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/135
Department of Electronic EngineeringNational Taipei University of Technology
/135
• PN BJT
•• BJT ( )
••
(CE) (CB) (CC)
••
2 Department of Electronic Engineering, NTUT
/135
PN BJT
3
/135
PN
• PN
• PN
PN
Cathode Anodepn
0t = 1t t= t = ∞pn pn pn
(Depletion region)
E
4 Department of Electronic Engineering, NTUT
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PN
•
•
1F
T
V
Vtot SI I e
−
=
+− FV
pn2 pn
S iA n D p
DDI Aqn
N L N L
= +
26 mV@ 300 T
kTV T K
q= =≃
F TV V>F
T
V
Vtot SI I e
≃
F TV V<< tot SI I−≃
−+ RV
pn
DI
DV
D
T
V
VSI e
≃
SI−
I/V
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(Reverse Breakdown)
• PN IS
PN
• ( )
• PN(Zener effect) (Avalanche effect)
DI
DVBDV
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•
( 1V/µm)
n
−+ RV
pn E•
PN
3 ~ 8 V
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( )
• PN
•(impact ionization)
−+ RV
pn E• ()
8 Department of Electronic Engineering, NTUT
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( )
•
( )
0 1s 2s 3s 4st
BEV
0 1s 2s 3s 4st
BE BE bev V v= +
BEV bev ( ) BEv ( + )
beV phasor ( )
0 1s 2s 3s 4st
bev
9 Department of Electronic Engineering, NTUT
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•
•
•VCCS
VCVS CCVS
+-
+
-
v1 v = mv1+- v = gi1
i1
VCCS CCCS
+
-v1 i = gv1
i1
i = bi1
10 Department of Electronic Engineering, NTUT
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(VCCS)
•
• VCCS RL RL vout
+
−inv
1 1i kv=
1kv1i LR
L mkR V
mV
t tinv outv
+
−1v
+
−inv
+
−1v
+
−outv
VCVS
1out L L inv kv R kR v= − = − kRL 1 VCCS
11 Department of Electronic Engineering, NTUT
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• VCCS rin
+
−inv 1kv1i LR
+
−outv
+
−1vinr
1 1
1
out L LL
in in
v kv R kv RkR
v v v
− −= = = −
kRL 1 VCCS
12 Department of Electronic Engineering, NTUT
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BJT
• (bipolar-junction transistor, BJT) 1945Shockley Brattain Bardeen
• (BJT )
VBE ( ) VCE
e− (−IE )
Collector
Base
Emitter
(C)
(B)
(E)
+
−0.8 VBEV =
−
+1 VCEV =
+−
+
−
−+
13 Department of Electronic Engineering, NTUT
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BJT I/V
• IC VBE
• IC VCE
+
−BEV
CI+
−CEV
+
−BEV
CI+
−CEV
2B
T
V
VSI e
1B
T
V
VSI e
CEV
CI
1BE BV V=
2BE BV V=
BEV
CI
BE
T
V
VC SI I e= ⋅
14 Department of Electronic Engineering, NTUT
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BJT VCCS
• BJT exponential VCCS
CBV+
−
+−BEV
CEV
+
−
(C)
(B)
(E)
Collector
Base
Emitter
BEV
+
−
BE
T
V
VsI e
(C)(B)
(E)
BE
T
V
VC sI I e=
15 Department of Electronic Engineering, NTUT
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( ) (I)
BEV BEV BEV BEV
CEVCEV
CEV CEV
CI
BE
T
V
VC SI I e= ⋅
CI
VBE
IC
(VBE=0 V)
VCE
(VCE>VBE)IC
(VCE=0 V)
VCE
VBE
(VCE=VBE)IC
VCE VBE
(VCE<VBE)IC
VCE
IC
CI
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( ) (II)
BEV+
−CEV
+
−
VCE
VCE
IC
VBE1
VBE2
VBE3
BEV
CEV
BE
T
V
VC SI I e= ⋅
BEV
CEV
CEV
BEV
BJT
IC VCE
VBE
BEV+
−
CEV
+
−
BE
T
V
VSI e⋅
IC
VCECEV
+
−
BJT
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• VOUT165 10 ASI −= ⋅
1.69 mABE
T
V
VC SI I e= ⋅ =
( )33 V 3 V 1.69 10 1000 1.31 VCE C LV I R −= − = − ⋅ ⋅ =
1.31 VOUTV =
750 mV
3 V
+
−
+
−CILR
OUTV
+
−
1 kΩ
Q:
VBE IC
3 V 2.155 VOUT C LV I R= − =
18 Department of Electronic Engineering, NTUT
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C BI Iβ=
1 11
BE
T
V
VE C B C SI I I I I e
ββ β
+= + = + = ⋅
BE
T
V
VC SI I e= ⋅
1 BE
T
V
VB SI I e
β= ⋅
1C E EI I Iβ α
β= =
+
β IC IE
+
−BEV
CEV+
−
CI
BI
EI
IE IC
IB IC
C BI Iβ=
IB IE
( )1E BI Iβ= +
β
IB IC
β
( β
)VCCS
( )expC S BE TI I V V= ⋅
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• BJT VBE
750 mV β
50~200 IB IE
1.685 mABE
T
V
VC SI I e= ⋅ =
200 50C B CI I I< <
8.43 A 33.7 ABIµ µ< <
1.005 1.02C E CI I I< <
1.693 mA 1.719 mAEI< <
165 10 ASI −= ⋅
50 200 1.05 1.002β α< < ⇒ < <
VBE( VCCS )
+
−BEV
BE
T
V
VSI e
BE
T
V
VSIe
β
CB
E
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− BJT RC
• VBE = 800 mV β=100BJT BJT
RC
X+
−BEV
CICR500 Ω
+2 VCCV =
−
( ) VXV
( ) CR Ω
2.0
1.424
0.800
500 1041
175 10 ASI −= ⋅
1.153 mABE
T
V
VC SI I e= ⋅ = 1
11.53 µABE
T
V
VB SI I e
β= ⋅ =
11.165 mA
BE
T
V
VE SI I e
ββ+= ⋅ =
1.424 VCC C C X XV R I V V= + ⇒ =
1.424 VCE X BEV V V= = >
800 mVCE XV V= = 1041 CC XC C
C
V VR R
I
−= ⇒ = Ω
RC
VBE IC
(VCE VBE )
21 Department of Electronic Engineering, NTUT
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•
10 VCCV =
2 kCR = Ω
220 kBR = Ω
CI
BI
4 VBBV =
+
−
CEV+
−BEV
4 0.715 µA
220kBB BE
BB
V VI
R
− −= = =
200 15 µA 3 mAC BI Iβ= = × =
200β =
( )1 3.015 mAE BI Iβ= + =
10 3 mA 2 k 4 VCE CC C CV V I R= − = − × Ω =
0.015 0.7 3 4 12 mWT B BE C CE C CEP I V I V I V= + = × + × =≃
(mA)Ci
,C satI
,CE satV
(V)CEv0 2 4 6 8 10
1
2
3
4
5
6
(Cut-off)
Q-point
5 µABi =
10 µA
15 µABQI =
20 µA
25 µA
30 µA
CE CC C CV V I R= − CC CEC
C
V VI
R
−=
y x
22 Department of Electronic Engineering, NTUT
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gm (I)
• +
• VBE ( )
•
+
−
BEV∆
CI∆+
CEV
−
0BEas VC C
BE BE
I dI
V dV
∆ →∆ =∆
Cm
BE
dIg
dV=
BE
T
V
VC SI I e= ⋅ 1BE BE
T T
V V
V VC Cm S S
BE BE T T
dI Idg I e I e
dV dV V V
= = ⋅ = ⋅ =
gm
gm IC !!
