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Bipolar Junction
Transistors (BJTs)
1
• Bipolar Junction Transistors, BJT, a three
terminal, non-linear electronic device.
• BJT’s are used as amplifiers in analog
electronics.
• BJTs are used as switches in digital
electronics.
• Invented in 1948 by Bardeen, Brattain, and
Shockley at Bell Telephone Labs.
• Popular for three decades before being
overtaken by Field Effect Transistors, FETs.
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A simplified structure of the npn transistor.
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A simplified structure of the pnp transistor
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• Still used in harsh environment and high frequency
applications, also Bi-CMOS applications.
• BJTs have the following four modes of operation.
• The cutoff and saturation modes are used in digital
electronics to obtain a switch.
• The active mode is used in analog electronics to
obtain an amplifier.
Mode
Cuttoff
Active
Reverse-Active
Saturation
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EBJ
Reverse
Forward
Reverse
Forward
CBJ
Reverse
Reverse
Forward
Forward
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Current flow in an npn transistor biased to
operate in the active mode. (Reverse current
components due to drift of thermally generated
minority carriers are not shown.)
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• Ignore the very small drift currents.
• The EBJ is a forward biased pn junction.
• Holes are injected from the base to the emitter
and electrons injected from the emitter to the
base.
• These two components combine to form the
emitter current, iE.
• A highly doped emitter and a lightly doped
base keep the hole component of iE small.
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Profiles of minority-carrier concentrations in the
base and in the emitter of an npn transistor
operating in the active mode: vBE > 0 and vCB ≥ 0.
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• The concentration np(0), using the Law of the
Junction is:
n p (0)  n p 0evBE / VT and n p (W )  0
• The electron diffusion current, In, points in the
positive x-direction.
dn p
n p (0)
 dn p 
, AE  Emitter Area ,
I n  AE (q) Dn  

dx
W
 dx 
 n p (0) 
, (negative means I n flows in the negative x direction)
I n  AE qDn  
 W 
• Recombination of electrons with holes in the base
cause np(x) to deviate a small amount from ideal.
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• The collector current, ic, points in the negative xdirection and is equal in magnitude to In.
iC   I n
AE qDn n p (0)
iC 
, n p (0)  n p 0 e vBE / VT
W
 AE qDn n p 0  vBE / VT
ni2

iC  
e
, n p0 


W
NA


2
A
qD
n
n i
iC  I s e vBE / VT , where I s  E
N AW
• The collector current is directly proportional to the
emitter area, AE, and inversely proportional to the
effective width of the base, W.
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• The base current, iB, is composed of two
components, iB1 and iB2 (iB= iB1+ iB2).
• The first component, iB1, is due to holes injected
into the emitter from the base.
iB1 
AE qD p ni2
N D Lp
e vBE / VT
• The second component, iB2, is due to the
recombination of holes and electrons in the base.
iB 2 
Qn
b
where Qn  Minority carrier charge in base,  b  Minority carrier lifetime
AE qWni2 vBE / VT
iB 2 
e
, Qn  AE q 1 2 n p (0)W 
2 b N A
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• The base current is the sum of these two components
iB  iB1  iB 2
AE qD p ni2 vBE / VT AE qWni2 vBE / VT
iB 
e

e
N D Lp
2 b N A
 AE qD p ni2 AE qWni2  v / V
e BE T
iB  

 N L

2

N
D
p
b
A


2 
 AE qDn ni2  D p N AW
W
e vBE / VT

iB  



 N AW  Dn N D L p 2 b Dn 
v BE / VT
2 
 D p N AW
I
e
iC
W
v
/
V
s
BE
T


iB  I s

e


D N L



 n D p 2 b Dn 
1
 D p N AW
W 

where  

, Common  Emitter current gain
D N L

 n D p 2 b Dn 
2
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• The emitter current, iE, (using KCL) is equal to the
base current plus the collector current.
iE  iC  iB
  1
iC
iE  iC   
   
iC
   1  vBE / VT
 I s e
iE  
  
I s vBE / VT iC

iE  e
 , 
, Common  Base current gain


 1
• α = αF, β = βF forward active mode, αR and βR for
the reverse active mode.
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Summary of the BJT Current-Voltage
Relationships in the Active Mode
iC  I s e vBE / VT
 Is
iB 
 
 
i
I
iE  C   s
 
 vBE / VT
e

 vBE / VT
e

iC  iE
iE
iB  (1   )iE 
 1
iE  (   1)iB
iC
iC   iB

 
1
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

 1
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Large-signal equivalent-circuit models of the npn
BJT operating in the forward active mode.
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• Scale current relations
 F I SE   R I SC  I S
AE I SE  R


