I've the following filter and I tried to write the transfer function for it:
simulate this circuit – Schematic created using CircuitLab
And I wrote for the current nodes the following equations:
- $$\text{I}_1=\frac{\text{V}_\text{in}-\text{V}_1}{\text{R}_1}+\frac{\text{V}_1}{\frac{1}{\text{s}\text{C}_1}}+\frac{\text{V}_1-\text{V}_2}{\text{R}_2}=0\tag1$$
- $$\text{I}_2=\frac{\text{V}_2-\text{V}_1}{\text{R}_2}+\frac{\text{V}_2-\text{V}_\text{out}}{\frac{1}{\text{s}\text{C}_3}}+\frac{\text{V}_2-\text{V}_3}{\text{R}_3}=0\tag2$$
- $$\text{I}_3=\frac{\text{V}_3-\text{V}_2}{\text{R}_3}+\frac{\text{V}_3}{\frac{1}{\text{s}\text{C}_2}}=0\tag3$$
- $$\text{V}_+=\text{V}_-\space\implies\space\text{V}_3=\text{V}_+=\text{V}_-=\text{V}_\text{out}\tag4$$
Question: are my equations correct? And how can I find \$\frac{\text{V}_\text{out}}{\text{V}_\text{in}}\$ from this (if they are correct of coruse)?