Neamen D. Microelectronics: Circuit Analysis and Design
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458 Part 1 Semiconductor Devices and Basic Applications
current
i
C
if the total instantaneous collector current is
i
C
≥ 0.1
mA and the
total instantaneous C–E voltage is in the range
1 ≤ v
CE
≤ 21
V.
6.37 For the circuit in Figure P6.20, the transistor parameters are
β = 100
and
V
A
= 100
V. The values of
R
C
,
R
E
, and
R
L
are as shown in the figure.
Design a bias-stable circuit to achieve the maximum undistorted swing in
the output voltage if the total instantaneous C–E voltage is to remain in
the range
1 ≤ v
CE
≤ 8
V and the minimum collector current is to be
i
C
(min) = 0.1
mA.
6.38 In the circuit in Figure P6.22 with transistor parameters
β = 180
and
V
A
=∞
, redesign the bias resistors
R
1
and
R
2
to achieve maximum sym-
metrical swing in the output voltage and to maintain a bias-stable circuit.
The total instantaneous C–E voltage is to remain in the range
0.5 ≤
v
CE
≤ 4.5
V and the total instantaneous collector current is to be
i
C
≥
0.25 mA.
6.39 For the circuit in Figure P6.24, the transistor parameters are
β = 100
and
V
A
=∞
. (a) Determine the maximum undistorted swing in the output
voltage if the total instantaneous E–C voltage is to remain in the range
1 ≤ v
EC
≤ 9
V. (b) Using the results of part (a), determine the range of col-
lector current.
Section 6.6 Common-Collector (Emitter-Follower) Amplifier
6.40 Figure P6.40 shows the ac equivalent circuit of an emitter follower. (a) The
transistor parameters are
β = 120
and
V
A
=∞
. For
R
E
= 500
, deter-
mine
I
CQ
such that the small-signal voltage gain is
A
v
= 0.92
. (b) Using
the results of part (a), determine the voltage gain if
V
A
= 20
V. (c) Deter-
mine the small-signal output resistance
R
o
for both parts (a) and (b).
6.41 Consider the ac equivalent circuit in Figure P6.40. The transistor parameters
are
β = 80
and
V
A
=∞
. (a) Design the circuit (find
I
CQ
and
R
E
)
such that
R
ib
= 50
k
and
A
v
= 0.95
. (b) Using the results of part (a), find
R
o
.
6.42 For the ac equivalent circuit in Figure P6.42,
R
S
= 1
k
and the transistor
parameters are
β = 80
and
V
A
= 50
V. (a) For
I
CQ
= 2
mA, find
A
v
,
R
i
,
and
R
o
. (b) Repeat part (a) for
I
CQ
= 0.2
mA.
R
ib
V
i
V
o
R
o
R
E
Figure P6.40
V
i
V
o
R
o
R
S
I
Q
Figure P6.42
V
o
R
o
I
Q
V
i
R
S
Figure P6.43
6.43 The circuit and transistor parameters for the ac equivalent circuit in Figure
P6.43 are
R
S
= 0.5
k
,
β = 120
, and
V
A
=∞
. (a) Determine the required
value of
I
Q
to produce a small-signal output resistance of
R
o
= 15
.
(b) Using the results of part (a), find the small-signal voltage gain if
V
A
= 50
V.
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Chapter 6 Basic BJT Amplifiers 459
6.44 The transistor parameters for the circuit in Figure P6.44 are
β = 180
and
V
A
=∞
. (a) Find
I
CQ
and
V
CEQ
. (b) Plot the dc and ac load lines. (c) Cal-
culate the small-signal voltage gain. (d) Determine the input and output
resistances
R
ib
and
R
o
.
6.45 Consider the circuit in Figure P6.45. The transistor parameters are
β = 120
and
V
A
=∞
. Repeat parts (a)–(d) of Problem 6.44.