, AE and AC  Emitter and Collector Areas
AC I SC  F
Cross-section of an npn BJT.
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Model for the npn transistor when operated in
the reverse active mode (i.e., with the CBJ
forward biased and the EBJ reverse biased).
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The Ebers-Moll (EM) model of the npn
transistor.
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• This structure yields positive values of iC, iE, and iB
in the forward-active mode and is valid for all modes.
iE  iDE   R iDC
iC  iDC   F iDE
iB  (1   F )iDE  (1   R )iDC
• The diode equations for iDE and iDC are as follows.
iDE  I SE (e vBE / VT  1)
iDC  I SC (e vBC / VT  1)
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• Substituting the diode equations into the expressions
for iC, iE, and iB and using the scale current relations
we obtain the following equations.
 IS
iE  
F
 vBE / VT
(e
 1)  I S (e vBC / VT  1)

 I S  vBC / VT
v BE / VT
(e
iC  I S (e
 1)  
 1)
R 
 I S  vBE / VT
 I S  vBC / VT
(e
(e
iB  
 1)  
 1)
 F 
 R 
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• In the forward active mode vBE is between 0.6 V and
0.8 V, and vBC is negative. The exponential terms
containing vBC will be negligibly small and we obtain
 IS


 F
 v BE / VT

1 

iE
 IS 
e
1   

F 


 1

v BE / VT
iC  I S e
 IS 
   1

 R

 I S  v BE / VT
 1
1


iB  
e

I

S
 
R
 F 
 F




• Note that if we ignore the very small second term in
these equations we obtain the relations derived earlier.
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The iC –vCB characteristic of an npn transistor fed with a constant
emitter current IE. The transistor enters the saturation mode of
operation for vCB < –0.4 V, and the collector current diminishes.
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Concentration profile of the minority carriers
(electrons) in the base of an npn transistor operating in
the saturation mode.
Ignoring small terms:
iC  I S e
vBE / VT
 IS
 
 R
 vBC / VT
e

Law of the Junction:
n p (W )  n p 0evBC /VT  0
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Current flow in a pnp transistor biased to operate in the
active mode.
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Large-signal model for the pnp transistor operating in
the active mode.
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Circuit symbols for BJTs.
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Voltage polarities and current flow in transistors
biased in the active mode.
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Figure 5.15 Circuit for Example 5.1.
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Figure E5.10
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Figure E5.11
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The iC –vBE characteristic for an npn
transistor.
iC  I S e
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v BE / VT
31
Effect of temperature on the iC–vBE
characteristic. At a constant emitter current
(broken line), vBE changes by –2 mV/°C.
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• Under normal forward-active and saturation
modes vBE is between 0.6 V and 0.8 V.
• Use vBE ≈ 0.7 V for rapid calculation.
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The iC–vCB characteristics of an npn transistor,
common-base characteristic.
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• Not quite horizontal lines, some increase in iC as vCB is
increased.
• CBJ will breakdown at BVCB0, typically greater than 50 V.
• The collector current in the saturation region (vCB < −0.4 V)
can be obtained using the EM equations.
 I 
iE   S (e vBE / VT  1)  I S (e vBC / VT  1), EM equation
F 
I S (e vBE / VT  1)   F iE   F I S (e vBC / VT  1)
 I 
iC  I S (e vBE / VT  1)   S (e vBC / VT  1), EM equation
R 
 I 
iC   F iE   F I S (e vBC / VT  1)   S (e vBC / VT  1)
R 
 1

