GATE EE 2015 Set 2 — Question 24
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Analog & Digital Electronics → Operational Amplifiers → Active Filters (Sallen-Key)
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Question
The filters F1 and F2 having characteristics as shown in Figures (a) and (b) are connected as shown in Figure (c).
The cut-off frequencies of F1 and F2 are and respectively. If , the resultant circuit exhibits the characteristic of a
Correct answer
(B) Band-stop filter
Solution
1.Analyze Filter Characteristics:
- Figure (a) shows the characteristic of a Low Pass Filter (LPF) with a cut-off frequency .
- Figure (b) shows the characteristic of a High Pass Filter (HPF) with a cut-off frequency .
- Figure (c) shows the input signal being fed into both filters F1 and F2 in parallel.
- Each filter output reaches the non-inverting (+) input through an equal resistor , so the + input sits at the average of the two outputs: .
- The op-amp's only feedback is from the output to the inverting (−) input, with no resistor from − to ground, so it is a unity-gain voltage follower: .
- Hence , i.e. .
- Since , the LPF (F1) passes frequencies from to , and the HPF (F2) passes frequencies from to .
- In the frequency range between and , neither filter provides a significant output.
- Therefore, the combined circuit passes low frequencies and high frequencies but rejects the middle band .
- This is the defining characteristic of a Band-stop filter.
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