Low-pass filter regarding Laplace.

  • Thread starter Thread starter aryise
  • Start date Start date
  • Tags Tags
    Filter Laplace
Click For Summary

Discussion Overview

The discussion revolves around the application of Laplace transforms in analyzing a low-pass filter circuit. Participants are attempting to understand how to apply the Laplace transform to the circuit equations involving resistors, capacitors, and inductors, particularly in the context of voltage and current relationships.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant states that a low-pass filter allows low-frequency signals to pass while attenuating high-frequency signals, and expresses confusion about solving the circuit problem.
  • Another participant suggests the need to represent circuit components in the s-domain and provides a link for reference.
  • A participant emphasizes the necessity of using the Laplace transform for the excitation voltage and understanding the Laplace representations of R, C, and L.
  • Several participants share their attempts at applying the Laplace transform, with one expressing uncertainty about the correctness of their approach involving sin(wt) and the relationship between current and impedance.
  • Another participant corrects a misunderstanding regarding the impedance of R and C, affirming that they are not the same type of impedance.
  • One participant describes their process of using partial fractions and inverse Laplace transforms to find the current, while questioning whether differentiation is needed in the solution.
  • Another participant confirms the correctness of a specific equation and encourages showing detailed math to clarify any mistakes.
  • A later reply indicates that an algebraic mistake was made in a participant's solution, noting dimensional inconsistencies in the terms presented.

Areas of Agreement / Disagreement

Participants express varying levels of understanding and correctness in their approaches, with some confirming the validity of certain equations while others highlight mistakes. The discussion remains unresolved regarding the final solution and specific algebraic errors.

Contextual Notes

There are limitations in the clarity of the mathematical steps presented, and some participants express confusion about the relationships between circuit components and their representations in the Laplace domain.

aryise
Messages
2
Reaction score
0

Homework Statement



Low-pass filter allows signals of low frequency to pass while attenuating high frequency signals; similarly, a high-pass filter allows signals of high frequency to pass while attenuating low frequency signals. The signals here can refer to voltage or current in the circuit. There is a link to a picture. I don't quite understand how to solve it.

Link: http://img198.imageshack.us/img198/5677/mathb.png

Homework Equations



I understand that Vin = Vc + Vr.
How do I use Laplace transform on Vin = Vc + Vr. AnD if Vout is the voltage across the resistor R.

The Attempt at a Solution



I am totally stuck.
 
Last edited by a moderator:
Physics news on Phys.org
Do you know how to represent circuits and basic components R, C, L in s domain?
This following link may help.
http://tintoretto.ucsd.edu/jorge/teaching/mae140/lectures/6sdomain.pdf


aryise said:

Homework Statement



Low-pass filter allows signals of low frequency to pass while attenuating high frequency signals; similarly, a high-pass filter allows signals of high frequency to pass while attenuating low frequency signals. The signals here can refer to voltage or current in the circuit. There is a link to a picture. I don't quite understand how to solve it.

Link: http://img198.imageshack.us/img198/5677/mathb.png

Homework Equations



I understand that Vin = Vc + Vr.
How do I use Laplace transform on Vin = Vc + Vr. AnD if Vout is the voltage across the resistor R.

The Attempt at a Solution



I am totally stuck.
 
Last edited by a moderator:
You will need the Laplace transform for the excitation voltage U(t)sin(wt). You also need to know how to express L, C and R in terms of their Laplace representations, as klondike points out.
 
Thank you! I finally solve it... :)
 
aryise said:
Thank you! I finally solve it... :)

Hey how did you solve it? i have a simillar question. Help would be greatly appreciated
 
Cfty said:
Hey how did you solve it? i have a simillar question. Help would be greatly appreciated

See my post of June 24.
 
rude man said:
See my post of June 24.

I can't understand. Argh.kNot so good in this.

I understand SinWt = iR + iC

Then i applied laplace : W/(s^2+w^2) = IR + IC.

Is this correct?
 
Cfty said:
I can't understand. Argh.kNot so good in this.

I understand SinWt = iR + iC

Then i applied laplace : W/(s^2+w^2) = IR + IC.

Is this correct?

sin(wt) = iR + iC is not correct. R and C are not the same type of impedance!
But you got the right transform for sin(wt).
 
rude man said:
sin(wt) = iR + iC is not correct. R and C are not the same type of impedance!
But you got the right transform for sin(wt).

I tried it with W/(S^2 + W^2) = IR + I/CS

Do i need to diffrentiate anywhere in this question?. I got the first two parts for the showing right. I can't seem to get the final part. I followed the laplace transform on top by making I the subject and doing partial fractions. Then when i found I i laplace inversed it to Find i. And Since Vout is VR : i took the i*R.
 
  • #10
Cfty said:
I tried it with W/(S^2 + W^2) = IR + I/CS
This is correct

Do i need to diffrentiate anywhere in this question?.
No.
I got the first two parts for the showing right. I can't seem to get the final part. I followed the laplace transform on top by making I the subject and doing partial fractions. Then when i found I i laplace inversed it to Find i.
That is correct.
And Since Vout is VR : i took the i*R.
Yes, if I understand you correctly, Vout= iR.
Show your math in detail.
 
  • #11
Hey This is my written solutions. If you could tell me where i went wrong I would greatly appreciate it.
 

Attachments

  • 001.jpg
    001.jpg
    12.6 KB · Views: 513
  • 002.jpg
    002.jpg
    14.7 KB · Views: 509
  • #13
rude man said:
This is correct



Show your math in detail.


Hope It helps
 
  • #14
Your equation at the top of page 1 is correct. And your answer is almost correct, obviously.

You just made an algebraic mistake somewhere. You can see that the last term in your answer is incorrect since it's dimensionally incorrect. Each term must be dimensionless
(actually it's Volts but you didn't include volts in your excitation function).

I can't follow your math from the pictures. I will leave it to you to find the mistake you made.

Good luck and good work!
 

Similar threads

Engineering How to determine circuit components of ´Mystery Box’ ?
  • · Replies 4 ·
Replies
4
Views
2K
How do I determine the resistance for RLC low pass filter?
  • · Replies 4 ·
Replies
4
Views
1K
Engineering Is it possible for a low pass filter to have such a transfer function?
  • · Replies 16 ·
Replies
16
Views
2K
[Homework] Identify Filter type
  • · Replies 4 ·
Replies
4
Views
2K
Engineering Signal Conditioning and Processing
  • · Replies 3 ·
Replies
3
Views
2K
High School Multiple frequency EMFs and capacitors
  • · Replies 9 ·
Replies
9
Views
1K
Engineering Bode plot for active low pass filters
  • · Replies 9 ·
Replies
9
Views
5K
Low Pass Filters and Laplace Transform
  • · Replies 6 ·
Replies
6
Views
4K
Engineering Laplace tranforms, transient current series CR circuit
  • · Replies 2 ·
Replies
2
Views
2K
Problems designing an FIR band pass filter on MATLAB?
  • · Replies 11 ·
Replies
11
Views
3K