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7/27/2019 Lecture17(20-3-11)
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EE 332
DEVICES AND CIRCUITS II
Lecture 17
AC Coupled Multi-Stage Amplifier
AC‐COUPLED MULTI‐STAGE AMPLIFIER
/INTRODUCTION
Coupling capacitors de‐couple the circuit into 3 stages
CE amplifier
R1
R2 R4
R3
RE2
C3
RL
C2
CE1RE1
RC1
C1
VCC
Q 2Q 1
vo
CC amplifier (voltage follower)
vi
AC‐COUPLED MULTI‐STAGE AMPLIFIER
/EXAMPLE AND GAIN
R1
R2R4
R3
RE2
C3
RL
C2
CE1RE1
RC1
C1
VCC
Q 2Q 1
vo
vi
, ,,
1,2
70 0.7
70 , 15
B E O N
A CC
V V Q
V V V V
β = = ⎫= ⎨ ⎬
= = ⎭
Analyze the given multi‐stage amplifier
Given:
1 2 1 1
3 4
160 , 43 , 4.7 , 1.6 ,
91 , 120 , 2.5 ,
C E
L
R k R k R k R k
R k R k R k
1 1 2 3
10 ,E
C C C C F
= Ω = Ω = Ω = Ω ⎫⎪ ⎪
= Ω = Ω = Ω ⎬⎪ ⎪= = = = ⎭
Lecture Goals
Understanding of concepts related to:
• AC-Coupled Multi-Stage Amplifier
• AC-Coupled Multi-Stage Amplifier/Gain
• AC-Coupled Multi-Stage Amplifier/Current Gain
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AC‐COUPLED MULTI‐STAGE AMPLIFIER
/1ST STAGE DC
ANALYSIS
R1
R2 R4
R3
RE2
C3
RL
C2
CE1RE1
RC1
C1
VCC
Q 2Q 1
vo
vi
Step 1: DC analysis DC effects on the dash box
→ Two “4‐resistor” BJT circuits
AC‐COUPLED MULTI‐STAGE AMPLIFIER
/ 1ST STAGE DC ANALYSIS
and
1
1 1
16.82
,
1.18 1.19
B
C E
I A
then
I m A I m A
μ
= =
Solve RHS loop
1 1 1
1 1 1
1 1 1
5.53
1.91
7.56
RC C C
RE E E
CE CC RC RE
V R I V
V R I V
V V V V V
= × =
= × =
= − − =
Since VCE=7.56 >VCE,sat=0.1V
The BJT operates in Forward Active region
REQ
VEQ
RC
RE
Q1
VCC
vo
IC
IE
IB
AC‐COUPLED MULTI‐STAGE AMPLIFIER
/ 1ST STAGE SMALL SIGNAL PARAMETERS
Step 2: Small Signal Parameters:
1
1
1
1
1
1
1
1.18
47.225
701.48
47.2
77.5665.7
1.18
C
m
T
m
A CE
o
C
I mA
g mS V mV
r k g mS
V V V r k
I mA
π
β
= = =
= = = Ω
+= = = Ω
AC‐COUPLED MULTI‐STAGE AMPLIFIER
/ 1
ST
STAGE DC
ANALYSIS
Assuming BJT operating in forward active mode,
Theveninizing LHS circuit
2
1 2
1 2
3.18
( / / ) 33.89
EQ CC
EQ
R V V V
R R
R R R k
= × =+
= = Ω
Solve the loop
1 1 , 1
1 1
,
1
1
( 1)
2.4816.82
( 1) 33.89 71 1.6
EQ E E BE ON B E Q
E B
EQ BE ON
B
EQ E
V I R V I R
I I
V V I A
R R k k
β
μβ
= + +⎨
= +
−⇒ = = =
+ + + ×
REQ
VEQ
RC
RE
Q1
VCC
vo
IC
IE
IB
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AC‐COUPLED MULTI‐STAGE AMPLIFIER
/2ND STAGE DC
ANALYSIS
R1
R2 R4
R3
RE2
C3
RL
C2
CE1RE1
RC1
C1
VCC
Q 2Q 1
vo
vi
Step 1: DC analysis DC effects on the dash box
→ Two “4‐resistor” BJT circuits
AC‐COUPLED MULTI‐STAGE AMPLIFIER
/ 2ND STAGE SMALL SIGNAL PARAMETERS
