PROBLEMS

Computer Simulations Problems Case E B C Mode

Problems identified by this icon are intended to 1 0 0.7 0.7
demonstrate the value of using SPICE simulation to verify 2 0 0.8 0.1
hand analysis and design, and to investigate important issues 3 −0.7 0 1.0
such as allowable signal swing and amplifier nonlinear 4 −0.7 0 −0.6
distortion. Instructions to assist in setting up simulations for 5 1.3 2.0 5.0
all the indicated problems can be found in the corresponding 6 0 0 5.0
files on the website. Note that if a particular parameter value
is not specified in the problem statement, you are to make a
reasonable assumption.
In this table, 0 indicates the reference terminal to which the
Section 4.1: Device Structure and Physical black (negative) probe of the voltmeter is connected. For
Operation each case, identify the mode of operation of the transistor.

4.1 The terminal voltages of various npn transistors are 4.2 Two transistors, fabricated with the same technology
measured during operation in their respective circuits with but having different junction areas, when operated at a
the following results (in volts): base-emitter voltage of 0.75 V, have collector currents of

problems with green numbers are considered essential; * = difficult problem; ** = more difficult; *** = very challenging
= simulation; D = design problem;
 282 Chapter 4 Bipolar Junction Transistors (BJTs)

and the collector is connected to a negative supply of −5 V

PROBLEMS

0.5 mA and 2 mA. Find IS for each device. What are the
relative junction areas? via a 8.2-k resistor, find the collector voltage, the emitter
current, and the base voltage.
4.3 In this problem, we contrast two BJT integrated-circuit
fabrication technologies: For the “old” technology, a typical
4.10 A pnp power transistor operates with an
npn transistor has IS = 2 × 10−15 A, and for the “new”
emitter-to-collector voltage of 5 V, an emitter current of 5 A,
technology, a typical npn transistor has IS = 2 × 10−18 A.
and VEB = 0.8 V. For β = 20, what base current is required?
CHAPTER 4

These typical devices have vastly different junction areas and

What is IS for this transistor? Compare the emitter–base
base width. For our purpose here we wish to determine the
junction area of this transistor with that of a small-signal
vBE required to establish a collector current of 1 mA in each
transistor that conducts iC = 1 mA with vEB = 0.70 V. How
of the two typical devices. Assume active-mode operation.
much larger is it?
4.4 In a particular BJT, the base current is 10 µA, and the
collector current is 800 µA. Find β and α for this device. 4.11 In a particular technology, a small BJT operating at
vBE = 30VT conducts a collector current of 200 µA. What
4.5 An npn transistor of a type whose β is specified to is the corresponding saturation current? For a transistor
range from 50 to 300 is connected in a circuit with emitter in the same technology but with an emitter junction
grounded, collector at + 10 V, and a current of 10 µA that is 32 times larger, what is the saturation current?
injected into the base. Calculate the range of collector and What current will this transistor conduct at vBE = 30VT ?
emitter currents that can result. What is the maximum power What is the base–emitter voltage of the latter transistor
dissipated in the transistor? (Note: Perhaps you can see why at iC = 1 mA? Assume active-mode operation in all
this is a bad way to establish the operating current in the cases.
collector of a BJT.)
4.6 Measurements made on a number of transistors 4.12 Two transistors have EBJ areas as follows: AE1 =
operating in the active mode with iE = 1 mA indicate base 200 µm × 200 µm and AE 2 = 0.4 µm × 0.4 µm. If the two
currents of 10 µA, 20 µA, and 50 µA. For each device, find transistors are operated in the active mode and conduct equal
iC , β, and α. collector currents, what do you expect the difference in their
vBE values to be?
4.7 Using the npn transistor model of Fig. 4.5(b), consider
the case of a transistor for which the base is connected to 4.13 Find the collector currents that you would expect
ground, the collector is connected to a 5-V dc source through for operation at vBE = 700 mV for transistors for which
a 2-k resistor, and a 2-mA current source is connected to −13 −18
IS = 10 A and IS = 10 A. For the transistor with the
the emitter with the polarity so that current is drawn out of larger EBJ, what is the vBE required to provide a collector
−15
the emitter terminal. If β = 100 and IS = 5 × 10 A, find current equal to that provided by the smaller transistor
the voltages at the emitter and the collector and calculate the at vBE = 700 mV? Assume active-mode operation in all
base current. cases.
*4.8 In order to investigate the operation of the npn transis-
tor in saturation using the model of Fig. 4.9, let IS = 10 A,
−15 4.14 Consider an npn transistor whose base–emitter drop is
vBE = 0.7 V, β = 100, and ISC /IS = 100. For each of three 0.76 V at a collector current of 5 mA. What current will it
values of vCE (namely, 0.4 V, 0.3 V, and 0.2 V), find vBC , iBC , conduct at vBE = 0.70 V? What is its base–emitter voltage for
iBE , iB , iC , and iC /iB . Present your results in a table. Also find iC = 5 µA?
vCE that results in iC = 0.
4.15 Find the values of β that correspond to α values of 0.5,
4.9 Consider the pnp large-signal model of Fig. 4.11(b) 0.8, 0.9, 0.95, 0.98, 0.99, 0.995, and 0.999.
−14
applied to a transistor having IS = 10 A and β = 50. If
the emitter is connected to ground, the base is connected to 4.16 Find the values of α that correspond to β values of 1,
a current source that pulls 10 µA out of the base terminal, 2, 10, 20, 50, 100, 200, 500, and 1000.