IC = 1mA VT = 26mV 110.0385 0.0385 S 38.5 mS
26 mg −= = Ω = =Ω
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gm (II)
• gm=dIC/dVBE IC-VBE
IC0 VBE0
• IC-VCE IC1
IC2
mg V∆
BEV0BEV
0CI
CI
V∆
2BE BV V V= + ∆
2BE BV V=
1BE BV V=1BE BV V V= + ∆
CI
2CI
1CI
2mg V∆
1mg V∆
CEV
VBE0 ±∆VIC0 ±gm∆V
gm= IC0/VT gm IC0 IC0
( )
VBE ∆V IC2 IC1
IC gm2> gm1
m C BEg dI dV=
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BJT
• BJT
+
−
BEV∆
+CEV
−
BI∆
EI∆
CI∆
rπrπ E
CB
vπ
−
+mg vπrπ
mr gπ β=
BE BE beV V v∆ = ++
−
B B bI I i∆ = +
BEV∆+
−
BE
T
V
VSI e
∆
C C cI I i∆ = +b ci i β=
+CEV
−
!
CB
E
bev−
+c m bei g v=
bi
ib B-E
b c m bei i g vβ β= =
be
b m
vr
i gπβ= =
BJT
m C Tg I V=
26 Department of Electronic Engineering, NTUT
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• v1 Q1
(a) (b) 1 mV C B?
165 10 ASI −= ⋅ 100β =
1
3.75 C
mT
Ig
V= =
Ω
6.92 mABE
T
V
VC SI I e= =
800 mVBEV =
375 m
rgπβ= = Ω
+
−1v
+ci
−
bi
rπ vπ mg vπ
1v vπ =
1
1 mV0.267 mA
3.75 c m mi g v g vπ= = = =Ω
1 1 mV26.7 µA=
375 c
b
v ii
rπ β= = =
Ω
+
−1v
+1.8 V−
CI
−
+800 mV
(1)
(2) gm rπ
(3)
VBE IC
27 Department of Electronic Engineering, NTUT
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v.s.
•
+
−1v
+
CR−rπ vπ mg vπ
+
−outv
+
−1v
+3.6 VCCV =
−200 CR = Ω
−
+800 mV
+
−OUT OUT outv V v= +3.6 6.92 mA 200 2.216 VCV = − × Ω = (>VBE, )
1out m C m Cv g v R g R vπ= − = −
1
outv m C
vA g R
v= = −
1
3.75 mg =Ω 200 CR = Ω 53.4vA = −
RC
BJT
800 mVBEV = 6.92 mABE
T
V
VC SI I e= =
28 Department of Electronic Engineering, NTUT
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(Early Effect)
• (VA )
BJT IC VBE VCE
( ) VBE IC VCE IC
1BE
T
V
V CEC S
A
VI I e
V
+
≃
1 11
BE BE
T T
V V
V VC CE CS S
CE CE A A A o
I d V II e I e
V dV V V V r
∂ = + = ⋅ = ∂ ≃
CI
BE
T
V
VSIe
β
w/ Early Effect
w/o Early Effect
CEV
1BE
T
V
VS CE
A
I Ve
Vβ
+
BJTro
CI
CEVAV−
CdICEdV
1
or
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1BE BE
T T
V V
V VCE ce ceC C c S C S
A A
V v vI I i I e I I e
V V
+∆ = + = + = +
BE
T
V
V cec S
A
vi I e
V=
BE
T
ce A Ao V
c CVS
v V Vr
i II e
= = ≃
+
−BEV
C C cI I i∆ = +
CE CE ceV V v∆ = +
rπ
+
−vπ mg vπ or
B C
E
Early effect BJT
BJT (gm, vπ, ro)
mr gπ β=m C Tg I V=
o A Cr V I=IC
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• BJT IC = 1 mA β = 100 VA=15 V
+
−BEV
CI∆
V∆rπ
+
−
vπ mg vπ or
B C
E
1
26 C
mT
Ig
V= =
Ω
2600 m
rgπβ= = Ω
15 kAo
C
Vr
I= = Ω
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PNP
• PNP NPN
BEV+
−CEV
+
−BI
EI
CI
EB
T
V
VC sI I e=
EB
T
V
VsB
II e
β= 1 EB
T
V
VE sI I e
ββ+=
1EB
T
V
V ECC s
A
VI I e
V
= +
+
−vπ mg vπ orrπ
cibi
ei
B C
E
+
−vπ mg vπ orrπ
cibi
ei
B C
Enpn
( )
32 Department of Electronic Engineering, NTUT
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BJT
• BJT B-C 2 VA
+
−Xv
Xi
rπ
+
−vπ mg vπ
Xm X
vg v i
r ππ
+ =
1mg rπ β= >> 1
1 1X T
X m m C
v V
i g r g Iπ−= =
+≃
BC diode
IC=1 mA ?
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(I) –
+
−INv
CR
CCV
+
−OUTv
+
−inv rπ
+
−vπ mg vπ or CR
+
−outv
+
−INv
CR
CCV
+
−OUTv
+
−inv
rπ−
+vπ mg vπ or
CR+
−outv
+
−inv rπ
+
−vπ mg vπ or CR
+
−outv
VCCS
NPN
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(II) –
−
+INv
CR
CCV
+
−OUTv
−
+inv rπ
−
+vπ mg vπ or
CR+
−outv
+
−inv rπ
+
−vπ mg vπ or CR
+
−outv
+
−INv
1CR
CCV
+
−OUTv
2CR
1Q
2Q
−
+inv 1rπ
−
+1vπ 1 1mg vπ 1or
1CR
+
−outv
2rπ−
+2vπ 2 2mg vπ 2or
2CR
35 Department of Electronic Engineering, NTUT
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• MOSFET
MOSFET IV
( ) ( )2 212 2
2D n ox GS TH DS DS n GS TH DS DS
WI C V V V V K V V V V
Lµ = − ⋅ − = − ⋅ −
( ) ( ) ( ) ( )2 211 1
2D n ox GS TH DS n GS TH DS
WI C V V V K V V V
Lµ λ λ= − + = − +
,DS sat GS THv v V= −Di
0GSv
DSv
1GSv
2GSv
3GSv
4GSv
5GSv
2GS THv V−
( ) ( )2
2 1D n GS TH DSi K v V vλ= − +
(Triode Region)
(Saturated Region)
+
−GSV
D
G
S
+
−DSV
DI
DSV( )1
2DS
D n GS TH
VR
I K V V= =
−
36 Department of Electronic Engineering, NTUT
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MOSFET
•
•
•
( ) ( ) 22
2D n D
m GS TH n ox GS TH n ox DGS GS TH
I K W W W Ig V V C V V C I
V L L L V Vµ µ∂= = − = − = =
∂ −
( ) ( )2 21
2D n ox GS TH n GS TH
WI C V V K V V
Lµ= − = − gm ID !!
( ) ( ) ( )2 2 11D
n GS TH DS n GS TH DDS DS o
I dK V V V K V V I
V dV rλ λ λ∂ = − + = − = =
∂
MOSro
CI
CEV1AV λ− = −
DdIDSdV
1
or
( ) ( )21D n GS TH DSI K V V Vλ= − +
1o
D
rIλ
=
+
−gsv
DG
S
m gsg vor
BJT !
