# Chaper 5

```Fundamentals of Microelectronics
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CH5
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Why Microelectronics?
Basic Physics of Semiconductors
Diode Circuits
Physics of Bipolar Transistors
Bipolar Amplifiers
Physics of MOS Transistors
CMOS Amplifiers
Operational Amplifier As A Black Box
1
Chapter 5
Bipolar Amplifiers
 5.1 General Considerations
 5.2 Operating Point Analysis and Design
 5.3 Bipolar Amplifier Topologies
 5.4 Summary and Additional Examples
2
Bipolar Amplifiers
CH5 Bipolar Amplifiers
3
Voltage Amplifier
 In an ideal voltage amplifier, the input impedance is infinite
and the output impedance zero.
 But in reality, input or output impedances depart from their
ideal values.
CH5 Bipolar Amplifiers
4
Input/Output Impedances
Rx 
Vx
ix
 The figure above shows the techniques of measuring input
and output impedances.
CH5 Bipolar Amplifiers
5
Input Impedance Example I
vx
ix
 r
 When calculating input/output impedance, small-signal
analysis is assumed.
CH5 Bipolar Amplifiers
6
Impedance at a Node
 When calculating I/O impedances at a port, we usually
ground one terminal while applying the test source to the
other terminal of interest.
CH5 Bipolar Amplifiers
7
Impedance at Collector
R out  ro
 With Early effect, the impedance seen at the collector is
equal to the intrinsic output impedance of the transistor (if
emitter is grounded).
CH5 Bipolar Amplifiers
8
Impedance at Emitter
vx
1

ix
gm 
R out 
1
gm
(V A   )
 The impedance seen at the emitter of a transistor is
approximately equal to one over its transconductance (if
the base is grounded).
CH5 Bipolar Amplifiers
9
1
r
Three Master Rules of Transistor Impedances
 Rule # 1: looking into the base, the impedance is r if
emitter is (ac) grounded.
 Rule # 2: looking into the collector, the impedance is ro if
emitter is (ac) grounded.
 Rule # 3: looking into the emitter, the impedance is 1/gm if
base is (ac) grounded and Early effect is neglected.
CH5 Bipolar Amplifiers
10
Biasing of BJT
 Transistors and circuits must be biased because (1)
transistors must operate in the active region, (2) their smallsignal parameters depend on the bias conditions.
CH5 Bipolar Amplifiers
11
DC Analysis vs. Small-Signal Analysis
 First, DC analysis is performed to determine operating point
and obtain small-signal parameters.
 Second, sources are set to zero and small-signal model is
used.
CH5 Bipolar Amplifiers
12
Notation Simplification
 Hereafter, the battery that supplies power to the circuit is
replaced by a horizontal bar labeled Vcc, and input signal is
simplified as one node called Vin.
CH5 Bipolar Amplifiers
13
 The microphone is connected to the amplifier in an attempt
to amplify the small output signal of the microphone.
 Unfortunately, there’s no DC bias current running thru the
transistor to set the transconductance.
CH5 Bipolar Amplifiers
14
 The base of the amplifier is connected to Vcc, trying to
establish a DC bias.
 Unfortunately, the output signal produced by the
microphone is shorted to the power supply.
CH5 Bipolar Amplifiers
15
Biasing with Base Resistor
IB 
V CC  V BE
RB
, IC  
V CC  V BE
RB
 Assuming a constant value for VBE, one can solve for both
IB and IC and determine the terminal voltages of the
transistor.
 However, bias point is sensitive to  variations.
CH5 Bipolar Amplifiers
16
Improved Biasing: Resistive Divider
VX 
R2
R1  R 2
I C  I S exp(
V CC
R2
V CC
R1  R 2 V T
 Using resistor divider to set VBE, it is possible to produce
an IC that is relatively independent of  if base current is
small.
CH5 Bipolar Amplifiers
17
)
Accounting for Base Current
IC
 V Thev  I B R Thev 
 I S exp 

VT


 With proper ratio of R1 and R2, IC can be insensitive to ;
however, its exponential dependence on resistor deviations
makes it less useful.
