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Solution+HW18 - Sections 9-4 and 9-5 Passive Filters...

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Sections 9-4 and 9-5: Passive Filters Problem 9.20 The element values of a series RLC bandpass filter are R = 5 , L = 20 mH, and C = 0 . 5 μ F. (a) Determine ϖ 0 , Q , B , ϖ c 1 , and ϖ c 2 . (b) Is it possible to double the magnitude of Q by changing the values of L and/or C , while keeping ϖ 0 and R unchanged? If yes, propose such values, and if no, why not? Solution: (a) ϖ 0 = 1 LC = 1 20 × 10 3 × 0 . 5 × 10 6 = 10 4 rad/s , Q = ϖ 0 L R = 10 4 × 20 × 10 3 5 = 40 , B = ϖ 0 Q = 10 4 40 = 250 rad/s , ϖ c 1 = ϖ 0 B 2 = 10 4 250 2 = 9875 rad/s , ϖ c 2 = ϖ 0 + B 2 = 10 4 + 250 2 = 10125 rad/s . (b) Q = ϖ 0 L R = ϖ 0 R = Q L . Since ϖ 0 and R are constants, doubling Q requires that L be doubled, but to keep ϖ 0 constant would require C to be reduced to one half. Thus, the new set of element values are: R = 5 , L = 40 mH , and C = 0 . 25 μ F . The corresponding values of ϖ 0 and Q are: ϖ 0 = 10 4 rad/s (unchanged) Q = ϖ 0 L R = 80 .
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Problem 9.24 Design a parallel RLC filter with f 0 = 4 kHz, Q = 100, and an input impedance of 25 k at resonance.
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