6.46 For the circuit shown in Figure P6.46, let
V
CC
= 3.3
V,
R
L
= 4k
,
R
1
= 585 k
,
R
2
= 135
k
, and
R
E
= 12
k
. The transistor parameters
are
β = 90
and
V
A
= 60
V. (a) Determine the quiescent values
I
CQ
and
V
ECQ
. (b) Plot the dc and ac load lines. (c) Determine
A
v
= v
o
/v
s
and
A
i
= i
o
/i
s
. (d) Find
R
ib
and
R
o
.
v
o
v
s
V
+
= +9 V
V
–
= – 9 V
R
1
= 10 kΩ
R
S
= 1 kΩ
R
2
=
10 kΩ
C
C1
C
C2
R
E
=
500 Ω
R
L
=
300 Ω
R
o
R
ib
+
–
Figure P6.44
v
o
v
s
–10 V
R
1
= 10 kΩ
R
S
= 5 kΩ
R
2
=
10 kΩ
C
C1
C
C2
R
E
=
2 kΩ
R
C
= 1 kΩ
R
L
=
2 kΩ
R
ib
R
o
+
–
Figure P6.45
v
o
v
s
R
L
R
E
R
2
R
1
C
C2
V
CC
C
C1
i
s
R
o
R
ib
i
o
+
–
Figure P6.46
v
s
v
o
R
B
=
10 kΩ
V
+
= +5 V
V
–
= –5 V
R
L
=
0.5 kΩ
C
C2
I
Eo
= 0.5 mA
C
C1
i
o
i
s
+
–
Figure P6.47
6.47 For the transistor in Figure P6.47,
β = 80
and
V
A
= 150
V. (a) Determine
the dc voltages at the base and emitter terminals. (b) Calculate the small-
signal parameters
g
m
,
r
π
, and
r
o
. (c) Determine the small-signal voltage
gain and current gain. (d) Repeat part (c) if a 2 k
source resistor is in series
with the
v
s
signal source.
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460 Part 1 Semiconductor Devices and Basic Applications
6.49 The transistor parameters for the circuit in Figure P6.49 are
β = 110
,
V
A
= 50
V, and
V
EB
(on) = 0.7
V. (a) Determine the quiescent values
I
CQ
and
V
ECQ
. (b) Find
A
v
,
R
ib
, and
R
o
. (c) The signal source is
v
s
(t) = 2.8 sin ωt
(V). Determine
i
s
(t)
,
i
o
(t)
,
v
o
(t)
, and
v
eb
(t)
.
D6.50 For the transistor in Figure P6.50, the parameters are
β = 100
and
V
A
=∞
.
(a) Design the circuit such that
I
EQ
= 1
mA and the Q-point is in the cen-
ter of the dc load line. (b) If the peak-to-peak sinusoidal output voltage is 4
V, determine the peak-to-peak sinusoidal signals at the base of the transistor
and the peak-to-peak value of
v
s
. (c) If a load resistor
R
L
= 1k
is
connected to the output through a coupling capacitor, determine the peak-
to-peak value in the output voltage, assuming
v
s
is equal to the value deter-
mined in part (b).
6.48 Consider the emitter-follower amplifier shown in Figure P6.48. The transis-
tor parameters are
β = 100
and
V
A
= 100
V. (a) Find the output resistance
R
o
. (b) Determine the small-signal voltage gain for (i)
R
L
= 500
and
(ii)
R
L
= 5k
.
v
o
v
s
v
eb
C
C
V
+
= +5 V
V
–
= –5 V
i
s
R
o
R
ib
i
o
+
–
R
E
=
3.3 kΩ
R
L
=
1 kΩ
+
–
Figure P6.49
v
s
v
o
R
S
= 10 kΩ
V
+
= +3 V
V
–
= –3 V
R
L
R
o
I
Q
=
2 mA
C
C
+
–
Figure P6.48
+
–
R
S
= 0.7 kΩ
R
B
V
CC
= +10 V
R
E
C
C
v
s
v
O
Figure P6.50
v
o
v
s
R
L
=1 kΩ
V
CC
= +10 V
R
E
=
5 kΩ
R
2
=
60 kΩ
R
1
=
40 kΩ
R
S
= 4 kΩ
C
C2
C
C1
R
o
R
is
i
o
i
s
+
–
Figure P6.51
6.51 In the circuit shown in Figure P6.51, determine the range in small-signal
voltage gain
A
v
= v
o
/v
s
and current gain
A
i
= i
o
/i
s
if
β
is in the range
75 ≤ β ≤ 150
.