iC   F iE  I S 
  F (e vBC / VT  1)
R

 1

iC   F iE  I S 
  F e vBC / VT , Ignoring the minus one.
R


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Common-Emitter Characteristics.
Early Voltage
(a) Conceptual circuit for measuring the iC –vCE characteristics of
the BJT. (b) The iC –vCE characteristics of a practical BJT.
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• The linear dependence of the collector current, iC, on
the collector-emitter voltage, vCE, is called “The Early
Effect”.
iC  I S e
v BE / VT

vCE
1 
VA




• The output resistance, ro
 i


ro   C
 vCE vBE constant 
VA
ro 
I S eVBE / VT
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Large-signal equivalent-circuit models of an npn BJT
operating in the active mode in the common-emitter
configuration.
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Figure 5.21 Common-emitter characteristics. Note that the horizontal scale is expanded
around the origin to show the saturation region in some detail.
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• Large-signal or dc CE current gain, βdc, (hFE in data
books)
 dc 
I CQ
I BQ
• Incremental or ac CE current gain, βac, (hfe in data
books)
 ac 
iC
iB
vCE  constant
• βdc and βac differ by 10% to 20%
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• Typical dependence of β on IC and on temperature in a
modern integrated-circuit npn silicon transistor intended for
operation around 1 mA.
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• An expanded view of the common-emitter
characteristics in the saturation region.
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• βac is high in the active region and low in the
saturation region.
• IC,sat < βFIB
• βForced = IC,sat /IB < βF
• Overdrive factor: βF / βForced
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Figure 5.24 (a) An npn transistor operated in saturation mode with a constant base current IB. (b) The iC–vCE characteristic curve corresponding to
iB = IB. The curve can be approximated by a straight line of slope 1/RCEsat. (c) Equivalent-circuit representation of the saturated transistor. (d) A
simplified equivalent-circuit model of the saturated transistor.
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• Saturation Resistance, RCEsat (~ 3 to 30 ohms)
RCEsat 
vCE
iC
iB  I B
iC  I Csa t
• Model of the saturated transistor
VCEsat  VCEoff  I Csat RCEsat  0.2 V
• Using the EM equations for the saturated BJT one
obtains the following expression for RCEsat.
RCEsat  1 /(10 F I B )
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Figure 5.25 Plot of the normalized iC versus vCE for an npn transistor with F = 100 and
R = 0.1. This is a plot of Eq. (5.47), which is derived using the Ebers-Moll model.
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Figure E5.18
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Table 5.3
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Table 5.3 (Continued)
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Figure 5.26 (a) Basic common-emitter amplifier circuit. (b) Transfer characteristic of the circuit in (a). The amplifier is biased at a point Q, and a
small voltage signal vi is superimposed on the dc bias voltage VBE. The resulting output signal vo appears superimposed on the dc collector voltage
VCE. The amplitude of vo is larger than that of vi by the voltage gain Av.
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• Amplification using the common-emitter (CE)
configuration.
vI (t )  vi (t )  VBE  vbe (t )  VBE  vBE (t )
• Lowercase letters with lowercase subscripts refer to
the ac signal or small–signal component.
• Capital letters with capital subscripts refer to the dc
or constant component of the signal.
• Lowercase letters with capital subscripts refer to the
total signals, dc signal plus the ac signal (small –
signal).
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• The output voltage of the amplifier using the CE
configuration biased to operate at the quiescent
point, Q, in the active region.
vO
vO
vO
vO
 vo  VO  vo  VCE
v I / VT
 VCC  RC iC  VCC  RC I s e
( vi VBE ) / VT
 VCC  RC I s e
vi / VT
VBE / VT
  RC I s e
 VCC  RC I s e

vO   RC ic  VCC  RC I C 
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
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Small-signal Amplification gain, Av
dvO
Av 
dvI
v I VBE

