quiz 4 solutions - ECE 412 INTRODUCTION TO FILTER SYNTHESIS...

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Unformatted text preview: ECE 412 INTRODUCTION TO FILTER SYNTHESIS University of Illinois at Chicago Quiz #4 Spring 2013 Name (print): M UIN: é Problem 1 (4 points) A second order Butterworth lowpass filter implemented with a. Sallen-Key circuit is shown below. Determine the 3dB—frequency of this filter in Hz. Hint: You don’t have to use the transfer function to answer this question. C1=3.206 nF 3J8 freiuemj =04 04%) $ 71,0 3 £3; ’Uin “out 1.0. 27,452 112 27,4g amp» A»??? “707; L—rw J. ’6", __ 27000 DAV”; CK/féf—Uon 6" 16min = “I”; = 91/40st 6 3. 205,; I “(I z 44/135710: _ f 22000 “ [.6335 .: M: w, = lé‘, 335 rad/5 K 524; 2’ 2. gm DR. VAHE CALISKAN 1 of 3 Handed out: March 15, 2013 ECE 412 INTRODUCTION TO FILTER SYNTHESIS University of Illinois at Chieago Quiz #4 Spring 2013 Problem 2 (6 points) In this problem, you are to design a. Butterworth filter to meet the specifications shown below. a(f) .. 15dB “my- 1J5 OOH/32 3 ME I 1.2kHz 2kHz w, = zzrlzaa a5: ZWZDDD —-,vw (rd/5) (a) (1 pt) Determine the order 11, required for a. Butterworth response. [ [Calm/Mo __ l ] l0 ’-5_I ll ’ , -- , = 4 5 a 27-2000 ' 2 5’3’( VWI’) 2 7 (Zn/zoo) (b) (1 pts) Find the 3dB frequency we so that the specs are met exactly at the edge of the stop band. 50‘ Z 7!” 1000 (Mo : dmi ’ 10-7)!" [-74% [/0 I';’/]7l; 2’ 8725" mall? I 350 ~0,6’07¢jam 0, 5/00 = 62. ~0,3091J'0,95/ /, (If: (9; DR. VAHE CALISKAN 2 of 3 Handed out: March 15, 2013 ECE 412 INTRODUCTION TO FILTER SYNTHESIS University of Illinois at Chicago Quiz #4 Spring 2013 (d) (1 pt) Design the unsealed version of the filter. Make sure to denote the ago and Q for each stage. Do not scale the circuit yet. r I 2431.230: I 22;: 3.2?{F : J 0 Ifl l l l - I ‘ —. I 7 é9=:/ra4/f ' i I _ J 0:000 : MW ' A ; 6L: /,é/g , 510:0,5' (e) (2 pts) Scale the filter (magnitude and frequency) in part (d) so that the final values for all resistors in your design are 33kfl. Make sure that you indicate the scaling factors for your design. This is your final scaled circuit. 06”: 33,000 +0 000/00 0// m ——> 33m {F :2 0,), : 3725’ 00% from, part (‘1 Co/J .— 6 -= ———— ... new 15ml; 175’. 53mg" t/.20.F NM: 3.911,: “H 175an /.05'n::Z- ,- - fll/ rcxistor: are 33/07, DR. VAHE CALISKAN 3 of 3 Handed out: March 15, 2013 ...
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