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Chapter 6 Basic BJT Amplifiers 461
6.52 The transistor current gain
β
in the circuit shown in Figure P6.52 is in the
range
50 ≤ β ≤ 200
. (a) Determine the range in the dc values of
I
E
and
V
E
.
(b) Determine the range in the values of input resistance
R
i
and voltage gain
A
v
= v
o
/v
s
.
6.53 Consider the circuit shown in Figure P6.47. The transistor current gain is in
the range
100 ≤ β ≤ 180
and the Early voltage is
V
A
= 150
V. Determine
the range in small-signal voltage gain if the load resistance varies from
R
L
= 0.5k
to
R
L
= 500 k
.
6.54 For the circuit in Figure P6.54, the parameters are
V
CC
= 5
V and
R
E
= 500
. The transistor parameters are
β = 120
and
V
A
=∞
. (a) De-
sign the circuit to obtain a small-signal current gain of
A
i
= i
o
/i
s
= 10
for
R
L
= 500
. Find
R
1
,
R
2
, and also the small-signal output resistance
R
o
.
(b) Using the results of part (a), determine the current gain for
R
L
= 2
k
.
v
o
v
s
R
L
=
1 kΩ
V
CC
= 9 V
R
E
=
1 kΩ
V
E
R
B
=
100 kΩ
R
S
= 10 kΩ
C
C 2
C
C1
R
i
+
–
Figure P6.52
v
o
v
s
R
L
V
CC
R
E
R
2
R
1
C
C2
C
C1
R
o
i
o
i
s
+
–
Figure P6.54
D6.55 Design an emitter-follower circuit with the configuration shown in Fig-
ure 6.49 such that the input resistance
R
i
, as defined in Figure 6.51, is
120 k
. Assume transistor parameters of
β = 120
and
V
A
=∞
. Let
V
CC
= 5
V and
R
E
= 2k
. Find new values of
R
1
and
R
2
. The Q-point
should be approximately in the center of the load line.
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462 Part 1 Semiconductor Devices and Basic Applications
D6.56 (a) For the emitter-follower circuit in Figure P6.54, assume
V
CC
= 24
V,
β = 75
, and
A
i
= i
o
/i
s
= 8
. Design the circuit to drive an
8
load.
(b) Determine the maximum undistorted swing in the output voltage.
(c) Determine the output resistance
R
o
.
*D6.57 The output of an amplifier can be represented by
v
s
= 4 sin ωt
(V) and
R
S
= 4k
. An emitter-follower circuit, with the configuration shown in
Figure 6.54, is to be designed such that the output signal does not vary by
more than 5 percent when a load in the range
R
L
= 4
to
10 k
is connected
to the output. The transistor current gain is in the range
90 ≤ β ≤ 130
and
the Early voltage is
V
A
=∞
. For your design, find the minimum and max-
imum possible value of the output voltage.
*D6.58 An emitter-follower amplifier, with the configuration shown in Figure 6.54,
is to be designed such that an audio signal given by
v
s
= 5 sin(3000t)
V but
with a source resistance of
R
S
= 10 k
can drive a small speaker. Assume
the supply voltages are
V
+
=+12
V and
V
−
=−12
V. The load, repre-
senting the speaker, is
R
L
= 12
. The amplifier should be capable of de-
livering approximately 1 W of average power to the load. What is the signal
power gain of your amplifier?
Section 6.7 Common-Base Amplifier
6.59 Figure P6.59 is an ac equivalent circuit of a common-base amplifier. The
transistor parameters are
β = 120
,
V
A
=∞
, and
I
CQ
= 1
mA. Determine
(a) the voltage gain
A
v
= V
o
/V
i
, (b) the current gain
A
i
= I
o
/I
i
, (c) the
input resistance
R
i
, and (d) the output resistance
R
o
.
R
i
I
i
I
o
R
C
=
2 kΩ
R
o
V
i
V
o
Figure P6.59
R
i
I
i
I
o
R
C
=
1.5 kΩ
I
Q
=
2 mA
R
L
=
2.5 kΩ
R
oc
R
o
V
i
V
o
Figure P6.60
6.60 The transistor in the ac equivalent circuit shown in Figure P6.60 has
parameters
β = 80
and
V
A
=∞
. Determine (a) the voltage gain
A
v
= V
o
/V
i
, (b) the current gain
A
i
= I
o
/I
i
, and (c) the input resistance
R
i
.