CH5 Bipolar Amplifiers
18
Emitter Degeneration Biasing
 The presence of RE helps to absorb the error in VX so VBE
stays relatively constant.
 This bias technique is less sensitive to  (I1 >> IB) and VBE
variations.
CH5 Bipolar Amplifiers
19
Design Procedure
 Choose an IC to provide the necessary small signal
parameters, gm, r, etc.
 Considering the variations of R1, R2, and VBE, choose a
value for VRE.
 With VRE chosen, and VBE calculated, Vx can be
determined.
 Select R1 and R2 to provide Vx.
20
Self-Biasing Technique
 This bias technique utilizes the collector voltage to provide
the necessary Vx and IB.
 One important characteristic of this technique is that
collector has a higher potential than the base, thus
guaranteeing active operation of the transistor.
CH5 Bipolar Amplifiers
21
Self-Biasing Design Guidelines
RB
(1)
R C 
(2)
 V BE  V CC  V BE

 (1) provides insensitivity to  .
 (2) provides insensitivity to variation in VBE .
CH5 Bipolar Amplifiers
22
Summary of Biasing Techniques
CH5 Bipolar Amplifiers
23
PNP Biasing Techniques
 Same principles that apply to NPN biasing also apply to
PNP biasing with only polarity modifications.
CH5 Bipolar Amplifiers
24
Possible Bipolar Amplifier Topologies
 Three possible ways to apply an input to an amplifier and
three possible ways to sense its output.
 However, in reality only three of six input/output
combinations are useful.
CH5 Bipolar Amplifiers
25
Study of Common-Emitter Topology



Analysis of CE Core
Inclusion of Early Effect
Emitter Degeneration
Inclusion of Early Effect
CE Stage with Biasing
26
Common-Emitter Topology
CH5 Bipolar Amplifiers
27
Small Signal of CE Amplifier
Av 

v out
RC
v out
v in
 g m v   g m v in
Av   g m R C
CH5 Bipolar Amplifiers
28
Limitation on CE Voltage Gain
Av 
I C RC
VT
Av 
V RC
VT
Av 
V CC  V BE
VT
 Since gm can be written as IC/VT, the CE voltage gain can
be written as the ratio of VRC and VT.
 VRC is the potential difference between VCC and VCE, and
VCE cannot go below VBE in order for the transistor to be in
active region.
CH5 Bipolar Amplifiers
29
CH5 Bipolar Amplifiers
30
I/O Impedances of CE Stage
R in 
vX
iX
 r
R out 
vX
iX
 RC
 When measuring output impedance, the input port has to
be grounded so that Vin = 0.
CH5 Bipolar Amplifiers
31
CH5 Bipolar Amplifiers
32
Inclusion of Early Effect
Av   g m ( R C || rO )
R out  R C || rO
 Early effect will lower the gain of the CE amplifier, as it
appears in parallel with RC.
CH5 Bipolar Amplifiers
33
Intrinsic Gain
A v   g m rO
Av 
VA
VT
 As RC goes to infinity, the voltage gain reaches the product
of gm and rO, which represents the maximum voltage gain
the amplifier can have.
 The intrinsic gain is independent of the bias current.
CH5 Bipolar Amplifiers
34
Current Gain
AI 
i out
AI

CE
i in
 Another parameter of the amplifier is the current gain,
which is defined as the ratio of current delivered to the load
to the current flowing into the input.
 For a CE stage, it is equal to .
CH5 Bipolar Amplifiers
35
Emitter Degeneration
 By inserting a resistor in series with the emitter, we
“degenerate” the CE stage.
 This topology will decrease the gain of the amplifier but
improve other aspects, such as linearity, and input
impedance.
CH5 Bipolar Amplifiers
36
Small-Signal Model
Av  
Av  
g m RC
1  g m RE
RC
1
gm
 RE
 Interestingly, this gain is equal to the total load resistance
to ground divided by 1/gm plus the total resistance placed in
series with the emitter.
