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21 Pages

Exam308_merged

Course: ECE 302, Fall 2010
School: N.C. State
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Word Count: 2631

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302, ECE Section 2 Spring 2008 April 11, 2008 Exam III Printed Name: ________________ KEY _________________________________ Honor Pledge: I certify that I have neither given nor received unauthorized aid while taking this exam. Signature: ____________________________________________________ - This is a closed book, closed notes test. You may use a calculator Please show all work to get partial credit....

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302, ECE Section 2 Spring 2008 April 11, 2008 Exam III Printed Name: ________________ KEY _________________________________ Honor Pledge: I certify that I have neither given nor received unauthorized aid while taking this exam. Signature: ____________________________________________________ - This is a closed book, closed notes test. You may use a calculator Please show all work to get partial credit. Attach any extra pages that were necessary. DO NOT write on the backs of the pages. SHOW ALL UNITS!!!!! Points will be deducted for incorrect or absence of units. Problem Possible Points 1 30 2 25 3 30 4 15 Total 100 1 Missed Points Total Points Small Signal Model Equations 1 FET gm 2I D = 2K n I D V V TN GS ro = S I BJT gm = C V T +V I D V ro = A I C S DS 1 I D vgs 0.2V V V TN GS V r = o T I C v 5 mV be VT = 0.025 V at room temperature Single Stage Amplifier Terminal Equations Common Collector Common Emitter Terminal Voltage Gain Input Terminal Resistance Output Terminal Resistance Terminal Current Gain Terminal Voltage Gain Input Terminal Resistance Output Terminal Resistance Terminal Current Gain gR mL 1+ g m R Common Base g mR L 1 1+ g m R L r (1+ gmR ) L E r (1+ gm R ) E gm R L 1 gm 1 Rth + gm o ro1 + g m R E o + 1 o Common Source gR mL 1+ g m R S Common Drain ro1 + gm R th o + 1 Common Gate g mR L 1 1+ g m R L 1 gm ro 1+ g m R S 2 gm R L 1 gm ro1+ gm R th +1 1. FET Amplifier Small Signal Analysis (30 points total) 80 io 50 2 ii 100 Q-point: (100A, 6 V) 500 7 VGS = 4 V 53 a. Find gm and ro for the circuit above. gm = 2K n I = 2 * 50 *100 = 0.1 mS D ro = 1 1 = = 752 k I 0.0133*100 D b. Draw the small signal equivalent circuit for the amplifier. Draw the small signal equivalent circuit for the amplifier. 500 500 k vg 44.4 k 1M 7k 3 c. For what values of vi is the small signal model valid? Assume ro approaches infinity. Let vg be the voltage from the gate to Ground, then vg = vgs + (g m * vgs * RS ) = vgs (1 + g m RS ) = vgs (1 + 0.1m * 7 k ) = 1.7 vgs and vg = vi * RG vi * 1M 2v = = i therefore RI + RG 500k + 1M 3 1.7 vgs = 2vi which implies vi 2.55 vgs 3 For the model to be valid v gs 0.2V V = 0.2 4 2 = 0.4 V TN GS substituting in the inequality above, vi 2.55 * 0.4 = 1.02 V d. Find the voltage gain ( Av = vo / vi ) for the amplifier. Show all work. Assume ro approaches infinity. Av = vo g m vgs RL = using the results from above and substituting circuit values, vi vi Av = 0.1* 44.4k * vgs 2.55* vgs = 1.74 4 2. FET/BJT Terminal Equation Derivations (25 point total) a. Draw the small signal equivalent circuit and derive the equation given on the equation sheet for the Terminal Input Resistance, RiB , of the following AC equivalent circuit. Assume ro approaches infinity. RI ib + vi + r vbe + _ o ib _ RB vb + RL vo _ _ RL = R6 || R3 RiB = vb r ib + (ib + oib )RL r ib + (1 + o )ib RL = = = r + (1 + o )RL r + o RL ib ib ib substituting RiB = r + g m r RL = r (1 + g m RL ) 