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EE3115 Exam2 Solutions F2010

# EE3115 Exam2 Solutions F2010 - Department of Electrical...

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Unformatted text preview: Department of Electrical Engineering University of Minnesota Hour Exam #2 EE3115 Nov. 15, 2010 Instructions 1 1. Closed Book Exam — single 85 x11" crib sheet permitted 2. Work problems in space provided. 3. Exam begins at 9:05 AM and ends at 9:55 A.M. 4. Calculators permitted. \3 O /U 7/7?) n5 Name: |.D.#: 1. /7O 2. I65 3. /65 Total /200 l. (70 points) Consider the feedback ampliﬁer shown below. The characteristics of the open—loop op amp are also shown below. Blank log-log and linear—log graphs are provided on the following pages for constructing Bode plots, if needed. Op Amp Characteristics 10“ 2 (1+ jf/104)(1+ jf/105)(l+ 17/106) 00 ; Rozo a. (20 points) For what range of values of Rf is the feedback ampliﬁer shown above unstable? : 1.5. o F Bale. his 076 B MM’FJ o;x/O°P§£N}phase = /o" I 716 “MRS be” -7. ﬂ . :- r5 1 . l0 ’15? a ‘F Irish-6 l} aux ' b. (30 points) V o The closed loop ampliﬁer gain V__ is to be 20 db. Dominant pole compensation of the 1n open-loop ampliﬁer is to be used to provide a phase margin of 45° in this application. What should be the value of the dominant pole? .510. Bede/94,75- 6, we c. (20 points) The terminals labeled A and B in the circuit below are internal nodes of the open loop op amp which are brought to the outside world for purposes of frequency compensation. The circuit shown below represents the internal equivalent circuit of the open loop op amp at that node pair. Connect an external circuit element or elements to implement the dominant pole found in part b. The values of the external circuit elements must be speciﬁed. 500 k!) 0 800 RC! I. t. y 12:} 3’15) I c ' Edy—315,555: ‘ C [Db] 100 80 60 4O 20 3 ' . 8 10 10 1o 10 1o 10 10 10 Frequency [Hz] I 2. (65 points) The ampliﬁer shown in the circuit below must have an input resistance Rin .<_ 20 S2 and an output resistance Rout s 1 k9. An op amp having the equivalent shown below is available for constructing the required ampliﬁer. Op amp equivalent circuit a. (20 points) Specify the type of feedback that should be used with the op amp in order to realize the desired input resistance. Sketch the amplifier topology (open—loop op amp with negative feedback circuit). Make sure to label the op amp terminals with the node numbers shown in the above diagram. No component values are required for this step. .S'huviT—S/i Midi" ‘fegoQbaIc/f b. (25 points) Specify the required value of the feedback parameter [3 and the resulting values of the components in the feedback network. The loading effects of the feedback network can be neglected. MK ‘4 4 q ~F - 423,—” ,D Fou+~EI+ 9:035 ‘17 r -- ’2 m c. (20 points) xS‘l/D With the value of [3 found in part b), what is the value of closed loop voltage gainV—S‘? ) 4 5 ,, 2' aX/o 3. (65 points) Consider the oscillator circuit shown. The op amp is ideal. a. (30 points) Develop an expression for the oscillation frequency f 0 in terms of the circuit parameters. Law/+5; (ml/56,) R I £2516, Raf/272L212? L(S) :(Iyt V C (Iii—SR9)+ é—CLR—I—SJZ)] 0" J. Q 1 L(<)‘(/+ Ki 5 1? 92+ S/Q(CifCl>7P/ ‘ i K ' gagic} 76/?[29 7417+ / r l I [:Lijﬁ) : 1+ 235) gage 992+ (7;, aﬁCcﬁ‘Qj ’2‘ ‘ I Rﬁmj Term /~ («g R'qu /:S nu Apﬂnam/Iafcﬂbh gm/ c/en/OM/Amﬁor 1 / 2:1: ﬁlm/(7L (71146/2640’ b. (20 points). C1 = 4C2 : 4 nanofarad. Find the required value of R so that f o = 10 kHz. ,2 _ Leif—— 1: I 5 (vi/77027477 \$600" x/zf‘ q (9772(é)2</ D 5 5 P 2 / 0 2 13/ 4 W / 21,5 0. (15 points) Find the required value of Assume R1 = 10 k9. , r - --s P“ Inna 1N4n 723045 //€/ /-//7L—ﬁ 0 ‘ g (7* ﬂit g 2g +C‘l : /7L CA r—~ f» / .72 /9/6 ...
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