Active Filter Circuits-2

Active Filter Circuits-2 - Active Filter Circuits Higher...

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1 ECE 307 -9 1 Active Filter Circuits Z. Aliyazicioglu Electrical and Computer Engineering Department Cal Poly Pomona Higher Order Op Amp Filter ECE 307 -9 2 Higher Order Op Amp Filter Cascading Identical Filter To obtain a sharper transition between the pass-band and stop- band, we can add more identical filter in cascade. One filter gives us 20dB/dec slope, two identical cascade filters give us 40 dB/dec slope transition. N identical cascade low-pas filters give us fram the corner frequency n20dB/dec slope Low-Pass Filter Low-Pass Filter Low-Pass Filter Vi Vo ( ) ... cc c c Hs ss s ωω ω ⎛⎞ −− = ⎜⎟ ++ + ⎝⎠ () n c c s = + Transfer function
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2 ECE 307 -9 3 Higher Order Op Amp Filter Cascading Identical Filter R2 R1 C + + - OUT Vo R2 R2 + - OUT C + R1 Vi + - OUT R1 C 1 () 2 n c cn c Hj j ω ωω == + ( ) 21 n cn c =− New Cutoff frequency ECE 307 -9 4 Higher Order Op Amp Filter Example Vo + R1 1 C 1F + - OUT R1 1 Vi Design 4 order low-pass filter with cut-off frequency is 500Hz and a pass-band gain is 10. Use capacitor 1 µ F capacitors From the cutoff frequency ( ) n cn c 4 25 0 0 7222.39 / 0.435 cn c rad s π = 1 c RC = 6 11 138.45 7222.39(10 ) c R C = For gain specification, we need to change R f 2 10(138.45) 1383.5 f RG R =
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3 ECE 307 -9 5 >> f=10:1:1000; >> w=2*pi*f; >> wc=7222.39; >> h=20*log10(10)- 80*log10(abs(1+j*w/wc)); >> semilogx(f,h) >> grid on >> xlabel(‘F[Hz]') >> ylabel('|H(jf)| dB') >> Example Higher Order Op Amp Filter 4 4 1 ( ) ( 10) ( 10) 1 c c c Hj j j ω ωω ⎛⎞ ⎜⎟ =− + ⎝⎠ + 10 10 20log (10) 20log 1 dB c j A =+ + 7222.39 rad/s c = 2 500 rad/s cn π = Final Cutoff frequency Each filter Cutoff frequency ECE 307 -9 6 Butterworth Filters Butterworth Filters A unity gain Butterworth Filter Transfer function We can set ω c equal to 1 rad/s in the transfer function, then we use scaling transform
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This note was uploaded on 03/12/2008 for the course ECE 307 taught by Professor Z.aliyazicioglu during the Winter '07 term at Cal Poly Pomona.

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Active Filter Circuits-2 - Active Filter Circuits Higher...

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