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BJT
38
/135
•
•
−
+inv out inv v=
sR
+
−
( )
−
+inv
Lout in
s L
Rv v
R R=
+
sR
+
−LR
vin
39 Department of Electronic Engineering, NTUT
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/
•
−
+thv
ocv
thR
+
−ocv
+
−−
+thv
sR
LR
+outv
−LR +
outv
−
th outR R=
outR
th inR R=
inR
40 Department of Electronic Engineering, NTUT
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• 1010-mV 200Ω 8Ω
(a) 2 kΩ 500Ω
(b) 10Ω 2Ω
10vA =10 mV
+
−mv
200 Ω
8 Ω
200 Ω 8 Ω
outRinR
inin m
in s
Rv v
R R=
+2 k 0.91in in mR v v= Ω ⇒ =
500 0.71in in mR v v= Ω ⇒ =
Lout amp
L o
Rv v
R R=
+ 2 0.8o out ampR v v= Ω ⇒ =
10 0.44o out ampR v v= Ω ⇒ =
41 Department of Electronic Engineering, NTUT
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••
•
xv
+
−
inR
xi xi
outR
xv
+
−
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• (a) a-b
(b) Rth
v
+−
b
a
V
+
−v
Rth
vV2i1
i−i1
6 Ω4 Ωi1 +
−
i
a
b
3 Ω
16v i=( )1 1 16 2 4i i i i= + −
1 0.5 , 3i i v i= =
( )3 th
vR
i= = Ω
+−a
b(a)
6 Ω
V2i1
i14 Ω
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• B ( )
+
−xv rπ+
−vπ mg vπ or
CRxi
xin
x
vR r
i π= = T
m C
Vr
g Iπβ β= =
1. β ( IC IB
)
2. (CE ) RC
( BJT )
BB
inv
CR
CCV
outv
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• C ( )
rπ+
−vπ mg vπ or
invoutR
outR
0vπ = 0mg vπ = out oR r=
(CE )
CC
outv
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• E ( Early Effect)
rπ+
−vπ mg vπ
xv
v
rπ
π
inv
outR
xi
CCV
xv vπ = −
m x
vg v i
rπ
ππ
+ = −
1 11
xout
x mm
vR
i ggrπ
= =+≃
1 m
mm
gr g
g rππ
ββ
= → = <<
CE ( vbe )
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• E AC rπ• E AC ro
• B AC 1/gm
m
rgπβ=
AC
Ao
C
Vr
I=
AC
1 T
m C
V
g I=
AV = ∞
AC
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(I)
• (B-E B-C ) BJT VCCS
• BJT gm rπ ro
IC
•
( )
T
m C
Vr
g Iπβ β= = A
oC
Vr
I=C
mT
Ig
V=
rπ = ∞1A
oD D
Vr
I Iλ= =2 D
mGS TH
Ig
V V=
−
BJT
MOSFET
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(II)
•
β
VBE
IC IB ( β)IB RB
VBE
BR CR
CCV
1R CR
2R
CCV
1R CR
2RERREV
−
+
CCV
BR CR
CCV
VBE IC
()
R1 R2
RE
BJT(thermal
runaway)
RB
BJT
BJT
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( )
+
− inv
1CR
CCV
1CICBV
+−BEV
2CI−
+
outv
−
+
()
()
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• BJT
BR CR
CCV
BI
CI
X
Y
B B BE CCR I V V+ = CC BEB
B
V VI
R
−= CC BEC B
B
V VI I
Rβ β −= =
CC BECE CC C C CC C
B
V VV V I R V R
Rβ −= − = −
RB RC VCE
RB RC
( )CC BECE CC C C CC C BE
B
V VV V I R V R V
Rβ −= − = − >
+
−BEV
(1)
(2)
VBE VBE 700 mV 800 mV( 800 mV) VBE
IC=ISexp(VBE/VT) VBE VBE IC=ISexp(VBE/VT) VCC−IBRB
VBE
52 Department of Electronic Engineering, NTUT
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• BJT
BR CR
BI
CI
X
Y
2.5 VCCV =
100 kΩ 0.5 kΩ
1710 ASI −= 100β =
17 µACC BEB
B
V VI
R
−= ≃
1.675 V CE CC C C BEV V I R V= − = >
( ) 800 mVBEV =
17 µA 100 1.7 mACI = × =
IC VBE ln 852 mVCBE T
S
IV V
I= =
16.5 µACC BEB
B
V VI
R
−= =
17 µA 100 1.65 mACI = × =VBE
VBE 850 mVIC
1.65 mAIB (VCC−VBE)
VBE VCC
IB IC
(1)
VBE IB IC
(2)
52 mV?
ln 851.2 mVCBE T
S
IV V
I= =
( )
53 Department of Electronic Engineering, NTUT
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− BJT VBE
• ( IB )
1R CR
CCV
CI
XY
2R
2
1 2BE X CC
RV V V
R R= =
+
BE
T
V
VC SI I e=
IC VBE VBE R1 R2
1R CR
CI
X
Y
2.5 VCCV =
17 kΩ 5 kΩ
2R8 kΩ100β =
1710 ASI −=
231 µABE
T
V
VC SI I e= =2
1 2
800 mVX CC
RV V
R R= =
+2.31 µABI =
11 2
100 µA 43CCB
VI I
R R= =
+≃ (IB )
1.345 VCE CC C C BEV V I R V= − = > ( )
1I
IB IC/β β
IB IB I1
R1 VBE
IC
1I
54 Department of Electronic Engineering, NTUT
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IB
1R
2R
CCV
CR
CIY
X
1R
2R
thR
thV
XCI
CCV
CR
BI
1R
+
−
2RCCV+
−
+
−
2
1 2th CC
RV V
R R=
+
1 2||thR R R=
X th B thV V I R= −th B th
T
V I R
VC SI I e
−
=
1ln C
B th TS th
II V V
I R
= − ⋅
VBE ln CBE T B C BE B C
S
IV V I I V I I
I= → → → → → →⋯
R1 R2 IB VX IB
IC
R1 R2 I1>10IB
1I
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• R1 R2 VBE
β ( R1 R2 IB )
VBE
R2 1% VX 1%exp(0.01VBE/VT)=1.36 1%
36%
1R
2R
CR
CIY
X
EI
ERP
CCV
1
1 2
1E P E CC BE C
E
RI V R V V I
R R R
= = − +
≃
VX RE
VBE
( β >> 1)
•
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•
(1) I1 >> IB β (I1 10IB ) ( )
(2) VRE (~100 mV) VX VBE ( RE )
(3) RC RC BJT
1R
2R
CR
CIYX
BI
ER
P
CCV
1I1 BI I>>
+
−REV
RC BJT
VRE VX VBE
I1 IB 10 β
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•gm=1/(52Ω)
RC 3 kΩ
1
52 C
mT
Ig
V= =
Ω0.5 mACI =
778 mVBEV =
200 mVRE E CV R I =≃ 400 ER = Ω
2
1 2
978 mVX BE E C CC
RV V R I V
R R= + = =
+
5 µABI =
11 2
10 50 µACCB
VI I
R R= > =
+ 1 2
2.5 V50 k
50 µAR R+ = = Ω
1 30.45 kR = Ω 2 19.55 kR = Ω