CH5 Bipolar Amplifiers
37
Emitter Degeneration Example I
Av  
RC
1
g m1
 R E || r 2
 The input impedance of Q2 can be combined in parallel with
RE to yield an equivalent impedance that degenerates Q1.
CH5 Bipolar Amplifiers
38
Emitter Degeneration Example II
R C || r 2
Av  
1
 RE
g m1
 In this example, the input impedance of Q2 can be
combined in parallel with RC to yield an equivalent collector
impedance to ground.
CH5 Bipolar Amplifiers
39
Input Impedance of Degenerated CE Stage
VA  
v X  r i X  R E (1   ) i X
R in 
vX
iX
 r  (   1) R E
 With emitter degeneration, the input impedance is
increased from r to r + (+1)RE; a desirable effect.
CH5 Bipolar Amplifiers
40
Output Impedance of Degenerated CE Stage
VA  
v
v in  0  v      g m v 
 r
R out 
vX
iX

 R E  v   0

 RC
 Emitter degeneration does not alter the output impedance
in this case. (More on this later.)
CH5 Bipolar Amplifiers
41
Capacitor at Emitter
 At DC the capacitor is open and the current source biases
the amplifier.
 For ac signals, the capacitor is short and the amplifier is
degenerated by RE.
CH5 Bipolar Amplifiers
42
Example: Design CE Stage with Degeneration as a Black Box
VA  
i out  g m
Gm 
i out
v in
v in
1
1  ( r  g m ) R E

gm
1  g m RE
 If gmRE is much greater than unity, Gm is more linear.
CH5 Bipolar Amplifiers
43
Degenerated CE Stage with Base Resistance
VA  
v out

v in
v out

v in
Av 
CH5 Bipolar Amplifiers
v A v out
.
v in v A
  RC
r  (   1) R E  R B
 RC
1
gm
 RE 
RB
 1
44
Input/Output Impedances
VA  
R in 1  r  (   1) R E
R in 2  R B  r 2  (   1) R E
R out  R C
 Rin1 is more important in practice as RB is often the output
impedance of the previous stage.
CH5 Bipolar Amplifiers
45
Emitter Degeneration Example III
 ( R C || R1 )
Av 
1
RB
 R2 
gm
 1
R in  r   (   1) R 2
R out  R C || R1
CH5 Bipolar Amplifiers
46
Output Impedance of Degenerated Stage with VA< 
R out  1  g m ( R E || r ) rO  R E || r
R out  rO  ( g m rO  1)( R E || r )
R out  rO 1  g m ( R E || r ) 
 Emitter degeneration boosts the output impedance by a
factor of 1+gm(RE||r).
 This improves the gain of the amplifier and makes
the
circuit a better current source.
CH5 Bipolar Amplifiers
47
Two Special Cases
1 ) R E  r
R out  rO (1  g m r )   rO
2 ) R E  r
R out  (1  g m R E ) rO
CH5 Bipolar Amplifiers
48
Analysis by Inspection
R out  R 1 || R out 1
R out 1  1  g m ( R 2 || r ) rO
R out  1  g m ( R 2 || r ) rO || R 1
 This seemingly complicated circuit can be greatly simplified
by first recognizing that the capacitor creates an AC short
to ground, and gradually transforming the circuit to a
known topology.
CH5 Bipolar Amplifiers
49
Example: Degeneration by Another Transistor
R out  1  g m 1 ( rO 2 || r 1 ) rO 1
 Called a “cascode”, the circuit offers many advantages that
are described later in the book.
CH5 Bipolar Amplifiers
50
Study of Common-Emitter Topology



Analysis of CE Core
Inclusion of Early Effect
Emitter Degeneration
Inclusion of Early Effect
CE Stage with Biasing
51
 Since the microphone has a very low resistance that
connects from the base of Q1 to ground, it attenuates the
base voltage and renders Q1 without a bias current.
CH5 Bipolar Amplifiers
52
Use of Coupling Capacitor
 Capacitor isolates the bias network from the microphone at
DC but shorts the microphone to the amplifier at higher
frequencies.