5 and o = g m r Draw the small signal equivalent circuit and derive the equation given on the equation sheet for the Terminal Voltage Gain, Avt , of the following AC equivalent circuit. Assume ro approaches infinity. gmvgs RI S D + vi + _ + R6 vit = - vgs RL vo _ _ Avt = vo g m vgs RL = = g m RL vgs vit 6 G 3. Single Stage BJT/MOSFET Amplifier Problem (25 points) vb RC = 100 k R B = 80 k RE = 450 R I = 20 k R3 = 100 k o = 55 a. For the amplifier above, what is the DC collector current, IC, if the terminal voltage gain of the amplifier (Avt = vo / vb ) is - 100? Assume ro approaches infinity. From the equation sheet, Avt = 100 = Solving, g m = g m RL g m * 50k = 1 + g m RE 1 + g m * 450 100 = 20 mS 50k 45k From the equation sheet, I gm = C V T and VT = 0.025 V Therefore, I C = g mVT = 20m * 0.025 = 0.5 mA b. What is r and gm ? From part a, g m = 20 mS r = o gm = 55 = 2.75 k 20m 7 4. Multistage Amplifier Problem (15 points) Stage 1 Stage 3 Stage 2 +V 15 k 4.7 k 910 k 160 k v3 v2 M3 v1 10 k 1M vi 1.2 Mk 43 k 9k 3k 1.6 k 250 For the circuit above; gm1 = 2 mS gm2 = 54 mS, r2 = 1.97 k gm3 = 1.93 mS Avt1 = - 4.36 Avt2 = - 237 Avt3 = 0.308 a. What is the overall gain of the circuit above, Av = vo / vi ? Assume ro approaches infinity. Av = vo vo v3 v2 v1 1M 1M = = Avt 3 Avt 2 Avt1 = (0.308)( 237 )( 4.36 ) = 315 vi v3 v2 v1 vi 10k + 1M 10k + 1M b. What is the overall gain of the circuit if C4 is removed? Avt3 will remain unchanged. Avt2 will change. Avt1 will change since the input impedance to the second stage changes and therefore the load resistance to the first stage changes. Avt 2 = g m 2 RL 2 237 = = 2.71 1 + g m 2 RE 2 1 + 54m *1.6k Avt1 = g m1RL1 = g m1 (RD1 || RB 2 || (r 2 (1 + g m 2 RE 2 ))) = 2m(15k || 33.9k || (1.97 k (1 + 54m *1.6k ))) = 19.6 Av = Avt 3 Avt 2 Avt1 1M 1M = (0.308)( 2.71)( 19.6 ) = 16.2 10k + 1M 10k + 1M 8 ECE 302, Section 1 Fall 2009 November 11, 2009 Exam III Printed Name: ______________ KEY_______________________________ Honor Pledge: I certify that I have neither given nor received unauthorized aid while taking this exam. Signature: ____________________________________________________ - This is a closed book, closed notes test. You may use a calculator Carry all calculations to 3 significant digits Show all work to get partial credit. Attach any extra pages that were necessary. Use the backs of the pages if you need more space. SHOW ALL UNITS!!!!! Points will be deducted for incorrect or absence of units. Problem Possible Points 1 40 2 40 3 20 Total 100 1 Missed Points Total Points Small Signal Model Equations 1 FET gm 2I D = 2K n I D V V TN GS ro = S I BJT gm = C V T +V I D V ro = A I C S DS 1 I D vgs 0.2V V V TN GS V r = o T I C v 5 mV be VT = 0.025 V at room temperature Single Stage Amplifier Terminal Equations Common Collector Common Emitter Terminal Voltage Gain Input Terminal Resistance Output Terminal Resistance Terminal Current Gain Terminal Voltage Gain Input Terminal Resistance Output Terminal Resistance Terminal Current Gain gR mL 1+ g m R Common Base g mR L 1 1+ g m R L r (1+ gmR ) L E r (1+ gm R ) E gm R L 1 gm 1 Rth + gm o ro1 + g m R E o + 1 o Common Source gR mL 1+ g m R S Common Drain ro1 + gm R th o + 1 Common Gate g mR L 1 1+ g m R L 1 gm ro 1+ g m R S 2 gm R L 1 gm ro1+ gm R th +1 1. BJT/MOSFET Amplifier Problem (40 points) +5 Vdc Kn = 100 A/V2 VTN = 1.5 V = 0.01 /V 18 k 120 120 k io ii vi 100 10 k vo 390 k Q point: (107 A, 2.80 V) VGS = 2.96 V 8.2 k ro = 935 k gm = 0.146 mS a) Draw the small signal equivalent circuit for the circuit above. b) Using the terminal equations on the equation sheet, find Av = vo / vi and Ai = io / ii. Assume ro approaches infinity. Common Source Amplifier with Rs = 0, so Avt = - gm RL = -(0.146m)(18k||10k) = -0.939 v 91.8k v vv Av = o = o gs = Avt gs = (0.932) 91.8k + 100 = 0.938 vi v gs vi vi vo i R3 R + RG 91.8k + 100 Ai = o = = Av I = (0.932) = 8 . 