Transfer function for RC and RL circuits

In summary, to calculate the transfer function in this circuit, you can start by finding the equation for vout, which is equal to (1/C) times the integral of i2 with respect to time. Then, you can use Kirchoff's Laws to work backwards and substitute for i2. Keep applying Kirchoff's Laws until you have vout in terms of vin and no other unknowns. Remember to treat the capacitors as impedances, using the equation Z = 1/sC.
  • #1
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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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  • #2
Start with what you want to find, then work backwards.

vout = (1/C). 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.
 
  • #3
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.)
 

1. What is a transfer function?

A transfer function is a mathematical representation of the relationship between the input and output of a system, such as an RC or RL circuit. It describes how the output of the system changes in response to changes in the input.

2. How is the transfer function for an RC circuit calculated?

The transfer function for an RC circuit can be calculated using the formula H(s) = 1 / (1 + RCs), where H(s) is the transfer function, R is the resistance in the circuit, C is the capacitance, and s is the complex frequency variable.

3. What does the transfer function tell us about an RC or RL circuit?

The transfer function provides insight into how the circuit will behave in response to different input signals. It can help us understand the filtering and amplification properties of the circuit, as well as its stability and frequency response.

4. How does the transfer function for an RL circuit differ from an RC circuit?

The transfer function for an RL circuit is calculated using the formula H(s) = Ls / (R + Ls), where L is the inductance in the circuit. This formula takes into account the effects of inductance, which plays a different role in the circuit's behavior compared to capacitance in an RC circuit.

5. Can the transfer function be used to design an RC or RL circuit?

Yes, the transfer function can be used in the design process to determine the appropriate values of resistance, capacitance, and inductance for a desired circuit response. It can also help identify any potential issues or limitations in the circuit design.

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