E.E. Essential Knowledge Sereies My Online Courses: https://www.byparams.com/courses 基頻放大器設計

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Department of Electronic Engineering
National Taipei University of Technology

2. /135
• PN BJT
•
• BJT ( )
•
•
(CE) (CB) (CC)
•
•
2 Department of Electronic Engineering, NTUT

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PN BJT
3

4. /135
PN
• PN
• PN
PN
Cathode Anodepn
0t = 1t t= t = ∞
pn pn pn
(Depletion region)
E
4 Department of Electronic Engineering, NTUT

5. /135
PN
•
•
1F
T
V
V
tot SI I e
 
− 
 
=
+− FV
pn
2 pn
S i
A n D p
DD
I Aqn
N L N L
 
= +  
 
26 mV@ 300T
kT
V T K
q
= =≃
F TV V>
F
T
V
V
tot SI I e
 
 
 
≃
F TV V<< tot SI I−≃
−+ RV
pn
DI
DV
D
T
V
V
SI e
 
 
 
≃
SI−
I/V
5 Department of Electronic Engineering, NTUT

6. /135
(Reverse Breakdown)
• PN IS
PN
• ( )
• PN
(Zener effect) (Avalanche effect)
DI
DV
BDV
6 Department of Electronic Engineering, NTUT

7. /135
•
( 1V/µm)
n
−+ RV
pn E
•
PN
3 ~ 8 V
7 Department of Electronic Engineering, NTUT

8. /135
( )
• PN
•
(impact ionization)
−+
RV
pn E• (
)
8 Department of Electronic Engineering, NTUT

9. /135
( )
•
( )
0 1s 2s 3s 4s
t
BEV
0 1s 2s 3s 4s
t
BE BE bev V v= +
BEV bev ( ) BEv ( + )
beV phasor ( )
0 1s 2s 3s 4s
t
bev
9 Department of Electronic Engineering, NTUT

10. /135
•
•
•
VCCS
VCVS CCVS
+
-
+
-
v1 v = mv1
+
-
v = gi1
i1
VCCS CCCS
+
-
v1 i = gv1
i1
i = bi1
10 Department of Electronic Engineering, NTUT

11. /135
(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

12. /135
• VCCS rin
+
−
inv 1kv1i LR
+
−
outv
+
−
1vinr
1 1
1
out L L
L
in in
v kv R kv R
kR
v v v
− −
= = = −
kRL 1 VCCS
12 Department of Electronic Engineering, NTUT

13. /135
BJT
• (bipolar-junction transistor, BJT) 1945
Shockley Brattain Bardeen
• (BJT )
VBE ( ) VCE
e− (−IE )
Collector
Base
Emitter
(C)
(B)
(E)
+
−
0.8 VBEV =
−
+
1 VCEV =
+
−
+
−
−
+
13 Department of Electronic Engineering, NTUT

14. /135
BJT I/V
• IC VBE
• IC VCE
+
−
BEV
CI
+
−
CEV
+
−
BEV
CI
+
−
CEV
2B
T
V
V
SI e
1B
T
V
V
SI e
CEV
CI
1BE BV V=
2BE BV V=
BEV
CI
BE
T
V
V
C SI I e= ⋅
14 Department of Electronic Engineering, NTUT

15. /135
BJT VCCS
• BJT exponential VCCS
CBV
+
−
+
−BEV
CEV
+
−
(C)
(B)
(E)
Collector
Base
Emitter
BEV
+
−
BE
T
V
V
sI e
(C)(B)
(E)
BE
T
V
V
C sI I e=
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16. /135
( ) (I)
BEV BEV BEV BEV
CEV
CEV
CEV CEV
CI
BE
T
V
V
C 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
16 Department of Electronic Engineering, NTUT

17. /135
( ) (II)
BEV
+
−
CEV
+
−
VCE
VCE
IC
VBE1
VBE2
VBE3
BEV
CEV
BE
T
V
V
C SI I e= ⋅
BEV
CEV
CEV
BEV
BJT
IC VCE
VBE
BEV
+
−
CEV
+
−
BE
T
V
V
SI e⋅
IC
VCE
CEV
+
−
BJT
17 Department of Electronic Engineering, NTUT

18. /135
• VOUT
16
5 10 ASI −
= ⋅
1.69 mA
BE
T
V
V
C SI I e= ⋅ =
( )3
3 V 3 V 1.69 10 1000 1.31 VCE C LV I R −
= − = − ⋅ ⋅ =
1.31 VOUTV =
750 mV
3 V
+
−
+
−
CI
LR
OUTV
+
−
1 kΩ
Q:
VBE IC
3 V 2.155 VOUT C LV I R= − =
18 Department of Electronic Engineering, NTUT

19. /135
C BI Iβ=
1 1
1
BE
T
V
V
E C B C SI I I I I e
β
β β
  +
= + = + = ⋅ 
 
BE
T
V
V
C SI I e= ⋅
1
BE
T
V
V
B SI I e
β
= ⋅
1
C E EI I I
β
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= ⋅
19 Department of Electronic Engineering, NTUT

20. /135
• BJT VBE
750 mV β
50~200 IB IE
1.685 mA
BE
T
V
V
C 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< <
16
5 10 ASI −
= ⋅
50 200 1.05 1.002β α< < ⇒ < <
VBE( VCCS )
+
−
BEV
BE
T
V
V
SI e
BE
T
V
VSI
e
β
CB
E
20 Department of Electronic Engineering, NTUT

21. /135
− BJT RC
• VBE = 800 mV β=100
BJT BJT
RC
X
+
−
BEV
CI
CR500 Ω
+
2 VCCV =
−
( )VXV
( )CR Ω
2.0
1.424
0.800
500 1041
17
5 10 ASI −
= ⋅
1.153 mA
BE
T
V
V
C SI I e= ⋅ =
1
11.53 µA
BE
T
V
V
B SI I e
β
= ⋅ =
1
1.165 mA
BE
T
V
V
E SI I e
β
β
+
= ⋅ =
1.424 VCC C C X XV R I V V= + ⇒ =
1.424 VCE X BEV V V= = >
800 mVCE XV V= = 1041CC X
C C
C
V V
R R
I
−
= ⇒ = Ω
RC
VBE IC
(VCE VBE )
21 Department of Electronic Engineering, NTUT

22. /135
•
10 VCCV =
2 kCR = Ω
220 kBR = Ω
CI
BI
4 VBBV =
+
−
CEV
+
−
BEV
4 0.7
15 µA
220k
BB BE
B
B
V V
I
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 CE
C
C
V V
I
R
−
=
y x
22 Department of Electronic Engineering, NTUT

23. /13523

24. /135
gm (I)
• +
• VBE ( )
•
+
−
BEV∆
CI∆
+
CEV
−
0BEas V
C C
BE BE
I dI
V dV
∆ →
∆
=
∆
C
m
BE
dI
g
dV
=
BE
T
V
V
C SI I e= ⋅
1BE BE
T T
V V
V VC C
m S S
BE BE T T
dI Id
g I e I e
dV dV V V
 
= = ⋅ = ⋅ = 
 
 
gm
gm IC !!
IC = 1mA VT = 26mV 11
0.0385 0.0385 S 38.5 mS
26
mg −
= = Ω = =
Ω
24 Department of Electronic Engineering, NTUT

