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lecture_08 - MIT OpenCourseWare http/ocw.mit.edu 2.161...

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MIT OpenCourseWare http://ocw.mit.edu 2.161 Signal Processing: Continuous and Discrete Fall 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms .

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1 Massachusetts Institute of Technology Department of Mechanical Engineering 2.161 Signal Processing - Continuous and Discrete Fall Term 2008 Lecture 8 1 Reading: Class handout: Introduction to Continuous Time Filter Design . Class Handout: Introduction to Operational Amplifiers . Class Handout: Op-Amp Implementation of Analog Filters . Second-Order Filter Sections (a) Low-Pass Filter a 0 H lp ( s ) = s 2 + a 1 s + a 0 High Frequency Behavior: The number of poles exceeds the number of zeros ( n m = 2) so that lim | H ( j Ω) | = 0 . Ω →∞ and the high frequency asymptotic slope is -40dB/decade. Low Frequency Behavior: lim | H ( j Ω) | = 1 Ω 0 Mid Frequency Behavior: The response in the region Ω a 0 is determined by the systems damping ratio ζ , and will exhibit a resonant peak if ζ < 0 . 707. | H ( j 9 ) | 1 0 9 1 copyright c D.Rowell 2008 8–1
(b) High-Pass Filter 2 s H hp ( s ) = s 2 + a 1 s + a 0 High Frequency Behavior: The number of poles equals the number of zeros ( n = m ) so that lim | H ( j Ω) | = 1 . Ω →∞ Low Frequency Behavior: There are a pair of zeros at the origin so that lim | H ( j Ω) | = 0 Ω 0 and the low frequency asymptotic slope is +40dB/decade. Mid Frequency Behavior: The response in the region Ω a 0 is determined by the systems damping ratio ζ , and will exhibit a resonant peak if ζ < 0 . 707. 1 0 9 | H ( j 9 ) | (c) Band-Pass Filter a 1 s H bp ( s ) = s 2 + a 1 s + a 0 High Frequency Behavior: The number of poles exceeds the number of zeros ( n m = 1) so that lim | H ( j Ω) | = 0 . Ω →∞ and the high frequency asymptotic slope is -20dB/decade. Low Frequency Behavior: There is a single of zero at the origin so that lim | H ( j Ω) | = 0 Ω 0 and the low frequency asymptotic slope is +20dB/decade. Mid Frequency Behavior: When s = j a 0 , H ( j a 0 ) = 1 which defines the passband center frequency.

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