- #1
mankku
- 9
- 0
Hi everybody!
This is my first post, happy to be a part of this forum!
I have a problem that may be pretty easy to solve, and a few years ago I could've myself, but at the moment I'm stuck.
I enjoy fiddling with electronics during my free time, and I'd like to study the use of a capacitor to remove DC offset from a signal (more specifically, how the capacitance, frequency and amplitude affect the outcome).
So I've made a simple assumption: I have a voltage source,
[tex]e(t)=2.5+A*sin(2*pi*ft)[/tex]
that feeds a circuit. The circuit consists of a capacitor C and resistor R in series, so that any current passes through both. I've based the case on Kirchoff's voltage law so that
[tex]e(t)=Vc(t)+Vr(t)[/tex]
where
[tex]i(t)=C*\frac{dVc(t)}{dt}[/tex]
and [tex]Vr(t)=R*i(t)[/tex]The equation becomes
[tex]e'(t)=\frac{1}{C}*i(t) + R*i'(t)[/tex]
From this I attempted to do a Laplace transform but I ended up with an expression that I cannot get past. I assumed that at t=0, e(t)=2.5 and i(0)=0.
Here's what I did:
[tex]sE(s)-e(0) = R*(sI(s)-i(0)) + I(s) * \frac{1}{C}[/tex]
from which I obtained
[tex]I(s) = \frac{sE(s)-2.5}{Rs+1/C}[/tex]
and substituting in E(s)
[tex]I(s) = \frac{As*\frac{2\pi f}{s^{2}+4\pi^{2}f^{2}}}{Rs+1/C}[/tex]
where I'm stuck... I can't modify the expression to be able to apply the inverse Laplace transform...
My question is, am I even doing the right thing? Have I gone wrong somewhere? I'm trying to obtain the function for the current i(t) so that I can work out the resistor voltage and thus the circuit output.
Any hints or helps will be greatly appreciated!
Mankku
This is my first post, happy to be a part of this forum!
I have a problem that may be pretty easy to solve, and a few years ago I could've myself, but at the moment I'm stuck.
I enjoy fiddling with electronics during my free time, and I'd like to study the use of a capacitor to remove DC offset from a signal (more specifically, how the capacitance, frequency and amplitude affect the outcome).
So I've made a simple assumption: I have a voltage source,
[tex]e(t)=2.5+A*sin(2*pi*ft)[/tex]
that feeds a circuit. The circuit consists of a capacitor C and resistor R in series, so that any current passes through both. I've based the case on Kirchoff's voltage law so that
[tex]e(t)=Vc(t)+Vr(t)[/tex]
where
[tex]i(t)=C*\frac{dVc(t)}{dt}[/tex]
and [tex]Vr(t)=R*i(t)[/tex]The equation becomes
[tex]e'(t)=\frac{1}{C}*i(t) + R*i'(t)[/tex]
From this I attempted to do a Laplace transform but I ended up with an expression that I cannot get past. I assumed that at t=0, e(t)=2.5 and i(0)=0.
Here's what I did:
[tex]sE(s)-e(0) = R*(sI(s)-i(0)) + I(s) * \frac{1}{C}[/tex]
from which I obtained
[tex]I(s) = \frac{sE(s)-2.5}{Rs+1/C}[/tex]
and substituting in E(s)
[tex]I(s) = \frac{As*\frac{2\pi f}{s^{2}+4\pi^{2}f^{2}}}{Rs+1/C}[/tex]
where I'm stuck... I can't modify the expression to be able to apply the inverse Laplace transform...
My question is, am I even doing the right thing? Have I gone wrong somewhere? I'm trying to obtain the function for the current i(t) so that I can work out the resistor voltage and thus the circuit output.
Any hints or helps will be greatly appreciated!
Mankku
Last edited: