55:041 Electronic Circuits

Size: px
Start display at page:

Download "55:041 Electronic Circuits"

Transcription

1 55:04 Electronc Crcuts Feedback & Stablty Sectons of Chapter 2. Kruger Feedback & Stablty

2 Confguraton of Feedback mplfer S o S ε S o ( S β S ) o Negate feedback S S o + β β s the feedback transfer functon f + β + T Implct ssumptons Made T s the loop gan Input sgnal s transmtted through amplfer and not through β network Output sgnal s transmtted through β network only There are no loadng effects β network does not load amplfer mplfer (wth/wthout β network) does not load source. Kruger Feedback & Stablty 2

3 β s the feedback transfer functon T s the loop gan β β >> f + β β β Profound result: Closed-loop gan s ndependent from open-loop gan, and we can control the closedloop gan wth the amount of feedback. Kruger Feedback & Stablty 3

4 Example How good s the /β approxmaton? ssume open-loop gan s 0 5, and the closed-loop gan s f 50. Then f 50 + β β 0 5 β f / β ssume open-loop gan s 0 6, wth the same β f + β β Practcally the same closed-loop gan. Kruger Feedback & Stablty 4

5 Op-mp Example VV + Σ VV oo 2 β + 2 Ideal case: + 2 β >> β Kruger Feedback & Stablty 5

6 f d f d d f + β d ( + β) 2 Gan Senstty Ddng both sdes wth closed-loop gan yelds d f f β + β + d ( + β) + β 2 ( + β) 2 ( β) 2 + β d d f f d + β Ths shows that the % change n closed-loop gan s smaller, by a factor +β, than the % change n open-loop gan.. Kruger Feedback & Stablty 6

7 Gan Senstty n engneer desgned a feedback amplfer β , and 0 5. By how much does the closed-loop gan change when the same feedback network s used, but an amplfer wth open-loop gan 0 6 s used? d f f + β d + ( ) % In other words, the open-loop gan changed by a factor 0, whle the closed loop gan changed about 0.5%.. Kruger Feedback & Stablty 7

8 . Kruger Feedback & Stablty 8 Gan Versus Frequency ssume we can characterze the frequency response of an amplfer wth a sngle pole (ths s true for many op-amps) H o s s ω + ) ( ) ( ) ( ) ( s s s f β + ( ) o H o o f s s β ω β ) ( We assume the feedback network s ndependent from frequency The closed-loop gan s smaller than the open-loop gan by a factor (+β) The 3 db bandwdth s larger by a factor (+β)

9 Gan-Bandwdth Product Gan-bandwdth product of a feedback amplfer s constant We can ncrease bandwdth at the expense of gan. Kruger Feedback & Stablty 9

10 Nose Senstty o n S o N o S N o n n S N o o S 0 N Conclusons. Negate feedback can reduce nternallygenerated addte amplfer nose Same closed-loop gan as preous amplfers 2 2 o + n S (mproe S/N) + β 2 + β 2 N 2. Negate feedback per 00se + wll 0. not reduce S/N wth respect to external nose o β 2 ( + ) + 00 n n o S o N S N o o 000 S N. Kruger Feedback & Stablty 0

11 educton of Nonlnear Dstorton Open-Loop Gan Non-lnear because the gan depends on the sgnal f + β β Closed-loop gan, β Kruger Feedback & Stablty

12 dantages of Negate Feedback. Gan Senstty aratons n gan s reduced 2. Bandwdth Extenson larger than that of basc amplfer 3. Nose Senstty may ncrease S/N rato 4. educton of Nonlnear Dstorton 5. Control of Impedance Leels nput and output mpedances can be ncreased or decreased Dsadantages of Negate Feedback. Crcut Gan reduced compared to that of basc amplfer 2. Stablty possblty that feedback crcut wll become unstable and oscllate at hgh frequences. Kruger Feedback & Stablty 2

13 Ideal Basc Feedback Confguratons Voltage mplfer Very Common Current mplfer Transconductance mplfer (oltage n-current out) Conerts current to oltage Transresstance mplfer (current n-oltage out) Conerts oltage to current. Kruger Feedback & Stablty 3

14 Ideal Seres-Shunt Feedback f + β Sample output oltage and feed t back to nput Ideal: assume feedback network does not load output/nput Voltage mplfer KVL: V x + I x + β V o 0 V x I x + β V ε f V I x x + β I I + x I x x ( β ) ( + β ). Kruger Feedback & Stablty 4

15 Seres-Shunt Feedback Output esstance How do we determne output resstance? Fast V β V ε x. Turn off ndependent sources 2. dd test oltage V x 3. See what test current I x flows 4. Determne V x /I x I x V V of x x V x V o ε ( β V ) o ( + β ) V I x x o x o ( + β ) KCL. Kruger Feedback & Stablty 5

16 Equalent Crcut: Seres-Shunt Feedback Crcut f + ( β ) f + β of o + β ( ) Useful to thnk of ths as the mproement factor BW f ( + β )BW. Kruger Feedback & Stablty 6

17 Ideal Basc Feedback Confguratons Voltage mplfer Current mplfer Transconductance mplfer (oltage n-current out) Conerts current to oltage Transresstance mplfer (current n-oltage out) Conerts oltage to current. Kruger Feedback & Stablty 7

18 Ideal Shunt-Seres Feedback Sample output current and feed t back to nput Ideal: assume feedback network does not load output, so that I o s unaffected Current mplfer f + β Feedback Subtract, educe, Steal From Fast I I V ε f I I ε I ε ε + βi + β I + o ( I ) ( β ) V I e I ( + β ) ( + β ). Kruger Feedback & Stablty 8

19 Ideal Shunt-Seres Feedback How do we determne output resstance?. Turn off ndependent sources 2. dd test current I x output 3. See what test current V x results 4. Determne V x /I x Iε βi x V x ( I x Iε ) o ( I x ( β I x )) o I x ( β ) o + of V I x x ( + β ) o Fast. Kruger Feedback & Stablty 9

20 Equalent Crcut: Shunt-Seres Feedback Crcut Current mplfer f + β ( ) Useful to thnk of ths as the mproement factor f + β of V I x x ( + β ) o. Kruger Feedback & Stablty 20

21 ecap - Ideal Basc Feedback Confguratons Voltage mplfer Current mplfer Transconductance mplfer (oltage n-current out) Conerts current to oltage Transresstance mplfer (current n-oltage out) Conerts oltage to current. Kruger Feedback & Stablty 2

22 Ideal Seres-Shunt Feedback f + β Sample output oltage and feed t back to nput Ideal: assume feedback network does not load output/nput Voltage mplfer V x I I x x + + β V β V ε o Fast f V I x x + β I I + x I x x ( β ) ( + β ). Kruger Feedback & Stablty 22

23 Ideal Seres-Seres Feedback Crcut Sample output current and feed t back to nput as a oltage Ideal: assume feedback network does not load output, so that I o s unaffected Transconductance mplfer (oltage n-current out) gf g + β z g Unts of β Z? V/ Fast I + β I z o ( ) I + βz gv ε f? (neglect S ) f I + β z I g I ( + β ) z g Conerts output current to a oltage. Kruger Feedback & Stablty 23

24 Ideal Seres-Seres Feedback Crcut I x V x Fast I o I x I of V x x + I x o V x o V V β I z + ε gv ε g x o I x ( + β ) z x ( β I ) z x g of? (neglect S ). Kruger Feedback & Stablty 24

25 Equalent Crcut: Seres-Seres Feedback Crcut Transconductance mplfer (oltage n-current out) f ( + β z g ) gf of o ( + βz g ) Useful to thnk of ths as the mproement factor g + β z g. Kruger Feedback & Stablty 25

26 ecap-ideal Basc Feedback Confguratons Voltage mplfer Current mplfer Transconductance mplfer (oltage n-current out) Conerts current to oltage Transresstance mplfer (current n-oltage out) Conerts oltage to current. Kruger Feedback & Stablty 26