61 vi ii R3 10k RI + RG 3 2. BJT/MOSFET Terminal Equation Derivations (40 points) a. Draw the small signal equivalent circuit and derive the equation given on the equation sheet for the Terminal Input Resistance, RiE, of the following AC equivalent circuit. Assume ro approaches infinity. RI ib + vi + vbe + _ oib r _ RB vb + RL vo _ _ RL = R6 || R3 + vbe - o ib Applying a voltage source to the Emitter and shorting the independent source, the circuit for finding RiE is shown below. Let RiE = Rth = RI || RB v x vbe + vb i r + (ib Rth ) r + Rth r + Rth = = b = = o ib oib 1 + o ix ix 4 r o + Rth o = r R R 1 + th = + th r g m o gm o b. the Draw small signal equivalent circuit and derive the equation given on the equation sheet for the Terminal Voltage Gain, Avt, of the following AC equivalent circuit. Assume ro approaches infinity. gmvgs RI S D + vi + _ + R6 vit = - vgs RL vo _ _ Avt = vo g m vgs RL = = g m RL vgs vit 5 G 3. BJT/MOSFET Design Problem (20 points) +5 V RD RG2 120 k 3900 RI In the circuit to the right; 2k vi Av = vo / vi = 0.494 RG1 3900 ROUT = 41 R6 68 k R3 100k ROUT a) Redesign the circuit above such that Av > 0.9 and the operating point is unchanged. RI and R3 cannot be changed. From the equation sheet , Then Av = Avt Avt 1 Let RG = RG1 || RG 2 RG RG = 1* 2k + RG RI + RG So the following must be true RG > 0 .9 2k + RG Solving RG > 18 k Since the operating point cannot change, RG1 must equal RG2 and be greater than 36 k Any solution where RG1 = RG2 and each is greater than 36 k is acceptable. b) What value of ROUT for the redesigned circuit? Explain your answer? ROUT = 1 / gm and since IC is unchanged, gm is unchanged. Therefore, ROUT = 41 6 vo ECE 302, Section 2 Spring 2010 April 7, 2010 Exam III Printed Name: ________________ KEY_________________________________ Honor Pledge: I certify that I have neither given nor received unauthorized aid while taking this exam. Signature: ____________________________________________________ - This is a closed book, closed notes test. You may use a calculator Carry all calculations to 3 significant digits Show all work to get partial credit. Attach any extra pages that were necessary. Use the backs of the pages if you need more space. SHOW ALL UNITS!!!!! Points will be deducted for incorrect or absence of units. Problem Possible Points 1 20 2 20 3 40 4 20 Total 100 1 Missed Points Total Points Small Signal Model Equations 1 FET gm 2I D = 2K n I D V V TN GS ro = S I BJT gm = C V T +V I D V ro = A I C S DS 1 I D vgs 0.2V V V TN GS V r = o T I C v 5 mV be VT = 0.025 V at room temperature Single Stage Amplifier Terminal Equations Common Collector Common Emitter Terminal Voltage Gain Input Terminal Resistance Output Terminal Resistance Terminal Current Gain Terminal Voltage Gain Input Terminal Resistance Output Terminal Resistance Terminal Current Gain gR mL 1+ g m R Common Base g mR L 1 1+ g m R L r (1+ gmR ) L E r (1+ gm R ) E gm R L 1 gm 1 Rth + gm o ro1 + g m R E o + 1 o Common Source gR mL 1+ g m R S Common Drain ro1 + gm R th o + 1 Common Gate g mR L 1 1+ g m R L 1 gm ro 1+ g m R S 2 gm R L 1 gm ro1+ gm R th +1 1. General Single Stage Amplifier Questions (20 points) a. In the following circuit, select a value of R3 such that Avt = - gm +5 Vdc 18 k 120 120 M From the Equation Sheet, Avt = - gm RL when RE = 0. 