See figures attached for problem statement as well as my work.
I managed to derive the transfer function without any troubles, however when it comes to part b) I'm not sure what route to take to solve it.
Since,
\(z_{1} = \frac{R}{1 + jRwc_{1}}\)
and
\(z_{2} = \frac{1}{jwc_{2}}\)
My transfer function,
\(H(w) = \frac{z_{1}}{z_{2} - z_{1}}\)
turns into a big algebra mess. This algebra mess makes finding the values of C1 and C2 to create a pole at 200 rad.Hz difficult.
I think if I could get a "clean" expression for the transfer function H(w) I would be able to solve the problem, but the algebra is so messy.
Does anyone have any suggestions? Or perhaps tips to make the algebra a little bit easier?
Thanks again!
Edit: I decided to man up an try to tackle the algebra and here's what I came up see. (See 2nd and 3rd pages of my work attached)
The 2nd page of my work is just finding \(z_{2} - z_{1}\).
The 3rd page shows me rewriting the transfer function and extracting the pole out of the denominator and solving for the difference between \(c_{1},c_{2}\).
Just a note when replying, WE DID NOT LEARN LAPLACE TRANSFORMS! When given a quadratic like in this example, we simply focused on the term with the highest power of \(w\) and solved it accordingly. We don't even consider if our the roots of our quadratic equation are real or complex.
Sorry if that last part is confusing but that's how we learnt it, and it was very vaguely explained.
I managed to derive the transfer function without any troubles, however when it comes to part b) I'm not sure what route to take to solve it.
Since,
\(z_{1} = \frac{R}{1 + jRwc_{1}}\)
and
\(z_{2} = \frac{1}{jwc_{2}}\)
My transfer function,
\(H(w) = \frac{z_{1}}{z_{2} - z_{1}}\)
turns into a big algebra mess. This algebra mess makes finding the values of C1 and C2 to create a pole at 200 rad.Hz difficult.
I think if I could get a "clean" expression for the transfer function H(w) I would be able to solve the problem, but the algebra is so messy.
Does anyone have any suggestions? Or perhaps tips to make the algebra a little bit easier?
Thanks again!
Edit: I decided to man up an try to tackle the algebra and here's what I came up see. (See 2nd and 3rd pages of my work attached)
The 2nd page of my work is just finding \(z_{2} - z_{1}\).
The 3rd page shows me rewriting the transfer function and extracting the pole out of the denominator and solving for the difference between \(c_{1},c_{2}\).
Just a note when replying, WE DID NOT LEARN LAPLACE TRANSFORMS! When given a quadratic like in this example, we simply focused on the term with the highest power of \(w\) and solved it accordingly. We don't even consider if our the roots of our quadratic equation are real or complex.
Sorry if that last part is confusing but that's how we learnt it, and it was very vaguely explained.
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