27 Ideal Shunt-Shunt Feedback Crcut Sample output oltage and feed t back to nput as a current Ideal: assume feedback network does not load output, so that V o s unaffected Transresstance mplfer (current n-oltage out) zf z + β g z f of + β ( ) g + β z o ( ) g z Conerts output oltage to a current. Kruger Feedback & Stablty 27

28 Equalent Crcut: Shunt-Shunt Feedback Crcut Transresstance mplfer (current n-oltage out) Useful to thnk of ths as the mproement factor f o of ( + β ) ( ) g z + β z + β g. Kruger Feedback & Stablty 28 g z zf z

29 Summary of Feedback mplfer Functons. Kruger Feedback & Stablty 29

30 Notes on Unts and Subscrpts Transresstance mplfer (current n-oltage out) z V I o Unts of resstance/mpedance (Z) I fb β g I V fb o Unts of conductance (g) Conerts output oltage to current f + β z zf of ( + β g z ) + β g z ( g z ) Product should be dmensonless. Kruger Feedback & Stablty 30

31 . Kruger Feedback & Stablty 3 Op-mp Seres-Shunt Feedback Crcut Seres-shunt feedback Input mpedance wll ncrease Output mpedance wll decrease Bandwdth wll ncrease Seres-shunt feedback Take some of the output oltage Feed t back n seres wth nput ssume ery large o o fb V V V β β ( ) f β f β 2 2 f + + ( ) o o of β

32 Op-mp Shunt-Shunt Feedback Current-n, oltage-out Transresstance Z Ideal op-amp, neglect nput current: Output oltage and 2 generate a feedback current that reduces current flowng nto op-amp β g 2 Feedback reduces nput mpedance Shunt-Shunt Feedback. Kruger Feedback & Stablty 32

33 Op-mp Shunt-Seres Feedback f + + F / + β. Kruger Feedback & Stablty 33

34 Op-mp Seres-Seres Feedback I L Transconductance amplfer (oltage n, current out) What s II LL f EE 00Ω and VV 2 V? nswer: m I L Voltage-controlled current source Feedback oltage s a functon of output current E conerts current to oltage Feedback: oltage n seres wth nput oltage Ideal op-amp, neglect base current: gf I V L E β Z E Seres-Seres Feedback What happens to and oo? Both ncrease. Kruger Feedback & Stablty 34

35 Dscrete Transstor Crcut Current-n, oltage-out Transresstance Z Output oltage and F generate a feedback current that reduces current flowng nto transstor base β g F Feedback reduces nput mpedance Shunt-Shunt Feedback. Kruger Feedback & Stablty 35

36 Dscrete Shunt-Seres Transstor Crcut. Kruger Feedback & Stablty 36

37 Dscrete Transstor Crcut Voltage out Current n Note that o C2 E 2 E 2 so that ths crcut s really samplng the output oltage Output oltage and F generate a feedback current that reduces current flowng nto amplfer Shunt-Shunt Feedback. Kruger Feedback & Stablty 37

38 Multstage Feedback Crcut I fb I Output oltage and F generate a feedback current that reduces current flowng nto transstor base Feedback reduces nput mpedance Shunt-Shunt Feedback. Kruger Feedback & Stablty 38

39 ecap-confguraton of Feedback mplfer Negate feedback β s the feedback transfer functon Implct ssumptons Made T s the loop gan f + β + T Input sgnal s transmtted through amplfer and not through β network Output sgnal s transmtted through β network only There are no loadng effects β network does not load amplfer mplfer (wth/wthout β network) does not load source. Kruger Feedback & Stablty 39

40 Stablty Secton 2.9 ecall defnton of loop gan: T β We assume β s not a functon of frequency Howeer, the amplfer gan,, s a functon of frequency (s), and we normally set s jω, so (jω). Thus T(jω) β(jω). Closed-loop gan: If T(jω) -, then ( jω) f ( jω) + T( jω) f ( jω) ( jω) Instablty We can wrte T ( jω) T ( jω) φ Equalent condtons for stablty T( jω) < or φ less than 80 Gan margn: when the amplfer phase shft s80 o, how much headroom/margn before the gan s and the amplfer becomes unstable? Phase margn: when the amplfer gan s, how much more headroom/margn before the phase shft s 80 o amplfer becomes unstable?. Kruger Feedback & Stablty 40

41 Complex Number eew T + ja 2 + ja a φ tan T + a T + ja T + ja + a 2 φ tan a tan ( a) T K + ja + jb T K + ja + jb K + a 2 + b 2 φ tan a tan b tan ( a) tan ( b). Kruger Feedback & Stablty 4

42 . Kruger Feedback & Stablty 42? ), ( tan 80 b b M 2 0 ) ( f j K f T ) ( f j K f T +?, 0 0 ) ( f f K f j K f T M b 80 tan f K

43 . Kruger Feedback & Stablty ) ( f j f j K f T ) ( + + f f K f T?, 0 0 ) ( f f f K f T Numercal soluton, tral-and-error

44 (jω). Kruger Feedback & Stablty 44

45 - -. Kruger Feedback & Stablty 45

46 - -. Kruger Feedback & Stablty 46

47 - -. Kruger Feedback & Stablty 47

48 - -. Kruger Feedback & Stablty 48

49 (jω). Kruger Feedback & Stablty 49

50 . Kruger Feedback & Stablty 50

51 Bode Plot: Phase and Gan Margns Loop Gan T(jω) β ( jω) Secton db Gan Margn 0 T ( f ) 80 db f f 80 Phase Margn 80 +φ( f). Kruger Feedback & Stablty 5

52 Bode Plot: Phase and Gan Margns The loop gan TT jjjj for a feedback amplfer s shown. Is the amplfer stable? Gan Margn 0 TT ff 80 db db dddd 0.8 db Phase Margn 80 + φφ(ff ) 80 + ( 75 ) 5 Yes, amplfer s stable.. Kruger Feedback & Stablty 52

53 Plottng Loop Gan If β s ndependent of frequency, then the loop gan T(jω) β(jω) s smply a scaled erson of the open-loop gan.. Kruger Feedback & Stablty 53

54 Plottng Loop Gan If β s ndependent of frequency, then the loop gan T(jω) β (jω) s smply a scaled erson of the open-loop gan. T( jω) 20log β 20log + 20log β db 20log 20log β We can determne the loop gan by graphcally subtractng a plot of 20log(/β) from the open loop Bode plot. powerful araton of the graphcal subtracton technque s the followng. Often 20log s aalable n graphcal form. It s ery conenent to plot 20log(/β) on ths graph, and consder ths the new frequency axs.. Kruger Feedback & Stablty 54

55 Graphcal Subtracton n amplfer has open-loop gan shown below. The amplfer s used n a feedback confguraton and the closed-loop gan s 4,000. What are the phase- and gan margns? Ths s where loop gan s (0 db) 0 db New axs closed loop o + β o β 32 db closed loop 4,000 β 20 log β 72 db Gan margn s 32 db 87 o Phase margn s 87 o mplfer s stable. Kruger Feedback & Stablty 55

56 Graphcal Subtracton n amplfer has open-loop gan shown below. The amplfer s used n a feedback confguraton and the closed-loop gan s,000. What s the phase margn? Open Loop Voltage Gan and Phase s Frequency closed loop closed loop o + β o,000 β β 20 log β 60 db Phase margn s 90 o. Kruger Feedback & Stablty 56

57 Draw ββ n amplfer has open-loop gan shown left. The amplfer s used n a feedback confguraton and the closed-loop gan s 00. What are the phase- and gan margns? What s the closed-loop bandwdth? 45 db closed loop o + β o β closed loop 00 β 20 log β 40 db 90 o Phase margn s 90 o Gan margn s 45 db Bandwdth ~ MHz. Kruger Feedback & Stablty 57

58 Wll ths amplfer be stable f used as a 30 amplfer? log db Draw ββ ββ 30 db Frequency where loop gan ββ oo, s 2 MHz. Kruger Feedback & Stablty 58

59 Wll ths amplfer be stable f used as a 30 amplfer? log db Phase 90 Phase margn 90 Draw ββ ββ 30 db. Kruger Feedback & Stablty 59

60 What s the phase margn f the amplfer s used n a feedback confguraton wth so the feedback amplfer has a gan of 5-dB? Open Loop Voltage Gan and Phase s Frequency Phase 80 Phase margn 00 Draw ββ ββ 5 db. Kruger Feedback & Stablty 60

61 What s the phase margn and bandwdth f closed loop gan 2 db?. What wll the rse tme for a step nput be? 2 db Method : Draw loop gan ββ oo ββ s ndependent of ff so the loop gan s just a scaled erson of the open loop gan TT ββ oo Open Loop Voltage Gan (db) Closed-loop response Loop Gan ff 2 db 3.98~ 4 shch mples that ββ Further, oooo 65 dddd , so that ββ oooo db. Consequently, the loop gan magntude plot s smply the open-loop magntude plot, shfted down 2 db. The phase plot s the same. The phase s 95 where the loop gan s 0 db, so the phase margn s 85. The 3-dB bandwdth of the feedback amplfer s 00 MHz. The rse tme s 0.35 BB 3.5 ns Open Loop Voltage Gan (db). Kruger Feedback & Stablty 6

62 What s the phase margn and bandwdth f closed loop gan 2 db?. What wll the rse tme for a step nput be? Method 2: Graphcal subtracton Draw ββ, whch s practcally the same as the closed-loop gan. Open Loop Voltage Gan (db) The phase s 95 where the loop gan s 0 db, so the phase margn s 85. The 3-dB bandwdth of the feedback amplfer s 00 MHz. The rse tme s 0.35 BB 3.5 ns Open Loop Voltage Gan (db). Kruger Feedback & Stablty 62

63 mplfer has an open-loop gan f j f j 0 5 Is amplfer stable f used so that closed-loop gan - 00? closed loop + β β 00, β β 0.0 Loop gan T s T ( f ) β (0.0) T( f ) + f j 0 3 ( 0 ) 3 + f j 0 5 Stable? examne phase- and gan margns T ( f ) f ( 0 ) φ tan tan f Kruger Feedback & Stablty Sole for f How? f 30 khz 8 o phase margn > amplfer s stable

64 . Kruger Feedback & Stablty 64

65 . Kruger Feedback & Stablty 65

66 . Kruger Feedback & Stablty 66

67 . Kruger Feedback & Stablty 67

68 . Kruger Feedback & Stablty 68

69 Next: Same Problem, but use Graphcal Subtracton. Kruger Feedback & Stablty 69

70 . Kruger Feedback & Stablty 70

71 Draw ββ ββ 00 Phase 90 Phase margn 90. Kruger Feedback & Stablty 7

72 . Kruger Feedback & Stablty 72

73 . Kruger Feedback & Stablty 73

74 . Kruger Feedback & Stablty 74

75 Draw ββ ββ Phase 90 Frequency where ββ oo s 0 6 Phase margn 90. Kruger Feedback & Stablty 75

76 . Kruger Feedback & Stablty 76

77 . Kruger Feedback & Stablty 77

78 . Kruger Feedback & Stablty 78

79 . Kruger Feedback & Stablty 79

80 . Kruger Feedback & Stablty 80

81 . Kruger Feedback & Stablty 8

82 . Kruger Feedback & Stablty 82

83 Nyqust Stablty Crteron (Secton 2.9.3) Not Coered. Kruger Feedback & Stablty 83

84 Determnng Loop Gan The term (+β) s used frequently n feedback amplfer analyss Loop gan T β s mportant n determnng stablty Step : Break the feedback loop Step 2: Termnate so that ports see same mpedances Step 3: Insert a test current/oltage and measure response: T -V r /V t Can be used as an analyss technque, n SPICE, as well as n some actual crcuts. Kruger Feedback & Stablty 84

85 T β V V r t. Kruger Feedback & Stablty 85

86 p n Loop gan? t t 0. t β n t > n 20 p n t > β p o 000 ( ) , p n o 3,000 t T o t 00. Kruger Feedback & Stablty 86

87 Frequency Compensaton Secton 2.0 Consder a feedback amplfer wth the loop gan TT as shown. How many poles? Stable or Unstable?. Kruger Feedback & Stablty 87

88 Frequency Compensaton Where loop gan TT, the phase s nearly 270, and the amplfer s unstable. How can we make the amplfer stable?. Kruger Feedback & Stablty 88

89 Frequency Compensaton Introduce a new, lowfrequency pole (ff DD ) at ery low frequency. In ths example, at ff DD 0 Hz. ff DD. Kruger Feedback & Stablty 89

90 Frequency Compensaton Introduce a new, lowfrequency pole (ff DD ) at ery low frequency. In ths example, at ff DD 0 Hz. ff DD Where TT, the phase not yet 80, so the amplfer s now stable. Where the phase s 80, TT <, stable. Kruger Feedback & Stablty 90

91 Frequency Compensaton How do we ntroduce low-frequency (domnant) pole nto a crcut? Nae approach Mller Compensaton Perhaps n f 3 db 2π C C M (+)C For compensaton to work f 3dB must be low > large compensaton capactors can be ery large > small (pf) capactors can be used. Kruger Feedback & Stablty 9

92 Frequency Compensaton Many op-amps hae the followng structure Dfferental Input Hgh-gan, nertng amplfer Power stage (gan ) The purpose of CC FF s to create a domnant pole at a low frequency, usng the Mller effect. Ths s called Mller compensaton.. Kruger Feedback & Stablty 92

93 Frequency Compensaton Smplfed Schematc of a 3-stage Op mp Dff Input Compensaton Capactor Mrrors Hgh-gan stage (nertng) Buffer. Kruger Feedback & Stablty 93

94 Beware Internally-compensated amplfers can also become unstable n way that are not obous to the unntated. Ths s often the case when drng capacte loads. Example of a capacte load? C L L C L nteracts wth L o and forms another pole wth addtonal phase shft If C L and/or L o s small, the pole s at ery hgh frequency and may not be mportant. Closed-loop gan 5 db Howeer, remember that phase shft starts at /0 of pole frequency Een what seems small capactances, the addtonal phase shft may remoe phase margn and the system s unstable. Phase margn 70 o Smlar problems wth capactances at nput Soluton? External compensaton. Kruger Feedback & Stablty 94

95 . Kruger Feedback & Stablty 95

55:041 Electronic Circuits

55:041 Electronic Circuits 55:04 Electronc Crcuts Feedback & Stablty Sectons of Chapter 2. Kruger Feedback & Stablty Confguraton of Feedback mplfer Negate feedback β s the feedback transfer functon S o S S o o S S o f S S S S fb

More information

55:041 Electronic Circuits

55:041 Electronic Circuits 55:04 Electrnc Crcuts Feedback & Stablty Sectns f Chapter 2. Kruger Feedback & Stablty Cnfguratn f Feedback mplfer S S S S fb Negate feedback S S S fb S S S S S β s the feedback transfer functn Implct

More information

55:141 Advanced Circuit Techniques Two-Port Theory

55:141 Advanced Circuit Techniques Two-Port Theory 55:4 Adanced Crcut Technques Two-Port Theory Materal: Lecture Notes A. Kruger 55:4: Adanced Crcut Technques The Unersty of Iowa, 03 Two-Port Theory, Slde What Are Two-Ports? Basc dea: replace a complex

More information

55:141 Advanced Circuit Techniques Two-Port Theory

55:141 Advanced Circuit Techniques Two-Port Theory 55:4 Adanced Crcut Technques Two-Port Theory Materal: Lecture Notes A. Kruger 55:4: Adanced Crcut Technques The Unersty of Iowa, 205 Two-Port Theory, Slde Two-Port Networks Note, the BJT s all are hghly

More information

EE C245 ME C218 Introduction to MEMS Design

EE C245 ME C218 Introduction to MEMS Design EE C45 ME C8 Introducton to MEM Desgn Fall 7 Prof. Clark T.C. Nguyen Dept. of Electrcal Engneerng & Computer cences Unersty of Calforna at Berkeley Berkeley, C 947 Dscusson: eew of Op mps EE C45: Introducton

More information

FEEDBACK AMPLIFIERS. v i or v s v 0

FEEDBACK AMPLIFIERS. v i or v s v 0 FEEDBCK MPLIFIERS Feedback n mplers FEEDBCK IS THE PROCESS OF FEEDING FRCTION OF OUTPUT ENERGY (VOLTGE OR CURRENT) BCK TO THE INPUT CIRCUIT. THE CIRCUIT EMPLOYED FOR THIS PURPOSE IS CLLED FEEDBCK NETWORK.

More information

Department of Electrical and Computer Engineering FEEDBACK AMPLIFIERS

Department of Electrical and Computer Engineering FEEDBACK AMPLIFIERS Department o Electrcal and Computer Engneerng UNIT I EII FEEDBCK MPLIFIES porton the output sgnal s ed back to the nput o the ampler s called Feedback mpler. Feedback Concept: block dagram o an ampler

More information

Copyright 2004 by Oxford University Press, Inc.

Copyright 2004 by Oxford University Press, Inc. JT as an Amplfer &a Swtch, Large Sgnal Operaton, Graphcal Analyss, JT at D, asng JT, Small Sgnal Operaton Model, Hybrd P-Model, TModel. Lecture # 7 1 Drecton of urrent Flow & Operaton for Amplfer Applcaton

More information

ELG 2135 ELECTRONICS I SECOND CHAPTER: OPERATIONAL AMPLIFIERS

ELG 2135 ELECTRONICS I SECOND CHAPTER: OPERATIONAL AMPLIFIERS ELG 35 ELECTONICS I SECOND CHAPTE: OPEATIONAL AMPLIFIES Sesson Wnter 003 Dr. M. YAGOUB Second Chapter: Operatonal amplfers II - _ After reewng the basc aspects of amplfers, we wll ntroduce a crcut representng

More information

Lecture 10: Small Signal Device Parameters

Lecture 10: Small Signal Device Parameters Lecture 0: Small Sgnal Dece Parameters 06009 Lecture 9, Hgh Speed Deces 06 Lecture : Ballstc FETs Lu: 0, 394 06009 Lecture 9, Hgh Speed Deces 06 Large Sgnal / Small Sgnal e I E c I C The electrcal sgnal

More information

Two Port Characterizations

Two Port Characterizations lectronc Crcuts Two Port Characterzatons Contents Input and output resstances Two port networks Models Prof. C.K. Tse: -port networks Impedances and loadng effects Voltage amplfers R s R out smaller the

More information

Coupling Element and Coupled circuits. Coupled inductor Ideal transformer Controlled sources

Coupling Element and Coupled circuits. Coupled inductor Ideal transformer Controlled sources Couplng Element and Coupled crcuts Coupled nductor Ideal transformer Controlled sources Couplng Element and Coupled crcuts Coupled elements hae more that one branch and branch oltages or branch currents

More information

VI. Transistor Amplifiers

VI. Transistor Amplifiers VI. Transstor Amplfers 6. Introducton In ths secton we wll use the transstor small-sgnal model to analyze and desgn transstor amplfers. There are two ssues that we need to dscuss frst: ) What are the mportant

More information

CHAPTER 13. Exercises. E13.1 The emitter current is given by the Shockley equation:

CHAPTER 13. Exercises. E13.1 The emitter current is given by the Shockley equation: HPT 3 xercses 3. The emtter current s gen by the Shockley equaton: S exp VT For operaton wth, we hae exp >> S >>, and we can wrte VT S exp VT Solng for, we hae 3. 0 6ln 78.4 mv 0 0.784 5 4.86 V VT ln 4

More information

Complex Numbers, Signals, and Circuits

Complex Numbers, Signals, and Circuits Complex Numbers, Sgnals, and Crcuts 3 August, 009 Complex Numbers: a Revew Suppose we have a complex number z = x jy. To convert to polar form, we need to know the magntude of z and the phase of z. z =

More information

Lecture 5: Operational Amplifiers and Op Amp Circuits

Lecture 5: Operational Amplifiers and Op Amp Circuits Lecture 5: peratonal mplers and p mp Crcuts Gu-Yeon We Dson o Engneerng and ppled Scences Harard Unersty guyeon@eecs.harard.edu We erew eadng S&S: Chapter Supplemental eadng Background rmed wth our crcut

More information

Electrical Engineering Department Network Lab.

Electrical Engineering Department Network Lab. Electrcal Engneerng Department Network Lab. Objecte: - Experment on -port Network: Negate Impedance Conerter To fnd the frequency response of a smple Negate Impedance Conerter Theory: Negate Impedance

More information

FE REVIEW OPERATIONAL AMPLIFIERS (OP-AMPS)( ) 8/25/2010

FE REVIEW OPERATIONAL AMPLIFIERS (OP-AMPS)( ) 8/25/2010 FE REVEW OPERATONAL AMPLFERS (OP-AMPS)( ) 1 The Op-amp 2 An op-amp has two nputs and one output. Note the op-amp below. The termnal labeled l wth the (-) sgn s the nvertng nput and the nput labeled wth

More information

Week 11: Differential Amplifiers

Week 11: Differential Amplifiers ELE 0A Electronc rcuts Week : Dfferental Amplfers Lecture - Large sgnal analyss Topcs to coer A analyss Half-crcut analyss eadng Assgnment: hap 5.-5.8 of Jaeger and Blalock or hap 7. - 7.3, of Sedra and

More information

Energy Storage Elements: Capacitors and Inductors

Energy Storage Elements: Capacitors and Inductors CHAPTER 6 Energy Storage Elements: Capactors and Inductors To ths pont n our study of electronc crcuts, tme has not been mportant. The analyss and desgns we hae performed so far hae been statc, and all

More information

Chapter 6. Operational Amplifier. inputs can be defined as the average of the sum of the two signals.

Chapter 6. Operational Amplifier.  inputs can be defined as the average of the sum of the two signals. 6 Operatonal mpler Chapter 6 Operatonal mpler CC Symbol: nput nput Output EE () Non-nvertng termnal, () nvertng termnal nput mpedance : Few mega (ery hgh), Output mpedance : Less than (ery low) Derental

More information

Transfer Characteristic

Transfer Characteristic Eeld-Effect Transstors (FETs 3.3 The CMS Common-Source Amplfer Transfer Characterstc Electronc Crcuts, Dept. of Elec. Eng., The Chnese Unersty of Hong Kong, Prof. K.-L. Wu Lesson 8&9 Eeld-Effect Transstors

More information

Design of Analog Integrated Circuits

Design of Analog Integrated Circuits Desgn f Analg Integrated Crcuts I. Amplfers Desgn f Analg Integrated Crcuts Fall 2012, Dr. Guxng Wang 1 Oerew Basc MOS amplfer structures Cmmn-Surce Amplfer Surce Fllwer Cmmn-Gate Amplfer Desgn f Analg

More information

Graphical Analysis of a BJT Amplifier

Graphical Analysis of a BJT Amplifier 4/6/2011 A Graphcal Analyss of a BJT Amplfer lecture 1/18 Graphcal Analyss of a BJT Amplfer onsder agan ths smple BJT amplfer: ( t) = + ( t) O O o B + We note that for ths amplfer, the output oltage s

More information

College of Engineering Department of Electronics and Communication Engineering. Test 1 With Model Answer

College of Engineering Department of Electronics and Communication Engineering. Test 1 With Model Answer Name: Student D Number: Secton Number: 01/0/03/04 A/B Lecturer: Dr Jamaludn/ Dr Jehana Ermy/ Dr Azn Wat Table Number: College of Engneerng Department of Electroncs and Communcaton Engneerng Test 1 Wth

