CHAPTER 4 BIPOLAR JUNCTION TRANSISTORS (BJTs)
Chapter Outline
4.1 Device Structure and Physical Operation
4.2 Current‐Voltage Characteristics
4.3 BJT Circuits at DC
4.4 Applying the BJT in Amplifier Design
4.5 Small‐Signal Operation and Models
4.6 Basic BJT Amplifier Configurations
4.7 Biasing in BJT Amplifier Circuits
4.8 Discrete‐Circuit BJT Amplifiers
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4‐1
4.1 Device Structure and Physical Operation
Physical structure of bipolar junction transistor (BJT)
Both electrons and holes participate in the conduction process for bipolar devices
BJT consists of two pn junctions constructed in a special way and connected in series, back to back
The transistor is a three‐terminal device with emitter, base and collector terminals
From the physical structure, BJTs can be divided into two groups: npn and pnp transistors
Modes of operation
The two junctions of BJT can be either forward or reverse‐biased
The BJT can operate in different modes depending on the junction bias
The BJT operates in active mode for amplifier circuits
Switching applications utilize both the cutoff and saturation modes
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Mode
EBJ
CBJ
Cutoff
Reverse
Reverse
Active
Forward
Reverse
Saturation
Forward
Forward
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Operation of the npn transistor in the active mode
Electrons in emitter regions are injected into base due to the forward bias at EBJ
Most of the injected electrons reach the edge of CBJ before being recombined if the base is narrow
Electrons at the edge of CBJ will be swept into collector due to the reverse bias at CBJ
Emitter injection efficiency ( ) = iEn/(iEn+iEp)
Base transport factor (T) = iCn/iEn
Common‐base current gain () = iCn/iE =  T < 1
Terminal currents of BJT in active mode:
iE(emitter current) = iEn(electron injection from E to B) + iEp(hole injection from B to E)
iC(collector current) = iCn(electron drift) + iCBO(CBJ reverse saturation current with emitter open) iB(base current) = iB1(hole injection from B to E) + iB2(recombination in base region) NTUEE Electronics – L. H. Lu
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Terminal currents:
AE qDnB ni2 vBE / VT
e
 I S e vBE /VT
Collector current: iC  iCn  AE qDnB dnB ( x) / dx  AE qDnB nB (0) / W 
N BW
Base current:
AE qD pE ni2 v
e
 Hole injection into emitter due to forward bias: iB1   AE qD pE dpE ( x) / dx 
BE
/ VT
N E L pE


 Eelectron‐hole recombination in base: iB 2  Qn /  n   AE q  nB (0)W  /  n 

 Total base current: iB  iB1  iB 2
Emitter current: iE  iC  iB 
1
2

AE qWni2 vBE / VT
e
2 N B n
D pE N B W 1 W 2 vBE / VT iC
 IS (

)e


DnB N E L pE 2 DnB n
i
I
 1
iC  C  S e v

 
BE
/ VT
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Large‐signal model and current gain for BJT in active region
Common‐emitter current gain
(1)
iC
iB

Common‐base current gain
(+1)
iE
iC

iB
iE
1
1
D pE N B W 1 W 2 1
iC

)   /(1   )
Common‐emitter current gain:    (
iB
DnB N E L pE 2 DnB n
Common‐base current gain:    /(   1)
The structure of actual transistors
In modern process technologies, the BJT utilizes a vertical structure
Typically,  is smaller and close to unity while  is large
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Operation of the npn transistor in the saturation mode
Saturation mode: both EBJ and CBJ are forward biased
Carrier injection from both emitter and collector into base
Base minority carrier concentraiton change accordingly  leading to reduced slope as vBC increases
Collector current drops from the value in active mode for negative vCB
For a given vBE, iC drops sharply to zero at vCB around 0.5 V and vCE around 0.2 V
BJT in saturation: VCEsat = 0.2 V
i
Current gain reduces (from  to forced):  forced  C saturation  
iB
np0exp(vBE/VT)
np0exp(vBC/VT)
vBC increases
np0
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Ebers‐Moll model
In EM model, the EBJ and CBJ are represented by two back to back diodes iDE and iDC
Current transported from one junction to the other is presented by F (forward) and R (reverse)
EM model can be used to describe the BJT in any of its possible modes of operation
EM model is used for more detailed dc analysis
v /V
 1) iDC  I SC (e v / V  1)  F I SE   R I SC  I S
The diode currents: iDE  I SE (e
iC  iDC   F iDE
iB  iE  iC
The terminal currents: iE  iDE   R iDC
BE
T
BC
T
Application of the EM model
The forward active mode:
 1

