Question: A second-order analog low-pass filter has a transfer function where Q is called the quality factor of the filter. (a) Show that the maximum of

A second-order analog low-pass filter has a transfer function

H(s) s +s/Q+1

where Q is called the quality factor of the filter.

(a) Show that the maximum of the magnitude

€¢ for Q < 1/ˆš2occurs at Ω = 0.

€¢ for Q ‰¥ 1/ˆš2occurs at a frequency different from zero.

(b) Show that for Q = 1/ˆš2 = 0.707, the half-power frequency of this filter is Ωhp = 1 rad/sec.

H(s) s +s/Q+1

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