More information

ECSE Linearity Superposition Principle Superposition Example Dependent Sources. 10 kω. 30 V 5 ma. 6 kω. 2 kω

ECSE Linearity Superposition Principle Superposition Example Dependent Sources. 10 kω. 30 V 5 ma. 6 kω. 2 kω S-00 Lnearty Superposton Prncple Superposton xample Dependent Sources Lecture 4. sawyes@rp.edu www.rp.edu/~sawyes 0 kω 6 kω 8 V 0 V 5 ma 4 Nodes Voltage Sources Ref Unknown Node Voltage, kω If hae multple

More information

Electrical Circuits II (ECE233b)

Electrical Circuits II (ECE233b) Electrcal Crcuts (ECE33b SteadyState Power Analyss Anests Dounas The Unersty of Western Ontaro Faculty of Engneerng Scence SteadyState Power Analyss (t AC crcut: The steady state oltage and current can

More information

The Decibel and its Usage

The Decibel and its Usage The Decbel and ts Usage Consder a two-stage amlfer system, as shown n Fg.. Each amlfer rodes an ncrease of the sgnal ower. Ths effect s referred to as the ower gan,, of the amlfer. Ths means that the sgnal

More information

Diode. Current HmAL Voltage HVL Simplified equivalent circuit. V γ. Reverse bias. Forward bias. Designation: Symbol:

Diode. Current HmAL Voltage HVL Simplified equivalent circuit. V γ. Reverse bias. Forward bias. Designation: Symbol: Dode Materal: Desgnaton: Symbol: Poste Current flow: ptype ntype Anode Cathode Smplfed equalent crcut Ideal dode Current HmAL 0 8 6 4 2 Smplfed model 0.5.5 2 V γ eal dode Voltage HVL V γ closed open V

More information

Prof. Paolo Colantonio a.a

Prof. Paolo Colantonio a.a Pro. Paolo olantono a.a. 3 4 Let s consder a two ports network o Two ports Network o L For passve network (.e. wthout nternal sources or actve devces), a general representaton can be made by a sutable

More information

Boise State University Department of Electrical and Computer Engineering ECE 212L Circuit Analysis and Design Lab

Boise State University Department of Electrical and Computer Engineering ECE 212L Circuit Analysis and Design Lab Bose State Unersty Department of Electrcal and omputer Engneerng EE 1L rcut Analyss and Desgn Lab Experment #8: The Integratng and Dfferentatng Op-Amp rcuts 1 Objectes The objectes of ths laboratory experment

More information

Boise State University Department of Electrical and Computer Engineering ECE 212L Circuit Analysis and Design Lab

Boise State University Department of Electrical and Computer Engineering ECE 212L Circuit Analysis and Design Lab Bose State Unersty Department of Electrcal and omputer Engneerng EE 1L rcut Analyss and Desgn Lab Experment #8: The Integratng and Dfferentatng Op-Amp rcuts 1 Objectes The objectes of ths laboratory experment

More information

I. INTRODUCTION. There are two other circuit elements that we will use and are special cases of the above elements. They are:

I. INTRODUCTION. There are two other circuit elements that we will use and are special cases of the above elements. They are: I. INTRODUCTION 1.1 Crcut Theory Fundamentals In ths course we study crcuts wth non-lnear elements or deces (dodes and transstors). We wll use crcut theory tools to analyze these crcuts. Snce some of tools

More information

Why working at higher frequencies?

Why working at higher frequencies? Advanced course on ELECTRICAL CHARACTERISATION OF NANOSCALE SAMPLES & BIOCHEMICAL INTERFACES: methods and electronc nstrumentaton. MEASURING SMALL CURRENTS When speed comes nto play Why workng at hgher

More information

Key component in Operational Amplifiers

Key component in Operational Amplifiers Key component n Operatonal Amplfers Objectve of Lecture Descrbe how dependent voltage and current sources functon. Chapter.6 Electrcal Engneerng: Prncples and Applcatons Chapter.6 Fundamentals of Electrc

More information

Flyback Converter in DCM

Flyback Converter in DCM Flyback Converter n CM m 1:n V O V S m I M m 1 1 V CCM: wth O V I I n and S 2 1 R L M m M m s m 1 CM: IM 2 m 1 1 V 1 Borderlne: O VS I n wth V nv 2 1 R 2 L 1 M m s O S m CM f R > R 2n crt 2 L m 2 (1 )

More information

TUTORIAL PROBLEMS. E.1 KCL, KVL, Power and Energy. Q.1 Determine the current i in the following circuit. All units in VAΩ,,

TUTORIAL PROBLEMS. E.1 KCL, KVL, Power and Energy. Q.1 Determine the current i in the following circuit. All units in VAΩ,, 196 E TUTORIAL PROBLEMS E.1 KCL, KVL, Power and Energy Q.1 Determne the current n the followng crcut. 3 5 3 8 9 6 5 Appendx E Tutoral Problems 197 Q. Determne the current and the oltage n the followng

More information

II. PASSIVE FILTERS. H(j ω) Pass. Stop

II. PASSIVE FILTERS. H(j ω) Pass. Stop II. PASSIE FILTES Frequency-selectve or flter crcuts pass to the output only those nput sgnals that are n a desred range of frequences (called pass band). The ampltude of sgnals outsde ths range of frequences

More information

I. INTRODUCTION. 1.1 Circuit Theory Fundamentals

I. INTRODUCTION. 1.1 Circuit Theory Fundamentals I. INTRODUCTION 1.1 Crcut Theory Fundamentals Crcut theory s an approxmaton to Maxwell s electromagnetc equatons n order to smplfy analyss of complcated crcuts. A crcut s made of seeral elements (boxes

More information

College of Engineering Department of Electronics and Communication Engineering. Test 2

College of Engineering Department of Electronics and Communication Engineering. Test 2 Name: Student D Number: Secton Number: 01/0/03/04 A/B Lecturer: Dr Jamaludn/ Dr Azn Wat/ Dr Jehana Ermy/ Prof Md Zan Table Number: ollege of Engneerng Department of Electroncs and ommuncaton Engneerng

More information

MAE140 - Linear Circuits - Winter 16 Final, March 16, 2016

MAE140 - Linear Circuits - Winter 16 Final, March 16, 2016 ME140 - Lnear rcuts - Wnter 16 Fnal, March 16, 2016 Instructons () The exam s open book. You may use your class notes and textbook. You may use a hand calculator wth no communcaton capabltes. () You have

More information

V V. This calculation is repeated now for each current I.

V V. This calculation is repeated now for each current I. Page1 Page2 The power supply oltage V = +5 olts and the load resstor R = 1 k. For the range of collector bas currents, I = 0.5 ma, 1 ma, 2.5 ma, 4 ma and 4.5 ma, determne the correspondng collector-to-emtter

More information

Electrical Circuits 2.1 INTRODUCTION CHAPTER

Electrical Circuits 2.1 INTRODUCTION CHAPTER CHAPTE Electrcal Crcuts. INTODUCTION In ths chapter, we brefly revew the three types of basc passve electrcal elements: resstor, nductor and capactor. esstance Elements: Ohm s Law: The voltage drop across

More information

( ) = ( ) + ( 0) ) ( )

( ) = ( ) + ( 0) ) ( ) EETOMAGNETI OMPATIBIITY HANDBOOK 1 hapter 9: Transent Behavor n the Tme Doman 9.1 Desgn a crcut usng reasonable values for the components that s capable of provdng a tme delay of 100 ms to a dgtal sgnal.

