I am trying to model this circuit in the s-plane, to prove that its transfer function is what I have written at the top.
The question I am asking the community is how to approach the first steps for this. I want to use Kirchhoff's current law, but I have forgotten how to express the different voltages and currents.
To be more specific, how can I express i1, i2 and i3 in terms of the voltages, resistances and capacitors? Could you explain your reasoning behind it as well?
I know that i1 is (Vi - Vx) / R1, because I am just taking the potential difference across the resistor, and dividing it by the resistors value, but I am unsure as to what to do next, for i2 and i3.
I know that it will depend on modelling the capacitor in the s-plane as sC, or 1/sC, depending on whether it is in parallel or in series, but again my circuit theory is rusty so when I looked at the solution I couldn't see how they derived it. I can post the solution if it helps.