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lec28 - Summary of Lecture#28 Analog filters Low pass...

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1 1 Summary of Lecture #28 10/30/09 Analog filters Realization of LP filters, examples Transformation from LP to HP, BP and BR Frequency and magnitude scalingT Examples Additional remarks on Sallen-Key circuit An example of active BP filters Transformation from LP filters to HP filters An example of RLC HP filters See me before next Friday, Nov. 6, 2009 if your test 2 score is less than 25. 2 Low pass filters Ideal specification of low pass filters Brick wall specification |H(j ϖ )| = 1 for ϖ ϖϖ < ϖ p |H(j ϖ )| = 0 for ϖ ϖϖ > ϖ p Realization or approximation Butterworth low pass transfer characteristic (maximum flat in pass band) Chebyshev low pass transfer characteristic (equal ripples in pass band) Inverse Chebyshev low pass transfer characteristic (equal ripples in stop band) Elliptic low pass transfer characteristic (equal ripples in pass and stop bands) Prototype circuit with ϖ p = 1 rad/s, rate of roll off and 1- ohm impedance level Frequency and magnitude scaling 2 examples, by coefficient matching |H(j ϖ )| 1 ϖ p 0 ϖ 3 Max. flat in pass band Equal ripples in pass band Equal ripples in stop band Equal ripples in pass and stop bands |H|’, |H|”, |H|’” … are 0 dB at ϖ = 0. 4 Ex. 2. Design a LP filters with ϖ p = 218.7 π rad/s , a roll off rate of 60 dB/dec . and for a 100 load. 60 dB/dec. third order filter By applying KCL to nodes 1 and 2, we obtain 2 1 2 1 2 1 2 2 1 3 2 1 C LC 2 s C LC C C L s ) C 1 C 1 ( s ) C LC /( 1 ) s ( H + + + + + + = 5 2 1 2 1 2 1 2 2 1 3 2 1 C LC 2 s C LC C C L s ) C 1 C 1 ( s ) C LC /( 1 ) s ( H + + + + + + = 1 s
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