 1
iC  I S e vBE /VT  I S 
 R 
 1
I
1 


iB  S e vBE / VT  I S 
F


R 
 F

I
1 

iE  S e vBE / VT  I S 1 
F

F 

iDE
RiDC
iC  I S e vBE / VT  I SC e vBC / VT
iE  I SE e
 ISe
iC
iE
The saturation mode:
v BE / VT
iDC
FiDE
iB
vBC / VT
iB  I SE (1   F )e vBE /VT  I SC (1   R )e vBC / VT
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The cutoff mode
 ICBO (CBJ reverse current with emitter open‐circuited)
ICBO = (1RF)ISC
Both EBJ and CBJ are reverse‐biased
In real case, reverse current depends on vCB
 ICEO (CBJ reverse current with base open‐circuited)
ICEO = ICBO/(1F)
F is always smaller than unity such that ICEO > ICBO
CBJ current flows from (C to B) so CBJ is reverse‐biased
EBJ current flows from (E to B) so EBJ is slightly forward‐biased

(3) RISC
B
iB
+
(3) iDE
C
iC
iE = 0
(2) RISC
C
iE
iC
iC = ICBO = (1RF)ISC (5)
FiDE (4)
(2) RISC

RFISC (4)
ISC (1)
E
ISC (1)
E
iB = 0
B
+
iB = (R1)ISC+(1F)iDE = 0  iDE = ISC(1R)/(1F) (5)
iC = ISC+FiDE = ISC(1RF)/(1F)  ICEO = ICBO/(1F) (6)
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The pnp transistor
Transistor structure:  emitter and collector are p‐type
 base is n‐type
Operation of pnp is similar to that of npn
Operation of pnp in the active mode
Collector current: iC  I S e
Base current: iB  iC / 
Emitter current: iE  iC  iB
vEB / VT
Large‐signal model and current gain for BJT in active region
Common‐emitter current gain
(1)
iC
iB

Common‐base current gain
(+1)
iE
iC

iB
iE
1
1
Exercise 4.1 (Textbook)
Exercise 4.3 (Textbook)
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4.2 Current‐Voltage Characteristics
Circuit symbols, voltage polarities and current flow
Terminal currents are defined in the direction as current flow in active mode
Negative values of current or voltage mean in opposite polarity (direction)
Summary of the BJT current‐voltage relationships in the active mode
The terminal currents for a BJT in active mode solely depend on the junction voltage of EBJ
The ratios of the terminal currents for a BJT in active mode are constant
The current directions for npn and pnp transistors are opposite
npn transistor
pnp transistor
iC  I S evBE /VT
i
I
iB  C  S e vBE / VT
iC  I S evEB / VT
i
I
iB  C  S e vEB / VT

iE 
iC



IS

e vBE / VT

iE 
iC



IS

e vEB / VT
iE  iC  iB


 1


1
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Current‐voltage characteristics of BJT
The iC‐vCB characteristics
The iC‐vCE characteristics
The Early effect
As CBJ reverse bias increases, the effective base width Weff reduces due to the increasing depletion
For a constant junction voltage vBE:
 The slope of nB(x) increases  iC increases
nB (0)
VZ
 Charge storage Qn reduces  iB decreases
VY
 Current gain  and  increases
VX
Early voltage (VA) is used for the linear approximation of Early Effect
Linear dependence of iC on vCE: iC  I S e v /V (1  vCE / VA )
BE
 i
Exhibit finite output resistance: ro   C
 vCE
T
1