problems with green numbers are considered essential; * = difficult problem; ** = more difficult; *** = very challenging
= simulation; D = design problem;
 Problems 283

*4.17 For a transistor with α close to unity, show that if α

CHAPTER 4
*4.23 Use Eqs. (4.14), (4.15), and (4.16) to show
changes by a small per-unit amount (α/α), the correspond- that an npn transistor operated in saturation exhibits a
ing per-unit change in β is given approximately by collector-to-emitter voltage, VCEsat , given by
    
β α ISC 1 + β forced
β VCEsat = VT ln
β α IS 1 − β forced /β
Now, for a transistor whose nominal β is 100, find the Use this relationship to evaluate VCEsat for β forced = 50, 10, 5,

PROBLEMS
percentage change in its α value corresponding to a drop in 1, and 0 for a transistor with β = 100 and with a CBJ area
its β of 10%. 100 times that of the EBJ. Present your results in a table.
−15
4.18 A BJT is specified to have IS = 5 × 10 A and β that 4.24 A pnp transistor has vEB = 0.7 V at a collector current
falls in the range of 50 to 200. If the transistor is operated of 1 mA. What do you expect vEB to become at iC = 10 mA?
in the active mode with vBE set to 0.700 V, find the expected At iC = 100 mA?
range of iC , iB , and iE .
4.25 A pnp transistor modeled with the circuit in Fig. 4.11
(b) is connected with its base at ground, collector at –2.0 V,
4.19 Measurements of VBE and two terminal currents taken
and a 1-mA current is injected into its emitter. If the transistor
on a number of npn transistors operating in the active
is said to have β = 10, what are its base and collector
mode are in the following table. For each, calculate the
currents? In which direction do they flow? If IS = 10−15 A,
missing current value as well as α, β, and IS as indicated by
what voltage results at the emitter? What does the collector
the table.
current become if a transistor with β = 1000 is substituted?
(Note: The fact that the collector current changes by less than
Transistor a b c d e 10% for a large change in β illustrates that this is a good way
to establish a specific collector current.)
VBE (mV) 700 690 580 780 820
IC (mA) 1.000 1.000 10.10 4.26 While Fig. 4.5 provides four possible large-signal
IB (µA) 10 5 120 1050 equivalent circuits for the npn transistor, only two equivalent
IE (mA) 1.020 0.235 75.00 circuits for the pnp transistor are provided in Fig. 4.11.
α Supply the missing two.
β
4.27 By analogy to the npn case shown in Fig. 4.9, give the
IS
equivalent circuit of a pnp transistor in saturation.