25. /135
gm (II)
• gm=dIC/dVBE IC-VBE
IC0 VBE0
• IC-VCE IC1
IC2
mg V∆
BEV
0BEV
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 ∆V
IC0 gm∆V
gm= IC0/VT gm IC0 IC0
( )
VBE ∆V IC2 IC1
IC gm2 > gm1
m C BEg dI dV=
25 Department of Electronic Engineering, NTUT

26. /135
BJT
• BJT
+
−
BEV∆
+
CEV
−
BI∆
EI∆
CI∆
rπ
rπ E
CB
vπ
−
+
mg vπrπ
mr gπ β=
BE BE beV V v∆ = +
+
−
B B bI I i∆ = +
BEV∆
+
−
BE
T
V
V
SI 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
v
r
i g
π
β
= =
BJT
m C Tg I V=
26 Department of Electronic Engineering, NTUT

27. /135
• v1 Q1
(a) (b) 1 mV C B
?
16
5 10 ASI −
= ⋅ 100β =
1
3.75
C
m
T
I
g
V
= =
Ω
6.92 mA
BE
T
V
V
C SI I e= =
800 mVBEV =
375
m
r
g
π
β
= = Ω
+
−
1v
+
ci
−
bi
rπ vπ mg vπ
1v vπ =
1
1 mV
0.267 mA
3.75
c m mi g v g vπ= = = =
Ω
1 1 mV
26.7 µA=
375
c
b
v i
i
rπ β
= = =
Ω
+
−
1v
+
1.8 V
−
CI
−
+
800 mV
(1)
(2) gm rπ
(3)
VBE IC
27 Department of Electronic Engineering, NTUT

28. /135
v.s.
•
+
−
1v
+
CR−
rπ vπ mg vπ
+
−
outv
+
−
1v
+
3.6 VCCV =
−
200CR = 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
out
v m C
v
A g R
v
= = −
1
3.75
mg =
Ω 200CR = Ω 53.4vA = −
RC
BJT
800 mVBEV = 6.92 mA
BE
T
V
V
C SI I e= =
28 Department of Electronic Engineering, NTUT

29. /135
(Early Effect)
• (VA )
BJT IC VBE VCE
( ) VBE IC VCE IC
1
BE
T
V
V CE
C S
A
V
I I e
V
 
+ 
 
≃
1 1
1
BE BE
T T
V V
V VC CE C
S S
CE CE A A A o
I d V I
I e I e
V dV V V V r
  ∂
= + = ⋅ =  
∂    
≃
CI
BE
T
V
VSI
e
β
w/ Early Effect
w/o Early Effect
CEV
1
BE
T
V
VS CE
A
I V
e
Vβ
 
+ 
 
BJT
ro
CI
CEV
AV−
CdI
CEdV
1
or
29 Department of Electronic Engineering, NTUT

30. /135
1
BE BE
T T
V V
V VCE ce ce
C C c S C S
A A
V v v
I I i I e I I e
V V
 +
∆ = + = + = + 
 
BE
T
V
V ce
c S
A
v
i I e
V
=
BE
T
ce A A
o V
c CV
S
v V V
r
i I
I 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
30 Department of Electronic Engineering, NTUT

31. /135
• BJT IC = 1 mA β = 100 VA=15 V
+
−
BEV
CI∆
V∆
rπ
+
−
vπ mg vπ or
B C
E
1
26
C
m
T
I
g
V
= =
Ω
2600
m
r
g
π
β
= = Ω
15 kA
o
C
V
r
I
= = Ω
31 Department of Electronic Engineering, NTUT

32. /135
PNP
• PNP NPN
BEV
+
−
CEV
+
−BI
EI
CI
EB
T
V
V
C sI I e=
EB
T
V
Vs
B
I
I e
β
=
1 EB
T
V
V
E sI I e
β
β
+
=
1
EB
T
V
V EC
C s
A
V
I I e
V
 
= + 
 
+
−
vπ mg vπ orrπ
cibi
ei
B C
E
+
−
vπ mg vπ orrπ
cibi
ei
B C
E
npn
( )
32 Department of Electronic Engineering, NTUT

33. /135
BJT
• BJT B-C 2 VA
+
−
Xv
Xi
rπ
+
−
vπ mg vπ
X
m X
v
g v i
r
π
π
+ =
1mg rπ β= >> 1
1 1X T
X m m C
v V
i g r g Iπ
−
= =
+
≃
BC diode
IC=1 mA ?
33 Department of Electronic Engineering, NTUT

34. /135
(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
34 Department of Electronic Engineering, NTUT

35. /135
(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

36. /135
• MOSFET
MOSFET IV
( ) ( )2 21
2 2
2
D n ox GS TH DS DS n GS TH DS DS
W
I C V V V V K V V V V
L
µ    = − ⋅ − = − ⋅ −   
( ) ( ) ( ) ( )
2 21
1 1
2
D n ox GS TH DS n GS TH DS
W
I C V V V K V V V
L
µ 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
2
DS
D n GS TH
V
R
I K V V
= =
−
36 Department of Electronic Engineering, NTUT

37. /135
MOSFET
•
•
•
( ) ( )
2
2
2
D n D
m GS TH n ox GS TH n ox D
GS GS TH
I K W W W I
g V V C V V C I
V L L L V V
µ µ
∂
= = − = − = =
∂ −
( ) ( )
2 21
2
D n ox GS TH n GS TH
W
I C V V K V V
L
µ= − = − gm ID !!
( ) ( ) ( )
2 2 1
1D
n GS TH DS n GS TH D
DS DS o
I d
K V V V K V V I
V dV r
λ λ λ
∂  = − + = − = =
 ∂
MOS
ro
CI
CEV
1AV λ− = −
DdI
DSdV
1
or
( ) ( )
2
1D n GS TH DSI K V V Vλ= − +
1
o
D
r
Iλ
=
+
−
gsv
DG
S
m gsg v or
BJT !
37 Department of Electronic Engineering, NTUT

38. /135
BJT
38

39. /135
•
•
−
+
inv out inv v=
sR
+
−
( )
−
+
inv
L
out in
s L
R
v v
R R
=
+
sR
+
−
LR
vin
39 Department of Electronic Engineering, NTUT

40. /135
/
•
−
+
thv
ocv
thR
+
−
ocv
+
−
−
+
thv
sR
LR
+
outv
−
LR +
outv
−
th outR R=
outR
th inR R=
inR
40 Department of Electronic Engineering, NTUT

41. /135
• 10
10-mV 200 8
(a) 2 k 500
(b) 10 2
10vA =
10 mV
+
−
mv
200 Ω
8 Ω
200 Ω 8 Ω
outRinR
in
in m
in s
R
v v
R R
=
+
2 k 0.91in in mR v v= Ω ⇒ =
500 0.71in in mR v v= Ω ⇒ =
L
out amp
L o
R
v 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

42. /135
•
•
•
xv
+
−
inR
xi xi
outR
xv
+
−
42 Department of Electronic Engineering, NTUT

43. /135
• (a) a-b
(b) Rth
v
+−
b
a
V
+
−
v
Rth
v
V2i1
i−i1
6 Ω4 Ω
i1
+
−
i
a
b
3 Ω
16v i=
( )1 1 16 2 4i i i i= + −
1 0.5 , 3i i v i= =
( )3th
v
R
i
= = Ω
+−
a
b(a)
6 Ω
V2i1
i1
4 Ω
43 Department of Electronic Engineering, NTUT

