How Do I Calculate Transfer Function from Input and Output Voltage?

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Discussion Overview

The discussion revolves around calculating the transfer function from input voltage Uin(t) and output voltage Uout(t) in an electrical engineering context. Participants explore the relationships between various circuit components and their respective equations, focusing on the application of circuit theory and differential equations.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant presents a series of equations related to the input and output voltages, including relationships involving resistors, inductors, and capacitors.
  • Another participant requests a circuit diagram to better visualize the problem, indicating that the textual representation is insufficient for understanding.
  • There is a suggestion to use a KCL (Kirchhoff's Current Law) equation for the node between the input resistor and the RLC load, proposing a different approach to solving the problem.
  • A later reply emphasizes that calculating a transfer function typically requires transitioning to the frequency domain using Laplace transformations, suggesting that the initial approach in the time domain may not be necessary.

Areas of Agreement / Disagreement

Participants express differing views on the appropriate method for calculating the transfer function, with some advocating for time-domain analysis and others suggesting a frequency-domain approach. No consensus is reached on the best method to proceed.

Contextual Notes

There are limitations regarding the clarity of the equations presented and the assumptions made about the circuit components. The discussion also highlights the need for visual aids to facilitate understanding.

Who May Find This Useful

This discussion may be useful for students or practitioners in electrical engineering who are exploring circuit analysis, particularly in relation to transfer functions and the application of Laplace transformations.

Suiluas
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Hi guys, I'm new to this engineering problem solving and I just wanted to ask for your help getting a transfer function of the input voltage Uin(t) and the output voltage Uout(t).1. Uin(t) = U_R(t) + u_out(t)
2. i(t) = i_L(t) + i_C(t)
3. u_r(t) = R_i(t)
4. u_out(t) = L d_iL / dt
5. i_C = C d_uout / dt3. The attempt:

Dv_c(t) / dt = 1/C i_c(t) = [ 1/C (i(t) - i_out(t) ] = - 1/RC_vc(t) + 1/C i (t)
Di(t) / dt = 1/L v_L(t) = 1/L...
 
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Suiluas said:
Hi guys, I'm new to this engineering problem solving and I just wanted to ask for your help getting a transfer function of the input voltage Uin(t) and the output voltage Uout(t).1. Uin(t) = U_R(t) + u_out(t)
2. i(t) = i_L(t) + i_C(t)
3. u_r(t) = R_i(t)
4. u_out(t) = L d_iL / dt
5. i_C = C d_uout / dt3. The attempt:

Dv_c(t) / dt = 1/C i_c(t) = [ 1/C (i(t) - i_out(t) ] = - 1/RC_vc(t) + 1/C i (t)
Di(t) / dt = 1/L v_L(t) = 1/L...
Welcome to the PF.

Is there a circuit diagram that you could UPLOAD for us to look at. For me, it's hard to visualize the problem. Thanks :smile:
 
Sure, attached is the circuit. :) http://postimg.org/image/7a4mj5c6b/

<< Link removed by Mentor >>
 
Suiluas said:
Sure, attached is the circuit. :) http://postimg.org/image/7a4mj5c6b/

<< Link removed by Mentor >>
Could you instead please use the UPLOAD button at the lower right to upload your image to the PF? The website you have linked to has some questionable advertisements on it. Thanks. :smile:
 
Sorry for that, here is the picture of the system.
 

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Suiluas said:
Sorry for that, here is the picture of the system.
No worries. Thanks for the diagram.

I'm not able to follow what you are doing with your equations, but it seems like you are working with each component individually (I could be wrong). Instead, I would write the one KCL equation for the node between the input resistor and the RLC load. Write that differential equation and solve for the currents and voltages. Can you give that approach a try? :smile:
 
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berkeman said:
No worries. Thanks for the diagram.

I'm not able to follow what you are doing with your equations, but it seems like you are working with each component individually (I could be wrong). Instead, I would write the one KCL equation for the node between the input resistor and the RLC load. Write that differential equation and solve for the currents and voltages. Can you give that approach a try? :smile:
I will try, but it's not as easy for me. anyways, thanks for advice.
 
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Suiluas - are you aware that a system`s "transfer function" requires to find voltage-current relations in the frequency domain?
You have started in the time domain - this is not necessary and requires application of the Laplace transformation. Instead, you can start directly with impedances in the frequency domain
Examples: inductice impedance: ZL=jωL, capcitive impedance: ZC=1/jωC.
 
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