d
v I / VT
Av 
VCC  RC I S e
dvI

v I VBE
VBE / VT
RC I S e
Av  
VT
RC I C
Av  
VT
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Figure 5.27 Circuit whose operation is to be analyzed graphically.
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Figure 5.28 Graphical construction for the determination of the dc base current in the
circuit of Fig. 5.27.
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Figure 5.29 Graphical construction for determining the dc collector current IC and the
collector-to-emitter voltage VCE in the circuit of Fig. 5.27.
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Figure 5.30 Graphical determination of the signal components vbe, ib, ic, and vce when a
signal component vi is superimposed on the dc voltage VBB (see Fig. 5.27).
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Figure 5.31 Effect of bias-point location on allowable signal swing: Load-line A results
in bias point QA with a corresponding VCE which is too close to VCC and thus limits the
positive swing of vCE. At the other extreme, load-line B results in an operating point too
close to the saturation region, thus limiting the negative swing of vCE.
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Figure 5.32 A simple circuit used to illustrate the different modes of operation of the
BJT.
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• Switching using the CE configuration as an inverter.
 VCC , vI  0.5 V, Switch open, cutoff.
vC  
 VCEsat  0.2 V, vI  0.8 V, Switch closed, saturation
• The BJT will be cutoff with vI < 0.5 V.
• The BJT at the edge of saturation (EOS).
vI  VBE
iB 
,
RB
iC   iB ,
vC  VCC  RC iC
• The BJT at the edge of saturation (EOS) will have
vCB = −0.4 V and vBE = 0.7 V, therefore vC will be
0.3 V (using KVL).
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• The collector and base currents at the edge of
saturation (EOS).
I C ( EOS)
VCC  0.3

,
RC
iB ( EOS) 
I C ( EOS)

• The corresponding value of vI required to drive the
transistor to the edge-of-saturation.
VI ( EOS)  I B ( EOS) RB  VBE
• The ratio of IB to IB(EOS) is known as the overdrive
factor.
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Figure 5.33 Circuit for Example 5.3.
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Figure 5.34 Analysis of the circuit for Example 5.4: (a) circuit; (b) circuit redrawn to remind the reader of the convention used in this book to
show connections to the power supply; (c) analysis with the steps numbered.
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Figure 5.35 Analysis of the circuit for Example 5.5. Note that the circled numbers indicate the order of the analysis steps.
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Figure 5.36 Example 5.6: (a) circuit; (b) analysis with the order of the analysis steps indicated by circled numbers.
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Figure 5.37 Example 5.7: (a) circuit; (b) analysis with the steps indicated by circled numbers.
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Figure 5.38 Example 5.8: (a) circuit; (b) analysis with the steps indicated by the circled numbers.
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Figure 5.39 Example 5.9: (a) circuit; (b) analysis with steps numbered.
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Figure 5.40 Circuits for Example 5.10.
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Figure 5.41 Circuits for Example 5.11.
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Figure E5.30
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Figure 5.42 Example 5.12: (a) circuit; (b) analysis with the steps numbered.
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Figure 5.43 Two obvious schemes for biasing the BJT: (a) by fixing VBE; (b) by fixing IB. Both result in wide variations in
IC and hence in VCE and therefore are considered to be “bad.” Neither scheme is recommended.
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Figure 5.44 Classical biasing for BJTs using a single power supply: (a) circuit; (b) circuit with the voltage divider
supplying the base replaced with its Thévenin equivalent.
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Figure 5.45 Biasing the BJT using two power supplies. Resistor RB is needed only if the signal is to be capacitively
coupled to the base. Otherwise, the base can be connected directly to ground, or to a grounded signal source, resulting in
almost total -independence of the bias current.
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Figure 5.46 (a) A common-emitter transistor amplifier biased by a feedback resistor RB. (b) Analysis of the circuit in (a).
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Figure 5.47 (a) A BJT biased using a constant-current source I. (b) Circuit for implementing the current source I.
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Small-signal circuit.
Figure 5.48 (a) Conceptual circuit to illustrate the operation of the transistor as an
amplifier. (b) The circuit of (a) with the signal source vbe eliminated for dc (bias)
analysis.
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Q-(VBE, IC ),
dc bias point or
quiescent point
Figure 5.49 Linear operation of the transistor under the small-signal condition: A small signal
vbe with a triangular waveform is superimposed on the dc voltage VBE. It gives rise to a collector
signal current ic, also of triangular waveform, superimposed on the dc current IC. Here, ic =
gmvbe, where gm is the slope of the iC–vBE curve at the bias point Q.
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• DC currents and voltages, capital letters with capital subscripts.
• DC voltages: VBE, VC, VCE, and VCC.
• DC currents: IC, IE, and IB.
• AC (small-signal) currents and voltages, lowercase letter with
lowercase subscripts.
• AC voltages: vbe, vc, and vce
• AC currents: ic, ie, and ib
• Total currents and voltages, lowercase letters with capital
subscripts.
• Total voltages: vBE = VBE + vbe, vC = VC + vc, and vCE = VCE + vce.
• Total currents: iC = IC + ic, iE = IE +ie, and iB = IB + ib.
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• Small-signal approximation, valid for vbe < 10 mV.
iC  I S e vBE / VT
iC  I S e
VBE  vb e  / VT

