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Bipolar Junction Transistors (BJTs)
1
Introduction
- The invention of the BJT in 1947 at the Bell Laboratories ushered in the era
of solid-state circuits.
Bardeen, Shockley, and Brattain at Bell
Labs - Brattain and Bardeen invented
the bipolar transistor in 1947.
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The first germanium bipolar transistor.
Roughly 50 years later, electronics
account for 10% (4 trillion dollars) of
the world GDP.
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• BJT >> MOSFET until 1980s. Now, BJT << MOSFET, CMOS
• Nevertheless, the BJT remains a significant device that excels in certain applications.
- For instance, the reliability of BJT circuits under severe environmental
conditions makes them the dominant devices in automobile electronics, an
important and still-growing area.
- The BJT remains popular in discrete-circuit design, in which a very wide
selection of BJT types are available to the design.
• The characteristics of the BJT are so well understood that we can design transistor
circuits whose performance is remarkably predicted and quite insensitive to
variations in device parameters.
• The BJT is still preferred device in RF circuits, very-high-speed digital logic circuit
family, such as emitter-coupled logic.
• BJT+CMOS = BiCMOS : high-input impedance, low-power operation (MOSFET)
very-high-frequency operation, high-current-driving capability (BJT)
Chap. 6, 7, 9, 11
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5.1 Device Structure and Physical Operation
Figure 5.1 A simplified structure
of the npn transistor.
• Electrons and holes participate
in the current-conduction
process. – Bipolar!
Figure 5.2 A simplified
structure of the pnp transistor.
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Amplifier
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Switch
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5.1.2 Operation of the npn Transistor in the Active Mode
Thin enough to neglect recombination.
Very thin!
1. Due to forward-biased EB junction, current flows.
- Base current by recombined holes and electrons. (small)
- This means E, B act as a resistance that is function of the
base voltage VBE.
Heavily doped emitter
Lightly doped base
V
V
2. Then, electrons from VCB arrives at BC junction.
3. Electrons flow to C due to VCB .
4. Collector current from C to E!
Figure 5.3 Current flow in an npn transistor biased to operate in the active mode.
5. This Ic is a function of base voltage!
(Reverse current components due to drift of thermally generated minority carriers are
6. Amplifier if VCE > VBE!!!
not shown.)
Diode equation np (0)  np0eBE / VT (5.1)
Electron diffusion current in the base reion
E 0
I n  A E qDn
E
E
E 0
E 0
dn p ( x )
dx
 n p (0) 
 A E qDn  

W


(5.2)
Should be zero since the positive collector voltage causes the
electron at the end to be swept across CBJ depletion region.
Figure 5.4 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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Diode equation np (0)  np0eBE / VT (5.1)
• The Collector Current
Electron diffusion current in the base reion
 n p (0) 
I n  A E qDn  

W


(5.2)
saturation current I S  A E qDn n p 0 / W
A E qDn ni2
n po  n / N A  I S 
N AW
2
i
(5.4)
Since base region is very thin and lightly doped,
iC  I n  I S e BE / VT
* IC is;
- inversely proportional to the base width W.
- Proportional to the area of the EBJ (scale current).
- Typically in the range of 10-12 A to 10 -18 A.
- Proportional to ni2. (doubling for every 5oC rise)
 E 
n i2  BT 3 exp  G  cm -6
 kT 
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cf )
iB2 
Qn
b
iD 
1 W
kn
(GS  Vt )2
2
L
(5.6)
Qn  AE q  12 np (0)W
- Base current = current due to holes injected from
 base to emitter.(iB1) + current due to holes to
supply recombined holes (iB2).
(5.5)
iC is independent of CB !
 b : minority-carrier life time
• The Base Current
A E qDn ni2  BE / VT
i B1 
e
N D Lp
(5.3)
A E qWni2  BE / VT
Qn 
e
2NA
1 A E qWni2  BE / VT
iB2 
e
2  b NA
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(5.7)
(5.8)
6
 Dp N A W 1 W 2   / V
iB  I S 

e BE T
 Dn N D Lp 2 Dn b 


iC  I n  I S e BE / VT
iB 
  BE / VT
e

iC

(5.11)

 1
iC   iE
(5.3)
 Dp N A W 1 W 2 
  1 


D
N
L
2
D

n b 
 n D p
I
iB   S


(5.9)
(5.12)


1
(5.17) Common-base current gain
(5.16)
iE   I S   eBE / VT (5.18)
cf ) i D  i S
(5.19)
  100,   0.99
Recapitulation and Equivalent Circuit model
(5.10)
npn transistor   50~1000
common emitter current gain
* β is;
- Highly depend on the base width W.
- Highly depend on relative dopings (NA/ND)
• The Emitter Current
i E  iC  iB
(5.13)
 1
iE 
i
 C
iE 
 1 
I e
 S
  100,   0.99
(5.14)
BE
/ VT
iC  iE
(5.15)
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5.1.3 Structure of Actual Transistors
In reverse active mode,
 R =0.01~0.5,  R =0.01~1
Scale currents
 F I SE   R I SC =I S (5.20)
Figure 5.6 Cross-section of an npn BJT.
Figure 5.7 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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5.2 Current-Voltage Characteristics
5.2.1 Circuit Symbols and Conventions
An npn transistor whose EBJ is forward biased will
operate in the active mode as long as the collector
voltage does not fall below that of the base by more
than 0.4 V. Otherwise, saturation mode.
An pnp transistor whose EBJ is forward biased will
operate in the active mode as long as the collector
voltage does not allowed to rise above that of the base
by more than 0.4 V. Otherwise, saturation mode.
BJT voltage-current relationship in the active mode
Figure 5.13 Circuit symbols for BJTs.
Figure 5.14 Voltage polarities and current flow in
transistors biased in the active mode.
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EXAMPLE 5.1
  100
 BE  0.7 V@iC  1 mA
Design the circuit such
that iC =2 mA, υC =5 V.
Figure 5.15 Circuit for Example 5.1.
CBJ is reverse biased, active mode!
RC 
10 V
 5 k
2 mA
 2
VBE  0.7  VT ln    0.717 V
1
VE  0.717 V
IE 
IC