CC C C XV R I V− > 1.522 VC CR I < 3.044 kCR < Ω
175 10 ASI −= ×
100β =
1R
2R
CR
CIY
X
EI
ERP
2.5 VCCV =
VX
1I
BJT
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• 500 mVREV =1 100 BI I≥
500 mV 0.5 mA 1 kER = = Ω
2
1 2
1.278 VX BE E C CC
RV V R I V
R R+ = =
+≃
1 2
100CCB
VI
R R≥
+ 1 2 5 kR R+ ≤ Ω
1 1.45 kR = Ω 2 3.55 kR = Ω
1.044 kCC XC
C
V VR
I
−< = ΩVRE
VX RC BJTRC I1 IB
R1 R2 R1 R2
175 10 ASI −= ×
100β =
1R
2R
CR
CIYX
EI
ERP
2.5 VCCV =1
52 C
mT
Ig
V= =
Ω0.5 mACI =
778 mVBEV =5 µABI =
BJT
RC 1 kΩ
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( )
• IC
BR CR
CCV
BI
X
Y
CI
X Y B BV V R I= −
RC
B CI I<< B CY CC C C B B BE BE
R IV V R I R I V V
β= − = + = + CC BE
CB
C
V VI
RR
β
−=+
VBE IC ln CBE T
S
IV V
I=
RC
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• IC
2 kCR = Ω
800 mVBEV =
ln 807.6 mVCBE T
S
IV V
I= =
154.5 mVB BR I = 0.955 VY B B BEV R I V= + ≃
ln 791 mVCBE T
S
IV V
I= =
81 mVB BR I = 0.881 VYV ≃
100β =
175 10 ASI −= ×
1 kCR = Ω10 kBR = Ω
2.5 VCCV =
BI
X
Y
CI
1.545 mACC BEC
BC
V VI
RR
β
−= =+
800 mVBEV = 0.81 mACC BEC
BC
V VI
RR
β
−= =+
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(1) VBE ( VBE )
(2) RC β
•
CC BEC
C
V VI
R
−≃
Y CC C C BEV V R I V= − ≃
( )CC BEV V−
BR β
10C BR R β=1.1CC BE
CC
V VI
R
−= ln CBE T
S
IV V
I=
1.1CC BE
CC
V VR
I
−=10
CB
RR
β=
CC BEC
BC
V VI
RR
β
−=+
1.8 VCCV =1
13 mg =Ω
BR CR
CCV
BI
X
Y
CI
175 10 ASI −= ×
100β =
1
13 C
mT
Ig
V= =
Ω 2 mACI = 754 mVBEV =
475 1.1
CC BEC
C
V VR
I
− Ω≃ ≃ 4.75 k10
CB
RR
β= = Ω 95 mVB BI R =
754 mV 95 mV 849 mVCV = + =
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BJT
• / 6
+
−inv
outv
outvoutv
+
−inv
+
−inv
B-EVCCS
CE CB CC
base ( )
CE
CC
CB
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(Common-Emitter Topology)
• B C E
+
−inv
outv
CCV
CR inv
rπ
+
−vπ mg vπ CR
outv
out
C
v
R−
Early Effect ( ro)
out m Cv g v Rπ= − outv m C
in
vA g R
v= = −inv vπ =
(1)
(2) gm IC
Cm
T
Ig
V= C C RC
vT T
I R VA
V V= =
RC CC BEV V V≤ −
CCv
T
VA
V≤
BJT
CC BEv
T
V VA
V
−<
(3) RC RC RC
BJT
RC VCC
VCC BJTVCC
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800 mV
1.8 VCCV =
CRpp2 mV
t
pp77 mV
800 mV
t
• RC 1 kΩ 21.7v m CA g R= − −≃
1 mWC CCP I V= =
0.556 mACI =
CC C C BEV I R V− = 800 mVBEV ≃
1.798 kCC BEC
C
V VR
I
−≤ = Ω
39v m CA g R= − −≃
0.02173mg =
VCC 38.46CC BEv
T
V VA
V
−< =
1 mW
2 mW
2 mWC CCP I V= = 1.1111 mACI = 0.04273mg = 900 CC BEC
C
V VR
I
−≤ = Ω 38.45v m CA g R= − −≃
• RC 1 kΩ 0.4 mA 27.66Cv m C C
T
IA g R R
V= − = − −≃
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CE
•
rπ
+
−vπ mg vπ CR
Xi
Xv
Xi
rπ
+
−vπ mg vπ CRXv
+
−
+
−
X Tin
X m C
v VR r
i g Iπββ= = = =
IC (IB )
0vπ =
Xout C
X
vR R
i= =
•
outv m C
in
RA g R
Rβ= − = − CE I/O
Early Effect
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CE
• RC ( VCC
BJT )
• CE IC=1 mA RC 1 kΩ β=100 VA=10 V ?
inv
rπ
+
−vπ mg vπ or CR
outv
( )||v m C oA g R r= −
inR rπ=
||out C oR R r=
1 26 m C Tg I V= = Ω
10 ko A Cr V I= = Ω( )|| 35v m C oA g R r= − ≃
2.6 kin mR r gπ β= = = Ω
|| 0.91 kout C oR R r= = Ω
VAV = ∞ 38vA ≃
RC
CR = ∞ Ω 384vA ≃
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CE
• RC
•
•
• CE VCC = 3 V VA = 5 V ? VCC 10 V ?
CR → ∞ v m oA g r= − (intrinsic gain)( )
Cm
T
Ig
V= A
oC
Vr
I= A
vT
VA
V=
intrinsic gainVA 5 V
intrinsic gain 200
CC BEv
T
V VA
V
−<VCC BJT
VCC
_384.6v VCC V
A =
192.3v VAA =
_10353.8v VCC V
A =
max84.6vA =
192.3v VAA = max
192.3vA =
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CE
••
CCV
CR
OUTv
V∆
ER
+
−
+
−
0ER = mV g V∆ → ∆
0ER ≠ m smallV g V∆ → ∆RE
( CE )
( )1in ER r Rπ β= + +
+
−inv rπ
+
−vπ mg vπ
outv
CR
ER
RE m E
vv g v R
rπ
ππ
= +
11in RE m E m E
vv v v v g v R v g R
r rπ
π π π ππ π
= + = + + = + +
1
1111
mg rout m C m C C
vin m E
Em Em
v g R g R RA
v g R Rg R gr
π
π
>>− −= = = −+ ++ +
≃
( CE ) 1 m Eg R+
bev
REv
vbe ( CE ) ic ib
( CE )( )in mR r gπ β> =
+
−REv
C
E
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CE
•
•
Xv i rπ π=
RE ( ) ( )1X m X Xi g r i iπ β+ = + ( )1X X E Xv r i R iπ β= + + ( )1Xin E
X
vR r R
i π β= = + +
+
−Xv rπ
+
−vπ mg vπ CR
outv
ER+REv−
P
+
−Xv rπ
+vπ
Xi
inR
( )1 ERβ+
−
rπ ib
RE ib+βib
ib (1+β)RE
emitter ground base (1+β)
+
− Xvrπ+
−vπ mg vπ CR
Xi
ER+REv−
0vπ =0in m E
vv v g v R
rπ
π ππ
= = + +
0vπ = 0mg vπ =
Xout C
X
vR R
i= =
Xi
Early Effect
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• CE
•BR
rπ
( )1 ERβ+
A
gm1m Eg R >>
out A out
in in A
v v v
v v v=
( )( )
1
1EA
in E B
r Rv
v r R Rπ
π
ββ
+ +=
+ + +
( )( ) ( )
1
1 1E m C
E B E
r R g r R
r R R r Rπ π
π π
ββ β
+ + −= ⋅+ + + + +
11
Cv
BE
m
RA
RR
g β
−
+ ++
≃
( )1in B ER R r Rπ β= + + +
out CR R=
1
