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ECE2260F09_HW3p45soln - 2260 F 09 HOMEWORK#3 probs 4 and 5...

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2260 F 09 HOMEWORK #3 probs 4 and 5 solution E X : v i + + v o L = 25 μ H C = 250 nF R 1 = 2.5 Ω R 2 = 5 Ω For the band-reject filter shown above, determine the transfer function V o /V i . Hint: Move R 1 to the right of L and C, place R 1 vertically, and suppose the output were tapped from the point between C and R 1 . Then use a v-divider. For the band-reject filter above, calculate the following quantities: a) ω o b) ω C1 and ω C2 c) β d) Q S OL ' N : a) Although we could calculate ω o without the transfer function, we derive the transfer function first in order to understand the nature of the circuit. As advised in the hint, we exchange the positions of the R 1 and the parallel LC so that the R 's are next to each other. + V 1 R 2 j ω L + V i V o + R 1 1 j ω C
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Putting the R 's together leaves the transfer function unaltered and allows us to consider an output signal taken across both R 's. If we consider the transfer function from V i to V 1 , we have a simple RLC filter. We use a
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