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Unformatted text preview: 1 1 Summary of Lecture #19 10/06/2010 • LP, HP, BP and BR filters • Normalized circuits or prototype circuits • 1 Ω ΩΩ and 1 rad/s • Magnitude scaling • How and its effect • Examples • Frequency scaling • How and its effect • Examples • Brief discussion leading to convolution integral • Flip, shift, multiply and integrate ∫ ∫ ∞ ∞ ∞ ∞ τ τ τ = τ τ τ = = d ) t ( h ) ( f d ) ( h ) t ( f ) t ( h ) t ( f ) t ( y HW #7, HW #7 Examples of low pass pass filters Roll off rate: 20 dB/decade (first order) 40 dB/decade (2nd order) RCs 1 1 ) s ( H + = 1 RCs 3 ) RCs ( 1 ) s ( H 2 + + = Pass band Stop band ϖ p or f p : pass band edge freq. ϖ s or f s : stop band edge freq. Roll off rate 3 First order LP filter 1 s 01 . 1 ) s ( H + = 20dB/dec. R = 1 Ω C = 0.01 F 4 Second order LP filter 1 s 003 . s 0001 . 1 ) s ( H 2 + + = 40 dB/dec. R = 1 Ω C = 0.01 F 5 Examples of high pass filters Roll off rate: +20 dB/decade (first order) + 40 dB/decade (2nd order) ) L / R ( s s ) s ( H + = 2 2 2 ) L R ( s L R 3 s s ) s ( H + + = Stop band Pass band High pass filters ϖ p or f p : pass band edge freq. ϖ s or f s : stop band edge freq. Roll off rate 6 First order HP filter s H(s) s 100 = + 20 dB/dec. R = 1 Ω L = 0.01 H 2 7 Second order HP filter 4 2 2 10 s 300 s s ) s ( H + + = +40 dB/dec. R = 1 Ω L = 0.01 H 8 Examples of band pass filters 1 RCs LCs RCs ) s ( H 2 + + = Pass band edge freq.: ϖ p1 ( or f p1 ) and ϖ p2 ( or f p2 ) 9 Second order band pass filter 100 s 10 s s 10 ) s ( H 2 + + = R = 1 Ω C = 0.1 F L = 0.1 H 10 Examples of band rejection filters 1 Cs ) R R ( LCs 1 Cs R LCs ) s ( H 2 1 2 2 2 + + + + + = Stop band edge freq : ϖ s1 ( or f s1 ) and ϖ s2 ( or f s2 ) 11 Second order band rejection filter...
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This document was uploaded on 01/13/2012.
 Spring '06

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