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 What is the cutoff frequency of the Butterworth filter with a pass band gain KP= -1 dB at ΩP= 4 rad/sec and stop band attenuation greater than or equal to 20dB at ΩS= 8 rad/sec? 
  • a)
    3.5787 rad/sec
  • b)
    1.069 rad/sec
  • c)
    6 rad/sec
  • d)
    4.5787 rad/sec
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
What is the cutoff frequency of the Butterworth filter with a pass ban...
Explanation: We know that the equation for the cutoff frequency of a Butterworth filter is given as

We know that KP= -1 dB, ΩP= 4 rad/sec and N=5
Upon substituting the values in the above equation, we get
Ω_C = 4.5787 rad/sec.
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Most Upvoted Answer
What is the cutoff frequency of the Butterworth filter with a pass ban...
The cutoff frequency of a Butterworth filter can be determined using the formula:

fc = 1 / (2 * π * RC)

where fc is the cutoff frequency, R is the resistor value, and C is the capacitor value.

However, in this case, the pass band gain is given as KP = -1 dB. The pass band gain is the gain at frequencies within the pass band of the filter. In a Butterworth filter, the pass band gain is generally 0 dB, so a KP of -1 dB indicates that there is some attenuation within the pass band.

Since the cutoff frequency is not directly given, it is not possible to determine the exact cutoff frequency of the Butterworth filter with a pass band gain of -1 dB without additional information.
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What is the cutoff frequency of the Butterworth filter with a pass band gain KP= -1 dB at ΩP= 4 rad/sec and stop band attenuation greater than or equal to 20dB at ΩS= 8 rad/sec?a)3.5787 rad/secb)1.069 rad/secc)6 rad/secd)4.5787 rad/secCorrect answer is option 'D'. Can you explain this answer?
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