- #1
Twinflower
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Homework Statement
I have this lowpass circuit which I have transformed to the S-domain.
The circuit is to be exposed to a unit step, and then I shall convert the transient response to the time domain.
Here's the transfer function of the lowpass circuit:
[tex]H(s) = \frac{\frac{1}{LC}}{s^2 + s \frac{1}{RC} + \frac{1}{LC}}[/tex]
[itex]\frac{1}{LC} = 1000000[/itex]
[itex]\frac{1}{RC} = 0,001415[/itex]
The function of the unit step is
[tex]x(t)=1 --> X(s) = \frac{1}{s}[/tex]
Homework Equations
[tex]
Y(s) = H(s) * X(s)
[/tex]
[tex]
Y(s) = \frac{\frac{1}{LC}}{s^2 + s \frac{1}{RC} + \frac{1}{LC}} * \frac{1}{s}
[/tex]
The Attempt at a Solution
Now, my problem is that I have great difficulties "arranging" the equation before converting it back to the time domain.
I know that it involves some partial fractions and some unknows (A, B, C and so forth), but even though I have studied the relevant subject in my textbook, I can't f*cking do it.
I'll show you what I got so far (wrong as it may be)
[tex]
1: \frac{A}{s} * \frac{B}{s^2 + s \frac{1}{RC} + \frac{1}{LC}} = \frac{\frac{1}{LC}}{s*(s^2 + s \frac{1}{RC} + \frac{1}{LC}})
[/tex]
[tex]
2: A*(s^2 + s \frac{1}{RC} + \frac{1}{LC}) + Bs = 1
[/tex]
I feel that I'am wondering in the dark, so if someone could point me in the right direction or even shed some light over what I am doing and how I am suppose to do it I would be very very happy :)