55:041 Electronic Circuits
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1 55:04 Electronic ircuit Frequency epone hapter 7 A. Kruger Frequency epone-
2 ee page 4-5 of the Prologue in the text Important eview co Thi lead to the concept of phaor we encountered in ircuit In Linear ytem we learn about complex frequency In thi coure, we normally tay on the imaginary axi 0 omplex impedance eitor apacitor 2 Inductor 2 A. Kruger Frequency epone-2
3 Frequency epone f o Av Vi Midband f o Av 2 Vi 20 log 0 A v f L f H log( f A. Kruger Frequency epone-3
4 Amplifier Gain Veru Frequency V i ( f A( V f o V o V ( f i ( f ect. 7. A. Kruger Frequency epone-4
5 Tranfer Function of omplex Frequency Voltage Amplifier urrent Amplifier Tranconductance Amplifier Tranreitance Amplifier Name of Function Voltage Tranfer Function urrent Tranfer Function Tranreitance Function Tranconductance Function Expreion T( = V o (/V i ( I o (/I i ( V o (/I i ( I o (/V i ( A. Kruger Frequency epone-5
6 A. Kruger Frequency epone-6 General Tranfer Function ( ( ( ( ( ( ( 2 2 n m p p p z z z K T Zero are where tranfer function i zero Zero are where tranfer function i zero Pole are where tranfer function diverge and become infinite Pole are where tranfer function diverge and become infinite omplex frequency omplex frequency j ( ( ( ( ( ( ( ( 2 2 n m j p j p j p j z j z j z j K T j T omplex frequency i the general cae. One can evaluate the tranfer function with a inuoidal excitation at a frequency ( = 2f by etting = j omplex frequency i the general cae. One can evaluate the tranfer function with a inuoidal excitation at a frequency ( = 2f by etting = j
7 omplex Impedance ecap omplex frequency j eitor apacitor Inductor L j j L A. Kruger Frequency epone-7
8 A. Kruger Frequency epone-8 erie oupling apacitor ircuit P P i o V V T ( ( ( τ = Time ontant τ = Time ontant Voltage Tranfer Function Voltage Tranfer Function P P p p P i o K K V V T 2 2 ( ( ( ( P P P P P P 2 K ( ( ( ( ( ( 2 2 n m p p p z z z K
9 A. Kruger Frequency epone-9 P P K T ( ( p p P i o K K V V T 2 2 ( ( ( ( Example of Firt-Order ircuit Example of Firt-Order ircuit More Example
10 A. Kruger Frequency epone-0 Bode Plot: Magnitude ect ect p p P K K T 2 2 ( ( ( 2 j j K j T ( 2 2 K j T 2 2 ( 2 2 f f K jf T 2 2 ( 2 p p f f jf T General cae General cae inuoidal excitation inuoidal excitation
11 T( jf 20log p p T ( jf 20log 2f 2f 2 20log 2f 20log 2f p p 2 20log0 T( jf p 20log 0 p 20 db Actual curve decade f f 0. 2 f 2 Log cale A. Kruger Frequency epone-
12 T( jf p p 2f 2f 2 T ( jf p p 2f 2 20log0 T( jf p 20log 0 p 3 db Actual curve Break-point frequency -3 db frequency f 2 f Log cale orner frequency A. Kruger Frequency epone-2
13 Bode Plot: Phae T( K2 P K2 ( p p A. Kruger Frequency epone-3
14 Bode Plot: Magnitude T ( K P ( P P P A. Kruger Frequency epone-4
15 Bode Plot: Phae T ( K P ( P P P A. Kruger Frequency epone-5
16 hort-ircuit and Open-ircuit Time ontant T( ( z K ( p ( ( z2 ( zm p ( p 2 n Pole and zero can interact hort- and open-circuit time contant: ueful implification when pole and zero don t interact trongly ect Low-Frequency epone Open-circuit time contant: et all independent ource to zero and treat P a open circuit ( P hort-circuit time contant: et all independent ource to zero and treat a hort circuit High-Frequency epone P ( f L f H 2 2 P P P A. Kruger Frequency epone-6
17 Frequency epone f o Av Vi Midband f o Av 2 Vi 20 log 0 A v f L f H log( f A. Kruger Frequency epone-7
