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GT ECE 3050 - ECE3050 — Assignment 17

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ECE3050 — A ssignmen t 171. The figures show in verting amplifier circuits.(a) For the circuit of Fig. (a), specify R1, RF,andROfor a voltag e ga in o f −50,aninput r esistan ce o f 2kΩ, and an output resistance of 1kΩ. If the op amp clips at apeak output voltage of 12 V, specify the maximum peak input v oltage if the op ampis not to be driv en into clipping. Answ ers: R1=2kΩ, RF=100kΩ, RO=1kΩ,and¯¯vI(peak)¯¯=0.24 V.(b) Fig. (b) sho w s th e circuit o f Fig. (a) with a load r esistor connected to the output.Calculate the new v oltage gain if RL=1kΩ. What is the maxim um peak outputvoltage if the op amp is n ot to clip? Answers: vO/vI= −25 and¯¯vO(peak)¯¯=6V.(c)Repeatpart(b)ifthecircuitismodifiedasshowninFig. (c). Answers: vO/vI=−50 and¯¯vO(peak)¯¯=5.97 V. Hin t, use voltage division to solve for¯¯vO(peak)¯¯in term sof¯¯¯v0O(peak)¯¯¯.2. Fig. (a) shows an inverting am plifier with a T feedback net work. Fig. (b) shows theamplifier with a Thévenin equivalent made looking in to the feedbac k netw o rk from theinput. The amplifier is to be designed for an input resistance of 1kΩ and a voltagegain of −1000.IfR2= R4and R3=100Ω, specify the value o f R2and R4.Answers:R1=1kΩ and R2= R4=9.9005 kΩ.13. Show that the same expression for the v olta ge gain of the circuit in figure (a) of problem2 is obtained if Norton equivalen t circuits are made looking ou t of the n egative inpu tthrough R1and R2and the su m of the two Norton currents is set to zero. Hint: Firstshow that the Norton curren t looking into R2is [vO/ (R4+ R2kR3)] × R3/ (R2+ R3).4. The figure sho w s a current to voltage con verter. The circuit is to be designed to con vertan input current of −50 µA into an output voltage of +4 V.(a) Calculate the required value of RF.Answer:RF=80kΩ.(b) If the op amp clips at a peak output v oltage of 12 V, calculate the maximum peakinput current. Answer: i1(peak)=150µA.(c) The circuit is driv en from an amplifie r which can be modeled b y a v o lt age-co ntrolledv oltage source with an open-circuit voltage gain of 10 and an output resistance of2kΩ. Calcu late the overall vo ltag e gain of the two circuits in combination. Answer:vO/vI= −400.5. The figure sho w s a no n-inverting amplifier. The circuit is to be designed for an inputresistance of 10 kΩ, and output resistance of 100 Ω, and an open-circuit v oltag e gainof 20. When the peak output voltage is 10 V, the current through RFand R1is tobe 0.2mA. Specify the resistors in the circuit. Answers: Ri=10kΩ, RO=100Ω,R1=2.5kΩ,andRF=47.5kΩ.6. For the inv e rting amplifier cir cuit of F ig. (c) in Proble m 1, let the open-loop gain ofthe op amp be denoted by A.Inthiscase,theopen-circuitoutputvoltageisgivenbyvO= A (v+− v−).