iC  I S e
VBE / VT
iC  I C e vb e / VT ,
e
vb e / VT
,
IC  I S e
e ax  1  ax ,
VBE / VT
ax  1
iC  I C 1  vb e VT   I C  I C VT vbe  I C  ic
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• Transconductance, gm, slope of the iC − vBE characteristic at the
quiescent point.
IC
iC

VT
v BE
gm 
iC  I C , v BE VBE
iC  I C  g m vbe
• Small-signal input resistance between the base and emitter,
rπ, looking into the base.
iB 
iC


I C  ic

 IC




 V



T

IC
ic
IC


vbe

iB  I B  ib
 IC
ib  
 V
T

v
r  be 
ib
Microelectronic Circuits - Fifth Edition

 gm 


v

  
vbe
 be




 VT
V

 T
gm
IC
IB
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• Small-signal resistance between base and emitter, looking
into the emitter, re.
iE 
iC


I C  ic

 IC




 V



T

IC
ic
IC


vbe

iE  I E  ie
 IC
ie  
 V
T

v
re  be 
ie

 gm

vbe   



 VT

gm
IC

vbe

V
1
 T 
IE
gm
• Relationship between re and rπ
vbe  ib r  ie re
i 
r   e re    1 re
 ib 
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• Voltage gain, Av
vC  VCC  iC RC  VCC  ( I C  ic ) RC
vC  (VCC  I C RC )  ic RC  VC  vc
vc  ic RC  ( g m vbe ) RC
vc
I C RC
Av 
  g m RC  
vbe
VT
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Figure 5.50 The amplifier circuit of Fig. 5.48(a) with the dc sources (VBE and VCC)
eliminated (short circuited). Thus only the signal components are present. Note that this is a
representation of the signal operation of the BJT and not an actual amplifier circuit.
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Figure 5.51 Two slightly different versions of the simplified hybrid- model for the small-signal
operation of the BJT. The equivalent circuit in (a) represents the BJT as a voltage-controlled
current source (a transconductance amplifier), and that in (b) represents the BJT as a currentcontrolled current source (a current amplifier).
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Figure 5.52 Two slightly different versions of what is known as the T model of the BJT.
The circuit in (a) is a voltage-controlled current source representation and that in (b) is a
current-controlled current source representation. These models explicitly show the
emitter resistance re rather than the base resistance r featured in the hybrid- model.
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Figure 5.53 Example 5.14: (a) circuit; (b) dc analysis; (c) small-signal model.
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Figure 5.54 Signal waveforms in the circuit of Fig. 5.53.
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Figure 5.55 Example 5.16: (a) circuit; (b) dc analysis; (c) small-signal model; (d) small-signal analysis performed directly
on the circuit.
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Figure 5.56 Distortion in output signal due to transistor cutoff. Note that it is assumed that no distortion due to the transistor
nonlinear characteristics is occurring.
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Figure 5.57 Input and output waveforms for the circuit of Fig. 5.55. Observe that this amplifier is noninverting, a property of
the common-base configuration.
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Figure 5.58 The hybrid- small-signal model, in its two versions, with the resistance ro included.
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Figure E5.40
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Table 5.4
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Figure 5.59 Basic structure of the circuit used to realize singlestage, discrete-circuit BJT amplifier configurations.
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Figure E5.41
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Table 5.5
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Figure 5.60 (a) A common-emitter amplifier using the structure of Fig.
5.59. (b) Equivalent circuit obtained by replacing the transistor with its
hybrid- model.
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• Input resistance, Rin
vi
Rin 
 RB || Rib ,
ii
Rin  RB || r ,
Rin  r ,
(since Rib  r )
(normally RB  r )
( Ri  Rin since unilateral )
• Input Voltage, vi
vi  vsig
Rin
,
Rin  Rsig
vi  vsig
RB || r
,
RB || r  Rsig
vi  vsig
r
r  Rsig
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( using voltage division)
(assuming RB  r )
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• Output voltage, vo
vo   g m v (ro || RC || RL ),
(since v  vi )
vo   g m vi (ro || RC || RL )
• Voltage Gain, Av
Av 
vo
vi
Av   g m (ro || RC || RL )
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• Open-circuit voltage Gain, Avo
vo
Avo 
vi R 
L
Avo   g m (ro || RC || )
Avo   g m (ro || RC ),
(typically ro  RC )
Avo   g m RC
• Output resistance, Rout
Rout  RC || ro ,
Rout  RC ,
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( typically ro  RC )
(since unilateral , Ro  Rout )
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• Overall voltage gain, Gv
 vi  vo   vi 
vo
   