More information

G = G 1 + G 2 + G 3 G 2 +G 3 G1 G2 G3. Network (a) Network (b) Network (c) Network (d)

G = G 1 + G 2 + G 3 G 2 +G 3 G1 G2 G3. Network (a) Network (b) Network (c) Network (d) Massachusetts Insttute of Technology Department of Electrcal Engneerng and Computer Scence 6.002 í Electronc Crcuts Homework 2 Soluton Handout F98023 Exercse 21: Determne the conductance of each network

More information

Physics Courseware Electronics

Physics Courseware Electronics Physcs ourseware Electroncs ommon emtter amplfer Problem 1.- In the followg ommon Emtter mplfer calculate: a) The Q pot, whch s the D base current (I ), the D collector current (I ) and the voltage collector

More information

COLLEGE OF ENGINEERING PUTRAJAYA CAMPUS FINAL EXAMINATION SPECIAL SEMESTER 2013 / 2014

COLLEGE OF ENGINEERING PUTRAJAYA CAMPUS FINAL EXAMINATION SPECIAL SEMESTER 2013 / 2014 OLLEGE OF ENGNEENG PUTAJAYA AMPUS FNAL EXAMNATON SPEAL SEMESTE 03 / 04 POGAMME SUBJET ODE SUBJET : Bachelor of Electrcal & Electroncs Engneerng (Honours) Bachelor of Electrcal Power Engneerng (Honours)

More information

Lecture 8: Small signal parameters and hybrid-π model Lecture 9, High Speed Devices 2016

Lecture 8: Small signal parameters and hybrid-π model Lecture 9, High Speed Devices 2016 Lecture 8: Small sgnal parameters and hbrdπ model π 08006 Lecture 9, Hgh Speed Deces 06 Lecture 8: Small sgnal parameters and hbrdπ model Lterature: Twoport networks Transstors for hgh frequences How to

More information

(8) Gain Stage and Simple Output Stage

(8) Gain Stage and Simple Output Stage EEEB23 Electoncs Analyss & Desgn (8) Gan Stage and Smple Output Stage Leanng Outcome Able to: Analyze an example of a gan stage and output stage of a multstage amplfe. efeence: Neamen, Chapte 11 8.0) ntoducton

More information

6.01: Introduction to EECS 1 Week 6 October 15, 2009

6.01: Introduction to EECS 1 Week 6 October 15, 2009 6.0: ntroducton to EECS Week 6 October 5, 2009 6.0: ntroducton to EECS Crcuts The Crcut Abstracton Crcuts represent systems as connectons of component through whch currents (through arables) flow and across

More information

EE215 FUNDAMENTALS OF ELECTRICAL ENGINEERING

EE215 FUNDAMENTALS OF ELECTRICAL ENGINEERING EE215 FUNDAMENTALS OF ELECTRICAL ENGINEERING TaChang Chen Unersty of Washngton, Bothell Sprng 2010 EE215 1 WEEK 8 FIRST ORDER CIRCUIT RESPONSE May 21 st, 2010 EE215 2 1 QUESTIONS TO ANSWER Frst order crcuts

More information

Linearity. If kx is applied to the element, the output must be ky. kx ky. 2. additivity property. x 1 y 1, x 2 y 2

Linearity. If kx is applied to the element, the output must be ky. kx ky. 2. additivity property. x 1 y 1, x 2 y 2 Lnearty An element s sad to be lnear f t satsfes homogenety (scalng) property and addte (superposton) property. 1. homogenety property Let x be the nput and y be the output of an element. x y If kx s appled

More information

6.01: Introduction to EECS I Lecture 7 March 15, 2011

6.01: Introduction to EECS I Lecture 7 March 15, 2011 6.0: Introducton to EECS I Lecture 7 March 5, 20 6.0: Introducton to EECS I Crcuts The Crcut Abstracton Crcuts represent systems as connectons of elements through whch currents (through arables) flow and

More information

+ v i F02E2P2 I. Solution (a.) The small-signal transfer function of the stages can be written as, V out (s) V in (s) = g m1 /g m3.

+ v i F02E2P2 I. Solution (a.) The small-signal transfer function of the stages can be written as, V out (s) V in (s) = g m1 /g m3. ECE 6440 Summer 003 Page 1 Homework Assgnment No. 7 s Problem 1 (10 ponts) A fourstage rng oscllator used as the VCO n a PLL s shown. Assume that M1 and M are matched and M3 and M4 are matched. Also assume

More information

Formulation of Circuit Equations

Formulation of Circuit Equations ECE 570 Sesson 2 IC 752E Computer Aded Engneerng for Integrated Crcuts Formulaton of Crcut Equatons Bascs of crcut modelng 1. Notaton 2. Crcut elements 3. Krchoff laws 4. ableau formulaton 5. Modfed nodal

More information

Advanced Circuits Topics - Part 1 by Dr. Colton (Fall 2017)

Advanced Circuits Topics - Part 1 by Dr. Colton (Fall 2017) Advanced rcuts Topcs - Part by Dr. olton (Fall 07) Part : Some thngs you should already know from Physcs 0 and 45 These are all thngs that you should have learned n Physcs 0 and/or 45. Ths secton s organzed

More information

Estimating Delays. Gate Delay Model. Gate Delay. Effort Delay. Computing Logical Effort. Logical Effort

Estimating Delays. Gate Delay Model. Gate Delay. Effort Delay. Computing Logical Effort. Logical Effort Estmatng Delas Would be nce to have a back of the envelope method for szng gates for speed Logcal Effort ook b Sutherland, Sproull, Harrs Chapter s on our web page Gate Dela Model Frst, normalze a model

More information

3.2 Terminal Characteristics of Junction Diodes (pp )

3.2 Terminal Characteristics of Junction Diodes (pp ) /9/008 secton3_termnal_characterstcs_of_juncton_odes.doc /6 3. Termnal Characterstcs of Juncton odes (pp.47-53) A Juncton ode I.E., A real dode! Smlar to an deal dode, ts crcut symbol s: HO: The Juncton

More information

5.6 Small-Signal Operation and Models

5.6 Small-Signal Operation and Models 3/16/2011 secton 5_6 Small Sgnal Operaton and Models 1/2 5.6 Small-Sgnal Operaton and Models Readng Assgnment: 443-458 Now let s examne how we use BJTs to construct amplfers! The frst mportant desgn rule

More information

Transfer Functions. Convenient representation of a linear, dynamic model. A transfer function (TF) relates one input and one output: ( ) system

Transfer Functions. Convenient representation of a linear, dynamic model. A transfer function (TF) relates one input and one output: ( ) system Transfer Functons Convenent representaton of a lnear, dynamc model. A transfer functon (TF) relates one nput and one output: x t X s y t system Y s The followng termnology s used: x y nput output forcng

More information

FE REVIEW OPERATIONAL AMPLIFIERS (OP-AMPS)

FE REVIEW OPERATIONAL AMPLIFIERS (OP-AMPS) FE EIEW OPEATIONAL AMPLIFIES (OPAMPS) 1 The Opamp An opamp has two nputs and one output. Note the opamp below. The termnal labeled wth the () sgn s the nvertng nput and the nput labeled wth the () sgn

More information

Massachusetts Institute of Technology Department of Electrical Engineering and Computer Science Circuits and Electronics Spring 2001

Massachusetts Institute of Technology Department of Electrical Engineering and Computer Science Circuits and Electronics Spring 2001 Massachusetts Insttute of Technology Department of Electrcal Engneerng and Computer Scence Read Chapters 11 through 12. 6.002 Crcuts and Electroncs Sprng 2001 Homework #5 Handout S01031 Issued: 3/8/2001

More information

Feedback Principle :-

Feedback Principle :- Feedback Prncple : Feedback amplfer s that n whch a part f the utput f the basc amplfer s returned back t the nput termnal and mxed up wth the nternal nput sgnal. The sub netwrks f feedback amplfer are:

More information

Revision: December 13, E Main Suite D Pullman, WA (509) Voice and Fax

Revision: December 13, E Main Suite D Pullman, WA (509) Voice and Fax .9.1: AC power analyss Reson: Deceber 13, 010 15 E Man Sute D Pullan, WA 99163 (509 334 6306 Voce and Fax Oerew n chapter.9.0, we ntroduced soe basc quanttes relate to delery of power usng snusodal sgnals.

