55:041 Electronic Circuits

Transcription

1 55:04 Electronic ircuit Frequency eone hater 7 A. Kruger Frequency eone-

2 ee age 4-5 o the Prologue in the text Imortant eview v = M co ωt + θ m = M e e j ωt+θ m = e M e jθ me jωt Thi lead to the concet o haor we encountered in ircuit In Linear ytem we learn about comlex requency = σ + jω In thi coure, we normally tay on the imaginary axi σ = 0 jω omlex imedance eitor aacitor jω jπ Inductor L jωl jπl A. Kruger Frequency eone-

3 Frequency o Av i o Av i 0log 0 A v L H log A. Kruger Frequency eone-3

4 Amliier Gain eru Frequency i A o o i ect. 7. A. Kruger Frequency eone-4

5 Traner Function o omlex Frequency oltage Amliier urrent Amliier Tranconductance Amliier Tranreitance Amliier Name o Function oltage Traner Function urrent Traner Function Tranreitance Function Tranconductance Function Exreion T = o / i I o /I i o /I i I o / i A. Kruger Frequency eone-5

6 A. Kruger Frequency eone-6 General Traner Function n m z z z K T Zero are where traner unction i zero Pole are where traner unction diverge and become ininite omlex requency j n m j j j j z j z j z j K T j T omlex requency i the general cae. One can evaluate the traner unction with a inuoidal excitation at a requency = by etting = j

7 omlex Imedance eca omlex requency j eitor aacitor Inductor L j j L A. Kruger Frequency eone-7

8 A. Kruger Frequency eone-8 erie ouling aacitor ircuit P P i o T τ = Time ontant oltage Traner Function P P P i o K K T P P P P P P K n m z z z K

9 A. Kruger Frequency eone-9 P P K T P i o K K T Examle o Firt-Order ircuit More Examle

10 A. Kruger Frequency eone-0 Bode Plot: Magnitude ect P K K T j j K j T K j T K j T j T General cae inuoidal excitation

11 0 db T j 0log T j 0log 0log 0log log 0T j 0log 0 Actual curve decade 0. Log cale A. Kruger Frequency eone-

12 A. Kruger Frequency eone- log 0 0 j T Log cale log db j T Actual curve Break-oint requency -3 db requency orner requency j T

13 Bode Plot: Phae T K P K A. Kruger Frequency eone-3

14 Bode Plot: Magnitude T K P P P P A. Kruger Frequency eone-4

15 Bode Plot: Phae T K P P P P A. Kruger Frequency eone-5

16 hort-ircuit and Oen-ircuit Time ontant T z K z zm n Pole and zero can interact hort- and oen-circuit time contant: ueul imliication when ole and zero don t interact trongly ect Low-Frequency eone Oen-circuit time contant: et all indeendent ource to zero and treat P a oen circuit P hort-circuit time contant: et all indeendent ource to zero and treat a hort circuit High-Frequency eone P L H P P P A. Kruger Frequency eone-6

17 Frequency o Av i o Av i 0log 0 A v L H log A. Kruger Frequency eone-7

18 hort-ircuit and Oen-ircuit Time ontant P L P P P H P A. Kruger Frequency eone-8

19 Examle Examle 7. = kω, P = 0 kω, = µf, P = 3 F τ = m and τ P =.73 n L = 4.5 Hz and H = 58.3 MHz L and H are order o magnitude aart => good aumtion A. Kruger Frequency eone-9

20 teady-tate Outut eone ouling aacitor ect Load aacitor Load aacitor ouling aacitor A. Kruger Frequency eone-0

21 elationhi Between ie-time and Bandwidth Not in text t order ytem, low-a v v o i e t / Time to reach 0% o inal value or te inut Time to reach 90% o inal value or te inut / 0. e t t0 0 / 0.9 e t t90 90 ln ln % ie time t r t90 t0 ln db bandwidth o a low a circuit with time contant BW 3dB Hz... ombine and BW 3dB tr. t r tr Hz A. Kruger Frequency eone-

22 elationhi Between ie-time and Bandwidth Not in text BW 3dB 0.35 t r Hz t r. t r t t t r r rn A. Kruger Frequency eone-