44. /135
• B ( )
+
−
xv rπ
+
−
vπ mg vπ or
CR
xi
x
in
x
v
R r
i
π= = T
m C
V
r
g I
π
β β
= =
1. β ( IC IB
)
2. (CE ) RC
( BJT )
B
B
inv
CR
CCV
outv
44 Department of Electronic Engineering, NTUT

45. /135
• C ( )
rπ
+
−
vπ mg vπ or
inv outR
outR
0vπ = 0mg vπ = out oR r=
(CE )
C
C
outv
45 Department of Electronic Engineering, NTUT

46. /135
• E ( Early Effect)
rπ
+
−
vπ mg vπ
xv
v
r
π
π
inv
outR
xi
CCV
xv vπ = −
m x
v
g v i
r
π
π
π
+ = −
1 1
1
x
out
x m
m
v
R
i gg
rπ
= =
+
≃
1 m
m
m
g
r g
g r
π
π
β
β
= → = <<
C
E ( vbe )
46 Department of Electronic Engineering, NTUT

47. /135
• E AC rπ
• E AC ro
• B AC 1/gm
m
r
g
π
β
=
AC
A
o
C
V
r
I
=
AC
1 T
m C
V
g I
=
AV = ∞
AC
47 Department of Electronic Engineering, NTUT

48. /13548

49. /135
(I)
• (B-E B-C ) BJT VCCS
• BJT gm rπ ro
IC
•
( )
T
m C
V
r
g I
π
β
β= = A
o
C
V
r
I
=C
m
T
I
g
V
=
rπ = ∞
1A
o
D D
V
r
I Iλ
= =
2 D
m
GS TH
I
g
V V
=
−
BJT
MOSFET
49 Department of Electronic Engineering, NTUT

50. /135
(II)
•
β
VBE
IC IB ( β)
IB RB
VBE
BR CR
CCV
1R CR
2R
CCV
1R CR
2R
ERREV
−
+
CCV
BR CR
CCV
VBE IC
(
)
R1 R2
RE
BJT
(thermal
runaway)
RB
BJT
BJT
50 Department of Electronic Engineering, NTUT

51. /135
( )
+
− inv
1CR
CCV
1CICBV
+
−BEV
2CI
−
+
outv
−
+
(
)
(
)
51 Department of Electronic Engineering, NTUT

52. /135
• BJT
BR CR
CCV
BI
CI
X
Y
B B BE CCR I V V+ = CC BE
B
B
V V
I
R
−
= CC BE
C B
B
V V
I I
R
β β
−
= =
CC BE
CE CC C C CC C
B
V V
V V I R V R
R
β
−
= − = −
RB RC VCE
RB RC
( )CC BE
CE CC C C CC C BE
B
V V
V V I R V R V
R
β
−
= − = − >
+
−
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

53. /135
• BJT
BR CR
BI
CI
X
Y
2.5 VCCV =
100 kΩ 0.5 kΩ
17
10 ASI −
= 100β =
17 µACC BE
B
B
V V
I
R
−
= ≃
1.675 VCE CC C C BEV V I R V= − = >
( ) 800 mVBEV =
17 µA 100 1.7 mACI = × =
IC VBE
ln 852 mVC
BE T
S
I
V V
I
= =
16.5 µACC BE
B
B
V V
I
R
−
= =
17 µA 100 1.65 mACI = × =VBE
VBE 850 mV
IC
1.65 mA
IB (VCC−VBE)
VBE VCC
IB IC
(1)
VBE IB IC
(2)
52 mV
?
ln 851.2 mVC
BE T
S
I
V V
I
= =
( )
53 Department of Electronic Engineering, NTUT

54. /135
− BJT VBE
• ( IB )
1R CR
CCV
CI
X
Y
2R
2
1 2
BE X CC
R
V V V
R R
= =
+
BE
T
V
V
C SI I e=
IC VBE VBE R1 R2
1R CR
CI
X
Y
2.5 VCCV =
17 kΩ 5 kΩ
2R8 kΩ
100β =
17
10 ASI −
=
231 µA
BE
T
V
V
C SI I e= =2
1 2
800 mVX CC
R
V V
R R
= =
+
2.31 µABI =
1
1 2
100 µA 43CC
B
V
I 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

55. /135
IB
1R
2R
CCV
CR
CI
Y
X
1R
2R
thR
thV
X
CI
CCV
CR
BI
1R
+
−
2RCCV
+
−
+
−
2
1 2
th CC
R
V V
R R
=
+
1 2||thR R R=
X th B thV V I R= −
th B th
T
V I R
V
C SI I e
−
=
1
ln C
B th T
S th
I
I V V
I R
 
= − ⋅ 
 
VBE ln C
BE T B C BE B C
S
I
V V I I V I I
I
= → → → → → →⋯
R1 R2 IB VX IB
IC
R1 R2 I1>10IB
1I
55 Department of Electronic Engineering, NTUT

56. /135
• R1 R2 VBE
β ( R1 R2 IB )
VBE
R2 1% VX 1%
exp(0.01VBE/VT)=1.36 1%
36%
1R
2R
CR
CI
Y
X
EI
ER
P
CCV
1
1 2
1
E P E CC BE C
E
R
I V R V V I
R R R
 
= = − 
+ 
≃
VX RE
VBE
( β >> 1)
•
56 Department of Electronic Engineering, NTUT

57. /135
•
(1) I1 >> IB β (I1 10IB ) ( )
(2) VRE (~100 mV) VX VBE ( RE )
(3) RC RC BJT
1R
2R
CR
CIY
X
BI
ER
P
CCV
1I
1 BI I>>
+
−
REV
RC BJT
VRE VX VBE
I1 IB 10 β
57 Department of Electronic Engineering, NTUT

58. /135
•
gm=1/(52 )
RC 3 k
1
52
C
m
T
I
g
V
= =
Ω
0.5 mACI =
778 mVBEV =
200 mVRE E CV R I =≃ 400ER = Ω
2
1 2
978 mVX BE E C CC
R
V V R I V
R R
= + = =
+
5 µABI =
1
1 2
10 50 µACC
B
V
I I
R R
= > =
+
1 2
2.5 V
50 k
50 µA
R 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
17
5 10 ASI −
= ×
100β =
1R
2R
CR
CI
Y
X
EI
ER
P
2.5 VCCV =
VX
1I
BJT
58 Department of Electronic Engineering, NTUT

59. /135
• 500 mVREV =
1 100 BI I≥
500 mV 0.5 mA 1 kER = = Ω
2
1 2
1.278 VX BE E C CC
R
V V R I V
R R
+ = =
+
≃
1 2
100CC
B
V
I
R R
≥
+ 1 2 5 kR R+ ≤ Ω
1 1.45 kR = Ω 2 3.55 kR = Ω
1.044 kCC X
C
C
V V
R
I
−
< = Ω
VRE
VX RC BJT
RC I1 IB
R1 R2 R1 R2
17
5 10 ASI −
= ×
100β =
1R
2R
CR
CIY
X
EI
ER
P
2.5 VCCV =
1
52
C
m
T
I
g
V
= =
Ω
0.5 mACI =
778 mVBEV =
5 µABI =
BJT
RC 1 k
59 Department of Electronic Engineering, NTUT