10 So, Avt = - AVt when RL = 1. RL = 18k || R3 = 1 R3 vi 390 M 8.2 k Therefore, R3 = 1 b. Two amplifiers, a common emitter with RE = 0 and a common base, have the same magnitudes of terminal voltage gain. Both amplifiers have the same 4 four resistor bias network, series source resistor RI, and parallel load resistor R3. Which amplifier would you expect to have the greater overall amplifier voltage gain? Why? AVt is the same for each amplifier, however, the input resistances are not. AV = AVt [RIN / (RI + RIN)] and the input resistance of a common base amplifier is small compared to a common emitter amplifier. So, [RIN / (RI + RIN)] is larger for a common emitter amplifier than for a common base when RI is non-zero. Therefore, AV is larger for a common emitter is expected to be larger for a common emitter amplifier. c. What are the input and output terminal for the following amplifiers? Input Output COMMON BASE __Emitter____ ____Collector____ COMMON DRAIN __Gate______ ____Source______ d. In a common gate amplifier, if you increase RI, how will the Output Terminal Resistance change? Why? Output Terminal Resistance = ro (1 + gmRth) where Rth= RI||R6. If RI increases, then Rth increases. Therefore, the Output Terminal Resistance increases. 3 2. Amplifier Small Signal Analysis (20 points) +10 V 270 k 3.9 M Qpt = (10.9 A, 5.74 V) KN = 100 A/V2 = 0.001 5k 1.5 M 200 120 k a) Draw the small signal equivalent circuit for the circuit above. ro RI S D gm v g vi - + _ s + R6 vgs RL vo _ + G b) Using the terminal equations on the equation sheet, find the Output Terminal Resistance, RiD, for the circuit above. ro = 1 / ID = 1 / (0.001 * 10.9) = 91.7 M gm = (2 KN ID ) = (2 * 100 * 10.9) = 46.7 S Rth = 120k || 200 = 200 RiD = ro ( 1 + gm Rth ) = 91.7 M [1+ 46.7 S * (200))] = 92.6 M 4 2. BJT/MOSFET Terminal Equation Derivations (40 points) a. Draw the small signal equivalent circuit and derive the equation given on the equation sheet for the Terminal Voltage Gain, Avt, for the AC equivalent circuit below. Assume ro approaches infinity. ib + RL o ib vb - AVt = RL = RC || R3 vo vo o ib RL o ib RL r g m RL = = = vb vbe + v RE r ib + ( o + 1)ib RE r ib + oib r + r g m RE 5 = g m RL 1 + g m RE b. Draw the small signal equivalent circuit and derive the equation given on the equation sheet for the Output Terminal Resistance, RiS, for the AC equivalent circuit below. Assume ro approaches infinity. D RI I R ib + vi + _ G ++ vvbe gs o b gm ivgs r _ R RBG vb - S + RL RL _ _ RL = R6 || R3 Applying a voltage to the Source and setting the input to zero, D gm vgs G vgs S RG RiS = v gs vx = = g m v gs ix vo 1 gm 6 3. BJT/MOSFET Design Problem (20 points) 12 V 12 V 1k BJT BJT or MOSFET Four Resistor Bias Circuit 68 k 3900 2.7 M 39 k 5k 200 1.5 M 27 k 2200 21.8 k Qpt = (1.1 mA, 5.27 V) VA = 1,000 V o = 80 Qpt = (90 A, 6.58 V) = 0.001 /V KN = 100 A/V2 VTN = 1.0 V The goal of this problem is to construct an Amplifier to fit in to the box at the left such that the magnitude of the voltage gain, |AV |= |vo / vi|, is greater than 50 using either the BJT circuit or the MOSFET circuit above. a) Would a Follower circuit (common collector or common drain) be a good choice? Why or why not? No. The Terminal Voltage Gain is approximately 1 so |Av| will be 1 or less. b) Would an Inverting circuit (common emitter or common source) be a good choice? Why or why not? Yes. The Terminal Voltage Gain, Avt, is -gmRL for both amplifiers and each has large RL. Av = Avt [RIN / (RI + RIN)] and both amplifiers have relatively large RIN so the gain is not reduced by the input resistance of either transistor. 