18 hort-ircuit and Open-ircuit Time ontant ( P f L 2 P ( P P f H 2 P A. Kruger Frequency epone-8
19 Example = kω, P = 0 kω, = µf, P = 3 pf τ = m and τ P = 2.73 n f L = 4.5 Hz and f H = 58.3 MHz Example 7.2 f L and f H are order of magnitude apart => good aumption A. Kruger Frequency epone-9
20 teady-tate Output epone oupling apacitor ect Load apacitor Load apacitor oupling apacitor A. Kruger Frequency epone-20
21 elationhip Between ie-time and Bandwidth Not in text t order ytem (, low-pa v v o i e t / Time to reach 0% of final value for tep input Time to reach 90% of final value for tep input / 0. e t t0 0 / 0.9 e t t90 90 ln( ln( % ie time t r t90 t0 ln( ( -3 db bandwidth of a low pa circuit with time contant BW ( 3dB (Hz...(2 2 ombine ( and ( BW ( 3dB 2 tr 2.2 2tr tr (Hz A. Kruger Frequency epone-2
22 elationhip Between ie-time and Bandwidth Not in text BW 3dB 0.35 t ( r (Hz t r 2.2 t r 2 t t 2 t 2 r r2 rn A. Kruger Frequency epone-22
23 Tak: plot frequency repone E with oupling apacitor ect. 7.3 f L 2 ( i i Alternative: ue time contant technique I i i B i r E B ib A v ( Vi g i m r i i B B ib A. Kruger Frequency epone-23
24 A. Kruger Frequency epone-24 f log 20 0 E f 2 i i L f ( 2 i i (? i E B i r E v A lope = 20 db/decade lope = 20 db/decade
25 ommon ource with Output oupling apacitor ect. 7.3 Time contant technique: et all independent ource to zero, and conider c. f L 2 ( D L A. Kruger Frequency epone-25
26 Emitter Follower with Output oupling apacitor Frequency repone = low pa Determine the lower -3 db frequency Example 7.5 o r o r B o ( o E L 2? f L 2 ( Alternative: Ue time contant technique: et all independent ource to zero and conider c2 o E Full analytical olution become quite complicated L Hz Great exam quetion A. Kruger Frequency epone-26
27 Emitter Follower with Output oupling apacitor Example 7.5 o r o r B 0 db ( o E L 2 0 db f L 2 ( o E L Hz lope = 20 db/decade f 2 f A. Kruger Frequency epone-27
28 ommon ource with Load apacitor Note the PMO tranitor. an you identify thi a a common ource amplifier? ect Frequency repone = low pa Time contant technique: et all independent ource to zero, and conider L f H 2 ( D L L A. Kruger Frequency epone-28
29 oupling and Parallel Load apacitor ect Low-pa (f H High-pa (f L 20 log 0 A v Midband Gain f L f H log( f A. Kruger Frequency epone-29
30 mall-ignal Equivalent ircuit: oupling and Parallel Load apacitor Derive an expreion for the voltage gain that include L and and then plot ignificant amount of work Ue PIE alo a fair amount of work A. Kruger Frequency epone-30
31 oupling and Parallel Load apacitor ect i r i E? Time contant technique: et independent ource to zero, and conider L, Low-pa (f H High-pa (f L f L 2 [ ( 2 ] i 20 log 0 A v Midband Gain f H 2 ( L L f L f H log( f A. Kruger Frequency epone-3
32 A. Kruger Frequency epone-32 mall-ignal Equivalent ircuit: oupling and Parallel Load apacitor i L f ] ( [ 2 2 L L H f ( 2 Time contant technique: et independent ource to zero, and conider L, Time contant technique: et independent ource to zero, and conider L, E i r
33 BJT impedance caling r E E Emitter Bypa apacitor mall-ignal Equivalent ect I b r V i E E A v 0 r ( r E g m v I br V g O m A v r r g m A. Kruger Frequency epone-33
34 A. Kruger Frequency epone-34 Bode Plot of Voltage Gain Magnitude: Emitter Bypa apacitor Both pole and zero in tranfer function Both pole and zero in tranfer function 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 oupling apacitor and a Emitter Bypa apacitor ect an you identify the type amplifier? PNP, E Amplifier Tend to increae gain a f increae Better coupling a f increae A detailed analytical analyi i complex A. Kruger Frequency epone-35
