinking about the case when VB is grounded. I think that there is current through RG, AO2 is a non inverting op amp with R4 as feedback resistor and $$\(R_3+R_2) \parallel R_G\$$ is the equivalent resistor.

To give you my thinking about the case when VA is grounded, well then AO2 is in inverting configuration, meaning there's a virtual ground at the inverting input, so RG is connected between 2 grounds, meaning that it has no current flowing through it. Then VO1 is $$\(1+R_2/R_1) \times V_b\$$. New contributor
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• Do you mean if Va is grounded Jan 13 at 0:22
• Why don't you sketch the two circuits you are trying to evaluate and figure out what Vo1 must be. Show us your work and explain your thinking. We won't do your homework for you. Jan 13 at 0:26
• @ElliotAlderson it's not about doing homework for me, it's not even a homework, I just want to understand how this circuit works. (yes, it's for school, listed as optional). I've sketched the circuit in different ways to help me visualize it better. All I was asking was confirmation if RG exists or not when Va is grounded. But to follow your objection I will explain my thinking: When VA is grounded, I think there isn't current through RG because AO2 inverting input is virtual ground, so RG would be situated between 2 grounds. So VO1 = (1+R2/R1)*VB Jan 13 at 0:43
• @ScottSeidman Yes, I was thinking in my native language that's why I wrote "shorted" because it starts with the same letter lol. I meant grounded for both Va and Vb Jan 13 at 0:44
• Please explain why you believe that the junction of R1, R2, and RG must be at ground potential for the case where VA is grounded but VB is not. Jan 13 at 1:47

Question : <<< I'm trying to find the output voltage using the superposition theorem for this circuit configuration when RG is connected. >>>

For helping a little ... here is the literal result for output ... (E&OE). Can be perhaps simplified. If all resistors = 10 kOhm, result is : $$\Vo = -4 * VB + 4 * VA\$$

Simulation. Two cases. <<< ... so RG is connected between 2 grounds ... >>>

Correction: RG is connected between 2 "virtual" "grounds" (which are different).

You can see this on the two simulated configurations, which are a direct Thevenin theorem application for the two inputs voltage.