More information

ELCT 503: Semiconductors. Fall 2014

ELCT 503: Semiconductors. Fall 2014 EL503 Semconductors Fall 2014 Lecture 09: BJ rcut Analyss Dr. Hassan Mostafa د. حسن مصطفى hmostafa@aucegypt.edu EL 503: Semconductors ntroducton npn transstor pnp transstor EL 503: Semconductors ntroducton

More information

Circuits II EE221. Instructor: Kevin D. Donohue. Instantaneous, Average, RMS, and Apparent Power, and, Maximum Power Transfer, and Power Factors

Circuits II EE221. Instructor: Kevin D. Donohue. Instantaneous, Average, RMS, and Apparent Power, and, Maximum Power Transfer, and Power Factors Crcuts II EE1 Unt 3 Instructor: Ken D. Donohue Instantaneous, Aerage, RMS, and Apparent Power, and, Maxmum Power pp ransfer, and Power Factors Power Defntons/Unts: Work s n unts of newton-meters or joules

More information

I = α I I. Bipolar Junction Transistors (BJTs) 2.15 The Emitter-Coupled Pair. By using KVL: V

I = α I I. Bipolar Junction Transistors (BJTs) 2.15 The Emitter-Coupled Pair. By using KVL: V Bpolar Juncton ransstors (BJs).5 he Emtter-oupled Par By usng KL: + + 0 Wth the transstors based n the forward-acte mode, the reerse saturaton current of the collector-base juncton s neglgble. / α F ES

More information

Module B3 3.1 Sinusoidal steady-state analysis (single-phase), a review 3.2 Three-phase analysis. Kirtley

Module B3 3.1 Sinusoidal steady-state analysis (single-phase), a review 3.2 Three-phase analysis. Kirtley Module B3 3.1 Snusodal steady-state analyss (sngle-phase), a reew 3. hree-phase analyss Krtley Chapter : AC oltage, Current and Power.1 Sources and Power. Resstors, Inductors, and Capactors Chapter 4:

More information

3.5 Rectifier Circuits

3.5 Rectifier Circuits 9/24/2004 3_5 Rectfer Crcuts empty.doc 1/2 3.5 Rectfer Crcuts A. Juncton ode 2-Port Networks - ( t ) Juncton ode Crcut ( t ) H: The Transfer Functon of ode Crcuts Q: A: H: teps for fndng a Juncton ode

More information

ECE 320 Energy Conversion and Power Electronics Dr. Tim Hogan. Chapter 1: Introduction and Three Phase Power

ECE 320 Energy Conversion and Power Electronics Dr. Tim Hogan. Chapter 1: Introduction and Three Phase Power ECE 3 Energy Conerson and Power Electroncs Dr. Tm Hogan Chapter : ntroducton and Three Phase Power. eew of Basc Crcut Analyss Defntons: Node - Electrcal juncton between two or more deces. Loop - Closed

More information

R. W. Erickson. Department of Electrical, Computer, and Energy Engineering University of Colorado, Boulder

R. W. Erickson. Department of Electrical, Computer, and Energy Engineering University of Colorado, Boulder R. W. Erckson Department of Electrcal, Computer, and Energy Engneerng Unersty of Colorado, Boulder 3.5. Example: ncluson of semconductor conducton losses n the boost conerter model Boost conerter example

More information

matter consists, measured in coulombs (C) 1 C of charge requires electrons Law of conservation of charge: charge cannot be created or

matter consists, measured in coulombs (C) 1 C of charge requires electrons Law of conservation of charge: charge cannot be created or Basc Concepts Oerew SI Prefxes Defntons: Current, Voltage, Power, & Energy Passe sgn conenton Crcut elements Ideal s Portland State Unersty ECE 221 Basc Concepts Ver. 1.24 1 Crcut Analyss: Introducton

More information

Digital Signal Processing

Digital Signal Processing Dgtal Sgnal Processng Dscrete-tme System Analyss Manar Mohasen Offce: F8 Emal: manar.subh@ut.ac.r School of IT Engneerng Revew of Precedent Class Contnuous Sgnal The value of the sgnal s avalable over

More information

Common Base Configuration

Common Base Configuration ommon Base onfguraton nput caracterstcs: s. B wt B const Output caracterstc: s. B wt const Pcture from ref [2] S. Lneykn, ntroducton to electroncs Slde [53] ommon Base Termnal caracterstcs [2] α BO FB

More information

ELECTRONICS. EE 42/100 Lecture 4: Resistive Networks and Nodal Analysis. Rev B 1/25/2012 (9:49PM) Prof. Ali M. Niknejad

ELECTRONICS. EE 42/100 Lecture 4: Resistive Networks and Nodal Analysis. Rev B 1/25/2012 (9:49PM) Prof. Ali M. Niknejad A. M. Nknejad Unversty of Calforna, Berkeley EE 100 / 42 Lecture 4 p. 1/14 EE 42/100 Lecture 4: Resstve Networks and Nodal Analyss ELECTRONICS Rev B 1/25/2012 (9:49PM) Prof. Al M. Nknejad Unversty of Calforna,

More information

i I (I + i) 3/27/2006 Circuits ( F.Robilliard) 1

i I (I + i) 3/27/2006 Circuits ( F.Robilliard) 1 4V I 2V (I + ) 0 0 --- 3V 1 2 4Ω 6Ω 3Ω 3/27/2006 Crcuts ( F.obllard) 1 Introducton: Electrcal crcuts are ubqutous n the modern world, and t s dffcult to oerstate ther mportance. They range from smple drect

More information

Revision of intermediate electronics

Revision of intermediate electronics Revson of ntermedate electroncs ports, feedback and flters Imperal College London EEE Generalsed Thevenn + Norton Theorems: port parameters Amplfers, flters etc have nput and output Input can be voltage

More information

ECEN 325 Electronics

ECEN 325 Electronics ECEN 325 Electronics Introduction Dr. Aydın İlker Karşılayan Texas A&M University Department of Electrical and Computer Engineering Ohm s Law i R i R v 1 v v 2 v v 1 v 2 v = v 1 v 2 v = v 1 v 2 v = ir

More information

Computer-Aided Circuit Simulation and Verification. CSE245 Fall 2004 Professor:Chung-Kuan Cheng

Computer-Aided Circuit Simulation and Verification. CSE245 Fall 2004 Professor:Chung-Kuan Cheng Computer-Aded Crcut Smulaton and Verfcaton CSE245 Fall 24 Professor:Chung-Kuan Cheng Admnstraton Lectures: 5:pm ~ 6:2pm TTH HSS 252 Offce Hours: 4:pm ~ 4:45pm TTH APM 4256 Textbook Electronc Crcut and

More information

Driving your LED s. LED Driver. The question then is: how do we use this square wave to turn on and turn off the LED?

Driving your LED s. LED Driver. The question then is: how do we use this square wave to turn on and turn off the LED? 0//00 rng your LE.doc / rng your LE s As we hae preously learned, n optcal communcaton crcuts, a dgtal sgnal wth a frequency n the tens or hundreds of khz s used to ampltude modulate (on and off) the emssons

More information

EE 508 Lecture 7. Degrees of Freedom The Approximation Problem

EE 508 Lecture 7. Degrees of Freedom The Approximation Problem EE 508 Lecture 7 Degrees of Freedom The Approxmaton Problem vew from Last Tme Desgn Strategy Theorem: A crcut wth transfer functon T(s) can be obtaned from a crcut wth normalzed transfer functon T n (s

More information

Chapter 10 Sinusoidal Steady-State Power Calculations

Chapter 10 Sinusoidal Steady-State Power Calculations Chapter 0 Snusodal Steady-State Power Calculatons n Chapter 9, we calculated the steady state oltages and currents n electrc crcuts dren by snusodal sources. We used phasor ethod to fnd the steady state

More information

INDUCTANCE. RC Cicuits vs LR Circuits

INDUCTANCE. RC Cicuits vs LR Circuits INDUTANE R cuts vs LR rcuts R rcut hargng (battery s connected): (1/ )q + (R)dq/ dt LR rcut = (R) + (L)d/ dt q = e -t/ R ) = / R(1 - e -(R/ L)t ) q ncreases from 0 to = dq/ dt decreases from / R to 0 Dschargng

More information

Designing Information Devices and Systems II Spring 2018 J. Roychowdhury and M. Maharbiz Discussion 3A

Designing Information Devices and Systems II Spring 2018 J. Roychowdhury and M. Maharbiz Discussion 3A EECS 16B Desgnng Informaton Devces and Systems II Sprng 018 J. Roychowdhury and M. Maharbz Dscusson 3A 1 Phasors We consder snusodal voltages and currents of a specfc form: where, Voltage vt) = V 0 cosωt

More information

(b) i(t) for t 0. (c) υ 1 (t) and υ 2 (t) for t 0. Solution: υ 2 (0 ) = I 0 R 1 = = 10 V. υ 1 (0 ) = 0. (Given).