60. /135
( )
• IC
BR CR
CCV
BI
X
Y
CI
X Y B BV V R I= −
RC
B CI I<< B C
Y CC C C B B BE BE
R I
V V R I R I V V
β
= − = + = + CC BE
C
B
C
V V
I
R
R
β
−
=
+
VBE IC ln C
BE T
S
I
V V
I
=
RC
60 Department of Electronic Engineering, NTUT

61. /135
• IC
2 kCR = Ω
800 mVBEV =
ln 807.6 mVC
BE T
S
I
V V
I
= =
154.5 mVB BR I = 0.955 VY B B BEV R I V= + ≃
ln 791 mVC
BE T
S
I
V V
I
= =
81 mVB BR I = 0.881 VYV ≃
100β =
17
5 10 ASI −
= ×
1 kCR = Ω10 kBR = Ω
2.5 VCCV =
BI
X
Y
CI
1.545 mACC BE
C
B
C
V V
I
R
R
β
−
= =
+
800 mVBEV = 0.81 mACC BE
C
B
C
V V
I
R
R
β
−
= =
+
61 Department of Electronic Engineering, NTUT

62. /135
(1) VBE ( VBE )
(2) RC β
•
CC BE
C
C
V V
I
R
−
≃ Y CC C C BEV V R I V= − ≃
( )CC BEV V−
BR β
10C BR R β=
1.1
CC BE
C
C
V V
I
R
−
= ln C
BE T
S
I
V V
I
=
1.1
CC BE
C
C
V V
R
I
−
=
10
C
B
R
R
β
=
CC BE
C
B
C
V V
I
R
R
β
−
=
+
1.8 VCCV =
1
13
mg =
Ω
BR CR
CCV
BI
X
Y
CI
17
5 10 ASI −
= ×
100β =
1
13
C
m
T
I
g
V
= =
Ω
2 mACI = 754 mVBEV =
475
1.1
CC BE
C
C
V V
R
I
−
Ω≃ ≃ 4.75 k
10
C
B
R
R
β
= = Ω 95 mVB BI R =
754 mV 95 mV 849 mVCV = + =
62 Department of Electronic Engineering, NTUT

63. /13563

64. /135
BJT
• / 6
+
−
inv
outv
outv
outv
+
−
inv
+
−
inv
B-E
VCCS
CE CB CC
base ( )
CE
CC
CB
64 Department of Electronic Engineering, NTUT

65. /135
(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= − out
v m C
in
v
A g R
v
= = −inv vπ =
(1)
(2) gm IC
C
m
T
I
g
V
= C C RC
v
T T
I R V
A
V V
= =
RC CC BEV V V≤ −
CC
v
T
V
A
V
≤
BJT
CC BE
v
T
V V
A
V
−
<
(3) RC RC RC
BJT
RC VCC
VCC BJT
VCC
65 Department of Electronic Engineering, NTUT

66. /135
800 mV
1.8 VCCV =
CR
pp2 mV
t
pp77 mV
800 mV
t
• RC 1 k 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 BE
C
C
V V
R
I
−
≤ = Ω
39v m CA g R= − −≃
0.02173mg =
VCC
38.46CC BE
v
T
V V
A
V
−
< =
1 mW
2 mW
2 mWC CCP I V= = 1.1111 mACI = 0.04273mg = 900CC BE
C
C
V V
R
I
−
≤ = Ω 38.45v m CA g R= − −≃
• RC 1 k 0.4 mA 27.66C
v m C C
T
I
A g R R
V
= − = − −≃
66 Department of Electronic Engineering, NTUT

67. /135
CE
•
rπ
+
−
vπ mg vπ CR
Xi
Xv
Xi
rπ
+
−
vπ mg vπ CRXv
+
−
+
−
X T
in
X m C
v V
R r
i g I
π
ββ
= = = =
IC (IB )
0vπ =
X
out C
X
v
R R
i
= =
•
out
v m C
in
R
A g R
R
β= − = − CE I/O
Early Effect
67 Department of Electronic Engineering, NTUT

68. /135
CE
• RC ( VCC
BJT )
• CE IC=1 mA RC 1 k 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 26m 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 ≃
68 Department of Electronic Engineering, NTUT

69. /135
CE
• RC
•
•
• CE VCC = 3 V VA = 5 V ? VCC 10 V ?
CR → ∞ v m oA g r= −
(intrinsic gain)
( )
C
m
T
I
g
V
= A
o
C
V
r
I
= A
v
T
V
A
V
=
intrinsic gain
VA 5 V
intrinsic gain 200
CC BE
v
T
V V
A
V
−
< VCC BJT
VCC
_3
84.6v VCC V
A =
192.3v VA
A =
_10
353.8v VCC V
A =
max
84.6vA =
192.3v VA
A = max
192.3vA =
69 Department of Electronic Engineering, NTUT

70. /135
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
v
v g v R
r
π
π
π
 
= + 
 
1
1in RE m E m E
v
v v v v g v R v g R
r r
π
π π π π
π π
    
= + = + + = + +    
    
1
111
1
mg r
out m C m C C
v
in m E
Em E
m
v g R g R R
A
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
70 Department of Electronic Engineering, NTUT

71. /135
CE
•
•
Xv i rπ π=
RE
( ) ( )1X m X Xi g r i iπ β+ = + ( )1X X E Xv r i R iπ β= + + ( )1X
in E
X
v
R 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
v
v v g v R
r
π
π π
π
 
= = + + 
 
0vπ = 0mg vπ =
X
out C
X
v
R R
i
= =
Xi
Early Effect
71 Department of Electronic Engineering, NTUT

72. /135
• CE
•
BR
rπ
( )1 ERβ+
A
gm
1m Eg R >>
out A out
in in A
v v v
v v v
=
( )
( )
1
1
EA
in E B
r Rv
v r R R
π
π
β
β
+ +
=
+ + +
( )
( ) ( )
1
1 1
E m C
E B E
r R g r R
r R R r R
π π
π π
β
β β
+ + −
= ⋅
+ + + + +
1
1
C
v
B
E
m
R
A
R
R
g β
−
+ +
+
≃
( )1in B ER R r Rπ β= + + +
out CR R=
1
1
m Eg R
m C C
v
m E E
g R R
A
g R R
>>
−
= −
+
≃
( )
( )
1
1 1
1
Eout m C
in E B
m E
r Rv g R
v r R R
g R
r
π
π
π
β
β
+ + −
= ⋅
+ + +  
+ + 
 
( )1
C
E B
R
r R Rπ
β
β
−
=
+ + +
CR
outv
ER
inv
BR
A
CCV
1
BR
β+
1
mg
72 Department of Electronic Engineering, NTUT

73. /135
( )
CCV
CR
outv
ER
inv
2rπ
CCV
CCV
CR
outv
ER
inv
2rπ
•
2||ER rπ
2
1
||
C
v
E
m
R
A
R r
g
π
= −
+
CCV
CR
outv
ER
inv
CCV
CCV
CR
outv
ER
inv
2rπ 2||
1
C
v
E
m
R r
A
R
g
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+
73 Department of Electronic Engineering, NTUT

