quiz 6 solutions

# quiz 6 solutions - ECE 412 INTRODUCTION TO FILTER SYNTHESIS...

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Unformatted text preview: ECE 412 INTRODUCTION TO FILTER SYNTHESIS S , University of Illinois at Chicago 0 W on 5 Quiz #6 Spring 2013 Name (print): UIN: Z 0 Problem 1 (2 points) The voltage gain transfer function of a second order bandpass ﬁlter (with we 2 10 rad/s and Q = 2) in standard form is given by we ""‘5 H(\$) _ ‘/out(s) : Q 55 Vin(s) 32+gs+wg 52+5s+100 Determine the voltage gain (in dB) at w = 20 rad/s. vol+age jam in dB at A) => 20kg /H(jw)/ 55w - gJW H HOW : ,_ ' Qw) +5jw+100 I05—w2—f- 5J1» /H(5w>/ = 5w /(Ioo--wz)2 + (5102' 5 (2°) [00 loo 4f w:20raJ/.< H ‘20) = .—: m: / (J / 1/000—(Zo)z)z+ (5720))“ 1/(:-3cm)‘,..(m,)z 316,23 /H()20)/ :: 0.31623 DR. VAHE CALISKAN 1 of 4 Handed out: April 26, 2013 ECE 412 INTRODUCTION TO FILTER SYNTHESIS University of Illinois at Chicago Quiz #6 Spring 2013 Problem 2 (6 points) We wish to design a ﬁlter with Chebyshev characteristics to meet the speciﬁcations shown below. Show all steps necessary to determine the 000 and Q for each stage along with the proper magnitude and frequency scaling factors. Final capacitor values should be 47nF. You don’t need to determine the midband gain w ignore this step. Note: all you need are the we, Q, km and 10f for each stage to draw the ﬁnal circuits. o/MI'A 3045 3000 2000 8W 5”” “1% 1000 1500 With, n=3 and dMayzzclB, C/zeé r/tei/ AP “CD‘S/M Oleque ' ._ 22 rJ'SZZ = —0, 1843;} 0,?23/ Gaffe a/jorl'é'hm ﬁr 22/,51; 3 c s 2214-522: 0. 88 (2 J p: 222/3; 0/055 : E _-: 4+ C/gc :: 43073? ; 4.4514172; 4,0503 : Q= = -> i 1 l I K: 2269/56; (.007! w: K+ﬁPTT= M‘f'fl DR. VAHE CALISKAN 2 of4 Handed out: April 26, 2013 ECE 412 INTRODUCTION To FILTER SYNTHESIS University of Illinois at Chicago Quiz #6 Spring 2013 Problem 2 (continued) 4/03 : /\$'/7’4J/J 7 Ca 5 caps: 5'3,Z§mF-'>3017'7/4F ' “(PS Jig/g/gzﬂF/ F .9 /7.‘7‘3//4IC km, low M was r . 30.74,“): ' k — “’52” 33 '. km:- ’7' I 37/ 14ml : 7 :654 " M2- 4-7»)5 :2 ' 47",: ‘2‘ hF 'I‘ __________________....__—-——-v , [SM/AL CII’V’CWT # 23H“; W + 0H Galbﬁol‘éors are Zf7nF DR. VAHE CALISKAN 3 of 4 Handed out: April 26, 2013 ECE 412 INTRODUCTION TO FILTER SYNTHESIS University of Illinois at Chicago Quiz #6 Spring 2013 Problem 3 (2 points) Determine the voltage gain transfer function of the circuit shown below and show that it is in the standard form of a bandpass ﬁlter given by 5393 H(s) : VVOUAS) Q Wn(5) 32+ gs—l—wg [Li/(5)1: Voat(\$/_ R 5K0 DR. VAHE CALISKAN 4 of 4 Handed out: April 26, 2013 ...
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