36 PIE eult for Two oupling apacitor and a Emitter Bypa apacitor oncept: Dominant Pole A. Kruger Frequency epone-36
37 The evere-biaed pn Junction depletion (nonconductive p (conductive n (conductive evere voltage electric field aid built-in electric field => increae depletion region j j0 V V bi More general cae / 2 V V j j0 bi 0.5 j0 V V bi m j0 = junction capacitance at zero applied voltage Varactor or varicap diode Junction grading coefficient A. Kruger Frequency epone-37
38 Forward-Biaed Diode & Diffuion apacitance More refined mall-ignal model r d d g d dq dv Even more complete mall ignal model D V I T DQ Tranit time I D T V T g d T hange in minority carrier tored charge with time-varying voltage uperimpoed on dc quiecent voltage. The change in tored charge lead to a diode diffuion capacitance. Diffuion capacitance i normally much larger than junction capacitance r d j g d d V I V V I D T V T j0 T DQ bi m g d T A. Kruger Frequency epone-38
39 Junction & Diffuion apacitance j V V j0 bi Junction capacitance mjc Junction capacitance j V V j0 bi mje Diffuion capacitance aociated with current flowing through the baeemitter junction d I T V T g m T A. Kruger Frequency epone-39
40 Expanded Hybrid- Equivalent ircuit ect 7.4. ~ 00 ~ M ~ 2 Paraitic element A. Kruger Frequency epone-40
41 PIE NOT IN TEXT PIE ue more complex model ome PIE parameter match up with hybrid- parameter, while other don t A. Kruger Frequency epone-4
42 PIE NOT IN TEXT B J I JE E BF VAF ~ 2 A. Kruger Frequency epone-42
43 Expanded Hybrid- Equivalent ircuit ect 7.4. π i normally >> µ However, becaue of the feedback from to B the effect of µ can be much bigger than that of π Both π, and µ are function of Q-point A. Kruger Frequency epone-43
44 hort ircuit Gain Ignore effect of and oupling capacitor 0 urrent amplifier A. Kruger Frequency epone-44
45 A. Kruger Frequency epone-45 hort-ircuit urrent Gain: BJT Frequency epone ect ect V V r V I b KL at input KL at input KL at output KL at output g V I m c 0 V I V g m r g h I I A m fe b c i r r g r g h m m fe With typical value for µ and g m With typical value for µ and g m fe b c i h I I A
46 h fe g m r g m r r r ecall that at dc we ued, f 2 r ( f T f o Beta cutoff frequency Tranition frequency A. Kruger Frequency epone-46
47 Expanded Hybrid- Equivalent ircuit Quiz later ~ 00 ~ M ~ 2 Paraitic element A. Kruger Frequency epone-47
48 Miller Effect and Miller apacitance ect B B E E mall (~ pf, but can have ignificant effect on frequency repone B E A. Kruger Frequency epone-48
49 A. Kruger Frequency epone-49 V o j I V V j I V o 2 Thevenin Equivalent Thevenin Equivalent Norton Equivalent Norton Equivalent
50 For typical value for dicrete BJT, we can ignore thi A. Kruger Frequency epone-50
51 We tarted here and went through a equence of tranformation, which reulted in thi circuit Thi i a much impler circuit to analyze (why? I V o V V j g m o L j v V V o I j [ M Miller apacitance gm ( L ] V [ gm( L ] A. Kruger Frequency epone-5
52 For typical value for dicrete BJT, we can ignore thi M [ gm( L ] A. Kruger Frequency epone-52
53 Phyical Origin of Miller Effect ect Inverting amplifier g ( ] M [ m L Voltage gain from B to (i.e., acro μ? M voltage gain acro Anwer g m L ead ection A. Kruger Frequency epone-53