CH5 Bipolar Amplifiers
53
DC and AC Analysis
A v   g m ( R C || rO )
R in  r || R B
R out  R C || rO
 Coupling capacitor is open for DC calculations and shorted
for AC calculations.
CH5 Bipolar Amplifiers
54
 Since the speaker has an inductor, connecting it directly to
the amplifier would short the collector at DC and therefore
push the transistor into deep saturation.
CH5 Bipolar Amplifiers
55
Still No Gain!!!
 In this example, the AC coupling indeed allows correct
biasing. However, due to the speaker’s small input
impedance, the overall gain drops considerably.
CH5 Bipolar Amplifiers
56
CE Stage with Biasing
Av   g m ( R C || rO )
R in  r || R1 || R 2
R out  R C || rO
CH5 Bipolar Amplifiers
57
CE Stage with Robust Biasing
VA  
 RC
Av 
1
 RE
gm
R in  r  (   1) R E  || R1 || R 2
R out  R C
CH5 Bipolar Amplifiers
58
Removal of Degeneration for Signals at AC
Av   g m R C
R in  r || R 1 || R 2
R out  R C
 Capacitor shorts out RE at higher frequencies and
removes degeneration.
CH5 Bipolar Amplifiers
59
Complete CE Stage
CH5 Bipolar Amplifiers
 R C || R L
Av 
R s || R1 || R 2
1
 RE 
gm
 1
60
Summary of CE Concepts
CH5 Bipolar Amplifiers
61
Common Base (CB) Amplifier
 In common base topology, where the base terminal is
biased with a fixed voltage, emitter is fed with a signal, and
collector is the output.
CH5 Bipolar Amplifiers
62
CB Core
Av  g m R C
 The voltage gain of CB stage is gmRC, which is identical to
that of CE stage in magnitude and opposite in phase.
CH5 Bipolar Amplifiers
63
Av 

IC
VT
.R C
V CC  V BE
VT
 To maintain the transistor out of saturation, the maximum
voltage drop across RC cannot exceed VCC-VBE.
CH5 Bipolar Amplifiers
64
Simple CB Example
A v  g m R C  17 . 2
R 1  22 . 3 K 
R 2  67 . 7 K 
CH5 Bipolar Amplifiers
65
Input Impedance of CB
R in 
1
gm
 The input impedance of CB stage is much smaller than that
of the CE stage.
CH5 Bipolar Amplifiers
66
Practical Application of CB Stage
 To avoid “reflections”, need impedance matching.
 CB stage’s low input impedance can be used to create a
match with 50 .
CH5 Bipolar Amplifiers
67
Output Impedance of CB Stage
R out  rO || R C
 The output impedance of CB stage is similar to that of CE
stage.
CH5 Bipolar Amplifiers
68
CB Stage with Source Resistance
Av 
RC
1
gm
 RS
 With an inclusion of a source resistor, the input signal is
attenuated before it reaches the emitter of the amplifier;
therefore, we see a lower voltage gain.
 This is similar to CE stage emitter degeneration; only the
phase is reversed.
CH5 Bipolar Amplifiers
69
Practical Example of CB Stage
 An antenna usually has low output impedance; therefore, a
correspondingly low input impedance is required for the
following stage.
CH5 Bipolar Amplifiers
70
Realistic Output Impedance of CB Stage
R out 1  1  g m ( R E || r ) rO   R E || r

R out  R C || R out 1
 The output impedance of CB stage is equal to RC in parallel
with the impedance looking down into the collector.
CH5 Bipolar Amplifiers
71
Output Impedance of CE and CB Stages
 The output impedances of CE, CB stages are the same if
both circuits are under the same condition. This is because
when calculating output impedance, the input port is
grounded, which renders the same circuit for both CE and
CB stages.
CH5 Bipolar Amplifiers
72
Fallacy of the “Old Wisdom”
 The statement “CB output impedance is higher than CE
output impedance” is flawed.