74. /135
•
C1
1
C
v
E
m
R
A
R
g
= −
+
( )1in ER r Rπ β= + +
out CR R=
CR
outv
ER
inv
biasI
CCV
1C
C1 AC
CR
outv
CCV
inv
BR
1I
1R
2R 1C
CR
BR
1R
outv
inv
2R
( ) 21in BR R r Rπ β= + + +
1||out CR R R=
1
2
||
1
1
C
v
B
m
R R
A
R
R
g β
= −
+ +
+
• I/O (C1
)
74 Department of Electronic Engineering, NTUT

75. /135
• 1 k 2 mV 1
mA CE 40 mV ( RE = 4/gm β = 100)
1 kBR = Ω
1
26
mg =
Ω
40 mV
20
2 mV
vA = =
4
104E
m
R
g
= = Ω
1
2.8 k
1
B
C v E
m
R
R A R
g β
 
= ⋅ + + Ω 
+ 
≃
1
1
C
v
B
E
m
R
A
R
R
g β
−
+ +
+
≃
75 Department of Electronic Engineering, NTUT

76. /135
• 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
xi
or
+
−
out o ER r R= +:
ix RE||rπ vπ 0
outR
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

77. /135
• 1 mA 20 k BJT β =100
VA=10 V
• (C1 )
10 kA
o
C
V
r
I
= = Ω ER rπ<< ( )1 2m Eg R+ =
1
26E
m
R
g
= = Ω
2.6 k E
m
r R
g
π
β
= = 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
77 Department of Electronic Engineering, NTUT

78. /135
CE (I)
• 100 CE
2.5 VCCV =
100 kΩ 1 kΩBR CR
X
OUTv
100
2.5 V 2.5 mV
100 k 100
XV
Ω
= ⋅
Ω + Ω
≃
RB VX ?
(1) RB
(2)
2.5 VCCV =
100 kΩ 1 kΩBR CR
X
OUTv1C
C1 AC
DC
78 Department of Electronic Engineering, NTUT

79. /135
CE (II)
CCV
BR CR
X
OUTv
1C
Y
1inR rπ=
CR
BR
CCV
BR CR
Y
X BR
CR
X
+
−
outv
inv
( ) ( )
outRCR
BR
CC BE
C
B
V V
I
R
β
−
=
CC BE
Y CC C BE
B
V V
V V R V
R
β
−
= − >
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=
79 Department of Electronic Engineering, NTUT

80. /135
CE (III)
• 8
2.5 VCCV =
100 kΩ 1 kΩBR CR
X OUTv1C
2.5 VCCV =
100 kΩ 1 kΩBR CR
X1C
2C
8spR = Ω8spR = Ω
(AC 8 DC
1 )
VCE BJT
heavy saturation
AC DC
80 Department of Electronic Engineering, NTUT

81. /135
CE (IV)
•
2.5 VCCV =
100 kΩ 1 kΩBR CR
X1C
2C
BR
CR
+
−
outv
inv 100 kΩ
1 kΩ 8spR = Ω
VC 1.5 V
17
5 10 ASI −
= ×
1.5 VCV = 2.5 1.5 1 VRCV = − =
1 V
1 mA
1 k
CI = =
Ω
ln 796 mVC
BE T
S
I
V V
I
= =
17 µACC BE
B
B
V V
I
R
−
= = 58.8C
B
I
I
β = =
( )|| 0.31v m C spA g R R= =
CE
CE
CE (buffer)
8spR = Ω
, ,m og r rπ
81 Department of Electronic Engineering, NTUT

82. /135
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
( )1
C
v
m E
R
A
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
82 Department of Electronic Engineering, NTUT

83. /135
• IC=1 mA RE VRE =400 mV
20 2 k
2.5 VCCV =
1R CR
X1C
2R
+
−
inv
ER 2C
1 mAC EI I= ≃ 400ER = Ω
1
26
mg =
Ω
20v m CA g R= = 512CR = Ω
400 mV ln 400 mV 736 mV 1.14 VC
X RE BE T
S
I
V V V V
I
= + = + = + =16
5 10 ASI −
= ×
100β =
400 mVREV =
1 µAC
B
I
I
β
= =
1 2
10CC
B
V
I
R R
>
+ 1 2 25 kR R+ < Ω
2
1 2
1.14 VX CC
R
V V
R R
= =
+ 2 11.4 kR = Ω
1 13.6 kR = Ω
1 2|| || 1.85 kinR r R Rπ= = Ω
RE R1 R2
1 2
5CC
B
V
I
R R
>
+ 1 2 50 kR R+ < Ω
2 22.4 kR = Ω
1 27.2 kR = Ω
1 2|| || 2.14 kinR r R Rπ= = Ω
83 Department of Electronic Engineering, NTUT

84. /135
CCV
1R CR
sR
1C 2R
+
−
inv
ER
2C LR
outv
+
−
inv
sR
1 2||R R
ER
||C LR R
outv
X
( )
( )
1 2
1 2
|| || 1
|| || 1
EX
in E s
R R r Rv
v R R r R R
π
π
β
β
+ +  =
+ + +  
( )
( )
1 2
1 2
|| || 1 ||
1|| || 1
Eout out C LX
in in X E s
E
m
R R r Rv v R Rv
v v v R R r R R R
g
π
π
β
β
+ +  = =
+ + +   +
R1 R2
DC AC
( )
DC
AC
84 Department of Electronic Engineering, NTUT

85. /135
(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
RC
out
m
C
v
g v
R
π− = out
in
m C
v
v v
g R
π = − = − out
m C
in
v
g R
v
=
85 Department of Electronic Engineering, NTUT

86. /135
• CB IC=0.2 mA
600 mV
• VB
1.8 VCCV =
CR
+
inv
BV
outv
600 mV
600 mV ln 600 mV 1.354 VC
B BE T
S
I
v V V
I
= + = + =
RC
1.8 V 1.354 V 0.446 V− =
17.2C
v m C C
T
I
A g R R
V
= = =
17
5 10 ASI −
= ×
100β =
Vb
+
−
inv 600 mV
outv
CR
1.8 VCCV =
1R
2R
BI1I
100β =
17
5 10 ASI −
= ×
1
1 2
10 20 µA CC
B
V
I I
R R+
≃ ≃ ≃
1 2 90 kR R+ = Ω 2
1 2
1.354 VB CC
R
V V
R R
=
+
≃
2 67.7 kR = Ω
1 22.3 kR = Ω
0.2 mACI = 0.2 100 mA 2 µABI = =
β
86 Department of Electronic Engineering, NTUT

87. /135
•
CCV
CR
inR 1
in
m
R
g
=
VA=∞ CB
IC=1 mA 26
(CE β/gm)
CCV
CR
BV
XI
+
−
XV V∆
1X
in
X m m
V V
R
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
out
v m out
in
R
A g R
R
= =
1 || ||out out C o CR R R r R= =
87 Department of Electronic Engineering, NTUT

88. /135
CB
CR
CCV
+
−
inv
sR
1
mg
outv
X
X
1
mg
sR
+
−
inv
1
1
1 1
m
X in in
m s
s
m
g
v v v
g RR
g
= =
++
out
m C
X
v
g R
v
= CB
11
out m C C
in m s
s
m
v g R R
v g R R
g
= =
+ +
CE ( Rs
)
88 Department of Electronic Engineering, NTUT