4.20 When operated in the active mode, a particular npn Section 4.2: Current–Voltage Characteristics
BJT conducts a collector current of 1 mA and has vBE = 0.7 V
4.28 For the circuits in Fig. P4.28, assume that the transis-
and iB = 10 µA. Use these data to create specific transistor
tors have very large β. Some measurements have been made
models of the form shown in Figs. 4.5(a) to (d).
on these circuits, with the results indicated in the figure. Find
D 4.21 Consider an npn transistor operated in the active the values of the other labeled voltages and currents.
mode and represented by the model of Fig. 4.5(d). Let the
4.29 Measurements on the circuits of Fig. P4.29 produce
transistor be connected as indicated by the equivalent circuit
labeled voltages as indicated. Find the value of β for each
shown in Fig. 4.6(b). Calculate the values of RB and RC
transistor.
that will establish a collector current IC of 0.5 mA and a
collector-to-emitter voltage VCE of 1 V. The BJT is specified D 4.30 Design the circuit in Fig. P4.30 to establish a current
to have β = 50 and IS = 5 × 10−15 A, and VCC = 5 V. of 0.5 mA in the emitter and a voltage of −0.5 V at the
collector. The transistor vEB = 0.64 V at IE = 0.1 mA, and
4.22 An npn transistor has a CBJ with an area 100 times
β = 100. To what value can RC be increased while the
that of the EBJ. If IS = 10−15 A, find the voltage drop
collector current remains unchanged?
across EBJ and across CBJ when each is forward biased
and conducting a current of 1 mA. Also find the forward D 4.31 Design the circuit in Fig. P4.31 to establish IC =
current each junction would conduct when forward biased 0.5 mA and VC = 0 V. The transistor exhibits vBE of 0.7 V
with 0.5 V. at iC = 1 mA, and β = 100.
 284 Chapter 4 Bipolar Junction Transistors (BJTs)
PROBLEMS

+5V

5.6 k

V3 9.1 k
I5
20 k V7
CHAPTER 4

V4
4V
V2 0V 0.7 V
2.4 k I6
10 k 3k

–5V
(a) (b) (c) (d)

Figure P4.28

7V

6.3 V
45 k
+ 3.0 V
200 k 27 k⍀
2k 750 ⍀ 1.5 k

(a) (b) (c)

Figure P4.29

2.5 V
1.5 V

RE
RC
IC
VC

RC
RE

2.5 V Figure P4.30 1.5 V Figure P4.31

problems with green numbers are considered essential; * = difficult problem; ** = more difficult; *** = very challenging
= simulation; D = design problem;
 Problems 285

3V

CHAPTER 4
4.32 A BJT whose emitter current is fixed at 1 mA has a
base–emitter voltage of 0.70 V at 25°C. What base–emitter
voltage would you expect at 0°C? At 100°C?

4.33 For a particular npn transistor operating at a vBE of

680 mV and IC = 1 mA, the iC –vCE characteristic has a slope RB 10 k
−5
of 0.8 × 10 . To what value of output resistance does this
correspond? What is the value of the Early voltage for this

PROBLEMS
transistor? For operation at 10 mA, what would the output
resistance become? VC

4.34 Measurements of the iC –vCE characteristic of a 1k

small-signal transistor operating at vBE = 710 mV show that
iC = 1.1 mA at vCE = 5 V and that iC = 1.3 mA at vCE = 15 V.
What is the corresponding value of iC near saturation? At
what value of vCE is iC = 1.2 mA? What is the value of the
Figure P4.36
Early voltage for this transistor? What is the output resistance
that corresponds to operation at vBE = 710 mV? 4.37 A very simple circuit for measuring β of an npn
4.35 For the circuit in Fig. P4.35 let VCC = 10 V, RC = 1 k, transistor is shown in Fig. P4.37. In a particular design, VCC
and RB = 10 k. The BJT has β = 50. Find the value of VBB is provided by a 9-V battery; M is a current meter with a
that results in the transistor operating 50-µA full scale and relatively low resistance that you can
neglect for our purposes here. Assuming that the transistor
(a) in the active mode with VC = 2 V; has VBE = 0.7 V at IE = 1 mA, what value of RC would
(b) at the edge of saturation; establish a resistor current of 1 mA? Now, to what value of
(c) deep in saturation with β forced = 10. β does a meter reading of full scale correspond? What is β if
the meter reading is 1/5 of full scale? 1/10 of full scale?
Assume VBE  0.7 V.
VCC