23 A. Kruger Frequency eone-3 E with ouling aacitor i i L ect. 7.3 i i i i I ib B E B i r ib B B i i m v r g A Alternative: ue time contant technique Tak: lot requency reone

24 A v E i i L i i i B i? r E 0 log 0 E loe = 0 db/decade A. Kruger Frequency eone-4

25 ommon ource with Outut ouling aacitor ect. 7.3 Time contant technique: et all indeendent ource to zero, and conider c L D L A. Kruger Frequency eone-5

26 Emitter Follower with Outut ouling aacitor Frequency reone = low a Determine the lower -3 db requency Examle 7.5 o r o r B o o E L? L Alternative: Ue time contant technique: et all indeendent ource to zero and conider c o E Full analytical olution become quite comlicated L 5.9 Hz Great exam quetion A. Kruger Frequency eone-6

27 Emitter Follower with Outut ouling aacitor Examle 7.5 o r o r B 0 db o E L 0 db L o E L 5.9 Hz loe = 0 db/decade A. Kruger Frequency eone-7

28 ommon ource with Load aacitor Note the PMO tranitor. an you identiy thi a a common ource amliier? ect 7.3. Frequency reone = low a Time contant technique: et all indeendent ource to zero, and conider L H D L L A. Kruger Frequency eone-8

29 ouling and Parallel Load aacitor ect Low-a H High-a L 0log 0 A v Midband Gain L H log A. Kruger Frequency eone-9

30 mall-ignal Equivalent ircuit: ouling and Parallel Load aacitor Derive an exreion or the voltage gain that include L and and then lot igniicant amount o work Ue PIE alo a air amount o work A. Kruger Frequency eone-30

31 ouling and Parallel Load aacitor ect i r i E? Time contant technique: et indeendent ource to zero, and conider L, Low-a H High-a L L [ ] i 0log 0 A v Midband Gain H L L L H log A. Kruger Frequency eone-3

32 A. Kruger Frequency eone-3 mall-ignal Equivalent ircuit: ouling and Parallel Load aacitor i L ] [ L L H Time contant technique: et indeendent ource to zero, and conider L, E i r

33 BJT imedance caling r E E Emitter Bya aacitor mall-ignal Equivalent ect I b r i E E A v 0 r r E g m v I br g O m A v r r g m A. Kruger Frequency eone-33

34 A. Kruger Frequency eone-34 Bode Plot o oltage Gain Magnitude: Emitter Bya aacitor Both ole and zero in traner unction E E A E E E B r r m E v g r r A 0 m v g r r A

35 Two ouling aacitor and a Emitter Bya aacitor ect an you identiy the tye amliier? PNP, E Amliier Tend to increae gain a increae Better couling a increae A detailed analytical analyi i comlex A. Kruger Frequency eone-35

36 PIE eult or Two ouling aacitor and a Emitter Bya aacitor oncet: Dominant Pole A. Kruger Frequency eone-36

37 The evere-biaed n Junction deletion nonconductive conductive n conductive evere voltage electric ield aid built-in electric ield => increae deletion region j j0 bi More general cae / j j0 bi 0.5 j0 bi m j0 = junction caacitance at zero alied voltage aractor or varica diode Junction grading coeicient A. Kruger Frequency eone-37

38 Forward-Biaed Diode & Diuion aacitance More reined mall-ignal model r d d g d dq d Even more comlete mall ignal model D I T DQ Tranit time I D T T g d T hange in minority carrier tored charge with time-varying voltage uerimoed on dc quiecent voltage. The change in tored charge lead to a diode diuion caacitance. Diuion caacitance i normally much larger than junction caacitance r d j g d d I I D T T j0 T DQ bi m g d T A. Kruger Frequency eone-38

39 Junction & Diuion aacitance j j0 bi Junction caacitance mjc Junction caacitance j j0 bi mje Diuion caacitance aociated with current lowing through the baeemitter junction d I T T g m T A. Kruger Frequency eone-39