2
 2.02 mA
0.99
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RE 

VE  ( 15)
IE
0.717  15
 7.07 k
2.02
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5.2.3 Dependence of iC on the Collector Voltage -The Early Effect
Due to the change of effective base width
cf) channel length modulation in MOSFET
Common Emitter Configuration
iC  I S e BE / VT
Figure 5.19 (a) Conceptual circuit for measuring the iC –vCE
of the BJT. (b) The iC –vCE characteristics of a practical BJT.
 i
ro   C
  CE
characteristics
ro 
VA
IC
  
iC  I S e BE / VT  1  CE 
VA 

1


 BE =constant 

(5.38a)
(5.37)
ro 
I C  I S e BE / VT
(5.36)
VA  VCE
IC
(5.38)
(5.38b)
It is rarely necessary to include the dependence of iC on υCE in dc bias design and analysis.
However, The finite output resistance can have a significant effect on the gain.
Figure 5.20 Large-signal equivalent-circuit models of an npn BJT operating in the active mode in the common-emitter configuration.
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5.2.4 The Common-Emitter Characteristics.
The Common-Emitter Current gain β
iB 
 dc 
 ac 
I CQ
I BQ
iC
iB
iC

(5.10)
(5.39) Large-signal or dc  (data sheet hFE )
(5.40) Incremental or ac  (dtat sheet h fe )
CE  constant
 dc and  ac differtypically by approximately 10% to 20%
In this book,  dc =  ac   F =
Figure 5.21 Common-emitter characteristics. Note that the horizontal
scale is expanded around the origin to show the saturation region in some
detail.
VCEsat and RCEsat
ΔiC
For the same I B ,
iC in active region (amp) > iC in saturation region(switch)
ΔiC
Therefore, β in saturation mode is smaller than β in active mode!
To make a transistor operate in saturation mode (switch mode,
given IC=ICsat), designer should establish VCE≈0.1~0.2 V, and
 forced =
Figure 5.23 An expanded view of the common-emitter
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characteristics in the saturation region.
ICsat
< F
IB
(5.41, 42)
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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.
RCEsat 
CE
iC
(a few tens Ohm)
(5.43)
iB  I B
iC  ICsat
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5.3 The BJT as an Amplifier
and as a Switch
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5.3.1 Large-Signal Operation-The Transfer Characteristic
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.
RC : to establish a desired dc bias voltage.
to convert the collector signal current ic to an output voltage.
O  CE  VCC  RC iC
(5.50)
For 0 <I  0.5, cutoff, iC  0, O  VCC
For  I > 0.5 and O >  I (  BE )  0.4, active mode
iC  I S e BE / VT
 I S e I / VT
 O  VCC  RC I S e
I
/ VT
(5.51)
}
For  I > 0.5 and O   I (  BE )  0.4, saturation mode
CE ( O )  VCEsat (0.1 ~ 0.2 V), ICsat 
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VCC  VCEsat
RC
}
(5.52)
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5.3.2 Amplifier Gain
Q (quiescent) point determined by a bias voltage,
RC and VBE.
We know I C  I S e BE /VT
(5.53) for BJT,
VCE  VCC  RC IC (5.54) for circuit.
Now,  I  VBE   i
Then, A 
d O
d I
(5.55)
 I VBE
1
I S eVBE /VT RC (inverting amp!)
VT
I R
V
Using (5.54), A   C C   RC
(5.56)
VT
VT
Using (5.53), A  
where VRC  VCC  VCE
(5.57)
- The voltage gain of CE amp is the ratio of the dc voltage drop
across RC to the thermal voltage VT (~25 mV at room temp).
- For a given VCC, to increase VRC, we have to operate at a lower
VCE.
- But, too low VCE results in negative peaks of output will be
flattened.
Theoretical maximum voltage gain (ignoring no negative swing),
V
V  VCEsat
A max   CC (5.59)
A   CC
(5.58)
VT
VT
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EXAMPLE 5.10
1. Find Thevenin’s equivalent
circuit of base bias circuit.
RB 2
50
 15
 5 V
RB1  RB 2
100  50
 ( RB1 // RB 2 )  (100 // 50)  33.3 k
VBB  15
RBB
2. Find IB and IE using loop equation around L.
VBB  I B RBB  VBE  I E RE
IE 
Find the voltage at all
nodes and currents
through all the branches.
(β = 100)
IB 
IE
 1
VBB  VBE
1.29
 0.0128 mA
 1.29 mA I B 
101
RE  [ RBB (   1)]
IC   I E  1.28 mA
VB  VBE  I E RE
VC  15  IC RC  15  1.28  5  8.6 V
 0.7  1.29  3  4.57 V
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(b) Equivalent circuit of the amplifier for small-signal analysis.
Figure 4.43 (a) Common-source amplifier based
on the circuit of Fig. 4.42.
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-p
model.
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