Mistake in finding KCL and KVL in op-amp circuit

Question

I have the following op-amp circuit:

^{simulate this circuit – Schematic created using CircuitLab}

I know that \$\text{V}_1=0\$ and \$\text{V}_3=0\$ in the case of an ideal op-amp circuit. I wrote the following KCL equations:

$$ \begin{cases} \text{I}_0=\text{I}_1+\text{I}_3\\ \\ \text{I}_4=\text{I}_1+\text{I}_2\\ \\ \text{I}_7=\text{I}_3+\text{I}_4\\ \\ \text{I}_7=\text{I}_5+\text{I}_6\\ \\ 0=\text{I}_5+\text{I}_6+\text{I}_8 \end{cases}\tag1 $$

And the following KVL equations:

$$ \begin{cases} \text{I}_1=\frac{\text{V}_\text{i}-\text{V}_1}{\text{R}_1}\\ \\ \text{I}_2=\frac{\text{V}_1-\text{V}_2}{\text{R}_2}\\ \\ \text{I}_3=\frac{\text{V}_\text{i}-\text{V}_3}{\text{R}_3}\\ \\ \text{I}_4=\frac{\text{V}_2-\text{V}_3}{\text{R}_4}\\ \\ \text{I}_5=\frac{\text{V}_3-\text{V}_4}{\text{R}_5}\\ \\ \text{I}_6=\frac{\text{V}_3-\text{V}_4}{\text{R}_6} \end{cases}\tag2 $$

Now, I tried to LTspice to simulate this circuit for me and I used Mathematica to find the mathematical result. But they did not gave the same result. Is there a mistake in my equations?

Thanks a lot.

Answer 1

Your second KVL equation is wrong. That should be I1 = (V1-V2)/R2, since I1 goes through R1 and then all of it goes through R2 as well. Otherwise you're saying that I2 completely cancels out I1, making I4=0, which you can't assume.