VCC
RC
M
VBB IC RC

VC
RB

Figure P4.37

Figure P4.35 4.38 Repeat Exercise 4.13 for the situation in which the
power supplies are reduced to ±2.5 V.
D 4.39 The table of standard values for resistors with 5%
4.36 The pnp transistor in the circuit in Fig. P4.36 has tolerance in Appendix J shows that the closest values to those
β = 50. Show that the BJT is operating in the saturation found in the design of Example 4.2 are 5.1 k and 6.8 k.
mode and find β forced and VC . To what value should RB be For these values, use approximate calculations (e.g., VBE 
increased in order for the transistor to operate at the edge of 0.7 V and α  1) to determine the values of collector current
saturation? and collector voltage that are likely to result.
 286 Chapter 4 Bipolar Junction Transistors (BJTs)
PROBLEMS

4.40 For each of the circuits shown in Fig. P4.40, find 4.43 A particular pnp transistor operating at an emitter
the emitter, base, and collector
 voltages and currents. Use current of 0.5 mA at 20°C has an emitter–base voltage of
β = 50, but assume VBE  = 0.8 V independent of current 692 mV.
level.
(a) What does vEB become if the junction temperature rises
1.5 V 1.5 V to 50°C?
(b) If the transistor is operated at a fixed emitter–base
CHAPTER 4

voltage of 700 mV, what emitter current flows at 20°C?

2.7 k 2k At 50°C?

4.44 Consider a transistor for which the base–emitter

voltage drop is 0.7 V at 10 mA. What current flows for
Q1 Q2 vBE = 0.5 V? Evaluate the ratio of the slopes of the iC –vBE
curve at vBE = 700 mV and at vBE = 500 mV. The large ratio
confirms the point that the BJT has an “apparent threshold”
2.7 k 2k at vBE  0.5 V.

4.45 Use Eq. (4.18) to plot iC versus vCE for an npn transistor
−15
having IS = 10 A and VA = 100 V. Provide curves for
1.5 V 1.5 V
vBE = 0.65, 0.70, 0.72, 0.73, and 0.74 volts. Show the
(a) (b) characteristics for vCE up to 15 V.
3V 3V
*4.46 In the circuit shown in Fig. P4.46, current source I is
1.1 mA, and at 25°C vBE = 680 mV at iE = 1 mA. At 25°C
with β = 100, what currents flow in R1 and R2 ? What voltage
10 k 8.2 k would you expect at node E? Noting that the temperature
1.0 V 1.5 V coefficient of vBE for IE constant is −2 mV/°C, what is the
TC of vE ? For an ambient temperature of 75°C, what voltage
Q3 Q4 would you expect at node E? Clearly state any simplifying
assumptions you make.

5.6 k 4.7 k

R2
68 k
(c) (d)

Figure P4.40

4.41 The current ICBO of a small transistor is measured to be

R1
10 nA at 25°C. If the temperature of the device is raised to
6.8 k
125°C, what do you expect ICBO to become?
4.42 Augment the model of the npn BJT shown in E
Fig. 4.19(a) by a current source representing ICBO . Assume
that ro is very large and thus can be neglected. In terms of I
this addition, what do the terminal currents iB , iC , and iE
become? If the base lead is open-circuited while the emitter
is connected to ground, and the collector is connected to a
positive supply, find the emitter and collector currents. Figure P4.46

problems with green numbers are considered essential; * = difficult problem; ** = more difficult; *** = very challenging
= simulation; D = design problem;
 Problems 287

CHAPTER 4
4.47 For a BJT having an Early voltage of 50 V, what is its 4.52 A single measurement indicates the emitter voltage of
output resistance at 1 mA? At 100 µA? the transistor in the circuit
 of Fig. P4.52 to be 1.0 V. Under
the assumption that VBE  = 0.7 V, what are VB , IB , IE , IC , VC ,
4.48 Give the pnp equivalent circuit models that correspond
β, and α ?
to those shown in Fig. 4.19 for the npn case.

