Transfer function for RC and RL circuits

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SUMMARY

The discussion focuses on calculating the transfer function for RC and RL circuits, specifically using the example of a circuit with a capacitor. The key equation derived is vout(s) = 1/(sC).i2(s), where i2 represents the current into the output capacitor C2. Participants emphasize the importance of applying Kirchhoff's Laws to express vout in terms of vin without any unknowns. The impedance of the capacitor is defined as 1/sC, allowing for the treatment of the circuit as impedances similar to resistors.

PREREQUISITES
  • Understanding of transfer functions in electrical circuits
  • Familiarity with Kirchhoff's Laws
  • Knowledge of capacitor impedance (Z = 1/sC)
  • Basic calculus for integration in circuit analysis
NEXT STEPS
  • Study the derivation of transfer functions for RL circuits
  • Learn about the application of Laplace transforms in circuit analysis
  • Explore advanced circuit analysis techniques using phasors
  • Investigate the role of feedback in transfer function stability
USEFUL FOR

Electrical engineering students, circuit designers, and anyone involved in analyzing or designing RC and RL circuits.

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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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