# Calculate the Laplace for the Ramp

1. Nov 7, 2014

### Davelatty

Hi, i am new to Laplace transforms/Algebra. I have been given a worked example by lecture to calculate the Laplace transform for a ramped input into a single pole RC high pass filter.

i have managed to calculate the Laplace for the Ramp and the Laplace for the Filter. however i cant figure out how to get to the final answer. any help would be great.

Dave

a ramped voltage of 5000s/V is inputted into the filter. R = 10K and c= 1u.

$τ = RC = 0.01$

$$\ T(L)= \frac{R}{R +\frac{1}{Jωc}} = \frac{JωRC}{JωRC +1} = \frac{Sτ}{Sτ+1}$$

$$\ Fin(L)= \frac{5000}{S^2}$$

$$\ Fout(L)= \frac{5000}{S^2} . \frac{Sτ}{Sτ+1}$$

The answer on the worked example is

$$\ Fout(L)= \frac{5}{τ} . \frac{1}{S(\frac{1}{τ}+S)}$$

Any help on the steps to get to the final answer would be great :)

Dave

2. Nov 7, 2014

### vela

Staff Emeritus
The constant factor of 5 or 5000 probably has to do with the units you're working in. The rest is just basic algebra. Surely, you've made some attempt. Show what you did.

3. Nov 8, 2014

### rude man

Meaning 5000V/s I presume.
What you did was correct. The given answer is wrong. The final answer, in any consistent units, must be of the form
Vout(s) = k/s(s + 1/T).
k being the ramp input rate, V/s
T = RC
BTW make your "s" lower case, not upper.

Last edited by a moderator: Nov 12, 2014
4. Nov 9, 2014

### Davelatty

Thanks for the two replies, i will speak to the lecturer on Thursday to see why he gave the answer he did.

I would still like to understand how he ended up with the final answerr, just so i can improve my basic algebra. I have had an attempt but quite quickly get stuck

$$\ Fout(L)= \frac{5000}{s^2} . \frac{sτ}{sτ+1}$$

$$\ Fout(L)= \frac{5000}{s^2} . \frac{sτ}{τ(\frac{1}{τ}+s)}$$

do both the τ cancel out ? leaving

$$\ Fout(L)= \frac{5000}{s^2} . \frac{s}{(\frac{1}{τ}+s)}$$

5. Nov 9, 2014

### Staff: Mentor

Now cancel that numerator s with one in the denominator.

6. Nov 9, 2014

### Davelatty

so now i have

$$\ Fout(L)= \frac{5000}{s} . \frac{1}{(\frac{1}{τ}+s)}$$

but how do i get the s to the denominator on the other side and where does the denominator τ come from ?

7. Nov 9, 2014

### rude man

You don't. It's still wrong.