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

[Suiluas]

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...

 

[berkeman]

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

 

[Suiluas]

Sure, attached is the circuit. :) http://postimg.org/image/7a4mj5c6b/

<< Link removed by Mentor >>

 

[berkeman]

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.

 

[Suiluas]

Sorry for that, here is the picture of the system.

 

[berkeman]

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?

 

[Suiluas]

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?

I will try, but it's not as easy for me. anyways, thanks for advice.

 

[LvW]

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.