(d) If
V
A
= 80
V, find (i) the output resistance
R
oc
and (ii) the output
resistance
R
o
.
6.61 Consider the ac equivalent common-base circuit shown in Figure P6.61.
The transistor has parameters
β = 110
and
V
A
=∞
. Determine (a) the
voltage gain
A
v
= V
o
/V
i
, (b) the current gain
A
i
= I
o
/I
i
, (c) the input re-
sistance
R
i
, and (d) the output resistance
R
o
.
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Chapter 6 Basic BJT Amplifiers 463
6.62 Figure P6.62 shows an ac equivalent circuit of a common-base amplifier.
The parameters of the transistor are
β = 120
,
V
BE
(on) = 0.7
V, and
V
A
=∞
. (a) Determine the quiescent values
I
CQ
and
V
CEQ
. (b) Find the
small-signal voltage gain
A
v
= V
o
/V
i
. (c) Find the small-signal current
gain
A
i
= I
o
/I
i
.
R
i
I
i
I
Q
=
0.5 mA
I
o
R
C
=
4 kΩ
R
o
V
i
V
o
R
S
= 1 kΩ
Figure P6.61
R
1
= 5 kΩ
V
i
V
o
R
2
=
2.8 kΩ
C
B
I
o
R
L
=
10 kΩ
C
C
I
Q
=
1.5 mA
I
i
Figure P6.62
6.63 The transistor in the circuit shown in Figure P6.63 has
β = 100
and
V
A
=∞
. (a) Determine the quiescent values
I
CQ
and
V
ECQ
. (b) Determine
the small-signal voltage gain
A
v
= v
o
/v
s
.
6.64 Repeat Problem 6.63 with a
100
resistor in series with the
v
s
signal
source.
V
+
= +10 V V
–
= –10 V
v
o
v
s
C
C1
C
C2
R
E
=
10 kΩ
R
C
=
5 kΩ
R
L
=
50 kΩ
+
–
Figure P6.63
v
o
v
s
C
C1
C
C2
R
C
=
2 kΩ
V
+
= +5 VV
–
= –5 V
R
L
=
10 kΩ
I
Q
=
1 mΑ
+
–
Figure P6.65
6.65 Consider the common-base circuit in Figure P6.65. The transistor has
parameters
β = 120
and
V
A
=∞
. (a) Determine the quiescent
V
CEQ
.
(b) Determine the small-signal voltage gain
A
v
= v
o
/v
s
.
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464 Part 1 Semiconductor Devices and Basic Applications
6.66 For the circuit shown in Figure P6.66, the transistor parameters are
β = 100
and
V
A
=∞
. (a) Determine the dc voltages at the collector, base, and
emitter terminals. (b) Determine the small-signal voltage gain
A
v
= v
o
/v
s
.
(c) Find the input resistance
R
i
.
+
–
V
CC
v
o
i
s
v
s
R
E
C
C1
C
C2
R
L
R
C
R
1
R
2
R
S
=
100 kΩ
Figure P6.67
v
o
v
s
C
C1
C
B
C
C2
R
i
R
S
=
50 Ω
R
E
=
1 kΩ
R
B
= 100 k
Ω
I
CC
= 0.5 mA
V
+
= +5 V
R
L
=
1 kΩ
+
–
Figure P6.66
6.67 The parameters of the circuit in Figure P6.67 are
V
CC
= 9
V,
R
L
= 4
k
,
R
C
= 6
k
,
R
E
= 3
k
,
R
1
= 150
k
, and
R
2
= 50
k
. The transistor pa-
rameters are
β = 125
,
V
BE
(on) = 0.7
V, and
V
A
=∞
. The input signal is a
current. (a) Determine the
Q
-point values. (b) Determine the transresistance
function
R
m
= v
o
/i
s
. (c) Find the small-signal voltage gain
A
v
= v
o
/v
s
.
6.68 For the common-base circuit shown in Figure P6.67, let
V
CC
= 5
V,
R
L
= 12
k
, and
R
E
= 500
. The transistor parameters are
β = 100
and
V
A
=∞
. (a) Design the circuit such that the minimum small-signal voltage
gain is
A
v
= v
o
/v
s
= 25
. (b) What are the
Q
-point values? (c) Determine
the small-signal voltage gain if
R
2
is bypassed by a large capacitor.