4.49 A BJT operating at iB = 10 µA and iC = 1.0 mA 2.5 V

undergoes a reduction in base current of 1.0 µA. When vCE

PROBLEMS
is held constant, the corresponding reduction in collector
current is 0.08 mA. What are the values of β and the 10 k
incremental β or β ac that apply? If the base current is
increased from 10 µA to 12 µA and vCE is increased from VE
8 V to 10 V, what collector current results? Assume VA =
100 V. VB
D *4.50 Consider the circuit of Fig. P4.35 for the 100 k
case VBB = VCC . If the BJT is saturated, use the equivalent
VC
circuit of Fig. 4.21 to derive an expression for β forced in
  10 k
terms of VCC and RB /RC . Also derive an expression for
the total power dissipated in the circuit. For VCC = 5 V,
design the circuit so that it operates at a forced β as 2.5 V
close to 10 as possible while limiting the power dissi-
pation to no larger than 20 mW. Use 1% resistors (see Figure P4.52
Appendix J).
4.53 For the circuit in Fig. P4.53, find VB , VE , and VC
for RB = 100 k, 10 k, and 1 k. Let β = 100.
Section 4.3: BJT Circuits at DC
4.51 The transistor in the circuit of Fig. P4.51 has a very 3
high β. Find VE and VC for VB (a) +2.0 V, (b) +1.7 V, and (c)
0 V.

5V

10 k
VB
VC

VE

Figure P4.53
10 k

4.54 For the circuits in Fig. P4.54, find values for the
labeled node voltages and branch currents. Assume β to be
Figure P4.51 very high.
 288 Chapter 4 Bipolar Junction Transistors (BJTs)

3V 3V
PROBLEMS

*4.55 Repeat the analysis of the circuits in Problem 4.54

using β = 100. Find all the labeled node voltages and branch
currents.
3.6 k 3.6 k
4.56 Design the circuit in Fig. P4.56 to obtain IE = 0.2 mA,
V2 V3
VE = +2 V, and VC = +5 V. Design for IB2 = 0.1 mA. Use
43 k standard 5% resistors (refer to Table J.1 in Appendix J). The
CHAPTER 4

transistor has VBE = 0.7 V and β = 100.

I4
V1 9V
4.7 k
0.5 mA

RC
3V
RB1
(a) (b)

3V 3V VC

3.6 k 6.2 k IB2

VE
V7 V8
0.75 V RB2 RE
43 k
IE
110 k
V6
V5 V9

4.7 k 10 k Figure P4.56

4.57 For the circuit in Fig. P4.57, find VB and VE for vI =

3V 3V 0 V, −2 V, +2.5 V, and +5 V. The BJTs have β = 50.

(c) (d) 2.5 V

3V

6.2 k
180 k
V11

V10

V12
300 k
10 k
2.5 V

Figure P4.57
3V

(e) 4.58 The transistor in the circuit of Fig. P4.51 has a very
high β. Find the highest value of VB for which the transistor
Figure P4.54 still operates in the active mode. Also, find the value of

problems with green numbers are considered essential; * = difficult problem; ** = more difficult; *** = very challenging
= simulation; D = design problem
 Problems 289

CHAPTER 4
VB for which the transistor operates in saturation with a D 4.61 Consider the circuit in Fig. P4.51 with the base
forced β of 3. voltage VB obtained using a voltage divider across the 5-V
supply. Assuming the transistor β to be very large (i.e.,
*4.59 Consider the operation of the circuit shown in
ignoring the base current), design the voltage divider to
Fig. P4.59 for VB at –1 V, 0 V, and +1 V. Assume that β is
obtain VB = 1.5 V. Design for a 0.1-mA current in the voltage
very high. What values of VE and VC result? At what value
divider. Now, if the BJT β = 100, analyze the circuit to
of VB does the emitter current reduce to one-tenth of its value
determine the collector current and the collector voltage.
for VB = 0 V? For what value of VB is the transistor just at