1
m Eg Rm C C
vm E E
g R RA
g R R
>>−= −+
≃
( )( )
1
1 11
Eout m C
in E Bm E
r Rv g R
v r R Rg R
r
π
π
π
ββ
+ + −= ⋅+ + +
+ +
( )1C
E B
R
r R Rπ
ββ
−=+ + +
CR
outv
ER
invBR
A
CCV
1BR
β+
1
mg
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( )
CCV
CR
outv
ER
inv
2rπ
CCV
CCV
CR
outv
ER
inv
2rπ
•
2||ER rπ2
1||
Cv
Em
RA
R rg π
= −+
CCV
CR
outv
ER
inv
CCV
CCV
CR
outv
ER
inv2rπ 2||
1C
v
Em
R rA
Rg
π= −+
2||CR rπ
( )( )1 ||in ER r R rπ πβ= + +
out CR R=
( )1in ER r Rπ β= + +
2||out CR R rπ=
( )1 ERβ+
( ) ( )21 ||ER rπβ+
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•C1
1C
v
Em
RA
Rg
= −+
( )1in ER r Rπ β= + +
out CR R=
CR
outv
ER
inv
biasI
CCV
1CC1 AC
CR
outv
CCV
invBR
1I
1R
2R 1C
CR
BR1R
outv
inv
2R
( ) 21in BR R r Rπ β= + + +
1||out CR R R=
1
2
||1
1
Cv
B
m
R RA
RR
g β
= −+ +
+
• I/O (C1
)
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• 1 kΩ 2 mV 1mA CE 40 mV ( RE = 4/gm β = 100)
1 kBR = Ω
1
26 mg =Ω
40 mV20
2 mVvA = =4
104 Em
Rg
= = Ω
12.8 k
1B
C v Em
RR A R
g β
= ⋅ + + Ω + ≃
11
Cv
BE
m
RA
RR
g β
−
+ ++
≃
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• ro Early Effect
ro
( BJT ) BJT
( )||x Ev i R rπ π= −
( )ro x m ov i g v rπ= −
( ) ( ) ( )|| ||x x m o x m x E o x Ev i g v r v i g i R r r i R rπ π π π= − − = + +
( ) ( ) ( )( )1 || || 1 ||out m E o E o m o ER g R r r R r r g r R rπ π π= + + = + +
( ) ( )|| 1 ||out o m o E o m ER r g r R r r g R rπ π+ + ≃ ≃1m og r >>
( )1 ||m Eg R rπ+
rπ
+
−vπ mg vπ
xi
ER
xv
P
xior
+
−
out o ER r R= +:
ix RE||rπ vπ 0outR
ER
inv or
ER rπ>> [ ]1out o m oR r g r rπ β+≃ ≃
ER rπ<< ( )1out o m ER r g R+≃
76 Department of Electronic Engineering, NTUT
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• 1 mA 20 kΩ BJT β =100VA=10 V
• (C1 )
10 kAo
C
Vr
I= = Ω ER rπ<< ( )1 2m Eg R+ =
126 E
m
Rg
= = Ω
2.6 k Em
r Rgπβ= = Ω >>
outR
1R
2R 1CbV+
−
1I
outR
2R
1R
( ) 1 1 2 1|| 1 || ||out out o mR R R r g R r Rπ= = +
( )1out o m ER r g R+≃
outR
1bV+
−
2bV+
−
outR
2or
( )1 1 2 11 ||out o m oR r g r rπ= +
Cascode
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CE (I)
• 100 Ω CE
2.5 VCCV =
100 kΩ 1 kΩBR CR
XOUTv
100 2.5 V 2.5 mV
100 k 100 XVΩ= ⋅
Ω + Ω≃
RB VX ?
(1) RB
(2)
2.5 VCCV =
100 kΩ 1 kΩBR CR
XOUTv1C
C1 ACDC
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CE (II)
CCV
BR CR
XOUTv
1CY
1inR rπ=
CR
BR
CCV
BR CR
YX BR
CRX
+
−
outv
inv
( ) ( )
outRCR
BR
CC BEC
B
V VI
Rβ −=
CC BEY CC C BE
B
V VV V R V
Rβ −= − >
2 ||in BR r Rπ=
, , m og r rπ
BJT
v m CA g R= −
( )||v m C oA g R r= −
out CR R=
||out C oR R r=
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CE (III)
• 8 Ω
2.5 VCCV =
100 kΩ 1 kΩBR CR
X OUTv1C
2.5 VCCV =
100 kΩ 1 kΩBR CR
X1C2C
8 spR = Ω8 spR = Ω
(AC 8 DC1 )
VCE BJTheavy saturation
AC DC
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CE (IV)
•2.5 VCCV =
100 kΩ 1 kΩBR CR
X1C2C
BR
CR+
−
outv
inv 100 kΩ
1 kΩ 8 spR = Ω
VC 1.5 V
175 10 ASI −= ×
1.5 VCV = 2.5 1.5 1 VRCV = − =1 V
1 mA1 kCI = =
Ω
ln 796 mVCBE T
S
IV V
I= =
17 µACC BEB
B
V VI
R
−= = 58.8C
B
I
Iβ = =
( )|| 0.31v m C spA g R R= =
CECE
CE (buffer)
8 spR = Ω
, , m og r rπ
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CCV
1R CR
X1C
2R+
−inv
2R+
−inv
1R
CR
outv
1 2|| ||inR r R Rπ=
||out o CR r R=
( )||v m C oA g R r= −
CCV
1R CR
X1C
2R+
−inv
ER
2R+
−inv 1R
CR
outv
ER
CCV
1R CR
X1C
2R+
−inv
ER 2C
( )1C
vm E
RA
g R
−=+
( ) 1 21 || ||in ER r R R Rπ β= + +
out CR R=
v m CA g R= −
1 2|| ||inR r R Rπ=
out CR R=
Bypass AC RE
AC
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• IC=1 mA RE VRE =400 mV20 2 kΩ
2.5 VCCV =
1R CR
X1C
2R+
−inv
ER 2C
1 mAC EI I= ≃ 400 ER = Ω1
26 mg =Ω
20v m CA g R= = 512 CR = Ω
400 mV ln 400 mV 736 mV 1.14 VCX RE BE T
S
IV V V V
I= + = + = + =165 10 ASI −= ×
100β =
400 mVREV =
1 µACB
II
β= =
1 2
10CCB
VI
R R>
+ 1 2 25 kR R+ < Ω
2
1 2
1.14 VX CC
RV V
R R= =
+ 2 11.4 kR = Ω1 13.6 kR = Ω
1 2|| || 1.85 kinR r R Rπ= = Ω
RE R1 R2
1 2
5CCB
VI
R R>
+ 1 2 50 kR R+ < Ω2 22.4 kR = Ω1 27.2 kR = Ω
1 2|| || 2.14 kinR r R Rπ= = Ω
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CCV
1R CR
sR
1C 2R+
−inv
ER
2CLR
outv
+
−inv
sR
1 2||R RER
||C LR R
outvX
( )( )
1 2
1 2
|| || 1
|| || 1EX
in E s
R R r Rv
v R R r R Rπ
π
ββ
+ + =+ + +
( )( )
1 2
1 2
|| || 1 ||1|| || 1
Eout out C LX
in in X E sE
m
R R r Rv v R Rv
v v v R R r R R Rg
π
π
ββ
+ + = =+ + + +
R1 R2
DC AC
( )
DCAC
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(Common-Base Topology)
• E C B
CCV
CR
+
− inv
+−bV
OUTv rπ+
−vπ mg vπ CR
outv
+
−inv
v m CA g R= CE CB
RCout
mC
vg v
R π− = outin
m C
vv v
g Rπ = − = − outm C
in
vg R
v=
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• CB IC=0.2 mA600 mV
