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Determine the transfer function H(s) for a high pass filter with the following characteristics:
1. a cutoff frequency of 100 kHz
2. a stopband attenuation rate of 40 dB/decade
3. a nominal passband gain of 20 dB, which drops to 14 dB at the cutoff frequency
Write the formula for H(s) that satisfies these requirements.

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Answer:

H(s) =  10 / [ 1 + s / (200*10^3π ) ]^2

Explanation:

Characteristics of the high pass filter

Cutoff frequency = 100 kHz

stopband attenuation rate = 40 dB/decade

nominal passband gain = 20dB  = 20logK = 20

Formula for H(s) satisfying the requirements above

given that the stopband attenuation = 40 dB/decade the formula for H(s) that will satisfy the requirements is a second order filter

H(s) = K / ( 1 + s/Wo ) ^2  ----- ( 1 )

Wo = 2πf = 2π ( 100 * 10^3 ) =  200 * 10^3 π

 K = 10

back to equation ( 1 )

H(s) =  10 / [ 1 + s / (200*10^3π ) ]^2

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