6.69 Consider the circuit shown in Figure P6.69. The transistor has parameters
β = 60
and
V
A
=∞
. (a) Determine the quiescent values of
I
CQ
and
V
CEQ
.
(b) Determine the small-signal voltage gain
A
v
= v
o
/v
s
.
v
o
v
s
C
C
C
B
R
S
=
50 Ω
R
B
= 100 kΩ
I
Q
= 1.0 mA
R
L
=
2 kΩ
+
–
V
+
= +5 V
Figure P6.69
*D6.70 A photodiode in an optical transmission system, such as shown in Fig-
ure 1.40, can be modeled as a Norton equivalent circuit with
i
s
in parallel
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Chapter 6 Basic BJT Amplifiers 465
with
R
S
as shown in Figure P6.67. Assume that the current source is given
by
i
s
= 2.5 sin ωtμA
and
R
S
= 50 k
. Design the common-base circuit of
Figure P6.67 such that the output voltage is
v
o
= 5 sin ωt mV
. Assume
transistor parameters of
β = 120
and
V
A
=∞
. Let
V
CC
= 5
V.
6.71 In the common-base circuit shown in Figure P6.71, the transistor is a
2N2907A, with a nominal dc current gain of
β = 80
. (a) Determine
I
CQ
and
V
ECQ
. (b) Using the h-parameters (assuming h
re
= 0
), determine the range
in small-signal voltage gain
A
v
= v
o
/v
s
. (c) Determine the range in input
and output resistances
R
i
and
R
o
.
*D6.72 In the circuit of Figure P6.71, let
V
EE
= V
CC
= 5
V,
β = 100
,
V
A
=∞
,
R
L
= 1k
, and
R
S
= 0
. (a) Design the circuit such that the small-signal
voltage gain is
A
v
= v
o
/v
s
= 25
and
V
ECQ
= 3
V. (b) What are the values
of the small-signal parameters
g
m
,
r
π
, and
r
o
?
Section 6.9 Multistage Amplifiers
6.73 Consider the ac equivalent circuit in Figure P6.73. The transistor parameters
are
β
1
= 120
,
β
2
= 80
,
V
A1
= V
A2
=∞
, and
I
CQ1
= I
CQ2
= 1
mA. (a)
Find the small-signal voltage gain
A
v1
= V
o1
/V
i
. (b) Determine the small-
signal voltage gain
A
v2
= V
o2
/V
o1
. (c) Find the overall small-signal voltage
gain
A
v
= V
o2
/V
i
.
R
i
+
–
+
–
+
–
V
CC
=
25 V
V
EE
=
20 V
C
C1
C
C2
v
o
v
s
R
E
=
10 kΩ
R
C
=
6.5 kΩ
R
S
= 1 kΩ
R
L
=
5 kΩ
R
o
+
–
Figure P6.71
R
C
=
4 kΩ
R
E
=
1 kΩ
V
o2
V
o1
V
i
Q
2
Q
1
Figure P6.73
R
C1
=
4 kΩ
R
E2
=
4 kΩ
V
o1
V
i
V
o2
Q
1
Q
2
Figure P6.74
6.74 The transistor parameters in the ac equivalent circuit shown in Figure P6.74
are
β
1
= β
2
= 100
,
V
A1
= V
A2
=∞
,
I
CQ1
= 0.5
mA, and
I
CQ2
= 2
mA.
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466 Part 1 Semiconductor Devices and Basic Applications
(a) Find the small-signal voltage gain
A
v1
= V
o1
/V
i
. (b) Determine the
small-signal voltage gain
A
v2
= V
o2
/V
o1
. (c) Determine the overall small-
signal voltage gain
A
v
= V
o2
/V
i
.
*6.75 The parameters for each transistor in the circuit shown in Figure P6.75 are
β = 100
and
V
A
=∞
. (a) Determine the small-signal parameters
g
m
,
r
π
,
and
r
o
for both transistors. (b) Determine the small-signal voltage gain
A
v1
= v
o1
/v
s
, assuming
v
o1
is connected to an open circuit, and determine
the gain
A
v2
= v
o
/v
o1
. (c) Determine the overall small-signal voltage gain
A
v
= v
o
/v
s
. Compare the overall gain with the product
A
v1
· A
v2
, using the
values calculated in part (b).