• VB
1.8 VCCV =
CR
+inv
BV
outv
600 mV
600 mV ln 600 mV 1.354 VCB BE T
S
Iv V V
I= + = + =
RC1.8 V 1.354 V 0.446 V− =
17.2Cv m C C
T
IA g R R
V= = =
175 10 ASI −= ×100β =
Vb
+
−inv 600 mV
outv
CR
1.8 VCCV =
1R
2R
BI1I
100β =175 10 ASI −= ×1
1 2
10 20 µA CCB
VI I
R R+≃ ≃ ≃
1 2 90 kR R+ = Ω 2
1 2
1.354 VB CC
RV V
R R=
+≃
2 67.7 kR = Ω1 22.3 kR = Ω
0.2 mACI = 0.2 100 mA 2 µABI = =
β
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•
CCV
CR
inR 1in
m
Rg
=
VA=∞ CBIC=1 mA 26
Ω (CE β/gm)
CCV
CR
BV
XI
+
−XV V∆
1Xin
X m m
V VR
I g V g
∆ ∆= = =∆ ∆
•
CR
outRor 1outR
1 || ||out out C o CR R R r R= =
1out oR r=
out CR R=
CB Rin Rout
outv m out
in
RA g R
R= =
1 || ||out out C o CR R R r R= =
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CB
CR
CCV
+
−inv
sR
1
mg
outv
X
X
1
mg
sR
+
−inv
11
1 1m
X in inm s
sm
gv v v
g RRg
= =++
outm C
X
vg R
v= CB
11out m C C
in m ss
m
v g R R
v g R Rg
= =+ +
CE ( Rs
)
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• CB 50 Ω RF50Ω CB 50Ω
( )
CR
CCV
CR
CCV
BV
outv
50 sR = Ω
outv
BV
+
−inv
150 in
m
Rg
= = Ω
0.52 mAC m TI g V= =
11 2
Cv
sm
RA
Rg
= =+
CB 50
1in
in
sm
vi
Rg
=+ 1
C inout
sm
R vv
Rg
=+
0.5C sR R≤
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CB
CCV
CRoutv
BRor
ER
BV
+
−inv
ER
orCR
1outR 2outR
150 in
m
Rg
= = Ω
0BR =
( ) ( )1 1 || ||out m E o ER g R r r R rπ π= + +
( ) ( ) || 1 || ||out C m E o ER R g R r r R rπ π= + +
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RB ro
rπ+
−vπ mg vπ CR
outvBR
ER+inv
−
P
outm
C
vg v
Rπ = − out
m C
vv
g Rπ = −
RBout out
m C C
v v v
r g r R Rπ
π π β= − = −
( ) ( )out outP B B
C C
v vv R r R r
R Rπ πβ β−= − + = +
P KCL P inm
E
v v vg v
r Rπ
ππ
−+ =
( )1
outB in
out Cm
m C E
vR r v
v Rg
r g R R
π
π
β+ −
−+ ⋅ = ( )
( )11
1
out C C
Bin E BE
m
v R RRv R R r R
gπ
ββ
β
=+ + + + +
+
≃
CERB RB
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RB
CCV
CR
+
−inv
ER
outvBR
CB Stage
rπ
+
−vπ mg vπ CR
outvBR
+
−Xv
Xi
XB
rv v
r Rπ
ππ
= −+
KCL m X
vg v i
rπ
ππ
+ = −
1m X X
B
rg v i
r r Rπ
π π
−+ = − +
1
1 1X B B
X m
v r R R
i gπ
β β+= ++ +≃
RB=0,Rin=1/gm
BR
ER
AV = ∞AV = ∞
1
1B
m
R
g β+
+
( )1 Er Rπ β+ +
emitter base RB (1+β) Emitterdegeneration base emitter RE (1+β)
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CR
CCV
BR
outv
CR
outv
CCV
1
1
1B
m
R
g β+
+
XReqR
XR
1
1
1B
eqm
RR
g β= +
+
2 2 1
1 1 1 1
1 1 1eq B
Xm m m
R RR
g g gβ β β
= + = + + + + +
• RX
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CB (I)
•
CCV
CR
OUTv
+
−inv
1C+
−BV
CCV
CR
OUTv
+
−inv
1C+
−BV
CCV
CR
outv
+
− inv
1C+
−BV
1
mg
ERER
emitter DC path emitter DC pathAC
RE emitter DC path
1||in E
m
R Rg
=
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CB (II)
CCV
CR
outv
+
−inv
1C+
−BV X
inRER
sR
1||in E
m
R Rg
=
Rin
( )
1||
11 1 1||
EX in m
in in s m E sE s
m
Rv R g
v R R g R RR Rg
= = =+ + ++
outm C
X
vg R
v=
( )1
1 1out
m Cin m E s
vg R
v g R R=
+ +
CCV
CR
outv
+
− inv1C
+
−bV
inRER
sRini
1i
2i
iin i1 RE(shunt ) i2 RC
RE
RC RE
RE 1/gm i2
1E
m
Rg
>>C E TI R V>>
RE RE VT
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CB (III) - Vb
• CECE CB bypass
AC CE bypass( common AC
)
CCV
CR
ER
1R
2R
1C
inv
1I
CCV
CR
ER
thR
+
−thV
CCV
CR
ER
1R
2R
BC
β I1>> IB2
1 2b CC
RV V
R R+≃
Base
1 2||thR R R=
bypass CB base ACground
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• CB 10 50 Ω
1E mR g>> 500 ER = Ω
1 50 in mR g = Ω≃ 0.52 mA, 899 mVC BEI V= =
bypass (AC )
500 CR = Ω10v m CA g R= =
RE 0.52 mA 500 260 mVE E C E TI R I R V= × Ω = >>≃
1.16 Vb E E BEV I R V= + =
R1 R2 10 52 µABI =
1
1 2
1.16 Vb CC
RV V
R R=
+≃
1 2
52 µACCV
R R=
+1 25.8 kR = Ω
2 22.3 kR = Ω
2.5 VCCV =
CR
ER
1R
2R
BC
OUTv
1Cinv
100β =
165 10 ASI −= ×
AV = ∞
900 MHzC1 CB
1
11
20mg
j Cω=
1
20 2071 pF
2 900 MHzm mg g
Cω π
= = =⋅
11 1
1 20m
B
g
j Cβ ω=
+
0.7 pFBC =
( 10 )
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(Common Collector Topology)
• B E C
CCV
ER
INV
OUTV1BEV
2BEV
1INV
1OUTV
1IN INV V+ ∆
1OUT OUTV V+ ∆
∆VOUT > ∆VIN VBE2 < VBE1
IE
IERE=VOUT
∆VOUT ∆VIN
1
rπ
+
−vπ mg vπ
ER
inv+
−
outv
outm
E
v vg v
r Rπ
ππ
+ =1
out
E
r vv
Rπ
π β=
+
in outv v vπ= +
11 1
11
out E
inE
E m
v Rrv R
R gπ
β
=+ +
+
≃
1
Early Effect
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CC
• CC
CCV
inv+
−
ER
CCV CCV
thR
inv+
− inv+
−out inv v=
ER
1th
m
Rg
=
outv
th inv v=
1in
m
Rg
=
CC Rth=1/gm
CC(CE CB
)
outv
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•
•
CCV
INv
OUTv
1I
1vA ≃
VBE out in BEv v V= −
VBE vOUT vIN
CCV
ERinv+
−
outv
sRsR
CCV
thR
th inv v=+
−
1
1s
m
R
g β+
+
ER
11
out E
sinE
m
v RRv R
gβ
=+ +
+
outv
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CC
rπ
