Design an RLC bandpass filter with a quality factor of 8 and a center frequency of 80 krad/s using a 10 nF capacitor. + R www + L3% a. Derive the transfer function equation. Show all your steps; the solution will not be worth any points. Ensure that the s² term in the denominator has a coefficient of 1. b. In terms of R, L, and C, what is the equation for this filter's bandwidth, quality factor, and center frequency? c. Calculate the values for the resistor, R, and inductor, L. d. Calculate the bandwidth, center frequency (f0), and the values of the two cutoff frequencies (fc1 and fc2) based on the values obtained in part c.

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Design an RLC bandpass filter with a quality factor of 8 and a center frequency of 80
krad/s using a 10 nF capacitor.
R
L
a. Derive the transfer function equation. Show all your steps; the solution will not be
worth any points. Ensure that the s² term in the denominator has a coefficient of 1.
b. In terms of R, L, and C, what is the equation for this filter's bandwidth, quality
factor, and center frequency?
c. Calculate the values for the resistor, R, and inductor, L.
d. Calculate the bandwidth, center frequency(f0), and the values of the two cutoff
frequencies (fc1 and fc2) based on the values obtained in part c.
Transcribed Image Text:Design an RLC bandpass filter with a quality factor of 8 and a center frequency of 80 krad/s using a 10 nF capacitor. R L a. Derive the transfer function equation. Show all your steps; the solution will not be worth any points. Ensure that the s² term in the denominator has a coefficient of 1. b. In terms of R, L, and C, what is the equation for this filter's bandwidth, quality factor, and center frequency? c. Calculate the values for the resistor, R, and inductor, L. d. Calculate the bandwidth, center frequency(f0), and the values of the two cutoff frequencies (fc1 and fc2) based on the values obtained in part c.
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