Lesson+22 - 1 Lesson 22 Lesson 22 Challenge 21 Op Amp...

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1 Lesson 22
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Challenge 21 Op Amp High-Order Filters and their Applications Ch15:4 Challenge 22 Time Magazine Lesson 22 2 Lesson 22
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Challenge 21 A very popular active filter architecture is called the Sallen-Key filter. With a Sallen-Key filter, a 2 nd order filter can be realized using 1 OpAmp. Shown is a Butterworth lowpass Sallen-Key filter. What is the filter’s -3dB frequency? R1 R2 C1 C2 GND AR 3 Lesson 22 (15:35) 2 1 2 1 1 1 1 2 2 2 1 2 1 1 1 1 1 C C R R s C R C R s C C R R s H ) ( Note: Formulas involving Q= 0 /BW relate to bandpass and bandstop filters.
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R1 R2 C1 C2 GND AR ) / ) ( ; ) ( ; ) ( 3dB ( 0.707 not 2 1 1 1 0 1 2 1 2 j H H s s s H 4 Lesson 22 The -3dB frequency is deifned by a non-linear equation that is hard to solve. Is there alternative? Cheat!
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Maximum gain at DC. H(j0)=1. Find -3dB frequency 0 s.t. |H(j 0 )|=0.707. n=[1]; d=[1 2 1]; [H,w]=freqs(n,d); plot(w,abs(H)) ~0.64. 5 Lesson 22 1 2 1 ) ( 2 s s s H
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n=[1]; d=[1 2 1]; [H,w]=freqs(n,d); plot(w,abs(H)) ~0.64. 6 Lesson 22 1 2 1 ) ( 2 s s s H 707 . 0 28 . 1 59 . 0 1 1 28 . 1 41 . 0 1 ) 64 . 0 ( j j j H
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Lesson 22 Broadband f 2 /f 1 2 The author discusses the design of passband and stopband filters in somewhat a non-traditional manner. The filters can also be classified as being narrowband or broadband. 0 f 1 f 0 f 2 7 Lesson 22
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Bandpass: The idea is as shown. 8 Lesson 22 O p t i o n a l Optional Optional
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Passband overlap Cascade: H(s)=H 1 (s)H 2( s) 9 Lesson 22
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Bandstop: The idea is as shown. 10 Lesson 22
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Bandstop (notch): 11 Lesson 22
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Express the bandpass filter’s transfer function as: H(s) = - K s /(s 2 + s+ o 2 ) : 12 Lesson 22 In-Class Problem C 2 R 2 R 1 C 1
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2 2 2 0 2 1000 70 70 57 3 s s s s s s K s H ) ( . ) ( ω β β 0 = 1000 = 31.6 r/s =70 r/s (BW) K= -3.57 Q= 0 / = 0.45 13 Lesson 22 Using the assigned component values (Section 15.3):
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These methods are not particularly practical. There are optimal design procedures based on the choice of classic filter model: Bessel Butterworth Chbeyshev I Chbeyshev II Elliptic These methods are designed using tables and graphs (old school) or today using dedicated computer programs (e.g., MATLAB). MATLAB-orchestrated designs to be studied in next lesson. 14 Lesson 22
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Author’s Butterworth motivation. Assume that a set of specifications can be translated into a 4 th order lowpass transfer function H(s). 2 nd order 2 nd order 15 Lesson 22
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Author’s Butterworth motivation. 4 th order Butterworth vs.
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