V
 A
v BE  constant 
IC

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nB0
0
WX WY WZ
4‐11
Common‐base output characteristics
Early effect
breakdown
iC versus vCB plot with various iE as parameter is known as common‐base output characteristics
The slope indicates that iC depends to a small extent on vCB  Early effect
iC increases rapidly at high vCB  breakdown
BCJ is slightly forward‐biased for 0.4V < vCB < 0
No significant change is observed in iC
The BJT still exhibits I‐V characteristics as in the active mode
BCJ turns on strongly and the iC starts to decrease for vBC < 0.4V
 I‐V characteristics in the saturation mode and vCEsat is considered a constant ( 0.2 V)
Current gain (): large‐signal   iC/iE and small‐signal (incremental)   iC/iE
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Common‐emitter output characteristics (I)
iC versus vCE plot with various vBE as parameter Common‐emitter current gain is defined as  = iC / iB
The BCJ turns on with a positive vBC at low vCE
BJT operates in saturation mode
The iC curve has a finite slope due to Early effect
The characteristics lines meet at vCE = VA
VA is called the Early Voltage (~ 50 to 100 V)
Common‐emitter output characteristics (II)
Plot of iC versus vCE with various iB as parameter
BJT in active region acts as a current source with high (but finite) output resistance
The cutoff mode in common‐emitter configuration is defined as iB = 0
Current gain: large‐signal bdc  iC/iB and bac  iC/iB
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Early effect
breakdown
4‐13
Saturation of common‐emitter configuration
In saturation region, it behaves as a closed switch with a small resistance RCEsat
The saturation IV curve can be approximated by a straight line intersecting the vCE axis at VCEoff
The saturation voltage VCEsat  VCEoff+ICsatRCEsat
VCEsat is normally treated as a constant of 0.2 V for simplicity regardless the value of iC
Incremental  in saturation is lower than that in active region:  forced  ICsat/IB < 
Overdrive factor  /forced
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Transistor breakdown
Transistor breakdown mechanism:
 Avalanche breakdown: avalanche multiplication mechanism takes place at CBJ or EBJ
 Base punch‐through effect: the base width reduces to zero at high CBJ reverse bias
In CB configuration, BVCBO is defined at iE = 0
The breakdown voltage is smaller than BVCBO for iE > 0
In CE configuration, BVCEO is defined at iB =0
The breakdown voltage is smaller than BVCEO for iB > 0
Typically, BVCEO is about half of BVCBO
Breakdown of the BCJ is not destructive as long as the power dissipation is kept within safe limits
Breakdown of the EBJ is destructive because it will cause permanent degradation of 
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Exercise 4.13 (Textbook)
Exercise 4.14 (Textbook)
Example 4.3 (Textbook)
Exercise 4.21 (Textbook)
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4.3 BJT Circuits at DC
BJT operation modes
The BJT operation mode depends on the voltages at EBJ and BCJ
The I‐V characteristics are strongly nonlinear
Simplified models and classifications are needed to speed up the hand‐calculation analysis
Mode
EBJ
CBJ
Active
Forward
Reverse
Cutoff
Reverse
Reverse
Saturation
Forward
Forward
Inverse
Reverse
Forward
pnp transistor
npn transistor
vBC
Inverse Mode
vBE < 0, vBC  0
Saturation Mode
vBE  0, vBC  0
Cutoff Mode
vBE < 0, vBC < 0
Active Mode
vBE  0, vBC  0
vCB
vBE
Inverse Mode
vEB < 0, vCB  0
Saturation Mode
vEB  0, vCB  0
Cutoff Mode
vEB < 0, vCB < 0
Active Mode
vEB  0, vCB  0
vEB
Simplified models and classifications for the operation of the npn BJT
Cut‐off mode:
 iE = iC = iB = 0
 vBE < 0.5 V and vBC < 0.4 V
Active mode:
 vBE = 0.7 V and iB : iC : iE = 1:  : (1+)
 vCE > 0.3 V
Saturation mode:
 vBE = 0.7 V and vCE = 0.2 V
 iC/iB = forced < 
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Equivalent circuit models NTUEE Electronics – L. H. Lu
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DC analysis of BJT circuits
Step 1: assume the operation mode
Step 2: use the conditions or model for circuit analysis
Step 3: verify the solution
Step 4: repeat the above steps with another assumption if necessary
Example 4.4
 = 100
Example 4.5
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Example 4.9 (Textbook)
Example 4.11 (Textbook)
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Exercise 4.22 (Textbook)
Exercise 4.23 (Textbook)
Exercise 4.24 (Textbook)
Exercise 4.25 (Textbook)
Exercise 4.28 (Textbook)
Example 4.12 (Textbook)
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4.4 Applying the BJT in Amplifier Design
BJT voltage amplifier
A BJT circuit with a collector resistor RC can be used as a simple voltage amplifier
Base terminal is used the amplifier input and the collector is considered the amplifier output
The voltage transfer characteristic (VTC) is obtained by solving the circuit from low to high vBE
 Cutoff mode:
0 V  vBE < 0.5 V and iC = 0
vO = vCE = VCC
 Active mode:
vBE > 0.5 V and iC = ISexp(vBE/VT)
vO = VCC  iCRC = VCC  RCISexp(vBE/VT)
 Saturation:
vBE further increases
vCE = vCEsat = 0.2 V
vO = 0.2 V
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Biasing the circuit to obtain linear amplification
The slope in the VTC indicates voltage gain
BJT in active mode can be used as voltage amplification
Point Q is known as bias point or dc operating point
IC = ISexp(VBE/VT)
The signal to be amplified is superimposed on VBE
vBE(t) = VBE+vbe(t)
The time‐varying part in vCE(t) is the amplified signal
The circuit can be used as a linear amplifier if:
 A proper bias point is chosen for gain
 The input signal is small in amplitude
The small‐signal voltage gain
The amplifier gain is the slope at Q:
Av 
dvCE
dvBE
vBE VBE

