# Homework Help: Low-pass filter regarding Laplace.

1. Jun 24, 2012

### aryise

1. The problem statement, all variables and given/known data

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.

2. Relevant 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.

3. The attempt at a solution

I am totally stuck.

Last edited by a moderator: May 6, 2017
2. Jun 24, 2012

### klondike

Do you know how to represent circuits and basic components R, C, L in s domain?
http://tintoretto.ucsd.edu/jorge/teaching/mae140/lectures/6sdomain.pdf

Last edited by a moderator: May 6, 2017
3. Jun 24, 2012

### rude man

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.

4. Jun 30, 2012

### aryise

Thank you! I finally solve it... :)

5. Jul 7, 2012

### Cfty

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

6. Jul 7, 2012

### rude man

See my post of June 24.

7. Jul 7, 2012

### Cfty

I cant 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?

8. Jul 7, 2012

### rude man

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).

9. Jul 7, 2012

### Cfty

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 cant 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. Jul 7, 2012

### rude man

This is correct

No.
That is correct.
Yes, if I understand you correctly, Vout= iR.

11. Jul 7, 2012

### Cfty

Hey This is my written solutions. If you could tell me where i went wrong I would greatly appreciate it.

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12. Jul 7, 2012

### Cfty

13. Jul 7, 2012

### Cfty

Hope It helps

14. Jul 7, 2012

### rude man

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!