(a) Solve for vOas a function of vI, R1, RF,andA(b) If A →∞,whatisvOgiven b y?7. Repeat Problem 5 for the non-inverting amplifier of Problem 4.8. The figure shows a 4 input inverting summer. The circuit is to be designed for anoutpu t voltag e given b y vO= − (2vI1+4vI2+6vI3+8vI4). When the peak output2voltage is 10 V, the current through RFis to be 0.5mA. Specify the resistors in thecircuit. A nswers: RF=20kΩ, R1=10kΩ, R2=5kΩ, R3=3.33 kΩ,andR4=2.5kΩ.9. The figure shows a non-in verting summer. The gain vO/v+is specified to be 50.IfR3= R4=1kΩ,specifyR1, R2,andRFfor an output v oltage given by vO=5vI1+2vI2.Answers: RF=49kΩ, R1=8.6kΩ,andR2=21.5kΩ.10. Fig. (a) sho ws a differen tial amplifier. Fig. (b) sho ws the equivalent circuit forthe special case R1= R3and R2= RF. It is desired to design the circuit so thatvO=10(vI1− vI2). In addition , the input resistance seen bet ween the t wo inputnodes is to be 10 kΩ.(a) Specify the resistors in the circuit. Answers: R1= R3=5kΩ, R2= RF=50kΩ.(b) For vI2=0, solv e fo r the resistance seen looking in to the vI1input. Answer: 55 kΩ.(c) For vI1=0, solve for the resistance seen looking in to the vI2input. A nswer: 5kΩ.11. The figure shows a differen tial am plifier w ith a source connected between its two inputs.3The circuit elemen ts values are the same as those found in problem 10. Solv e for thev oltage gain vO/vD, vI1, vI2, the voltage at each op amp input, and the common-modeinput v oltage vICM.Answers:vO/vD=10, vI1=5.5vD, vI2=4.5vD, v+= v−=5vD,vICM= vO/2=5vD.12. Fig. (a) show s a sw itch h itter circuit. Fig. (b) sho w s the equivalent circuit wh ichcan be used to calcula te vO. It is given that R1= RF=10kΩ, RP=100kΩ,theresistance belo w t he poten tio m et er wiper is xRP, and the resistance abo ve the wiperis (1 − x) RP,where0 ≤ x ≤ 1.NotethatxRP+(1− x) RP= RP.(a) Pro ve that the Thév en in equivalen t circuit seen looking out of the v+input isthe one sho w n in Fig. (b). What is the maxim um source resistance of this Thévenincircuit? Answer: 25 kΩ.(b) Solve for vO.Answer:vO=(2x − 1) vI.(c) The vInode of the switch hitter is connected to the vI1input of the inverting sum-mer in problem 8. The vOnode is connected to the vI2input of the inverting summ er.The other inputs to the in verting summ er are connected to ground. Solve for vOof theinv ertin g summer. Answer: vO=(2− 8x) vI.13. The figure shows a t wo op amp diff amp. Design the circuit for an output v oltagegiven by vO=50(vI1− vI2). Th e input resistance to eac h input is to be 5kΩ.An-swers: R1= R2= RF 1= R3=5kΩ, RF 2=250kΩ.414. The figure sh ows a three op amp instrumentation amplifier. (a) Design the circuit suchthat vO1− vO2=10(vI1− vI2) and vO=10(vO1− vO2).Answers:1+2RF 1/R1=10,choose R1=2kΩ and RF 1=9kΩ, RF 2/R2=10,chooseRF 2=10kΩ,andR2=1kΩ.(b) For vI1=0.03 V and vI2=0.01 V,calculatevO1, vO2,andvO.Answers:vO1=0.12 V, vO2= −0.08 V,andvO=2V.15. The figure show s a balanced output amplifier. Design the circuit so that vO1= −vO2=6vI.WhenvO1= ±12 V and vO2= ∓12 V, the current through RF 1and RF 2is not toexceed 1mA.Answers:for1mA, R1=2kΩ, RF 1=10kΩ,andRF 2=12kΩ.16. For the circuit shown, show that the Thévenin equivalent circuit seen looking into RFfrom the v−node consists of the voltage vOR2/ (R1+ R2) in series with the resistanceRF+R1kR2. Use superposition to sho w that v−= i1(RF+ R1kR2)+vOR2/ (R1+ R2).Set v−=0to show that vO= −i1[R1+ RF(1 + R1/R2)].517. For the circu it shown, let vObe the o p amp output v o ltage.(a) With the load open circuited, i.e. iL=0, use superposition of v1and vOto showthat vL(oc)=(v1R2+ vOR1) / (R1+ R2).ShowthatvO=


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