IC
RC
VT
Voltage gain depends on IC and RC
Maximum voltage gain of the amplifier
Av  
IC
V  VCE VCC
RC  CC

| Av max |
VT
VT
VT
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Determining the VTC by graphical analysis
Provides more insight into the circuit operation
Load line: the straight line represents in effect the load
iC = (VCCVCE)/RC
The operating point is the intersection point
Locating the bias point Q
The bias point (intersection) is determined by properly choosing the load line
The output voltage is bounded by VCC (upper bound) and VCEsat (lower bound)
The load line determines the voltage gain
The bias point determines the headroom or maximum upper/lower voltage swing of the amplifier NTUEE Electronics – L. H. Lu
4‐24
4.5 Small‐Signal Operation and Models
The collector current and the transconductance
The total quantities (ac + dc) of the collector current:
vBE  VBE  vbe
iC  I S e vBE / VT  ( I S eVBE / VT )e vbe / VT  I C e vbe / VT
Small‐signal approximation: vbe << VT
 v 
I
iC  I C  ic  I C 1  be   I C  C vbe
VT
 VT 
I
i
g m  C iC  I C  C
vBE
VT
The transconductance indicates the incremental change of iC versus change of vBE
The transconductance gm is determined by its dc collector current IC
General, BJTs have relatively high transconductance compared with FETs at the same current level
The base current and the input resistance at the base
The total quantities (ac + dc) of the base current:
iB 
IC


