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Unformatted text preview: EE202 Exam III April 13, 2006
Name: __________________________________
(Please print clearly) Student ID: _________________ CIRCLE YOUR DIVISION
DeCarlo 2:30 MWF Furgason 3:30 MWF
INSTRUCTIONS There are 10 multiple choice worth 5 points each and there is 1 workout problem worth 50 points. This is a closed book, closed notes exam. No scrap paper or calculators are permitted. A transform table will be handed out separately. Carefully mark your multiple choice answers on the scantron form. Work on multiple choice problems and marked answers in the test booklet will not be graded. Nothing is to be on the seat beside you. When the exam ends, all writing is to stop. This is not negotiable. No writing while turning in the exam/scantron or risk an F in the exam. All students are expected to abide by the customary ethical standards of the university, i.e., your answers must reflect only your own knowledge and reasoning ability. As a reminder, at the very minimum, cheating will result in a zero on the exam and possibly an F in the course. Communicating with any of your classmates, in any language, by any means, for any reason, at any time between the official start of the exam and the official end of the exam is grounds for immediate ejection from the exam site and loss of all credit for this exercise. Do not open, begin, or peek inside this exam until you are instructed to do so EE202, Ex 3 Sp 06 page 2 MULTIPLE CHOICE.
1. What is Vout ( t ) for the following circuit if Vin ( t ) = 10 cos( t ) V ? (1) 5 cos( t ! 90o ) V (5) 10 cos( t ! 90o ) V (2) 5 cos( t ) V (6) 10 cos( t ) V (3) 5 cos( t + 45o ) V (7) 10 cos( t + 90o ) V (4) 5 cos( t + 90o ) V (8) None of these EE202, Ex 3 Sp 06 page 3 2. The Q of the circuit shown below is: (1) 1 (2) 2 (3) 6 (4) 8 (5) 10 (6) 20 (7) 40 (8) none of these 10Ω Vin(s) 10Ω + Vout(s) 1 H 40 1 F 10 – EE202, Ex 3 Sp 06 page 4 3. Shown below is a lowpass Butterworth filter prototype having the following transfer function: 0.5 H ( s) = 3 s + 2s 2 + 2s + 1 The circuit is to be magnitude and frequency scaled so that the source and load resistances are 2kΩ and the new value of the capacitor is 4μF. What is the frequency of the 3dB point? (1) .5 rad/s (5) 500 rad/s (2) 2 rad/s (6) 1000 rad/s (3) 125 rad/s (7) 2500 rad/s (4) 250 rad/s (8) None of these EE202, Ex 3 Sp 06 page 5 4. The real coil shown below is characterized by an inductance 200 mH and a Q = 50 @ 2000 rad/s. The complex impedance, Z(s), of the oneport shown below is given by: (1) 4 +.2s (5) 12 +.2s (2) 4.8 +.2s (6) 4 + 5s (3) 5.25 +.2s (7) 8 + 5s (4) 8 +.2s (8) None of these EE202, Ex 3 Sp 06 page 6 5. In terms of the voltages and currents defined in the figure below, the correct expression for V2(s) is: (1) sL1I1 + sM I2 (5) sL2I2  sM I1 (2) sL1I1  sM I2 (6) sL2I2 + sM I2 (3) sL2I2 + sM I1 (7) sL2I2 + sM I1 (4) sL2I2  sM I1 (8) None of these EE202, Ex 3 Sp 06 page 7 6. The coupled inductors shown below highpass filter the input signal i(t). At what frequency will the 3dB point occur (i.e. at what frequency will the magnitude of the transfer function be 3dB below the maximum value)? (1) 1 rad/s 5 (2) 1 rad/s 3 (3) 15 rad/s 8 (4) 17 rad/s 7 (5) 3 rad/s (6) 5 rad/s (7) 7.5 rad/s (8) None of these EE202, Ex 3 Sp 06 page 8 7. A transfer function, H ( s) = K n( s) , has the polezero plot shown below. Given that K = 4, d ( s) determine the value of the zero phaseshift frequency (also the peak frequency), ωp, and the bandwidth, Bω. ωp and Bω are respectively (in radians/second):
(1) 2 & 4 (5) 2 5 & 4 (2) 4 & 4 (6) 16 & 2 (3) 4 & 2 (7) 16 & 4 (4) 2 5 & 2 (8) None of these EE202, Ex 3 Sp 06 page 9 8. For the circuit shown below with iL (0! ) = 0 A and vC (0! ) = 2 V , the current, iL (t ) , in amps for t > 0 is given by: 2 " t& 1# !t !2 t !t !2 t !t !2 t (1) ! e + 2e (2) 2 e ! e (3) !3e ! 4e (4) %3!(t ) " 8e 3 ( 9% ( $ ' 2& "t 2 1# ! e! t + 3 e!3t (5) !3e! t + 4e!2t (6) (7) (8) None of these %3!(t ) + 8e 3 ( 3 9% ( $ ' ( ) ( ) EE202, Ex 3 Sp 06 page 10 9. & 10. For the opamp filter shown below determine the Q and the maximum of the magnitude of the transfer function, H ( j!) .