CH5 Bipolar Amplifiers
73
CB with Base Resistance
v out
v in

RE 
RC
RB
 1

gm
 With an addition of base resistance, the voltage gain
CH5 Bipolar Amplifiers
1
74
Comparison of CE and CB Stages with Base
Resistance
 The voltage gain of CB amplifier with base resistance is
exactly the same as that of CE stage with base resistance
and emitter degeneration, except for a negative sign.
CH5 Bipolar Amplifiers
75
Input Impedance of CB Stage with Base Resistance
vX
iX

r  R B
 1

1
gm

RB
 1
 The input impedance of CB with base resistance is equal to
1/gm plus RB divided by (+1). This is in contrast to
degenerated CE stage, in which the resistance in series
with the emitter is multiplied by (+1) when seen from the
base.
CH5 Bipolar Amplifiers
76
Input Impedance Seen at Emitter and Base
CH5 Bipolar Amplifiers
77
Input Impedance Example
RX 
1
gm2
1  1
RB 




  1  g m1   1 
 To find the RX, we have to first find Req, treat it as the base
resistance of Q2 and divide it by (+1).
CH5 Bipolar Amplifiers
78
Bad Bias Technique for CB Stage
 Unfortunately, no emitter current can flow.
CH5 Bipolar Amplifiers
79
Still No Good
 In haste, the student connects the emitter to ground,
thinking it will provide a DC current path to bias the
amplifier. Little did he/she know that the input signal has
been shorted to ground as well. The circuit still does not
amplify.
CH5 Bipolar Amplifiers
80
Proper Biasing for CB Stage
R in 
v out
CH5 Bipolar Amplifiers
v in

1
gm
|| R E
1
1  1  g m R E  R S
g m RC
81
Reduction of Input Impedance Due to RE
 The reduction of input impedance due to RE is bad because
it shunts part of the input current to ground instead of to Q1
(and Rc) .
CH5 Bipolar Amplifiers
82
Creation of Vb
 Resistive divider lowers the gain.
 To remedy this problem, a capacitor is inserted from base to
ground to short out the resistor divider at the frequency of
interest.
CH5 Bipolar Amplifiers
83
Example of CB Stage with Bias
 For the circuit shown above, RE >> 1/gm.
 R1 and R2 are chosen so that Vb is at the appropriate value
and the current that flows thru the divider is much larger
than the base current.
 Capacitors are chosen to be small compared to 1/gm at the
required frequency.
CH5 Bipolar Amplifiers
84
Emitter Follower (Common Collector Amplifier)
CH5 Bipolar Amplifiers
85
Emitter Follower Core
 When the input is increased by V, output is also increased
by an amount that is less than V due to the increase in
collector current and hence the increase in potential drop
across RE.
 However the absolute values of input and output differ by a
VBE.
CH5 Bipolar Amplifiers
86
Small-Signal Model of Emitter Follower
VA  
v out
v in
1

1
r

1
  1 RE
RE

RE 
1
gm
 As shown above, the voltage gain is less than unity and
positive.
CH5 Bipolar Amplifiers
87
Unity-Gain Emitter Follower
VA  
Av  1
 The voltage gain is unity because a constant collector
current (= I1) results in a constant VBE, and hence Vout
follows Vin exactly.
CH5 Bipolar Amplifiers
88
Analysis of Emitter Follower as a Voltage Divider
VA  
CH5 Bipolar Amplifiers
89
Emitter Follower with Source Resistance
VA  
v out
v in
CH5 Bipolar Amplifiers

RE 
RE
RS

1
 1 gm
90
Input Impedance of Emitter Follower
VA  
vX
iX
 r  (1   ) R E
 The input impedance of emitter follower is exactly the
same as that of CE stage with emitter degeneration. This
is not surprising because the input impedance of CE with
emitter degeneration does not depend on the collector
resistance.