+
–
R
1
=
80 kΩ
R
2
=
20 kΩ
R
C1
=
2 kΩ
C
C1
C
C3
v
o1
C
C2
C
E1
R
C2
=
4 kΩ
V
CC
= +10 V
R
E2
=
0.5 kΩ
R
3
=
85 kΩ
R
4
=
15 kΩ
R
E1
=
1 kΩ
Q
1
C
E2
v
o
v
s
R
L
=
4 kΩ
Q
2
+
–
Figure P6.75
R
1
=
67.3 kΩ
R
2
=
12.7 kΩ
R
C1
=
10 kΩ
C
C1
C
C3
C
C2
C
E
V
CC
= +12 V
R
E2
=
1.6 kΩ
R
L
=
250 Ω
R
3
=
15 kΩ
R
4
=
45 kΩ
R
E1
=
2 kΩ
Q
1
v
o
v
s
Q
2
R
is
R
o
+
–
Figure P6.76
*6.76 Consider the circuit shown in Figure P6.76 with transistor parameters
β = 120
and
V
A
=∞
. (a) Determine the small-signal parameters
g
m
,
r
π
,
and
r
o
for both transistors. (b) Plot the dc and ac load lines for both tran-
sistors. (c) Determine the overall small-signal voltage gain
A
v
= v
o
/v
s
.
(d) Determine the input resistance
R
is
and the output resistance
R
o
. (e) De-
termine the maximum undistorted swing in the output voltage.
6.77 The transistor parameters for the circuit in Figure P6.77 are
β
1
= 120
,
β
2
= 80
,
V
BE1
(on) = V
BE2
(on) = 0.7
V, and
V
A1
= V
A2
=∞
. (a) Deter-
mine the quiescent collector current in each transistor. (b) Find the small-
signal voltage gain
A
v
= v
o
/v
s
. (c) Determine the input and output resis-
tances
R
ib
and
R
o
.
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Chapter 6 Basic BJT Amplifiers 467
*6.78 For each transistor in Figure P6.78, the parameters are
β = 100
and
V
A
=∞
. (a) Determine the Q-point values for both
Q
1
and
Q
2
. (b) Deter-
mine the overall small-signal voltage gain
A
v
= v
o
/v
s
. (c) Determine the
input and output resistances
R
is
and
R
o
.
6.79 An ac equivalent circuit of a Darlington pair configuration is shown in Fig-
ure P6.79. The transistor parameters are
β
1
= 120
,
β
2
= 80
,
V
A1
= 80
V,
and
V
A2
= 50
V. Determine the output resistance
R
o
for (a)
I
C2
= I
Bias
= 1
mA; (b)
I
C2
= 1
mA,
I
Bias
= 0.2
mA; and (c)
I
C2
= 2
mA,
I
Bias
= 0
.
+
–
V
CC
= 9 V
v
o
R
o
R
ib
Q
1
Q
2
v
s
50 Ω
0.5 kΩ
5 V
+
–
Figure P6.77
v
s
R
2
=
125 kΩ
R
1
=
335 kΩ
R
C
=
2.2 kΩ
R
E2
=
1 kΩ
C
C
C
E
v
o
R
is
R
o
Q
2
Q
1
+
–
V
CC
= +10 V
Figure P6.78
AC ground
Q
1
Q
2
I
C 2
R
o
I
Bias
Figure P6.79
Section 6.10 Power Considerations
6.80 Consider the circuit in Figure 6.31. The circuit and transistor parameters
are given in Exercise Ex 6.5. (a) Determine the average power dissipated
in the transistor,
R
C
, and
R
E
for
v
s
= 0
. (b) Repeat part (a) for
v
s
= 100 sin ω t
(mV).
6.81 Consider the circuit shown in Figure 6.38. The transistor parameters are
given in Exercise Ex 6.7. (a) Calculate the average power dissipated in the
transistor,
R
C
, and
R
E
for
v
s
= 0
. (b) Determine the maximum undistorted
signal power that can be delivered to
R
C
for the condition that
i
C
≥ 0
and
0.5 ≤ v
CE
≤ 9
V.
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