Step 2: Small Signal Parameters:
2
2
2
2
2
2
2
2.63105
25
70665
105
81.8831.13
2.63
C
m
T
m
A CE
o
C
I mAg mS
V mV
r g mS
V V V r k
I mA
π
β
= = =
= = = Ω
+= = = Ω
AC‐COUPLED MULTI‐STAGE AMPLIFIER
/ SMALL SIGNAL EQUIVALENT CIRCUIT
Step 3: Small Signal Equivalent Circuit
R1//R2
RE2
C2
RL
C1
E1
rπ1
RC1
vo
vi gmvbe1
vbe1
B1
ro1R3//R4
B2
E2
rπ2
gmvbe2
vbe2
ro2
Stage 1 :CE amplifier
Stage 2 :CC amplifier
AC‐COUPLED MULTI‐STAGE AMPLIFIER
/ 2
ND
STAGE DC
ANALYSIS
42
3 4
2 3 4
8.53
( / / ) 51.75
EQ CC
EQ
R V V V
R R
R R R k
= × =+
= = Ω
2 ,
2
2
7.8337.6
( 1) 51.75 71 2.2
EQ BE ON
B
EQ E
V V I A
R R k k μ
β
−= = =
+ + + ×
and2 2
2.63 2.67C E
I mA I mA=
Solve RHS
loop
2 2 211.88
CE CC RC RE V V V V V − − =
Since VCE2=11.88V >VCE,sat=0.1V
The BJT operates in Forward Active region
REQ
VEQ
RC
RE
Q1
VCC
vo
IC
IE
IB
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AC‐COUPLED MULTI‐STAGE AMPLIFIER
/ VOLTAGE
GAIN
R1//R2
RE2
C2
RL
C1
E1
rπ1
RC1
vo
vi gmvbe1
vbe1
B1
ro1R3//R4
B2
E2
rπ2
gmvbe2
vbe2
ro2
1 1 2
1 1 2
o be c b o
v i i be c b
v v v v v
A v v v v v = = × × ×
1 1be
i
v
v =
1 1 1 1 1 3 4 2
2 2 2
1
1
[ / / / / / / / / ]
( 1)[ / / ] 84.55
47.2 3.85 181.72
c m be C o b
b E L
c
be
v g v R r R R r
r r R R k
v
v
πβ
= − ×
= + + = Ω
⇒ = − × = −
Voltage gain
Calculate one term at a time:
AC‐COUPLED MULTI‐STAGE AMPLIFIER
/ CURRENT GAIN
R1//R2
RE2
C2
RL
C1
E1
rπ1
RC1
vo
vi gmvbe1
vbe1
B1
ro1R3//R4
B2
E2
rπ2
gmvbe2
vbe2
ro2
i
i v
L
R A A
R = ×
1 1 2 1 1 2 1
1 3 4 2
/ / / / / / / / 1.42
/ / / /
91 / /120 / /84.55 31.19
1.42
i b
L b
1181.72 8.27
31.19i
R R R r R R r k
R R R r
k k k k
k
π
Ak
= = = Ω
=
= Ω Ω Ω = Ω
= − × = −
1st stage:
11 1
1
i
i v
L
R A A
R = ×
1 1 11
1
181.72c be c
v
i i be
v v v A
v v v = = × = −
AC‐COUPLED MULTI‐STAGE AMPLIFIER
/ CURRENT GAIN
R1//R2
RE2
C2
RL
C1
E1
rπ1
RC1
vo
vi gmvbe1
vbe1
B1
ro1R3//R4
B2
E2
rπ2
gmvbe2
vbe2
ro2
2 3 4 2
2
/ / / / 31.19
2.5
31.190.960 12.35
2.5
i b
L
i
R R R r k
R k
k A
k
1 28.27 12.35 102.13
i i i A A A
= = Ω
= Ω
= × =
2nd stage:
= × = − × = −
2
2 2
2
i
i v
L
R A A
R = ×
2
2
1 1 2
0.99o b o
v
c c b
v v v A
v v b = = × =
i
i v
L
R A A
R = ×
AC‐COUPLED MULTI‐STAGE AMPLIFIER
/
VOLTAGE
GAIN
R1//R2
RE2
C2
RL
C1
E1
rπ1
RC1
vo
vi gmvbe1
vbe1
B1
ro1R3//R4
B2
E2
rπ2
gmvbe2
vbe2
ro2
Voltage gain
2
2 2 2
( 1)[ / / ]
( 1)[ / / ]
( 1) 11700.99
665 ( 1) 1170
1 ( 181.72) 1 0.99 179.9
o E L
b E L
v
v R R
v r R R
A
π
β
β
β
β
+=+ +
+ ×= =
+ + ×
= × − × × = −
Calculate one term at a time:
1 1 2
1 1 2
o be c b o
v i i be c b
v v v v v A
v v v v v = = × × ×
2
1
1b
c
v
v =
76