CH5 Bipolar Amplifiers
91
Emitter Follower as Buffer
 Since the emitter follower increases the load resistance to a
much higher value, it is suited as a buffer between a CE
stage and a heavy load resistance to alleviate the problem
CH5 Bipolar Amplifiers
92
Output Impedance of Emitter Follower
R out
 Rs
1 
 || R E
 

  1 gm 
 Emitter follower lowers the source impedance by a factor of
+1 improved driving capability.
CH5 Bipolar Amplifiers
93
Emitter Follower with Early Effect
Av 
R E || rO
RS
1
R E || rO 

 1 gm
R in  r     1  R E || rO 
 Rs
1 
 || R E || rO
R out  

  1 gm 
 Since rO is in parallel with RE, its effect can be easily
incorporated into voltage gain and input and output
impedance equations.
CH5 Bipolar Amplifiers
94
Current Gain
 There is a current gain of (+1) from base to emitter.
 Effectively speaking, the load resistance is multiplied by
(+1) as seen from the base.
CH5 Bipolar Amplifiers
95
Emitter Follower with Biasing
 A biasing technique similar to that of CE stage can be used
for the emitter follower.
 Also, Vb can be close to Vcc because the collector is also at
Vcc.
CH5 Bipolar Amplifiers
96
Supply-Independent Biasing
 By putting a constant current source at the emitter, the bias
current, VBE, and IBRB are fixed regardless of the supply
value.
CH5 Bipolar Amplifiers
97
Summary of Amplifier Topologies
 The three amplifier topologies studied so far have different
properties and are used on different occasions.
 CE and CB have voltage gain with magnitude greater than
one, while follower’s voltage gain is at most one.
CH5 Bipolar Amplifiers
98
Amplifier Example I
v out
v in
R 2 || R C
R1
 

R1 || R S
1
R1  R S

 RE
 1
gm
 The keys in solving this problem are recognizing the AC
ground between R1 and R2, and Thevenin transformation of
the input network.
CH5 Bipolar Amplifiers
99
Amplifier Example II
v out
v in
 
RC
R S || R1
 1

1
gm

 R2
R1
R1  R S
 Again, AC ground/short and Thevenin transformation are
needed to transform the complex circuit into a simple stage
with emitter degeneration.
CH5 Bipolar Amplifiers
100
Amplifier Example III
R in  r 1  R1  r 2
Av 
1
g m1

 RC
R1
 1

1
gm2
 The key for solving this problem is first identifying Req,
which is the impedance seen at the emitter of Q2 in parallel
with the infinite output impedance of an ideal current
source. Second, use the equations for degenerated CE
stage with RE replaced by Req.
CH5 Bipolar Amplifiers
101
Amplifier Example IV
R C || R1
Av 
1
RS 
gm
 The key for solving this problem is recognizing that CB at
frequency of interest shorts out R2 and provide a ground for
R 1.
 R1 appears in parallel with RC and the circuit simplifies to a
simple CB stage.
CH5 Bipolar Amplifiers
102
Amplifier Example V
 1
1  R B
1 
 || R E  
R in 

 
  1    1 g m 2 
 g m1
 The key for solving this problem is recognizing the
equivalent base resistance of Q1 is the parallel connection
of RE and the impedance seen at the emitter of Q2.
CH5 Bipolar Amplifiers
103
Amplifier Example VI
v out

v in
R out
R E || R 2 || rO
R1

R S || R 1 R1  R S
1
R E || R 2 || rO 

gm
 1
 R S || R1 1 
 || R E || R 2 || rO
 

gm 
  1
 The key in solving this problem is recognizing a DC supply
is actually an AC ground and using Thevenin
transformation to simplify the circuit into an emitter
follower.
CH5 Bipolar Amplifiers
104
Amplifier Example VII

R B1
1 

R in  r 1     1  R E 

  1 gm2 

R out  R C 
RB2
 1
RC 
Av  
R B1
 1
RB2
 1

1

1
gm2
g m3


1
g m3
1
g m1
 Impedances seen at the emitter of Q1 and Q2 can be lumped
with RC and RE, respectively, to form the equivalent emitter
and collector impedances.
CH5 Bipolar Amplifiers
105
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