54 Inherent eitance and apacitance in n- hannel MOFET ect 7.5 mall mall mall g gd WL 2 ox A. Kruger Frequency epone-54
55 Equivalent ircuit for n-hannel ommon ource MOFET A. Kruger Frequency epone-55
56 Unity-Gain Bandwidth ect Unity gain-band width i defined a the frequency where the magnitude of the hort circuit current gain goe to. KL at input node KL at output node I i Vg j g V g j gd I d g m V g V g j gd A i I I d i g m j m j g j gd gd g g gd et to f T gm 2 ( g gd imilar to BJT f T gm 2 ( A. Kruger Frequency epone-56
57 MOFET Miller apacitance ect Inverting amplifier M gd [ g ml ] Voltage gain from G to D (i.e., acro gd? Anwer g m L A. Kruger Frequency epone-57
58 E Amplifier ( i imilar ect eq High-gain becaue of E Inverting amplifier Ue time contant technique: f H 2 [ r B ]( eq f H 2 p A. Kruger Frequency epone-58
59 PIE eult for ommon Emitter A. Kruger Frequency epone-59
60 B Amplifier (G i imilar ect Thee are NOT inverting amplifier. Thu, Miller no multiplication effect. A. Kruger Frequency epone-60
61 B Amplifier Equivalent output circuit f H 2 ( L Equivalent input circuit f H r 2 E Either one could determine bandwidth (normally μ egardle, higher bandwidth than E A. Kruger Frequency epone-6
62 acode ircuit E i an inverting amplifier => Miller effect preent E voltage gain ~ => low Miller effect A. Kruger Frequency epone-62
63 acode ircuit f H 2 r ( H B M 2 ( L 2 f Either one could determine bandwidth (normally μ Wide bandwidth A. Kruger Frequency epone-63
64 PIE eult for acode A. Kruger Frequency epone-64
65 Emitter-Follower ircuit (ource-follower i imilar A. Kruger Frequency epone-65
66 A. Kruger Frequency epone-66 ' ' ( 2 L m L m B H g r g f ' ' ( L m L m B p g r g Wide bandwidth Wide bandwidth ' ' ' ' L L L b gm gm r Z
67 PIE eult for Emitter Follower A. Kruger Frequency epone-67
68 Bode Plot Example A. Kruger Frequency epone-68
69 ,000 0, Two pole at 0 and one zero at,000 A. Kruger Frequency epone-69
70 , , , dB A. Kruger Frequency epone-70
71 , Two pole Active after 0-40 db/decade lope i 40 db decade A. Kruger Frequency epone-7
72 , One zero become active at,000 lope i 40 db decade lope i 20 db decade A. Kruger Frequency epone-72
73 , tan 0 tan 0 tan,000 lope i 40 db decade lope i 20 db decade A. Kruger Frequency epone-73
74 , tan 0 tan 0 tan,000 lope i 40 db decade lope i 20 db decade lope i 90 decade A. Kruger Frequency epone-74
75 , tan 0 tan 0 tan,000 lope i 40 db decade lope i 20 db decade lope i 90 decade A. Kruger Frequency epone-75
76 , tan 0 tan 0 tan,000 lope i 40 db decade lope i 20 db decade lope i 90 decade A. Kruger Frequency epone-76
77 , tan 0 tan 0 tan,000 lope i 40 db decade lope i 20 db decade lope i 90 decade lope i 45 decade A. Kruger Frequency epone-77
78 , tan 0 tan 0 tan,000 lope i 40 db decade lope i 20 db decade lope i 90 decade lope i 45 decade A. Kruger Frequency epone-78
79 , lope i 40 db decade lope i 20 db decade lope i 90 decade lope i 45 decade A. Kruger Frequency epone-79
80 Plotting Tranfer Function in Matlab A. Kruger Frequency epone-80
81 A. Kruger Frequency epone-8
82 A. Kruger Frequency epone-82
83 A. Kruger Frequency epone-83
84 A. Kruger Frequency epone-84
85 A. Kruger Frequency epone-85
86 A. Kruger Frequency epone-86
87 A. Kruger Frequency epone-87
55:041 Electronic Circuits
55:04 Electronic ircuit Frequency eone hater 7 A. Kruger Frequency eone- 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
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