 Av
Gv 



vsig  vsig  vi   vsig 


R
||
r
B

 g m (ro || RC || RL ) 
Gv  
 R || r  R 
sig 
 B 
 (ro || RC || RL )
Gv  
, (for the case RB  r )
r  Rsig
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• Overall voltage gain, Gv, is highly dependent on β if Rsig
>> r π, an undesirable property.
• If Rsig << rπ then the overall voltage gain is almost
independent of β.
Gv   g m ( RC || RL || ro ), ( R sig  r and RB  r )
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• Short-circuit current gain, Ais
ios   g m vi ,
vi  v
vi  ii Rin
ios
Ais 
  g m Rin
ii
Ais   g m RB || r ,
Ais   g m r ,
r 
RB  r

gm
Ais   
• The common-emitter configuration provides large current and
voltage gains, but Rin is relatively low and Rout is relatively
high.
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Figure 5.61 (a) A common-emitter amplifier with an emitter resistance Re. (b)
Equivalent circuit obtained by replacing the transistor with its T model.
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• Input resistance, Rin
vi
Rin 
 RB || Rib
ii
vi
Rib  ,
ib
ie
vi
where ib 
and ie 
 1
re  Re
Rib  (   1)( re  Re )
• The input resistance looking into the base, Rib, is (β + 1)
times the total resistance in the emitter. This is known as
the resistance-reflection rule.
Rib ( with Re included ) (   1)( re  Re )

Rib ( without Re )
(   1)re
R
 1  e  1  g m Re
re
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• The voltage gain, Av
vo  ic ( RC || RL )
 ie ( RC || RL )
 vi 
( RC || RL )
  
 re  Re 
vo
Av 
vi

 ( RC || RL )
re  Re
( RC || RL )

,
re  Re
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• The open-circuit voltage gain, Avo, found by setting RL = ∞
Avo  
 RC
re  Re
RC


re 1  Re re
g m RC

, ( g m   re )
1  Re re
g m RC

, ( g m   re  1 re )
1  g m Re
• The open-circuit voltage gain, Avo, is reduced by the factor
(1 + gmRe). The factor by which Rib is increased. This allows
the designer to trade-off gain for input resistance.
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• The output resistance, Rout, is Rout = RC.
• The amplifier is unilateral so Ro = Rout
• The short-circuit current gain, Ais
io
Ais 
ii
ios  io
RL  0
RL  0
ios

ii
  ie
ii  vi Rin
Ais  
 Rin ie
vi

 ( RB || Rib )
re  Re
,
if RB  Rib and since Rib  (   1)( re  Re ) then :
Ais  
 (   1)( re  Re )
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re  Re
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 
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• The overall voltage gain, Gv
vo
vi vo vi
Rin  ( RC || RL )
Gv 

