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Chapter 9
Common-Emitter Amplifiers
Pictures are redrawn (with some modifications) from
Introductory Electronic Devices and Circuits
By
Robert T. Paynter
1
Objectives
• Describe AV, AI, AP associated with the three
amplifier configurations.
• Describe the input/output voltage and current
phase relationships.
• Calculate the ac emitter resistance of a transistor.
• Discuss two roles of the capacitors in the circuits.
• Derive the ac equivalent circuit for a given
amplifier.
• Explain how the voltage gain drift due to
temperature occurs.
• Discuss the relationship between the load
resistance and voltage gain of a CE amplifier.
2
Objectives (Cont.)
• Calculate Zin(base) and Zin for a CE amplifier
• Discuss the effects of swamping on the ac
characteristics of a CE amplifier
• List and describe the four ac h-parameters
3
Fig 9.1 Common-emitter input-
output phase relationship.
VB
+VCC
IB 15 A
10 A
5 A RC
RB
Q1
VC 8V
6V
Ai = 100 4V
IC 1.5 mA
1 mA
500 A 4
AC Emitter Resistance
25mV
re
IE
where r’e = ac emitter resistance
IE = the dc emitter current, found as VE / RE for
example.
5
Fig 9.2 Example 9.1.
R2 2.2kΩ
VB VCC 10V 1.8V
+10 V R1 R2 12.2kΩ
VE VB 0.7V
IE 1.1mA
RC RE 1kΩ
R1
10k 4k
25mV 25mV
re 22.7Ω
RL IE 1.1mA
hFE = 300 15k
R2
2.2k RE
1k
6
Fig 9.3 Graphical determination of
ac emitter resistance.
IE
IE Q2
VBE
re
Q1 I E
IE
VBE
VBE VBE 7
Fig 9.4 The determination of ac beta.
IC
I C ic
ac
I B ib
Q
hFE = dc beta
IC
hfe = ac beta
IB
IB
8
AC Model of A BJT
c
ic = acib
C C
B B b
ib
E E r'e
npn pnp
e
9
Roles of Capacitors in Amplifiers
1. A coupling capacitor passes an ac
signal from one amplifier to another,
while providing dc isolation between the
two.
2. A bypass capacitor is used to “short
circuit” an ac signal to ground while not
affecting the dc operation of the circuit.
1 The higher the freq.,
XC
2 fC the lower the capacitor impedance.
10
Fig 9.5 Coupling capacitors in a
multistage amplifer.
VCC
CC3
CC1
CC2
Load
11
Fig 9.6a AC coupling.
GND
CC3
CC1
CC2
Load
12
Fig 9.6b DC isolation.
VCC
CC3
CC1
CC2
Load
13
Fig 9.7 Capacitive vs. direct
coupling.
VCC VCC
CC
14
Fig 9.8-9 Bypass capacitors.
VCC GND VCC
CB CB CB
For AC analysis For DC analysis
15
Fig 9.10 Typical common-emitter
amplifier signals.
VCC 1.8V
5.6V
5.6V
1.8V
0V
0V
1.1VDC 1.1VDC
16
Fig 9.11 Deriving the CE ac-
equivalent circuit.
R1 RC R1 RC R1 RC
RS = 0
VCC (ideally)
R2 RE R2 RE R2 RE
(a) (b) (c)
17
Fig 9.12a Example 9.2.
VCC
RC
R1 CC2
CC1
Q1 RL
R2
RE CB
18
Fig 9.12b Example 9.2.
GND
RC
R1
Q1 RL
R2
RE
19
Fig 9.12c-d Example 9.2.
Q1 RC RL
(c)
R1 R2
Q1 RC||RL
(d)
R1||R2
20
Voltage Gain of CE
Q1 RC||RL
R1||R2
vout vout ic RC RL
ic = ib RC||RL ic rC where rC RC RL
vin ib
Q1 vin ie re
r'e
vout ir r
R1||R2 Av c C C
vin ie re re
21
Fig 9.13 Example 9.4. (1)
+20 V Transform the base circuit to its
Thevenin equivalent.