+
−vπ mg vπ
ER
Xv+
−
Xi
inR
0CR →
CCV
ER
CCV
inRER
Xi v vπ π=
iX gmvπ RE ( )X m Ei g v Rπ+
( ) ( )X X m E X X m Ev v i g v R i r i g v Rπ π π π= + + = + +
( )1XE
X
vr R
i π β= + +Follower RE
buffer ( )
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• CE 20 1 kΩ
(a) 8Ω ?(b) CC ? CC 5 mA
β=100 VA follower
CCV
1 kΩ CR8 spR = Ω
1C
1inRinv+
−1I
CCV
( )20 ||8 0.159v CA R= ⋅ Ω = ( )1 2 1 1058 in spR r Rπ β= + + = Ω
( )1||20 10.28C in
vC
R RA
R= ⋅ =
CCV
1 kΩ
inv+
−
CR
1C
8 spR = Ω
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CCV
sR
ER
outR
sR
CCV
1
1s
m
R
g β+
+
ER
1||
1s
out Em
RR R
g β
= + +
Followerdriver follower
( ) ( )ER
inv+
−inv+
−
CCV
sR
ER
or
sR
ER or||
1||
1
E ov
sE o
m
R rA
RR r
gβ
=+ +
+
( ) ( )1 ||in E oR r R rπ β= + +
1|| ||
1s
out E om
RR R r
gβ
= + +
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CC
CCV
ER
X
OUTv
1R
2R
1C
inv
−
+
inv
−
+
1C
CCV
BRBI
XY OUTv
ER
R1 R2 IB
β
VCC C VCC BJT
RB RE
β
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• RB=10 kΩ RE=1 kΩ VCC=2.5 V
KVL B CBE E C CC
R IV R I V
β+ + =
800 mVBEV ≃ 1.545 mACI =
ln 748 mVCBE T
S
IV V
I= = 1.593 mACI =
159 mVB BI R =1.593 VC EI R = C E B BI R I R>>inv
−
+
1C
CCV
BRBI
XY OUTv
ER
165 10 ASI −= ×100β =
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(I)
• 10 kΩ 10 mV0.1 W 8Ω
12 V
2 2, ,0.1 W 8L L rms L L rmsP i R i= = ⋅ = ⋅
, 0.112 AL rmsi =
, ,2 0.158 AL peak L rmsi i= =
, , 0.158 8 1.26 Vo peak L peak Lv i R= ⋅ = × ≃
1.26126
0.01vA = =
inv
−
+
10 ksR = Ω CC
8 LR = Ω
outv
Li126vA =
1. 8Ω CE2. 126 CC3. 10 kΩ CB
CE CC CB
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(II)
•
inv
−
+
10 ksR = Ω CC
8 LR = Ω
outv
1vA 2vA 3vA
1.CE CE CC
2.CC
3.CE CE
2.CE CE
3.
1.CE CE CB
1.CE CE CC
2.CC
3.CC
1 2 3v v v vA A A A= ⋅ ⋅
CC +CE +CC
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• 8Ω CC ( )
Li
CC
8 LR = Ω
ov
4ER
4BV
4BI3ov
4inR 12 VCCV =
(III) –
, 0.158 AL peaki = , 1.26 Vo peakv =
4 50β =
4
12 620
0.3CC CEQ
EEQ
V VR
I
− −= = = Ω
500.3 0.294 A
1 51CQ EQI Iβ
β= = ⋅ =
+
0.294 A11.3
26 mVC
mT
Ig
V= = = 4.42
m
rgπβ= = Ω
( )( )( )( )
( )( )
1 || 51 20 || 80.985
1 || 4.42 51 20 || 8E L
vE L
R RA
r R Rπ
ββ
+ ⋅= = =
+ + + ⋅
1.26 V vo3
1.28 V
0.158 A
0.158 A
Ci
CQ EQI I≃
CEvCEQV 12 VCCV =
1.26 V1.26 V
0.3 AEQI =
6 VCEV =
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(IV) –
• 10 kΩ CC
6 V, 1 mACEQ CQV I= =
1 2|| 100 kR R = Ω
1
12 66 k
0.001CC CE
EE
V VR
I
− −= = = Ω
10.0385
26 C
mT
Ig
V= = =
Ω2.6 k
m
rgπβ= = Ω
( )1 2|| || 1 85.9 kin ER R R r Rπ β= + + = Ω ( )
( )1
0.8921
Einv
in s E
RRA
R R r Rπ
ββ
+= =
+ + + 8.92 mVov =
1 155 kR = Ω 2 282 kR = Ω
+inv
−
sR
10 kΩ
12 VCCV =
1R
2R
1 100β =1ov
1ER
( ) ( )1 1 2 1 1 1|| || 1in ER R R r Rπ β= + +
CEv12 VCCV =CEQV
Ci
CQ EQI I≃
Rs 10
1 mACQI =
6 VCEV =
608.6 kΩ
10 mVinv =
( )
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(V) –
2 328.8, 5v vA A= =
3 4 4 4 6 0.7 6.7 VC B E BEV V V V= = + = + =
4
0.2945.88 mA
50BI = = 33 313 mA, 0.5C
C mT
II g
V= =≃
3 200 m
rgπβ= = Ω
( ) ( )( )
4 4 4 41 ||
4.42 51 20 ||8 296
in E LR r R Rπ β= + +
= + = Ω
( )( )
3 3 43
3 3 3
||5
1C in
vE
R RA
r Rπ
ββ
= =+ + 3 27.3 ER Ω≃
, , , ,126 0.892 0.985v v in v gain v o v gainA A A A A= = ⋅ ⋅ = ⋅ ⋅
, 144v gainA ≃
VBE4
33
3 3
12 6.7296 CC C
CRC RC
V VR
I I
− −= Ω = = 3 18.9 mARCI =
( ) ( )3 5 6 3 3 3|| || 1 50 k || 200 101 27.3 2.8 kin ER R R r Rπ β= + + = Ω + ⋅ Ω ≃
5 6|| 50 kR R = Ω ( ) 5 69.9 kR = Ω 6 176 kR = Ω
12 VCCV =
5R
6R
3R
4R
3CR
3ER
2CR
2ER
3inR2inR
1ov2ov
3 4C BV V=3 100β =2 100β =
22
12 61.2 k
5CC C
CCQ
V VR
I
− −= = = Ω 22
2
0.52 kT
CQ
Vr
Iπβ= = Ω
( )( )
2 2 32
2 2 2
||28.8
1C in
vE
R RA
r Rπ
ββ
= =+ + 2 23.7 ER Ω≃ 5 6|| 50 kR R = Ω ( ) 3 181 kR = Ω
4 69.1 kR = Ω
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(VI) –
•
• ( )headroom
•• decouple
181 kΩ
23.7 Ω
1.2 kΩ
69.9 kΩ
176 kΩ
296 Ω
20 Ω 8 Ω27.3 Ω
155 kΩ
282 kΩ
69.1 kΩ6 kΩ
12 VCCV =
10 kΩ
−
+sv
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(I)
PSRR
DDV
SSV
INv +
INv − −
+
OUTv
offsetCMRR
( )SR
0
(dB)
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(II)
• OPA (DVCVS)
• OPA A OPAvo
+
−
1v
2vov
+
−
− −
1v2v
( )1 2 oA v v v− =−
−A → ∞
1 2 0v v− =
1 2v v=
( )1 2ov A v v= −
v1 = v2 (virtual short)(v1=0)
(v2≈0)(virtual ground virtual earth)
non-inverting input
inverting input
+
++
+
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(I)
•
•
IvOv
1R
2R
−
+
2
1
Ov
I
v RA
v R= = −
0a bv v= =
1 2 1Ii i v R= =
av
0bv =
IvOv
1R
2R
−
+1i
2iZin
22 2
1O I
Rv i R v
R= − = −
2
1
1Ov
I
v RA
v R= = +
Ov−
+Iv
1R
2R
Ov−
+Iv
1R
2R
1i
2iav
a Iv v=
1 2 1ai i v R= = −Zin
( ) 22 1 2
1
1O I
Rv i R R v
R
= − + = +