 
 Av  
vsig vsig vi vsig
Rsig  Rin re  Re
Since Rin  RB || Rib , assuming RB  Rib and since Rib  (   1)( re  Re )
Gv  
 ( RC || RL )
Rsig  (   1)( re  Re )
• The gain is lower than that of the CE amplifier because of
the term (β+1)Re in the denominator. However, the gain is
also less sensitive to changes in β, a desirable property.
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• The CE amplifier with emitter resistor can handle larger
input signal without nonlinear distortion, since only a
fraction of the input signal at the base appears between the
base and emitter.
v
re
1


vi
re  Re 1  g m Re
• Thus, for the same vπ, the signal at the input terminal, vi,
can be greater than for the CE amplifier by the factor
(1+gmRe)
• Recall that vπ = vi for the CE amplifier
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Summary of the characteristics of the CE
amplifier with emitter resistor.
• The input resistance Rib is increased by the factor (1 + gmRe).
• The voltage gain from base to collector, Av, is reduced by the
factor (1 + gmRe).
• For the same nonlinear distortion, the input signal vi can be
increased by the factor (1 + gmRe).
• The overall voltage gain is less dependent on the value of β.
• The high-frequency response is significantly improved.
• The reduction in gain is the tradeoff for the other
improvements.
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Figure 5.62 (a) A common-base amplifier using the structure of Fig. 5.59. (b)
Equivalent circuit obtained by replacing the transistor with its T model.
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• The common-base (CB) amplifier, ignoring Early effect.
• The input resistance, Rin = Ri, since unilateral if ro is ignored.
Rin  re
• The voltage gain, Av
vi
vo   ie ( RC || RL ), and ie   , therefore
re
 vi 
vo     ( RC || RL ), so
 re 
vo 
Av 
 ( RC || RL )  g m ( RC || RL )
vi re
• Same as CE amplifier without minus sign.
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• The output resistance, Rout = Ro, ignoring Early effect.
Rout  RC
• The short-circuit current gain Ais.
Ais 
  ie
  ie