R2 20kΩ
Vth VCC 20V
R1 RC R1 R2 170kΩ
150k 12k 2.353V
Rth R1 R2 20kΩ 150kΩ
RL 17.65kΩ
hFE = 200 50k
R2
RE Vth VBE 2.353V 0.7V
20k IB
2.2k Rth (hFE 1) RE 17.65kΩ 201 2.2kΩ
3.595μA
22
Fig 9.13 Example 9.4. (2)
+20 V I C hFE I B 200 3.595μA 718.9μA
I E hFE 1 I B 201 3.595μA 722.5μA
VCE VCC I C RC I E RE
R1 RC
20V 718.9μA 12kΩ 722.5μA 2.2kΩ
150k 12k
9.784V active
RL 25mV 25mV
re 34.6Ω
hFE = 200 50k IE 722.5μA
rC RC RL 12kΩ 50kΩ 9.677kΩ
R2
20k RE rC 9.677kΩ
2.2k Av 279.7
re 34.6Ω
23
Fig 9.14 Example 9.5. (1)
+10 V
Transform the base circuit to its
Thevenin equivalent.
R2 4.7kΩ
RC Vth VCC 10V
R1 R1 R2 22.7kΩ
1.5k
18k 2.070V
Rth R1 R2 4.7kΩ 18kΩ
RL
hFE = 30 3.727kΩ
hfe = 200 5k
R2
4.7k RE Vth VBE 2.070V 0.7V
IB
1.2k Rth (hFE 1) RE 3.727kΩ 311.2kΩ
33.49μA
24
Fig 9.14 Example 9.5. (2)
+10 V I C hFE I B 30 33.49μA 1.005mA
I E hFE 1 I B 31 33.49μA 1.038mA
VCE VCC I C RC I E RE
RC 10V 1.005mA 1.5kΩ 1.038mA 1.2kΩ
R1 1.5k
18k 7.247V active
hFE = 30 RL re 25mV 25mV 24.08Ω
5k IE 1.038mA
hfe = 200 rC RC RL 1.5kΩ 5kΩ 1.154kΩ
R2
4.7k RE Av
rC
1.154kΩ
47.91
1.2k re 24.08Ω
25
CE Current Gain
iout
Ai
iin
Ai is always less than hfe due to two factors:
1.The input ac current is divided between
the transistor and the biasing network.
2.The output collector current is divided
between the collector resistor and the
load.
26
Power Gain
Ap Ai Av
Example 9.7 The amplifier shown in Fig. 9.5 has
values of Av = 45.3 and Ai = 20. Determine the
power gain (Ap) of the amplifier and the output
power when Pin = 80 W.
Ap AAv 2 4 . 0
i 0 53 9 6
Pot A P 9 6 8 μ 7 . 8 W
u pi
n 0 0 W 24 m
27
The Effects of Loading
RC RL RC RL
3k 12k 3k 6k
R1||R2 r'e=25 R1||R2 r'e=25
rC RC RL 2.4kΩ rC RC RL 2kΩ
rC rC
Av 96 Av 80
re re
The lower the load resistance is, the lower the voltage gain.
28
Example 9.8
The load in Fig. 9.16 is open. Calculate the
open-load voltage gain of the circuit.
rC RC 3kΩ
rC 3kΩ
Av 120 (max. gain)
re 25Ω
29
Calculating Amp.
Input Impedance
VCC
Z in R1 R2 Z in(base)
R1
DC: RIN(base) hFE 1 RE
hFE RE
R2
Zin Zin(base) AC: Z in(base) h fe 1 re
h fe re
Biasing circuit
30
Fig 9.17 Example 9.9.
+10 V
RC
R1 1.5k
18k
hFE = 30 RL Z in(base) h fe re
5k
hfe = 200
200 24Ω 4.8kΩ
R2
Zin Zin(base) RE
4.7k
1.2k Zin R1 R2 Zin(base)
18kΩ 4.7kΩ 4.8kΩ
Q1
RC RL 2.1kΩ
1.5k 5k
R1 R2
Zin Zin(base)
18k 4.7k
r'e = 24
hfe = 200 31
Calculating the Value of Ai
iout
ic
iin ib
Q1 RC v RL
out
vin
R1 R2
Zin Zin(base)
i i vin iin Zin ib Zin(base)
Ai out h fe c
iin ib ib Zin(base) ib h fe 1 re
iin
vout ic RL RC ic rC iout RL Zin Zin
ic rC Z in rC
iout Ai h fe
RL Z in(base) RL
32
Example 9.10
Calculate the value of Ai for the circuit shown in Fig.