IS

e vBE / VT 
IS

eVBE / VT e vbe / VT  I B e vbe / VT
Small‐signal approximation:
 v 
I
iB  I B  ib  I B 1  be   I B  B vbe
VT
 VT 
v
 VT
r  be 

ib
gm I B
Resistance r is the small‐signal input resistance between base and emitter (looking into the base)
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The emitter current and the input resistance at the emitter
The total quantities (ac + dc) of the emitter current:
iE  I E  ie 
iC


IC


ic

Small‐signal approximation:
IC
I
vbe  E vbe
VT
 
VT
v
1

V
re  be  T 

ie
I E gm gm
ie 
ic

gm
vbe 
Relation between r and re:
re 
r 

gm

 r  (1   )re
gm
Output resistance accounting for Early effect
Use the collector current equation with linear vCE dependence:
 v 
iC  I S e vBE / VT 1  CE 
 VA 
1

 iC
V
ro  
 A
v BE  constant 
IC

 vCE
The output resistance ro is included to represent Early Effect of the BJT
The resulting ro is typically a large resistance and can be neglected to simplify the analysis
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BJT small‐signal models
Two models are exchangeable and does not affect the analysis result
The hybrid‐ model
 Typically used as the emitter is grounded
Neglect ro
The T model
 Typically used as the emitter is not grounded
Neglect ro
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4.6 Basic BJT Amplifier Configuration
Three basic configurations
Common‐Emitter (CE)
Common‐Base (CB)
Common‐Collector (CC)
Characterizing amplifiers
The BJT circuits can be characterized by a voltage amplifier model (unilateral model)
The electrical properties of the amplifier is represented by Rin, Ro and Avo
The analysis is based on the small‐signal or linear equivalent circuit (dc components not included)
vo
RL

Avo
vi RL  Ro
v
Rin
Rin
RL
Overall voltage gain: Gv  o 
Av 
Avo
vsig Rin  Rsig
Rin  Rsig RL  Rso
Voltage gain: Av 
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The common‐emitter (CE) amplifier
Characteristic parameters of the CE amplifier
 Input resistance: Rin  r
 Output resistance: Ro  RC || ro  RC
 Open‐circuit voltage gain: Avo   g m ( RC || ro )   g m RC
 Voltage gain: Av   g m ( RC || RL || ro )   g m ( RC || RL )
 Overall voltage gain: Gv  
r
r
g m ( RC || RL || ro )   g m
( RC || RL )
r  Rsig
r  Rsig
CE amplifier can provide high voltage gain
Input and output are out of phase due to negative gain
Lower IC increases Rin at the cost of voltage gain
Output resistance is moderate to high
Small RC reduces Ro at the cost of voltage gain
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The common‐emitter (CE) with an emitter resistance
Characteristic parameters (by neglecting ro)
 Input resistance:
Rin  (1   )(re  Re )  r  (1   ) Re
 Output resistance:
Ro  RC
 Open‐circuit voltage gain:
Avo  
g m RC
g R
 m C
1  Re / re
1  g m Re
 Voltage gain:
Av  
g m RC
g ( R || RL )
RL
 m C
1  g m Re RL  RC
1  g m Re
 Overall voltage gain:
Gv  
r
g m RC
r
g m ( RC || RL )
RL

r  Rsig 1  g m Re RL  RC
r  Rsig 1  g m Re
Emitter degeneration resistance Re is adopted
Input resistance is increased by adding (1+)Re
Gain is reduced by the factor (1+gmRe)
The overall gain is less dependent on 
It is considered a negative feedback of the amplifier
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The common‐base (CB) amplifier
Characteristic parameters of the CE amplifier (by neglecting ro)
 Input resistance: Rin  re
 Output resistance: Ro  RC
 Open‐circuit voltage gain: Avo  g m RC
 Voltage gain: Av  g m ( RC || RL )
 Overall voltage gain: Gv 
re
g m ( RC || RL )
re  Rsig
CE amplifier can provide high voltage gain
Input and output are in‐phase due to positive gain
Input resistance is very low
A single CB stage is not suitable for voltage amplification
Output resistance is moderate to high
Small RC reduces Ro at the cost of voltage gain
The amplifier is no longer unilateral if ro is included
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The common‐collector (CC) amplifier
Characteristic parameters of the CC amplifier (by neglecting ro)
 Input resistance: Rin  (1   )(re  RL )
 Output resistance: Ro  re  Rsig / 
 Open‐circuit voltage gain: Avo  RL /( RL  re )  1
 Overall voltage gain: Gv 
Rin
(   1) RL
RL

