lec29 - Summary of Lecture #29 Analog filters General...

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1 1 Summary of Lecture #29 11/02/09 Analog filters General procedure Prototype LP filters Transformation from LP filters to HP filters Frequency and magnitude scaling An example of RLC HP filters Two examples of active HP filters Filter realization based on brick wall specification Find n and ϖ c from ϖ p , ϖ s , A max and A min Examples 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 Realization of high pass filters Low pass filters with ϖ c = 1 rad/s and 1 LP to HP Transformation: s 1/s Inductor in LP filter capacitor in HP filter Capacitor in LP filter inductor in HP filter Frequency scaling ( K f ) to desired ϖ c Magnitude scaling ( K m ) to desired impedance level LP HP LP LP LP L HP P 1 1 L s , L s ( )s L C s 1/ L 1/ L C = = = LP HP HP LP LP L P P L 1 L L 1/ C C 1 s C s s, C C s = = = 5 Ex. 6 A high pass RLC filter Design a second-order Butterworth HP filter with f c = 5500 Hz and two 1000 resistors. Begin with a LP filter of ϖ c = 1 rad/s and 1 . 2 nd order LP Butterworth filter Matching coefficients 2 1/(LC) H(s) 1 1 2 s ( )s L C LC = + + + 2 1 H(s) s 2 s 1 = + + 1 1 2 2, 1 L C LC + = = L 2 H, C 2 F = = LP LP L 2 H, C 2 F = = LP Write 6 Transformation to a HP filter of ϖ c = 1 rad/s and 1 . s
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lec29 - Summary of Lecture #29 Analog filters General...

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