PROBLEMS
the edge of conduction? (vBE = 0.5 V) What values of VE and D 4.62 Design a circuit using a pnp transistor for which
VC correspond? For what value of VB does the transistor reach α  1 using two resistors connected appropriately to ±3 V
the edge of saturation? What values of VC and VE correspond? so that IE = 0.5 mA and VBC = 1 V. What exact values of RE
Find the value of VB for which the transistor operates in and RC would be needed? Now, consult a table of standard
saturation with a forced β of 2. 5% resistor values (e.g., that provided in Appendix J) to
select suitable practical values. What values of resistors
3V
have you chosen? What are the values of IE and VBC that
result?
1k
4.63 In the circuit shown in Fig. P4.63, the transistor has
VC β = 40. Find the values of VB , VE , and VC . If RB is raised
to 100 k, what voltages result? With RB = 100 k, what
VB value of β would return the voltages to the values first
calculated?
VE

1k 3V

3V RE
Figure P4.59 2.2 k

VE
4.60 For the transistor shown in Fig. P4.60, assume α 1
and vBE = 0.5 V at the edge of conduction. What are the
VB
values of VE and VC for VB = 0 V? For what value of VB does
the transistor cut off? Saturate? In each case, what values of RB
20 k VC
VE and VC result?

+5 V RC
2.2 k

4 mA
3V
VC
Figure P4.63
1k
VB 4.64 In the circuit shown in Fig. P4.63, the transistor has
β = 50. Find the values of VB , VE , and VC , and verify that the
VE transistor is operating in the active mode. What is the largest
value that RC can have while the transistor remains in the
2 mA 1k active mode?

D *4.65 Design the circuit in Fig. P4.65 so that a current

of 1 mA is established in the emitter and a voltage of −1 V
–5 V
appears at the collector. The transistor used has a nominal β
Figure P4.60 of 100. However, the β value can be as low as 50 and as high
 290 Chapter 4 Bipolar Junction Transistors (BJTs)

3V
PROBLEMS

as 150. Your design should ensure that the specified emitter

current is obtained when β = 100 and that at the extreme
values of β the emitter current does not change by more 9.1 k
than 10% of its nominal value. Also, design for as large a 5.1 k
value for RB as possible. Give the values of RB , RE , and RC to V2
the nearest kilohm. What is the expected range of collector V1
V5
Q1
current and collector voltage corresponding to the full range
CHAPTER 4

of β values? 100 k V3 Q2

+5V
V4
9.1 k
4.3 k
E

3V

Figure P4.67

D *4.68 Using β = ∞, design the circuit shown in

C
Fig. P4.68 so that the emitter currents of Q1 , Q2 , and Q3
are 0.5 mA, 0.5 mA, and 1 mA, respectively, and V3 = 0,
–5V V5 = −2 V, and V7 = 1 V. For each resistor, select the nearest
Figure P4.65 standard value utilizing the table of standard values for 5%
resistors in Appendix J. Now, for β = 100, find the values of
D 4.66 The pnp transistor in Fig. P4.66 has β = 50. Find the V3 , V4 , V5 , V6 , and V7 .
value for RC that gives VC = +2 V. What happens if the
**4.69 All the transistors in the circuits of Fig. P4.69 are
transistor is replaced with another having β = 100? Give the
specified to have a minimum β of 50. Find approximate
value of VC in the latter case.
values for the collector voltages and calculate forced β for
each of the transistors. (Hint: Begin by assuming that all
3V transistors are operating in saturation, and then verify the
assumption.)

5V

R3
R2 R5
V4

Q2 V7

V3
Q1 Q3

V2 V5
Figure P4.66 V6
R4
R1 R6
*4.67 For the circuit shown in Fig. P4.67, find the labeled
node voltages for:
5V
(a) β = ∞
(b) β = 100 Figure P4.68

problem with green numbers are considered essential; * = difficult problem; ** = more difficult; *** = very challenging
= simulation; D = design problem
 Problems 291

CHAPTER 4
5V

5V 5V

PROBLEMS
20

5V

Figure P4.69