Engineering Transfer function for RC and RL circuits

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To calculate the transfer function for RC and RL circuits, start by determining the output voltage (Vout) in terms of the input voltage (Vin). Use the relationship Vout = (1/C)∫i2.dt, leading to Vout(s) = 1/(sC)i2(s), where i2 is the current into the output capacitor. Apply Kirchhoff's Laws to express i2 in terms of Vin, systematically working through the circuit. Remember to treat capacitors as impedances, using the formula Z = 1/sC. This approach allows for deriving Vout in relation to Vin without unknowns, facilitating the calculation of the transfer function.
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Homework Statement


I just want to understand, how to calculate transfer function.
Here is simple example:
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Homework Equations





The Attempt at a Solution


But in this circuit I don't understand how to do it.
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I have to find T and k as it is in preview. Which is the element for Vout in this circuit? Or what I shoud find first?
 
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Start with what you want to find, then work backwards.

vout = (1/C).∫[/size] i2.dt

→ vout(s) = 1/(sC).i2(s)

where i2 is the current into the output capacitor, C2.

Now, find equations that allow you to substitute something for i2. Keep going, applying Kirchoff's Laws as you work towards the left until you have vout in terms of vin but no other unknowns.
 
The impedance of a capacitor is 1/sC. So treat this network as impedances just as though the capacitors were resistors.

(This is per the fact that for a capacitor, i = C dv/dt or I = sCV so Z = V/I = 1/sC.)
 

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