7 c) Would a Non-Inverting circuit (common base or common gate) be a good choice? Why or why not? No. The Terminal Voltage Gain, Avt, is gmRL for both amplifiers and each has large RL. For both amplifiers, the terminal input resistance is 1/gm g m = 2 K N I D = 2 * 100 * 90 = 0.134 mS . I C 1.1m gm = = = 44.0 mS Vt 25m For the MOSFET, For the BJT, So RIN will be small Since Av = Avt [RIN / (RI + RIN)] and both amplifiers have relatively small RIN, the gain is reduced by the input resistance with either transistor. d) Draw the complete diagram of the circuit (including bypass capacitors) that will meet the criteria |AV| > 50 and calculate the actual value of AV. So either BJT common emitter or MOSFET common source are good candidates. 1 39 k 3.9 k 68 k k 2.7 M 1k 1k 5k 5k 200 27 k 1.5 M 21.8 k 2.2 k For the Common Emitter Amplifier, Av = g m RL RB || RiB 68k || 27 k || 1.82k = (0.044)(3.9k || 5k ) = 60.1 1k + (68k || 27 k || 1.82k ) RI + RB || RiB For the Common Source Amplifier with RS = 200, Av = g m RL RG (0.134m)(39.0k || 5k ) 1.5M || 2.7 M = = 0.572 1 + g m RS RI + RB 1 + (0.134m)(200) 1k + (1.5M || 2.7 M ) For the Common Source Amplifier with RS bypassed also, RG 1.5M || 2.7 M = (0.134m)(39.0k || 5k ) = 0.590 Av = g m RL 1k + (1.5M || 2.7 M ) R I + RB So Common Emitter Amplifier is the best choice. 8
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Appendix DCOM/220 Version 7Associate Program MaterialAppendix DBias, Rhetorical Devices, and ArgumentationThere are both good and bad arguments. Bad arguments consist of biases and fallacies. Goodarguments include rhetorical devices and logic. Argui
University of Phoenix - COM - 220
Appendix ECOM/220 Version 7Associate Program MaterialAppendix ESummary of the Research ProcessReview the following summary of the research process, print a hard copy, and refer to theinformation often as you work on your final project.1. Begin the
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Appendix FCOM/220 Version 7Associate Program MaterialAppendix FResearch PlanAs part of your Research Plan, you must draft a research question for your research paper. Aresearch question, which is more specific and focused than a general topic, is th
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Finding a Topic for Argument TranscriptCOM/220 Version 71Finding a Topic for Argument TranscriptCharacters: NarratorNARRATORIf youre having trouble finding a good subject for an argument, you can try this riddleexercise. Ask yourself, When people d
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Appendix GCOM/220 Version 7Associate Program MaterialAppendix GFinding, Evaluating, and Utilizing Credible InformationThis course requires a higher level of research than you may have undertaken in the past. Youmust find sources that are reliable, r
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Appendix HCOM/220 Version 7Associate Program MaterialAppendix HAppropriate Style GuidelinesA central aspect of the Teaching-Learning Model at University of Phoenix is the degree ofemphasis placed on written and verbal communication skills. To succee
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Appendix ICOM/220 Version 7Associate Program MaterialAppendix IStrategies for Gathering InformationFill in the following information for each of your sources:List the APA reference citation for the source.Determine the credibility of the source. Co
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Writing in Action: Narrowing a Topic Online TranscriptCOM/220 Version 71Writing in Action: Narrowing a Topic Online TranscriptCharacter: NarratorNARRATORWhen you conduct research on the Internet, you generally have two main goals. First,you want re