1
Rin  Rsig RL  re (   1)( RL  re )  Rsig
CC amplifier is also called emitter follower. Input resistance is very high
Output resistance is very low
The voltage gain is less than but can be close to 1
CC amplifier can be used as voltage buffer
It is noted that, in the analysis, the amplifier is not unilateral
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4.7 Biasing in BJT Amplifier Circuits
DC bias for BJT amplifier
The amplifiers are operating at a proper dc bias point
Linear signal amplification is provided based on small‐signal circuit operation
The DC bias circuit is to ensure the BJT in active mode with a proper collector current IC
The classical discrete‐circuit bias arrangement
A single power supply and resistors are needed
Thevenin equivalent circuit:
 VBB = VCCR2/(R1+R2)
 RB = R1||R2
VBB  VBE
BJT operating point: I C 
RB /   RE (1  1 /  )
RC is chosen to ensure the BJT in active (VCE > VCEsat)
A two‐power‐supply version of the classical bias arrangement
Two power supplies are needed
Similar dc analysis
VEE  VBE
BJT operating point: I C 
RB /   RE (1  1 /  )
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Biasing using a collector‐to‐base feedback resistor
A single power supply is needed
RB ensures the BJT in active (VCE > VBE  0.7 V)
BJT operating point: I C 
VCC  VBE
RB /   RC (1  1 /  )
The value of the feedback resistor RB affects the small‐signal gain
Biasing using a constant‐current source
The BJT can be biased with a constant current source I
The resistor RC is chosen to operate the BJT in active mode
The current source is typically implemented by a BJT current mirror
Current mirror circuit:
 Both BJT transistors Q1 and Q2 are in active mode
 Assume current gain  is very high:
I  I REF 
VCC  VEE  VBE
R
 When applying to the amplifier circuit, the voltage
V has to be high enough to ensure Q2 in active
Exercise 6.35 (Textbook)
Exercise 6.36(Textbook)
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4.8 Discrete‐Circuit BJT Amplifiers
Circuit analysis:
DC analysis:
 Remove all ac sources (short for voltage source and open for current source)
 All capacitors are considered open‐circuit
 DC analysis of BJT circuits for all nodal voltages and branch currents
 Find the dc current IC and make sure the BJT is in active mode AC analysis:
 Remove all dc sources (short for voltage source and open for current source)
 All large capacitors are considered short‐circuit
 Replace the BJT with its small‐signal model for ac analysis
 The circuit parameters in the small‐signal model are obtained based on the value of IC
Complete amplifier circuit
DC equivalent circuit
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AC equivalent circuit
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The common‐emitter (CE) amplifier
The common‐emitter amplifier with an emitter resistance
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The common‐base (CB) amplifier
The common‐collector (CC) amplifier
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The amplifier frequency response
The gain falls off at low frequency band due to the effects of the coupling and by‐pass capacitors
The gain falls off at high frequency band due to the internal capacitive effects in the BJTs
Midband:
 All coupling and by‐pass capacitors (large capacitance) are considered short‐circuit
 All internal capacitive effects (small capacitance) are considered open‐circuit
 Midband gain is nearly constant and is evaluated by small‐signal analysis
 The bandwidth is defined as BW = fH – fL
 A figure‐of‐merit for the amplifier is its gain‐bandwidth product defined as GB = |AM|BW
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Exercise 6.40 (Textbook)
Exercise 6.41 (Textbook)
Exercise 6.43 (Textbook)
Exercise 6.44 (Textbook)
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