The transfer function of the Butterworth low pass filter is given as H(s)=A(s2+0.518s+1)(s2+1.414s+1)(s2+1.932s+1)𝐻(𝑠)=𝐴(𝑠2+0.518𝑠+1)(𝑠2+1.414𝑠+1)(𝑠2+1.932𝑠+1)What is the maximum passband gain (A) of this filter?
Question
The transfer function of the Butterworth low pass filter is given as H(s)=A(s2+0.518s+1)(s2+1.414s+1)(s2+1.932s+1)𝐻(𝑠)=𝐴(𝑠2+0.518𝑠+1)(𝑠2+1.414𝑠+1)(𝑠2+1.932𝑠+1)What is the maximum passband gain (A) of this filter?
Solution
The maximum passband gain (A) of a Butterworth filter is always 1. This is because the Butterworth filter is designed to have a frequency response that is as flat as possible in the passband. Therefore, the maximum passband gain (A) of this filter is 1.
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