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Warrior Tours. (1997-2011). Retrieved November 2011, fromhttp:/www.warriortours.com/intro/education.htmThis site gives information on many aspects of live in China including the educations system. Icould use this site for information on the curriculum
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Appendix HCOM/220 Version 7Associate Program MaterialAppendix HAppropriate Style GuidelinesA central aspect of the Teaching-Learning Model at University of Phoenix is the degree ofemphasis placed on written and verbal communication skills. To succee
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Appendix JCOM/220 Version 71Associate Program MaterialAppendix JQuoting, Summarizing, and Paraphrasing SourcesSummarize:Be brief.Reflect key facts or ideas.Help readers understand context.Do not insert personal views.Write in your own words, ex
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Appendix JCOM/220 Version 71Associate Program MaterialAppendix JQuoting, Summarizing, and Paraphrasing SourcesSummarize:Be brief.Reflect key facts or ideas.Help readers understand context.Do not insert personal views.Write in your own words, ex
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Even though Americans hold a superior view of the United States, the education system in theUnited States is flawed because we are behind in Math and Science and Asia is more technologyadvanced then the United States.I plan to compare and contrast the
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Appendix LCOM/220 Version 71Associate Level MaterialAppendix LIntegrating Source MaterialsPart 1: Example PassagesExample Passage 1Integrate the quotation into the passage as if the passage is a sentence in yourresearch paper. Include appropriate
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Appendix DCOM/220 Version 7Associate Level MaterialAppendix DBias, Rhetorical Devices, and ArgumentationThere are both good and bad arguments. Bad arguments consist of biases and fallacies. Goodarguments include rhetorical devices and logic. Arguing
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Appendix KCOM/220 Version 7Associate Level MaterialAppendix KOrganizing Your Research PaperOnce you have researched sources and taken notes, you must complete the following steps inthe research process:1.2.3.4.5.6.Ensure your research is comp
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Appendix LCOM/220 Version 7Associate Level MaterialAppendix LIntegrating Source MaterialsPart 1: Example PassagesExample Passage 1Integrate the quotation into the passage as if the passage is a sentence in your research paper.Include appropriate t
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Appendix MCOM/220 Version 7Associate Level MaterialAppendix MDrafting Your Research PaperDrawing Readers InAs you begin to write the rough draft of your paper, think critically about how you might draw yourreaders into your argument in a compelling
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Appendix NCOM/220 Version 7Associate Level MaterialAppendix NPeer Review Checklist*Violent crimes committed by teenagers and why they are doingit.What is the main point of thispaper?What is the greatest strengthof this paper? Explain youranswer
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Appendix NCOM/220 Version 7Associate Level MaterialAppendix NPeer Review Checklist*What is the main point of thispaper?What is the greatest strengthof this paper? Explain youranswer.What material does not seemto fit the main point of thepaper