(b) i(t) for t 0. (c) υ 1 (t) and υ 2 (t) for t 0. Solution: υ 2 (0 ) = I 0 R 1 = = 10 V. υ 1 (0 ) = 0. (Given). Problem 5.37 Pror to t =, capactor C 1 n the crcut of Fg. P5.37 was uncharged. For I = 5 ma, R 1 = 2 kω, = 5 kω, C 1 = 3 µf, and C 2 = 6 µf, determne: (a) The equvalent crcut nvolvng the capactors for

More information

COMPOSITE BEAM WITH WEAK SHEAR CONNECTION SUBJECTED TO THERMAL LOAD

COMPOSITE BEAM WITH WEAK SHEAR CONNECTION SUBJECTED TO THERMAL LOAD COMPOSITE BEAM WITH WEAK SHEAR CONNECTION SUBJECTED TO THERMAL LOAD Ákos Jósef Lengyel, István Ecsed Assstant Lecturer, Professor of Mechancs, Insttute of Appled Mechancs, Unversty of Mskolc, Mskolc-Egyetemváros,

More information

Sections begin this week. Cancelled Sections: Th Labs begin this week. Attend your only second lab slot this week.

Sections begin this week. Cancelled Sections: Th Labs begin this week. Attend your only second lab slot this week. Announcements Sectons begn ths week Cancelled Sectons: Th 122. Labs begn ths week. Attend your only second lab slot ths week. Cancelled labs: ThF 25. Please check your Lab secton. Homework #1 onlne Due

More information

ENGR-4300 Electronic Instrumentation Quiz 4 Fall 2010 Name Section. Question Value Grade I 20 II 20 III 20 IV 20 V 20. Total (100 points)

ENGR-4300 Electronic Instrumentation Quiz 4 Fall 2010 Name Section. Question Value Grade I 20 II 20 III 20 IV 20 V 20. Total (100 points) ENGR-43 Electronc Instrumentaton Quz 4 Fall 21 Name Secton Queston Value Grade I 2 II 2 III 2 IV 2 V 2 Total (1 ponts) On all questons: SHOW LL WORK. EGIN WITH FORMULS, THEN SUSTITUTE VLUES ND UNITS. No

More information

EE C245 ME C218 Introduction to MEMS Design Fall 2007

EE C245 ME C218 Introduction to MEMS Design Fall 2007 EE C45 ME C18 Introducton to MEMS Desgn Fall 007 Prof. Clark T.C. Nguyen Dept. of Electrcal Engneerng & Computer Scences Unversty of Calforna at Berkeley Berkeley, CA 9470 Lecture 8: Mnmum Detectable Sgnal

More information

Selected Student Solutions for Chapter 2

Selected Student Solutions for Chapter 2 /3/003 Assessment Prolems Selected Student Solutons for Chapter. Frst note that we know the current through all elements n the crcut except the 6 kw resstor (the current n the three elements to the left

More information

Semistate Theory and Design of Analog VLSI Circuits

Semistate Theory and Design of Analog VLSI Circuits Semstate Theory and Desgn of Analog VLSI Crcuts Roert W. Newcom Electrcal and Computer Engneerng Department Unersty of Maryland, College Park, MD 74 USA URL: http://www.ece.umd.edu/~newcom/msla.html emal:

More information

Section 8.3 Polar Form of Complex Numbers

Section 8.3 Polar Form of Complex Numbers 80 Chapter 8 Secton 8 Polar Form of Complex Numbers From prevous classes, you may have encountered magnary numbers the square roots of negatve numbers and, more generally, complex numbers whch are the

More information

Physics 4B. A positive value is obtained, so the current is counterclockwise around the circuit.

Physics 4B. A positive value is obtained, so the current is counterclockwise around the circuit. Physcs 4B Solutons to Chapter 7 HW Chapter 7: Questons:, 8, 0 Problems:,,, 45, 48,,, 7, 9 Queston 7- (a) no (b) yes (c) all te Queston 7-8 0 μc Queston 7-0, c;, a;, d; 4, b Problem 7- (a) Let be the current

More information

I 2 V V. = 0 write 1 loop equation for each loop with a voltage not in the current set of equations. or I using Ohm s Law V 1 5.

I 2 V V. = 0 write 1 loop equation for each loop with a voltage not in the current set of equations. or I using Ohm s Law V 1 5. Krchoff s Laws Drect: KL, KL, Ohm s Law G G Ohm s Law: 6 (always get equaton/esor) Ω 5 Ω 6Ω 4 KL: : 5 : 5 eq. are dependent (n general, get n ndep. for nodes) KL: 4 wrte loop equaton for each loop wth

More information

Lesson 16: Basic Control Modes

Lesson 16: Basic Control Modes 0/8/05 Lesson 6: Basc Control Modes ET 438a Automatc Control Systems Technology lesson6et438a.tx Learnng Objectves Ater ths resentaton you wll be able to: Descrbe the common control modes used n analog

More information

Physics 1202: Lecture 11 Today s Agenda

Physics 1202: Lecture 11 Today s Agenda Physcs 122: Lecture 11 Today s Agenda Announcements: Team problems start ths Thursday Team 1: Hend Ouda, Mke Glnsk, Stephane Auger Team 2: Analese Bruder, Krsten Dean, Alson Smth Offce hours: Monday 2:3-3:3

More information

210 Calle Solana, San Dimas, CA Tel. (909) ; Fax (909)

210 Calle Solana, San Dimas, CA Tel. (909) ; Fax (909) 1 Crcuts and Systems Exposton THE GFT: A GENERAL YET PRACTICAL FEEDBACK THEOREM R. Dad Mddlebrook 210 Calle Solana, San Dmas, CA 91773 Tel. (909) 592-0317; Fax (909) 592-0698 EMal: rdm@rdmddlebrook.com

More information

ANALOG ELECTRONICS I. Transistor Amplifiers DR NORLAILI MOHD NOH

ANALOG ELECTRONICS I. Transistor Amplifiers DR NORLAILI MOHD NOH 241 ANALO LTRONI I Lectures 2&3 ngle Transstor Amplfers R NORLAILI MOH NOH 3.3 Basc ngle-transstor Amplfer tages 3 dfferent confguratons : 1. ommon-emtter ommon-source Ib B R I d I c o R o gnal appled

More information

COMPLEX NUMBERS AND QUADRATIC EQUATIONS

COMPLEX NUMBERS AND QUADRATIC EQUATIONS COMPLEX NUMBERS AND QUADRATIC EQUATIONS INTRODUCTION We know that x 0 for all x R e the square of a real number (whether postve, negatve or ero) s non-negatve Hence the equatons x, x, x + 7 0 etc are not

More information

AGC Introduction

AGC Introduction . Introducton AGC 3 The prmary controller response to a load/generaton mbalance results n generaton adjustment so as to mantan load/generaton balance. However, due to droop, t also results n a non-zero

More information