89. /135
• CB 50 RF
50 CB 50
( )
CR
CCV
CR
CCV
BV
outv
50sR = Ω
outv
BV
+
−
inv
1
50in
m
R
g
= = Ω
0.52 mAC m TI g V= =
1
1 2
C
v
s
m
R
A
R
g
= =
+
CB 50
1
in
in
s
m
v
i
R
g
=
+
1
C in
out
s
m
R v
v
R
g
=
+
0.5C sR R≤
89 Department of Electronic Engineering, NTUT

90. /135
CB
CCV
CR
outv
BR
or
ER
BV
+
−
inv
ER
or
CR
1outR 2outR
1
50in
m
R
g
= = 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= + +  
90 Department of Electronic Engineering, NTUT

91. /135
RB ro
rπ
+
−
vπ mg vπ CR
outv
BR
ER+
inv
−
P
out
m
C
v
g v
R
π = − out
m C
v
v
g R
π = −
RB
out out
m C C
v v v
r g r R R
π
π π β
= − = −
( ) ( )out out
P B B
C C
v v
v R r R r
R R
π π
β β
−
= − + = +
P KCL P in
m
E
v v v
g v
r R
π
π
π
−
+ =
( )
1
out
B in
out C
m
m C E
v
R r v
v R
g
r g R R
π
π
β
+ −
  −
+ ⋅ = 
  ( )
( )
11
1
out C C
Bin E B
E
m
v R R
Rv R R r R
g
π
β
β
β
=
+ + + + +
+
≃
CE
RB RB
91 Department of Electronic Engineering, NTUT

92. /135
RB
CCV
CR
+
−
inv
ER
outv
BR
CB Stage
rπ
+
−
vπ mg vπ CR
outv
BR
+
−
Xv
Xi
X
B
r
v v
r R
π
π
π
= −
+
KCL m X
v
g v i
r
π
π
π
+ = −
1
m X X
B
r
g v i
r r R
π
π π
  −
+ = − 
+ 
1
1 1
X B B
X m
v r R R
i g
π
β β
+
= +
+ +
≃
RB=0, Rin=1/gm
BR
ER
AV = ∞AV = ∞
1
1
B
m
R
g β
+
+
( )1 Er Rπ β+ +
emitter base RB (1+β) Emitter
degeneration base emitter RE (1+β)
92 Department of Electronic Engineering, NTUT

93. /135
CR
CCV
BR
outv
CR
outv
CCV
1
1
1
B
m
R
g β
+
+
XR
eqR
XR
1
1
1
B
eq
m
R
R
g β
= +
+
2 2 1
1 1 1 1
1 1 1
eq B
X
m m m
R R
R
g g gβ β β
 
= + = + + 
+ + + 
• RX
93 Department of Electronic Engineering, NTUT

94. /135
CB (I)
•
CCV
CR
OUTv
+
−
inv
1C+
−
BV
CCV
CR
OUTv
+
−
inv
1C+
−
BV
CCV
CR
outv
+
−
inv
1C+
−
BV
1
mg
ER
ER
emitter DC path emitter DC path
AC
RE emitter DC path
1
||in E
m
R R
g
=
94 Department of Electronic Engineering, NTUT

95. /135
CB (II)
CCV
CR
outv
+
−
inv
1C+
−
BV X
inRER
sR
1
||in E
m
R R
g
=
Rin
( )
1
||
1
1 1 1||
E
X in m
in in s m E s
E s
m
R
v R g
v R R g R RR R
g
= = =
+ + ++
out
m C
X
v
g R
v
=
( )
1
1 1
out
m C
in m E s
v
g R
v g R R
=
+ +
CCV
CR
outv
+
−
inv
1C
+
−
bV
inR
ER
sR
ini
1i
2i
iin i1 RE(shunt ) i2 RC
RE
RC RE
RE 1/gm i2
1
E
m
R
g
>> C E TI R V>>
RE RE VT
95 Department of Electronic Engineering, NTUT

96. /135
CB (III) - Vb
• CE
CE 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 >> IB
2
1 2
b CC
R
V V
R R+
≃
Base
1 2||thR R R=
bypass CB base AC
ground
96 Department of Electronic Engineering, NTUT

97. /135
• CB 10 50
1E mR g>> 500ER = Ω
1 50in mR g = Ω≃ 0.52 mA, 899 mVC BEI V= =
bypass (AC )
500CR = 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
R
V 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
1C
inv
100β =
16
5 10 ASI −
= ×
AV = ∞
900 MHz
C1 CB
1
1
1
20
mg
j Cω
=
1
20 20
71 pF
2 900 MHz
m mg g
C
ω π
= = =
⋅
1
1 1
1 20
m
B
g
j Cβ ω
=
+
0.7 pFBC =
( 10 )
97 Department of Electronic Engineering, NTUT

98. /135
(Common Collector Topology)
• B E C
CCV
ER
INV
OUTV
1BEV
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
out
m
E
v v
g v
r R
π
π
π
+ =
1
out
E
r v
v
R
π
π
β
=
+
in outv v vπ= +
1
1 1
1
1
out E
in
E
E m
v R
rv R
R g
π
β
=
+ +
+
≃
1
Early Effect
98 Department of Electronic Engineering, NTUT

99. /135
CC
• CC
CCV
inv
+
−
ER
CCV CCV
thR
inv
+
− inv
+
−
out inv v=
ER
1
th
m
R
g
=
outv
th inv v=
1
in
m
R
g
=
CC Rth=1/gm
CC
(CE CB
)
outv
99 Department of Electronic Engineering, NTUT

100. /135
•
•
CCV
INv
OUTv
1I
1vA ≃
VBE out in BEv v V= −
VBE vOUT vIN
CCV
ER
inv
+
−
outv
sR
sR
CCV
thR
th inv v=
+
−
1
1
s
m
R
g β
+
+
ER
1
1
out E
sin
E
m
v R
Rv R
gβ
=
+ +
+
outv
100 Department of Electronic Engineering, NTUT

101. /135
CC
rπ
+
−
vπ mg vπ
ER
Xv
+
−
Xi
inR
0CR →
CCV
ER
CCV
inR
ER
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= + + = + +
( )1X
E
X
v
r R
i
π β= + +
Follower RE
buffer ( )
101 Department of Electronic Engineering, NTUT

102. /135
• CE 20 1 k
(a) 8 ?
(b) CC ? CC 5 mA
β=100 VA follower
CCV
1 kΩ CR
8spR = Ω
1C
1inR
inv
+
−
1I
CCV
( )20 ||8 0.159v CA R= ⋅ Ω = ( )1 2 1 1058in spR r Rπ β= + + = Ω
( )1||
20 10.28C in
v
C
R R
A
R
= ⋅ =
CCV
1 kΩ
inv
+
−
CR
1C
8spR = Ω
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103. /135
CCV
sR
ER
outR
sR
CCV
1
1
s
m
R
g β
+
+
ER
1
||
1
s
out E
m
R
R R
g β
 
= + 
+ 
Follower
driver follower
( ) ( )ER
inv
+
−
inv
+
−
CCV
sR
ER
or
sR
ER or
||
1
||
1
E o
v
s
E o
m
R r
A
R
R r
gβ
=
+ +
+
( )( )1 ||in E oR r R rπ β= + +
1
|| ||
1
s
out E o
m
R
R R r
gβ
 
