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I'm working on a problem which has two parts.
1. Find the frequency response function H(f) for a circuit. A hint given is to find H(s) first and then plug in [itex]s=j2\pi f[/itex] to get H(f).
2. Find [itex]v_{out}(t)[/itex], which is the response of the LTIC system to the periodic input signal [itex]v_{in}(t) = \sum_{n=1, n \ odd}^{\infty} \frac{8}{\pi^2n^2}\cos\left(\frac{\pi}{4}nt\right)[/itex] using H(f).
I used KCL on the circuit to find the transfer function H(s):
[itex]H(s) = \frac{1}{1*10^{-10}s^2+2*10^{-5}s+1}[/itex]
Now, the problem hint said to evaluate the function at [itex]s=j2\pi f[/itex], so if I plug that in then the above equation becomes:
[itex]H(f) = H(s)|_{s=j2\pi f} = \frac{1}{-4\pi^2*10^{-10}f^2+j4\pi*10^{-5}f+1}[/itex]
So, although I don't really understand the above equation (for one thing, I don't get why there would be a "j" in an s-domain equation -- I've never seen that before), I guess I answered the first part of the problem.
My question is, how should I go about solving the second part of the problem, finding [itex]v_{out}(t)[/itex] for the crazy input signal?
Appreciate your advice.
1. Find the frequency response function H(f) for a circuit. A hint given is to find H(s) first and then plug in [itex]s=j2\pi f[/itex] to get H(f).
2. Find [itex]v_{out}(t)[/itex], which is the response of the LTIC system to the periodic input signal [itex]v_{in}(t) = \sum_{n=1, n \ odd}^{\infty} \frac{8}{\pi^2n^2}\cos\left(\frac{\pi}{4}nt\right)[/itex] using H(f).
I used KCL on the circuit to find the transfer function H(s):
[itex]H(s) = \frac{1}{1*10^{-10}s^2+2*10^{-5}s+1}[/itex]
Now, the problem hint said to evaluate the function at [itex]s=j2\pi f[/itex], so if I plug that in then the above equation becomes:
[itex]H(f) = H(s)|_{s=j2\pi f} = \frac{1}{-4\pi^2*10^{-10}f^2+j4\pi*10^{-5}f+1}[/itex]
So, although I don't really understand the above equation (for one thing, I don't get why there would be a "j" in an s-domain equation -- I've never seen that before), I guess I answered the first part of the problem.
My question is, how should I go about solving the second part of the problem, finding [itex]v_{out}(t)[/itex] for the crazy input signal?
Appreciate your advice.