KCL KVL ( )
v i i v
R2 5 kΩ 25 kΩR1
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(II)
• (level shifting)
IvOv
1R
2R
−
+
IvOv
1R
2R
−
+
−
+BIASV
2 2
1 1
1O I BIAS
R Rv v V
R R
= − + +
Ov−
+Iv
1R
2R
2 2
1 1
1O I BIAS
R Rv v V
R R
= + −
2R
1R
IvOv
+
−
−
+BIASV
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( )
•
•
IvOv
1 1 kR = Ω
2 10 kR = Ω
−
+
2
1O I
Rv v
R= −
IvOv
1 1 kR = Ω
2 10 kR = Ω
−
+
IvOv
1 1 kR = Ω
2 10 kR = Ω
−
+
−
+BIASV
2 2
1 1
1O I BIAS
R Rv v V
R R
= − + +
+VCC
−−−−VSS
100 mV1 V−
OPAOK
+VCC
GND
1 V−100 mV
OPA0 V
100 mV 1 V 2.475 V= − +
Level shiftingAC
VCC/2
+VCC
GND225 mV
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(III)
• /
1v
Ov
1R fR
−
+
2v
nv
2R
nR
1 21 2
f f fO n
n
R R Rv v v v
R R R
= − + + +
⋯
1 2f nR R R R= = = =⋯
( )1 2O nv v v v= − + + +⋯
−
+1v
2v
bR
aR
aR
bR
Ov
( )1 2b
Oa
Rv v v
R= −
( v2=0 v1 vo1 v1=0 v2
vo2 vo= vo1 +vo2 )
v i i v
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(IV)
•
−
+
1v2v
aR
aR3v
4vaR
aR
bR
bR
ov
( )1 2 3 4b
Oa
Rv v v v v
R= + − −
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(V)
•
•
0
ivov
R
C
−
+
( )0 0ov =
KCL 0i ov dvC
R dt+ =
0
1 t
o iv v dtRC
= − ∫
iVoV
R
1sC
−+
1 1o i i
sCV V VR sRC
= − = −
ivov
C
R
−
+
( )1o i i
RV V sRC V
sC
= − = −
v i i v
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(Voltage Follower)
• ( )
• (heavy load)
Iv Ov−
+
1Ov
I
vA
v= ≃
Iv
100 ksR = Ω
1 kLR = Ω+
−Ov+
−
Source Load
1k0.01
100k+1kO Iv v= ≃
Iv
100 ksR = Ω
1 kLR = Ω+
−
Ov+
−
Source Load
Buffer
O Iv v≃
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• ZL
+
−
SV
1R
OV
ILZ
1SI V R=
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• general
INv +
INv −
2R
1R
3R
4R
Ov−
+
BIASV
( )( )
( )( )
4 1 2 3 1 22
1 3 4 1 1 3 4O IN IN BIAS
R R R R R RRv v v V
R R R R R R R+ −
+ += − +
+ +
INv +4
3 4IN
Rv
R R ++4 2
3 4 1
1 IN
R Rv
R R R +
+ +
INv −2
1IN
Rv
R −−
3
3 4BIAS
RV
R R+BIASV 3 2
3 4 1
1 BIAS
R RV
R R R
+ +
31
2 4
RR KR R= =
1 1
1 IN
Kv
K K ++
+
2
1IN
Rv
R −−
( ) ( )11 1
1 1 BIASK VK
+ +
( )2
1O IN IN BIAS
Rv v v V
R + −= − +
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( )
( )2 41 2
3
21O BIAS
G
R Rv v v V
R R
= + − +
2v
1v
2R
4R
GROv
−
+ BIASV
+
− 4R
3R
3R2R
−
+ 1v
211
G
Rv
R
+
2v
221
G
Rv
R
+
3
3 4BIAS
RV
R R+BIASV 3 4
3 4 3
1 BIAS
R RV
R R R
+ +
21
G
Rv
R
−
22
G
Rv
R
−
2 21 21
G G
R Rv v
R R
− + +
2 22 11
G G
R Rv v
R R
− + +
4
3
R
R
× − +
4 4
3 4 3
1R R
R R R
× ⋅ + + +
( )2 41 2
3
21 BIAS
G
R Rv v V
R R
= + − +
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OPA
• OPA ( )1
oAA s
sτ=
+
12c cfω π
τ= =
fall-off rate:−6 dB/oct
f (Hz)fc fT
Gain (dB)
f (Hz)
Phase (deg.)
0
90−
oA
oAτ OPA ( )1 τ−
cf 3 dB
Tf 0 dB (1)OPA fT OPA (GBW)
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(Gain-Bandwidth Product)
•• OPA
• =
12c cfω π
τ= =
( )1
o
c
AA s
s
ω
=+
( )2
1
o
c
AA jω
ωω
=
+
( ) 1TA jω =
2
1 To
c
Aωω
+ =
2
1T
c
ωω
>>
To
c
Aωω≃
T o cAω ω=
3 dB
( )x x Tf A j fω⋅ =
OPA fx
( ) Tx
x
fA j
fω =
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OPA (I)
• (AOL)
OPA
•
Bipolar OPA Ri 150 kΩFETs (Mega ) OPA
•
Bipolar OPA 100Ω
OPA OPA1 kΩ 100 kΩ 10 kΩOPA
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OPA (II)
• (Input offset voltage,VOS VIO)
OPA 0 VAC
(VIO)
• (Input offset current,IOS IIO)
0OPA
BJT
1 1O f BV R I=IB1 (IB2=0)
2 2 21
1 fO B
RV I R
R
= − +
1 2 1 2 21
1 fO O O B f B
RV V V I R I R
R
= + = − +
IB1 = IB2
IB2 (IB1=0)
2BI
1BI
fR
1R
OV
SV
2R −+
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OPA (III)
• (VIN)
OPA ( )offset offset OPA
• (Vopp)
DC 0 V OPA
2 1iV V V− ≤ ≤
iV1V
2V−
oV
1oV
2oV−
Vi
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OPA (IV)
• Slew Rate (SR)
OPA (OPA
) SR OPA step(unit gain) zero crossing
• SR sino mv V tω=
cosom
dvV t
dtω ω=
0, ,2 ,
om
t
dvV
dt ω π π
ω=
=⋯
mSR V ω≥ mVSR
ω≥
SR OPA
OPA
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OPA (V)
• (Common-mode rejection ratio, CMRR)
OPA ( )
CMRR (dB)
CMRR 80 dB CMRR
• (Power supply sensitivity,∆VIO/∆VGG)
∆VGG ∆VIO
•
OPA
• Ci
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OPA (VI)
• (Full power response)
OPA
• (Gain-Bandwidth Product)
17 OPA
OPA
75 kHz
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OPA (VII)
• (Rise time, tr)
OPA OPA 10% 90%
• (Power supply voltage)
• (Power supply current)
• ( )
•( )
0.35r ct f× ≅
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• OPA
• datasheetAC
• 100
• Slew Rate
• OPAOPA datasheet
• bypassDC 1 MHz 1 µF
(10MHz MHz)0.1 µF
OPA
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•
• ( )gm rπ
ro
• BJTCE CB CB
CC CE CB CC
• OPA
135 Department of Electronic Engineering, NTUT