9.17.
RC RL
Q1
1.5k 5k
R1 R2
Zin Zin(base)
18k 4.7k
r'e = 24
hfe = 200
Z in rC
Z in(base) h fe re 200 24Ω 4.8kΩ Ai h fe
Z in(base) RL
Z in R1 R2 Z in(base) 2.1kΩ
2.1kΩ 1.15kΩ
200
rC RC RL 1.15kΩ 4.8kΩ 5kΩ
20.2 33
Multistage Amp.
Gain Calculations
AvT Av1 Av 2 Av 3 Procedure:
AiT Ai1 Ai 2 Ai 3 1. Do dc analysis
2. Find r’e for each stage
ApT AvT AiT
3. Find rC for each stage
4. Using r’e and rC to find Av
for each stage
Input impedance of next stage is the load of current stage.
(Zin of next stage is RL of current stage)
34
Fig 9.18 Example 9.11. (1)
+15V
R3 R7
R1 5k R5 5k
CC1 22k 15k
Q1 CC2 Q2 CC3 RL
10k
R2 R4 R6 R8
CB1 CB2 hFE = 150
3.3k 1k 2.5k 1k
hfe = 200
Determine Av of the 1st The input impedance of the 2nd stage:
stage. Assume that r’e
for the 1st stage is 19.8 Zin(base) h fe 1 re 20117.4 3.497kΩ
and r’e for the 2nd stage is
found to be 17.4 . For Z in R5 R6 Z in ( base ) 1.329kΩ
the 2nd stage, hfe is 200.
35
Fig 9.18 Example 9.11. (2)
+15V
R3 R7
R1 5k R5 5k
CC1 22k 22k
Q1 CC2 Q2 CC3 RL
10k
R2 R4 R6 R8
CB1 CB2 hFE = 150
3.3k 1k 3.3k 1k
hfe = 200
rC R3 Zin 5kΩ 1.33kΩ=1.05kΩ
Finally, Av for the 1st stage is found as
rC 1.05kΩ
Av 53.03
re 19.8Ω
36
Example 9.12. (1)
Determine the value of AvT for the amplifier in Figure
9.18.
rC for the 2nd stage can be found as
rC R7 RL 3.33kΩ
Av for the 2nd stage is found as
rC 3.33kΩ
Av 191.38
re 17.4Ω
AvT Av1 Av 2 53.03 191.38 10.15 103
37
Fig 9.19 The swamped CE amplifier
and its ac equivalent ckt.
+VCC Swamped amplifier is an
amplifier that uses a partially
bypassed emitter resistance to
RC increase ac emitter resistance.
R1 Also referred to as a gain-
C1 stabilized amplifier.
Q1 C2 RL
R2 rE rC
Q1
R1//R2
RE CB rE
38
Av of Swamped Amp.
rC
Q1
vout ic rC
Av
R1//R2
rE vin ie re rE
rC
vout Av
re rE
ic = acib rC
vin Q1
R1//R2 ib r'e
rE
39
Fig 9.20 Example 9.13. (1)
+10V
R2 4.7kΩ
Vth VCC 10V 2.070V
R1 R2 22.7kΩ
RC Rth R1 R2 18kΩ 4.7kΩ 3.727kΩ
R1 1.5k
18k Vth VBE
IB
hFE = 200 RL Rth hFE 1 rE RE
hfe = 150 10k
2.070V 0.7V
R2 rE
4.7k 300 3.727kΩ 2011210Ω
5.550μA
RE
910
CB I C hFE I B 200 5.550μA
1.110mA
I E hFE 1 I B 201 5.550μA
1.116mA 40
Fig 9.20 Example 9.13. (2)
+10V VCE VCC I C RC I E rE RE
10V 1.110mA 1.5kΩ 1.116mA 1210Ω
RC 6.985V (active)
R1 1.5k
18k 25mV 25mV
re 22.41Ω
hFE = 200 RL IE 1.116mA
hfe = 150 10k
R2 rE rC RC RL 1.304kΩ
4.7k 300
rC 1.304kΩ
RE Av 4.046
910
CB re rE 22.41Ω 300Ω
41
Example 9.14
Determine the change in gain for the amplifier in Example
9.13 when r’e doubles in value.