40 Exanded Hybrid- Equivalent ircuit ect 7.4. ~00 ~ M ~ Paraitic element A. Kruger Frequency eone-40

41 PIE NOT IN TEXT PIE ue more comlex model ome PIE arameter match u with hybrid- arameter, while other don t A. Kruger Frequency eone-4

42 PIE NOT IN TEXT B J I JE E BF AF ~ A. Kruger Frequency eone-4

43 Exanded Hybrid- Equivalent ircuit ect 7.4. π i normally >> µ However, becaue o the eedback rom to B the eect o µ can be much bigger than that o π Both π, and µ are unction o Q-oint A. Kruger Frequency eone-43

44 A. Kruger Frequency eone-44 hort-ircuit urrent Gain: BJT Frequency eone ect j j r I b KL at inut KL at outut j g I m c 0 j I g m j r j g h I I A m e b c i r j r g j r g h m m e With tyical value or µ and g m e b c i h I I A

45 A. Kruger Frequency eone-45 r o T r j r g h m e Beta cuto requency Tranition requency

46 Exanded Hybrid- Equivalent ircuit Quiz later ~00 ~ M ~ Paraitic element A. Kruger Frequency eone-46

47 Miller Eect and Miller aacitance ect B B E E mall ~ F, but can have igniicant eect on requency reone B E A. Kruger Frequency eone-47

48 A. Kruger Frequency eone-48 o j I j I o Thevenin Equivalent Norton Equivalent

49 For tyical value or dicrete BJT, we can ignore thi A. Kruger Frequency eone-49

50 A. Kruger Frequency eone-50 ] [ L m M g We tarted here and went through a equence o tranormation, which reulted in thi circuit Thi i a much imler circuit to analyze why? o o j j I v g L m o g j I L m ] [ Miller aacitance

51 For tyical value or dicrete BJT, we can ignore thi M [ gm L ] A. Kruger Frequency eone-5

52 Phyical Origin o Miller Eect ect Inverting amliier g ] M [ m L oltage gain rom B to i.e., acro μ? M voltage gain acro Anwer g m L ead ection A. Kruger Frequency eone-5

53 Inherent eitance and aacitance in n- hannel MOFET mall mall ect 7.5 mall g gd WL ox A. Kruger Frequency eone-53

54 Equivalent ircuit or n-hannel ommon ource MOFET A. Kruger Frequency eone-54

55 Unity-Gain Bandwidth ect 7.5. Unity gain-band width i deined a the requency where the magnitude o the hort circuit current gain goe to. KL at inut node KL at outut node I i g j g g j gd I d g m g g j gd A i I I d i g m j m j g j gd gd g g gd et to T gm g gd imilar to BJT T gm A. Kruger Frequency eone-55

56 MOFET Miller aacitance ect Inverting amliier M gd [ gml ] oltage gain rom G to D i.e., acro gd? Anwer g m L A. Kruger Frequency eone-56

57 E Amliier i imilar ect eq High-gain becaue o E Inverting amliier Ue time contant technique: H [ r B ] eq H A. Kruger Frequency eone-57

58 PIE eult or ommon Emitter A. Kruger Frequency eone-58

59 B Amliier G i imilar ect 7.6. Thee are NOT inverting amliier. Thu, Miller no multilication eect. A. Kruger Frequency eone-59

60 A. Kruger Frequency eone-60 B Amliier r E H L H Equivalent inut circuit Equivalent outut circuit Either one could determine bandwidth normally μ egardle, higher bandwidth than E

61 acode ircuit E i an inverting amliier => Miller eect reent E voltage gain ~ => low Miller eect A. Kruger Frequency eone-6

62 acode ircuit H r H B M L Either one could determine bandwidth normally μ Wide bandwidth A. Kruger Frequency eone-6

63 PIE eult or acode A. Kruger Frequency eone-63

64 Emitter-Follower ircuit ource-follower i imilar A. Kruger Frequency eone-64

65 A. Kruger Frequency eone-65 ' ' L m L m B H g r g ' ' L m L m B g r g Wide bandwidth ' ' ' ' L L L b gm gm r Z

66 PIE eult or Emitter Follower A. Kruger Frequency eone-66

67 A. Kruger Frequency eone-67