max 9. The Q of the circuit is? (1) R1C1 + R f Cf R1C1R f Cf
R f Cf R1C1 + R f Cf (2) R1C1R f Cf R1C1 + R f Cf R1C1R f Cf R1Cf + R f C1 (3) R1C1R f Cf R1C1 + R f Cf R1Cf R1C1 + R f Cf (4) R1C1 R1C1 + R f Cf (5) (6) (7) (8) None of above EE202, Ex 3 Sp 06 page 11 10. The maximum of the magnitude of the transfer function, H ( j!) (1)
R f Cf R1C1 R f Cf R1C1 + R f Cf max is? (4)
R1C1 R f Cf (2) R f C1 R1Cf R1C1 R1Cf + R f C1 (3) R1Cf R f C1 R f C1 R1C1 + R f Cf (5) (6) (7) (8) None of above EE202, Ex 3 Sp 06 page 12 WORKOUT PROBLEM. (50 points) All work is to be included and shown on the attached pages. ANSWERS without work = NO CREDIT!!!!! There are two parts. See following pages for part 2. PART 1: (41 points) Mickey “Mike” Farad and Millie “Nano” Ohm have designed a unique NORMALIZED low pass filter having transfer function
H NLP ( s) = 4 s2 + 0.5s + 4 (a) (6 pts) Determine ! p (the normalized pole frequency) and Q p (the Q of the filter): ! p = ___________ and Q p = ___________. (PROPERLY IDENTIFY AND SHOW WORK ON ATTACHED PAGES.) (b) (12 pt total) Realize the normalized transfer function using the Sallen and Key circuit below; the transfer function of the Sallen and Key circuit below is
2 1 s2 + s + 1 Q Note: The circuit gain will be adjusted in the next design step. H CIRCUIT (s ) = The FINAL values of the normalized circuit parameters are: R1 = ___________ R2 = ___________ C1 final = ___________ and C2 final = ___________ (PROPERLY IDENTIFY AND SHOW WORK ON ATTACHED PAGES.) (c) (16 point total) Use input attenuation (a voltage division circuit consisting of two resistors R A and RB to replace R1 ) to adjust the dc gain of the circuit. Determine the DC gains of the circuit and the
filter transfer function. DC Gain Transfer function = ___________
R A = ___________ DC Gain Circuit = ___________ RB = ___________ (PROPERLY IDENTIFY AND SHOW WORK ON ATTACHED PAGES.) EE202, Ex 3 Sp 06 page 13 (d) (7 points total) MickeyMike and Millie Nano want the normalized cutoff frequency of 2 rads/s (an unfortunate error in their original design) to be moved to 2000 rad/s. Further, they want the capacitor C1 final to become 0.5 micro Farads after frequency and magnitude scaling. Determine the scale factors K f and K m in that order. K f = ___________ K m = ___________ (PROPERLY IDENTIFY AND SHOW WORK ON ATTACHED PAGES.) EE202, Ex 3 Sp 06 page 14 PART 2. (9 points) In the blink of an eye, MikeyMike and Millie Nano realize they could have V ( s) 4 realized the NLP filter H NLP ( s) = out with a lot less work, even by inspection, using = Vin ( s) s2 + 0.5s + 4 the biquad below. The values for G1, G2, and G3 in mhos are:
G1 = _______ G2 = _______, G3 = _______ . EE202, Ex 3 Sp 06 page 15 EE202 Exam III April 10, 2008
Name: __________________________________
(Please print clearly) Student ID: _________________ CIRCLE YOUR DIVISION
Morning 8:30 MWF Afternoon 12:30 MWF INSTRUCTIONS There are 13 multiple choice worth 5 points each and there is 1 workout problem worth 35 points. This is a closed book, closed notes exam. No scrap paper or calculators are permitted. A transform table will be handed out separately. Carefully mark your multiple choice answers on the scantron form. Work on multiple choice problems and marked answers in the test booklet will not be graded. Nothing is to be on the seat beside you. When the exam ends, all writing is to stop. This is not negotiable. No writing while turning in the exam/scantron or risk an F in the exam. All students are expected to abide by the customary ethical standards of the university, i.e., your answers must reflect only your own knowledge and reasoning ability. As a reminder, at the very minimum, cheating will result in a zero on the exam and possibly an F in the course. Communicating with any of your classmates, in any language, by any means, for any reason, at any time between the official start of the exam and the official end of the exam is grounds for immediate ejection from the exam site and loss of all credit for this exercise. Do not open, begin, or peek inside this exam until you are instructed to do so EE202, Ex 3 Sp 08 page 2 MULTIPLE CHOICE.