= + 
+ 
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104. /135
CC
CCV
ER
X
OUTv
1R
2R
1C
inv
−
+
inv
−
+
1C
CCV
BR
BI
X
Y OUTv
ER
R1 R2 IB
β
VCC C VCC BJT
RB RE
β
104 Department of Electronic Engineering, NTUT

105. /135
• RB=10 k RE=1 k VCC=2.5 V
KVL B C
BE E C CC
R I
V R I V
β
+ + =
800 mVBEV ≃ 1.545 mACI =
ln 748 mVC
BE T
S
I
V V
I
= = 1.593 mACI =
159 mVB BI R =
1.593 VC EI R =
C E B BI R I R>>
inv
−
+
1C
CCV
BR
BI
X
Y OUTv
ER
16
5 10 ASI −
= ×
100β =
105 Department of Electronic Engineering, NTUT

106. /135
(I)
• 10 k 10 mV
0.1 W 8
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= ⋅ = × ≃
1.26
126
0.01
vA = =
inv
−
+
10 ksR = Ω CC
8LR = Ω
outv
Li126vA =
1. 8 CE
2. 126 CC
3. 10 k CB
CE CC CB
106 Department of Electronic Engineering, NTUT

107. /135
(II)
•
inv
−
+
10 ksR = Ω CC
8LR = 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
107 Department of Electronic Engineering, NTUT

108. /135
• 8 CC ( )
Li
CC
8LR = Ω
ov
4ER
4BV
4BI
3ov
4inR 12 VCCV =
(III) –
, 0.158 AL peaki = , 1.26 Vo peakv =
4 50β =
4
12 6
20
0.3
CC CEQ
E
EQ
V V
R
I
− −
= = = Ω
50
0.3 0.294 A
1 51
CQ EQI I
β
β
= = ⋅ =
+
0.294 A
11.3
26 mV
C
m
T
I
g
V
= = = 4.42
m
r
g
π
β
= = Ω
( )( )
( )( )
( )
( )
1 || 51 20 ||8
0.985
1 || 4.42 51 20 ||8
E L
v
E L
R R
A
r R Rπ
β
β
+ ⋅
= = =
+ + + ⋅
1.26 V vo3
1.28 V
0.158 A
0.158 A
Ci
CQ EQI I≃
CEv
CEQV 12 VCCV =
1.26 V1.26 V
0.3 AEQI =
6 VCEV =
108 Department of Electronic Engineering, NTUT

109. /135
(IV) –
• 10 k CC
6 V, 1 mACEQ CQV I= =
1 2|| 100 kR R = Ω
1
12 6
6 k
0.001
CC CE
E
E
V V
R
I
− −
= = = Ω
1
0.0385
26
C
m
T
I
g
V
= = =
Ω
2.6 k
m
r
g
π
β
= = Ω
( )1 2|| || 1 85.9 kin ER R R r Rπ β= + + = Ω  
( )
( )
1
0.892
1
Ein
v
in s E
RR
A
R R r Rπ
β
β
+
= =
+ + + 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= + +  
CEv
12 VCCV =CEQV
Ci
CQ EQI I≃
Rs 10
1 mACQI =
6 VCEV =
608.6 kΩ
10 mVinv =
( )
109 Department of Electronic Engineering, NTUT

110. /135
(V) –
2 328.8, 5v vA A= =
3 4 4 4 6 0.7 6.7 VC B E BEV V V V= = + = + =
4
0.294
5.88 mA
50
BI = = 3
3 313 mA, 0.5C
C m
T
I
I g
V
= =≃
3 200
m
r
g
π
β
= = Ω
( )( )
( )
4 4 4 41 ||
4.42 51 20 ||8 296
in E LR r R Rπ β= + +
= + = Ω
( )
( )
3 3 4
3
3 3 3
||
5
1
C in
v
E
R R
A
r Rπ
β
β
= =
+ +
3 27.3ER Ω≃
, , , ,126 0.892 0.985v v in v gain v o v gainA A A A A= = ⋅ ⋅ = ⋅ ⋅
, 144v gainA ≃
VBE4
3
3
3 3
12 6.7
296 CC C
C
RC RC
V V
R
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
1ov
2ov
3 4C BV V=
3 100β =2 100β =
2
2
12 6
1.2 k
5
CC C
C
CQ
V V
R
I
− −
= = = Ω 2
2
2
0.52 kT
CQ
V
r
I
π
β
= = Ω
( )
( )
2 2 3
2
2 2 2
||
28.8
1
C in
v
E
R R
A
r Rπ
β
β
= =
+ +
2 23.7ER Ω≃ 5 6|| 50 kR R = Ω ( ) 3 181 kR = Ω
4 69.1 kR = Ω
110 Department of Electronic Engineering, NTUT

111. /135
(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
111 Department of Electronic Engineering, NTUT

112. /135112

113. /135
(I)
PSRR
DDV
SSV
INv +
INv − −
+
OUTv
offset
CMRR
( )
SR
0
(dB)
113 Department of Electronic Engineering, NTUT

114. /135
(II)
• OPA (DVCVS)
• OPA A OPA
vo
+
−
1v
2v
ov
+
−
− −
1v
2v
( )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
+
+
+
+
114 Department of Electronic Engineering, NTUT

115. /135
(I)
•
•
Iv
Ov
1R
2R
−
+
2
1
O
v
I
v R
A
v R
= = −
0a bv v= =
1 2 1Ii i v R= =
av
0bv =
Iv
Ov
1R
2R
−
+
1i
2i
Zin
2
2 2
1
O I
R
v i R v
R
= − = −
2
1
1O
v
I
v R
A
v R
= = +
Ov
−
+Iv
1R
2R
Ov
−
+Iv
1R
2R
1i
2i
av
a Iv v=
1 2 1ai i v R= = −Zin
( ) 2
2 1 2
1
1O I
R
v i R R v
R
 
= − + = + 
 
KCL KVL ( )
v i i v
R2 5 k 25 k
R1
115 Department of Electronic Engineering, NTUT

116. /135
(II)
• (level shifting)
Iv
Ov
1R
2R
−
+
Iv
Ov
1R
2R
−
+
−
+
BIASV
2 2
1 1
1O I BIAS
R R
v v V
R R
 
= − + + 
 
Ov
−
+Iv
1R
2R
2 2
1 1
1O I BIAS
R R
v v V
R R
 
= + − 
 
2R
1R
Iv
Ov
+
−
−
+
BIASV
116 Department of Electronic Engineering, NTUT

117. /135
( )
•
•
Iv
Ov
1 1 kR = Ω
2 10 kR = Ω
−
+
2
1
O I
R
v v
R
= −
Iv
Ov
1 1 kR = Ω
2 10 kR = Ω
−
+
Iv
Ov
1 1 kR = Ω
2 10 kR = Ω
−
+
−
+
BIASV
2 2
1 1
1O I BIAS
R R
v v V
R R
 
= − + + 
 
+VCC
−−−−VSS
100 mV
1 V−
OPA
OK
+VCC
GND
1 V−
100 mV
OPA
0 V
100 mV 1 V 2.475 V= − +
Level shifting
AC
VCC/2
+VCC
GND
225 mV
117 Department of Electronic Engineering, NTUT

118. /135
(III)
• /
1v
Ov
1R fR
−
+
2v
nv
2R
nR
1 2
1 2
f f f
O n
n
R R R
v 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 2
b
O
a
R
v v v
R
= −
( v2=0 v1 vo1 v1=0 v2
vo2 vo= vo1 +vo2 )
v i i v
118 Department of Electronic Engineering, NTUT