rC 1.304kΩ
Av 3.782
re rE 44.82Ω 300Ω
Av 4.046 3.782 0.2639
Swamping improves the gain stability of a CE
amplifier when rE >> r’e.
42
The Effect of Swamping on Zin
c
b
Z in(base) h fe 1 re
r'e
Zin(base)
h fe re e c
b
Zin(base) h fe 1 re rE
r'e
Zin(base)
h fe re rE e
rE
43
Fig 9.22 Gain stabilization.
rE
RE RE
Av -rC / r’e -rC / (r’e+rE)
Zin(base) hfer’e hfe(r’e+rE)
Advantage Higher values of Av than Relatively stable Av.
the swamped amplifier. Much smaller distortion.
Disadvantage Relatively unstable values Lower Av than the
of Av. standard amplifier.
44
The Hybrid Equivalent Model
I1 I2
1 2
Two-Port
V1 System V2
1' 2'
Hybrid model is derived from two-port system.
45
Six Circuit-Parameter Models
for Two-Port Systems
Independent Dependent Circuit Parameters
Variables Variables
I1, I2 V1, V2 Impedance Z
V1, V2 I1, I2 Admittance Y
V1, I2 I1, V2 Inverse Hybrid g
I1, V2 V1, I2 Hybrid h
V2, I2 V1, I1 Transmission T
Inverse Transmission
V1, I1 V2, I2 T’
46
Equations for Hybrid Model
V1 h11I1 h12V2
I 2 h21I1 h22V2
Let V1 = Vi, I1 = Ii, V2 = Vo, and I2 = Io.
Then
Vi h11Ii h12Vo
I o h21Ii h22Vo
47
Equivalent Circuit for
Hybrid Model
Ii Io
1 2
hi
Vi hrVo hfIi ho Vo
1' 2'
Vi h11I i h12Vo hi I i hrVo
I o h21I i h22Vo h f I i hoVo
48
h-Parameters
Vi Vi
h11 h12
Ii Vo 0 Vo Ii 0
Io Io
h21 h22
Ii Vo 0 Vo Ii 0
h11 = hi = Input Resistance
h12 = hr = Reverse Transfer Voltage Ratio
h21 = hf = Forward Transfer Current Ratio
h22 = ho = Output Admittance
49
h-Parameters for CE Amp.
• hie = the base input impedance
• hfe = the base-to-collector current gain
• hoe = the output admittance
• hre = the reverse voltage feedback ratio
vbe hieib hre vce
ic h feib hoe vce
50
Hybrid Model for
CE Configuration
ib ic
b c
ic hie
ib c hfeib hoe
b hrevce
ie vbe vce
ie
e
e
vin ic
hie (output shorted) hoe (input open)
ib vce May be
neglected.
ic vbe
h fe (output shorted) hre (input open)
ib vce
51
h-parameters of 2N3904
52
Hybrid Model without hre and hoe
b c
ib ic
hie hfeib h fe ac
hie hfe 1 re hfe re Z in(base)
ie
c c
ic ic h fe rC
acib acib Av
ac+1)r'e hie
b b
ib ib
r'e Zin rC
ie ie Ai h fe
hie RL
e e
53
Determining h-Parameter Values
Use geometric means if given max. and min.
values.
hie hie(min) hie(max)
h fe h fe(min) h fe(max)
See examples 9.18 and 9.19.
54
Summary
• AC concepts
• Roles of capacitors in amplifiers
• Common-emitter ac equivalent
circuit
• Amplifier gain
• Gain and impedance calculations
• Swamped amplifiers
• h-parameters
55