1. In terms of the voltages and currents defined in the figure below, the correct expression for V2 ( s ) is: (1) L1sI1 + MsI 2 (5) ! MsI1 ! L2 sI 2 (2) L1sI1 ! MsI 2 (6) MsI 2 ! L2 sI 2 (3) MsI1 + L2 sI 2 (7) MsI1 ! L2 sI 2 (4) ! MsI1 + L2 sI 2 (8) None of above 2. Suppose R = 4 Ω. The real coil shown below is characterized by an inductance of 2 H and a Q = 25 at 200 rad/s. The input impedance, Zin ( s ) : (1) 16 + 2s (5) 12 + 2s (2) 20 + 2s (6) 4 + 2s (3) 404 + 2s (7) 16 – 2s (4) 8 + 2s (8) None of these EE202, Ex 3 Sp 08 page 3 3. If R = 0.6 Ω, L = 0.1 H, and C = 0.1 F, then the resonant frequency ! r " 0 in rad/sec of the circuit sketched below is: (1) 10 (2) 100 (3) 64 (4) 8 (5) 36 (6) 6 (7) 136 (8) none of above EE202, Ex 3 Sp 08 page 4 THE CIRCUIT BELOW IS FOR PROBLEMS 4 – 6. The band pass circuit shown below has transfer function R2 s Vout ( s) L H ( s) = = R + R2 Vin ( s) 1 s2 + 1 s+ L LC It is known that ! m = 10 rad/s, R1 = 0.2 , Bw = 5 , and H max = 0.8 . 4. The exact half power frequencies are !1 and ! 2 (in rad/s) (1) 5, 5 (5) 7.5, 12.5 (2) 5, 15 (6) 95, 105 (3) 0, 20 (7) 97.5, 102.5 (4) 8.5, 12.5 (8) None of these 5. The value of R2 is (in ohms): (1) 1 (5) 16 (6) 0.8 (2) 2 (7) 8 (3) 0.2 (8) None of these (4) 4 6. The values of L and C respectively are (in H and F): (1) 0.05, 0.2 (5) 0.25, 0.04 (2) 0.2, 0.05 (6) 0.01, 1 (3) 1, 0.01 (7) None of these (4) 0.1, 0.1 EE202, Ex 3 Sp 08 page 5 7. In the circuit below, L = 0.2 H, C = 0.05 F, Rs = 0.25 Ω, R p = 16 , then the approximate half power frequency !1 (rad/s) and the bandwidth Bw (in rad/s) are: (1) 7.5, 5 (5) 8.75, 2.5 (2) 7.5, 2.5 (6) 8.75, 1.25 (3) 7.5, 1.25 (7) None of these (4) 8.75, 5 8. Referring to the circuit of problem 7, the approximate value of H max is: (1) 1 (5) 5 (2) 2 (6) 0.25 (3) 2.5 (7) None of these (4) 4 EE202, Ex 3 Sp 08 page 6 THE FOLLOWING IS FOR PROBLEMS 9, AND 10. A 3rd order Butterworth HP filter has 3 dB down point at ! c = 10 rad/s. The 3rd order Butterworth NLP prototype circuit is given in the figure below and has transfer function 1 V (s) 1 LC1C2 H cir ( s ) = out = =3 2 Vin ( s ) s 3 + 1 s 2 + C1 + C2 s + 1 s + 2s + 2s + 1 C1 LC1C2 LC1C2 9. The values of L in H and C1 and C2 in F to realize the 3 dB NLP 3rd order prototype are: (1) 1, 2, 0.5 (2) 1.334, 0.5, 2 (3) 1.334, 0.5, 1.5 (4) 0.5, 2, 1 (5) 1, 0.5, 2 (6) 0.75, 1.334, 1 (7) none of above 10. Given the appropriate transformation of the NLP circuit to HP form, the value of C HP in F to realize the 3rd order HP filter in which ! c, HP = 10 rad/s and the source resistance is 3 Ω is:
1 40 4 (6) 90 (1) (2) 0.75 (3) 0.25 (4) 1 120 (5) 9 40 (7) none of above EE202, Ex 3 Sp 08 page 7 CIRCUIT FOR PROBLEMS 11, 12, AND 13. A Sallen and Key circuit with parameter choices as indicated is shown below The circuit transfer function is H cir ( s ) = 11. The value of the circuit Q is: (1) 0.5 (2) 2 (7) none of above (3) 0.04 12.5 2 . If this circuit is to realize H LP ( s ) = 2 . 1 2 s + 2 s + 25 s + s +1 Q (4) 0.25 (5) 5 (6) 2.5 12. The final values of C1 and C2 to realize H LP ( s ) are C1 f and C2 f in F which are: (1) 0.2, 0.4 (2) 1, 0.5 (3) 0.2, 0.1 (4) 0.2, 0.08 (5) 0.2, 0.8 (6) 0.2, 0.5 (7) 0.2, 0.1 (8) none of above 13. If input attenuation is used to adjust the DC gain using a combo of RA and RB as shown below, then the values of RA and RB (in ohms) are respectively: (1) 2, 2 (5) 1.25, 4 (2) 4, 1.333 (6) 4, 1.25 (3) 1.333, 4 (7) 3, 1.5 (4) 4, 3 (8) none of above EE202, Ex 3 Sp 08 page 8 WORKOUT PROBLEM (35 PTS) V 2 s + 0.1 Use the observable canonical form biquad realization technique to H nuts ( s ) = out = 2 as Vin s + 2s + 4
follows: (i) (5 pts) Construct the differential equation (time domain) in vout (t ) and vin (t ) associated with H nuts ( s ) . (s 2 !! ! ! + 2 s + 4 Vout = ( 2 s + 0.1)Vin !! !!! vout + 2 vout + 4 vout = 0.1vin + 2 vin ) (ii) (5 pts) Use the D k and D ! k notation as per the class examples to put the differential equation of part (i) into the proper form for constructing the observable canonical biquad realization.
D 2 vout + 2 Dvout + 4 vout = 0.1vin + 2 Dvin implies vout = D !2 ( 0.1vin ! 4 vout ) + D !1 ( 2 vin ! 2 vout ) (iii) (6 pts) Given your (correct) answer to (ii), define the variable x1 as per the class room derivation, and construct and draw an op amp circuit for vout (t ) in terms of vin (t ) and x1 (t ) . x1 = vout = D !2 ( 0.1vin ! 4 vout ) + D !1 ( 2 vin ! 2 vout )
No need for any op amp circuit. (iv) (9 pts) Given your (correct) definition of x1 , properly define the x2 , and construct and draw an op amp circuit whose output is x1 (t ) . Dx1 = D !1 ( 0.1vin ! 4 vout ) + ( 2 vin ! 2 vout ) = x2 + 2 vin ! 2 x1 . Thus
! ! " x1 = ! x1 = ! " x2 ! 2 " vin ! 2 " ! x1
(v) (10 pts) Construct the op amp circuit whose output is ± x2 (t ) depending on the sign needed for the input to the circuit for x1 (t ) . EE202, Ex 3 Sp 08 page 9 1. V2 ( s ) = MsI1 ( s ) ! L2 sI 2 ( s ) ; (7) 2. Q = !L 200 * 2 ! "! 25 = ! "! Rs = 16 Ω.; (2) Rs Rs L R # & +2 3. Yin ( j! ) = j! %C " 2 ; thus 2 2( R + L ! ' R + L2! 2 $
C! L R 2 + L2" 2 = 0 ! #!" 2 = 1 R2 ! 2 = 100 ! 36 = 64 ; (4) LC L 4. !1, 2 = ! m ! Bw = 7.5,12.5 ; (5) 2 5. H max = 0.8 = R2 R2 = ! !! R2 = 0.8 ! " . (6) R2 + R1 R2 + 0.2 6. Bw = 5 = R1 + R2 1 = ! !! L = 0.2 H and C = 0.05 F. (2) L L 7. Qcap = ! R pC = 10 * 16 * 0.05 = 8 . Then Rseries = Rp
2 Qcap = 16 = 0.25 . 64 Req = 0.5 Ω. Thus Bw = Req L = 2.5 . !1 = 10 " 1.25 = 8.75 rad/s. ANSWER (5) 8. H max 1 5 =L= = 2 ANSWER (2) Bw 2.5
4 H. ANSWER (3) 3 9. C1 = 0.5 F, C1 + C2 = 2 ! !! C2 = 1.5 F, and L = 10. C NHP = 1 1 3 1 F ANSWER (1) ! !! C HP = = = L LK m K f 4 * 3 * 10 40 11. Q = 5 = 2.5 ANSWER (6) 2 12. C1 f = 13. 1 = 1 1 2 8 1 = = = F. ANSWER (4) = 0.2 F and C2 f = 5Q 12.5 25 100 5 RA RB 1 = RA ! ! RA = 4 ! " ANSWER (2) RA + RB 4 EE202, Ex 3 Sp 08 page 10 Original Circuit Exact Equivalent Circuit at ω0 Approximate Equivalent circuit, for high Q, (QL > 6 and QC > 6) and ω within (1 ± 0.05) ! 0 ...
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