Calculate the Laplace for the Ramp

[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 can't 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

 

[vela]

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.

 

[rude man]

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

Meaning 5000V/s I presume.

$τ = RC = 0.01$

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

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

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

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

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.

 

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

 

[NascentOxygen]

Now cancel that numerator s with one in the denominator.

 

[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 ?

 

[rude man]

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 ?

You don't. It's still wrong.