119. /135
(IV)
•
−
+
1v
2v
aR
aR
3v
4v
aR
aR
bR
bR
ov
( )1 2 3 4
b
O
a
R
v v v v v
R
= + − −
119 Department of Electronic Engineering, NTUT

120. /135
(V)
•
•
0
iv
ov
R
C
−
+
( )0 0ov =
KCL 0i ov dv
C
R dt
+ =
0
1 t
o iv v dt
RC
= − ∫
iV
oV
R
1
sC
−
+
1
1
o i i
sCV V V
R sRC
= − = −
iv
ov
C
R
−
+
( )1o i i
R
V V sRC V
sC
= − = −
v i i v
120 Department of Electronic Engineering, NTUT

121. /135
(Voltage Follower)
• ( )
• (heavy load)
Iv
Ov
−
+
1O
v
I
v
A
v
= ≃
Iv
100 ksR = Ω
1 kLR = Ω
+
−
Ov
+
−
Source Load
1k
0.01
100k+1k
O Iv v= ≃
Iv
100 ksR = Ω
1 kLR = Ω+
−
Ov
+
−
Source Load
Buffer
O Iv v≃
121 Department of Electronic Engineering, NTUT

122. /135
• ZL
+
−
SV
1R
OV
ILZ
1SI V R=
122 Department of Electronic Engineering, NTUT

123. /135
• general
INv +
INv −
2R
1R
3R
4R
Ov
−
+
BIASV
( )
( )
( )
( )
4 1 2 3 1 22
1 3 4 1 1 3 4
O IN IN BIAS
R R R R R RR
v v v V
R R R R R R R
+ −
+ +
= − +
+ +
INv +
4
3 4
IN
R
v
R R
+
+
4 2
3 4 1
1 IN
R R
v
R R R
+
 
+ 
+  
INv −
2
1
IN
R
v
R
−−
3
3 4
BIAS
R
V
R R+BIASV 3 2
3 4 1
1 BIAS
R R
V
R R R
 
+ 
+  
31
2 4
RR
K
R R
= =
1 1
1
IN
K
v
K K
+
+ 
 
+  
2
1
IN
R
v
R
−−
( )
( )
1
1 1
1 1
BIASK V
K
+  +
( )2
1
O IN IN BIAS
R
v v v V
R
+ −= − +
123 Department of Electronic Engineering, NTUT

124. /135
( )
( )2 4
1 2
3
2
1O BIAS
G
R R
v v v V
R R
  
= + − +  
  
2v
1v
2R
4R
GR
Ov
−
+ BIASV
+
− 4R
3R
3R
2R
−
+ 1v
2
11
G
R
v
R
 
+ 
 
2v
2
21
G
R
v
R
 
+ 
 
3
3 4
BIAS
R
V
R R+BIASV 3 4
3 4 3
1 BIAS
R R
V
R R R
 
+ 
+  
2
1
G
R
v
R
 
− 
 
2
2
G
R
v
R
 
− 
 
2 2
1 21
G G
R R
v v
R R
   
− + +   
   
2 2
2 11
G G
R R
v v
R R
   
− + +   
   
4
3
R
R
 
× − + 
 
4 4
3 4 3
1
R R
R R R
   
× ⋅ + +   
+   
( )2 4
1 2
3
2
1 BIAS
G
R R
v v V
R R
  
= + − +  
  
124 Department of Electronic Engineering, NTUT

125. /135
OPA
• OPA ( )
1
oA
A s
sτ
=
+
1
2c cfω π
τ
= =
fall-off rate:
−6 dB/oct
f (Hz)
fc fT
Gain (dB)
f (Hz)
Phase (deg.)
0
90−
oA
oA
τ OPA ( )1 τ−
cf 3 dB
Tf 0 dB (1)
OPA fT OPA (GBW)
125 Department of Electronic Engineering, NTUT

126. /135
(Gain-Bandwidth Product)
•
• OPA
• =
1
2c cfω π
τ
= =
( )
1
o
c
A
A s
s
ω
=
+
( ) 2
1
o
c
A
A jω
ω
ω
=
 
+  
 
( ) 1TA jω =
2
1 T
o
c
A
ω
ω
 
+ = 
 
2
1T
c
ω
ω
 
>> 
 
T
o
c
A
ω
ω
≃
T o cAω ω=
3 dB
( )x x Tf A j fω⋅ =
OPA fx
( ) T
x
x
f
A j
f
ω =
126 Department of Electronic Engineering, NTUT

127. /135
OPA (I)
• (AOL)
OPA
•
Bipolar OPA Ri 150 k
FETs (Mega ) OPA
•
Bipolar OPA 100
OPA OPA
1 k 100 k 10 k
OPA
127 Department of Electronic Engineering, NTUT

128. /135
OPA (II)
• (Input offset voltage, VOS VIO)
OPA 0 V
AC
(VIO)
• (Input offset current, IOS IIO)
0
OPA
BJT
1 1O f BV R I=IB1 (IB2=0)
2 2 2
1
1 f
O B
R
V I R
R
 
= − + 
 
1 2 1 2 2
1
1 f
O O O B f B
R
V V V I R I R
R
 
= + = − + 
 
IB1 = IB2
IB2 (IB1=0)
2BI
1BI
fR
1R
OV
SV
2R −
+
128 Department of Electronic Engineering, NTUT

129. /135
OPA (III)
• (VIN)
OPA ( )
offset offset OPA
• (Vopp)
DC 0 V OPA
2 1iV V V− ≤ ≤
iV
1V
2V−
oV
1oV
2oV−
Vi
129 Department of Electronic Engineering, NTUT

130. /135
OPA (IV)
• Slew Rate (SR)
OPA (
OPA
) SR OPA step
(unit gain) zero crossing
• SR sino mv V tω=
coso
m
dv
V t
dt
ω ω=
0, ,2 ,
o
m
t
dv
V
dt ω π π
ω
=
=
⋯
mSR V ω≥ mV
SR
ω
≥
SR OPA
OPA
130 Department of Electronic Engineering, NTUT

131. /135
OPA (V)
• (Common-mode rejection ratio, CMRR)
OPA ( )
CMRR (dB)
CMRR 80 dB CMRR
• (Power supply sensitivity, ∆VIO/∆VGG)
∆VGG ∆VIO
•
OPA
• Ci
131 Department of Electronic Engineering, NTUT

132. /135
OPA (VI)
• (Full power response)
OPA
• (Gain-Bandwidth Product)
17 OPA
OPA
75 kHz
132 Department of Electronic Engineering, NTUT

133. /135
OPA (VII)
• (Rise time, tr)
OPA OPA 10% 90%
• (Power supply voltage)
• (Power supply current)
• ( )
•
( )
0.35r ct f× ≅
133 Department of Electronic Engineering, NTUT

134. /135
• OPA
• datasheet
AC
• 100
• Slew Rate
• OPA
OPA datasheet
• bypass
DC 1 MHz 1 µF
(10MHz MHz)
0.1 µF
OPA
134 Department of Electronic Engineering, NTUT

135. /135
•
• ( )
gm rπ
ro
• BJT
CE CB CB
CC CE CB CC
• OPA
135 Department of Electronic Engineering, NTUT