ii
 ie
• The overall voltage gain, Gv.
vi
re

vsig
Rsig  re
vo
vi vo
vi
re
Gv 



 Av 
g m ( RC || RL )
vsig vsig vi
vsig
Rsig  re

 ( RC || RL )
Rsig  re
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Summary of Common-Base amplifiers
• Very low input resistance.
• Short-circuit current gain nearly equal to one.
• Open-circuit voltage gain positive with same magnitude as CE.
• Relatively high output resistance, compared to input resistance.
• Excellent high-frequency performance.
• A significant application of the CB amplifier is as a current
buffer.
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Figure 5.63 (a) An emitter-follower circuit based on the structure of Fig. 5.59. (b) Small-signal
equivalent circuit of the emitter follower with the transistor replaced by its T model augmented with
ro. (c) The circuit in (b) redrawn to emphasize that ro is in parallel with RL. This simplifies the
analysis considerably.
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Figure 5.64 (a) An equivalent circuit of the emitter follower obtained from the circuit in Fig. 5.63(c) by reflecting all resistances in the emitter to
the base side. (b) The circuit in (a) after application of Thévenin theorem to the input circuit composed of vsig, Rsig, and RB.
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Figure 5.65 (a) An alternate equivalent circuit of the emitter follower obtained by reflecting all base-circuit resistances to the emitter side. (b) The
circuit in (a) after application of Thévenin theorem to the input circuit composed of vsig, Rsig / ( 1 1), and RB / ( 1 1).
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Figure 5.66 Thévenin equivalent circuit of the output of the emitter follower of Fig. 5.63(a). This circuit can be used to find vo and hence the
overall voltage gain vo/vsig for any desired RL.
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Summary of the common-collector properties
• The common-collector amplifier exhibits a high input
resistance.
• The common-collector amplifier exhibits a low output
resistance.
• The CC amplifier has a voltage gain smaller than, but very
close to unity.
• The CC amplifier is often used as the last stage in a multistage amplifier (voltage buffer).
• The CC amplifier is also used to connect a high-resistance
source to a low-resistance load.
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Summary and Comparisons
• The CE configuration is the best suited for realizing
the bulk of the gain required in an amplifier.
• Including a resistor in the emitter lead of the CE
amplifier provides a number of performance
improvements at the expense of gain reduction.
• The low input resistance of the CB amplifier makes it
useful only in specific applications, such as highfrequency applications and as a current buffer.
• The CC is used as a voltage buffer for connecting a
high-resistance source to a low-resistance load and as
the output stage in a multistage amplifier.
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Table 5.6
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Figure 5.67 The high-frequency hybrid- model.
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Figure 5.68 Circuit for deriving an expression for hfe(s) ; Ic/Ib.
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Figure 5.69 Bode plot for uhfeu.
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Figure 5.70 Variation of fT with IC.
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Table 5.7
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Figure 5.71 (a) Capacitively coupled common-emitter amplifier. (b) Sketch of the magnitude of the gain of the CE amplifier versus frequency.
The graph delineates the three frequency bands relevant to frequency-response determination.
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Figure 5.72 Determining the high-frequency response of the CE amplifier: (a) equivalent circuit; (b) the circuit of (a) simplified at both the input
side and the output side; (c) equivalent circuit with Cm replaced at the input side with the equivalent capacitance Ceq; (d) sketch of the frequencyresponse plot, which is that of a low-pass STC circuit.
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Figure 5.73 Analysis of the low-frequency response of the CE amplifier: (a) amplifier circuit with dc sources removed; (b) the effect of CC1 is
determined with CE and CC2 assumed to be acting as perfect short circuits;
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Figure 5.73 (Continued) (c) the effect of CE is determined with CC1 and CC2 assumed to be acting as perfect short circuits; (d) the effect of CC2 is
determined with CC1 and CE assumed to be acting as perfect short circuits;
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Figure 5.73 (Continued) (e) sketch of the low-frequency gain under the assumptions that CC1, CE, and CC2 do not interact and that their break (or
pole) frequencies are widely separated.
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Figure 5.74 Basic BJT digital logic inverter.
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Figure 5.75 Sketch of the voltage transfer characteristic of the inverter circuit of Fig. 5.74 for the case RB 5 10 kW, RC 5 1 kW,  5 50, and VCC 5
5 V. For the calculation of the coordinates of X and Y, refer to the text.
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Figure 5.76 The minority-carrier charge stored in the base of a saturated transistor can be divided into two components: That in blue produces the
gradient that gives rise to the diffusion current across the base, and that in gray results from driving the transistor deeper into saturation.
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Figure E5.53
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Figure 5.77 The transport form of the Ebers-Moll model for an npn BJT.
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Figure 5.78 The SPICE large-signal Ebers-Moll model for an npn BJT.
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Figure 5.79 The PSpice testbench used to demonstrate the dependence of dc on the collector bias current IC for the Q2N3904 discrete BJT
(Example 5.20).
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Figure 5.80 Dependence of dc on IC (at VCE 5 2 V) in the Q2N3904 discrete BJT (Example 5.20).
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Figure 5.81 Capture schematic of the CE amplifier in Example 5.21.
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Figure 5.82 Frequency response of the CE amplifier in Example 5.21 with Rce = 0 and Rce = 130 W.
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Figure P5.20
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Figure P5.21
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Figure P5.24
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Figure P5.26
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Figure P5.36
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Figure P5.44
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Figure P5.53
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Figure P5.57
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Figure P5.58
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Figure P5.65
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Figure P5.66
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Figure P5.67
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Figure P5.68
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Figure P5.69
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Figure P5.71
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Figure P5.72
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Figure P5.74
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Figure P5.76
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Figure P5.78
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Figure P5.79
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Figure P5.81
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Figure P5.82
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Figure P5.83
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Figure P5.84
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Figure P5.85
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Figure P5.86
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Figure P5.87
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Figure P5.96
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Figure P5.97
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Figure P5.98
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Figure P5.99
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Figure P5.100
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Figure P5.101
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Figure P5.112
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Figure P5.115
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Figure P5.116
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Figure P5.124
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Figure P5.126
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Figure P5.130
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Figure P5.134
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Figure P5.135
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Figure P5.136
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Figure P5.137
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Figure P5.141
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Figure P5.143
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Figure P5.144
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Figure P5.147
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Figure P5.148
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Figure P5.159
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Figure P5.161
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Figure P5.162
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Figure P5.166
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Figure P5.167
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Figure P5.171
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