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ECE 315 – Spring 2007 – Farhan Rana – Cornell University
Lecture 18
Bipolar Junction Transistors (BJTs)
In this lecture you will learn:
• The operation of bipolar junction transistors
• Forward and reverse active operations, saturation, cutoff
• Ebers-Moll model
• Small signal models
ECE 315 – Spring 2007 – Farhan Rana – Cornell University
Bipolar Transistors
First Bipolar Transistor (AT&T Bell Labs)
First Bipolar Transistor (AT&T Bell Labs)
William Shockley, John Bardeen, Walter Brattain(Nobel Prize for the Transistor, AT&T Bell Labs)
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ECE 315 – Spring 2007 – Farhan Rana – Cornell University
Emitter
N-doped
Collector
N-doped
aBNdEN
Base
P-doped
dCN
VBE VCB+ +- -
NPN Bipolar Junction Transistor
B
E
C
VBE
VCB
+-
+-
VGS+-
VDG+-
ECE 315 – Spring 2007 – Farhan Rana – Cornell University
Emitter
P-doped
Collector
P-dopedaEN dBN
Base
N-doped
VBE VCB+ +- -
PNP Bipolar Junction Transistor
B
E
C
VBE
VCB
+-
+-
aCN
VGS+-
VDG+-
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ECE 315 – Spring 2007 – Farhan Rana – Cornell University
Metal base contact Metal emitter contact Metal collector contact
P (base)N+ (emitter)
N (collector)
N+ (contact layer)
N (substrate)
Insulator (SiO2)
Insulator (SiO2)
Insulator (SiO2)
A Silicon NPN BJT
P+ (contact)
ECE 315 – Spring 2007 – Farhan Rana – Cornell University
NPN BJT: Basic Operation
Emitter
N-doped
Collector
N-dopeddEN aBN
Base
P-doped
VBE > 0 VCB=0+ +- -
WE WB WC
dCN
Suppose:
The base-emitter junction is forward biased
The base-collector junction is zero biased
0BEV
0CBV
This biasing scheme will put the device in the “forward active” operation (to be discussed fully later)
pxnx 0
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ECE 315 – Spring 2007 – Farhan Rana – Cornell University
NPN BJT: Basic Operation
dEN aBN
VBE>0+ +- -
WE WB WC
dCN
Consider the action in the base first (VBE > 0 and VCB = 0)
• The electrons diffuse from the emitter, cross the depletion region, and enter the base
• In the base, the electrons are the minority carriers
• In the base, the electrons diffuse towards the collector
• As soon as the electrons reach the base-collector depletion region they are immediately swept away into the collector by the strong electric fields in the depletion region
holes
electrons
pxnxE-field
0
swept electrons
VCB=0
ECE 315 – Spring 2007 – Farhan Rana – Cornell University
NPN BJT: Electron-Hole Populations
Consider the base first:
In the base, the electron population can be written as:
In the base, the excess electron population satisfies the differential equation:
xnnxn po '
Equilibrium electron density Excess electron densityaB
ipo N
nn
2
1'
2KT
Vq
aB
ip
BE
eNn
xn 0
''22
2
nL
xn
x
xn
Boundaryconditions
dEN aBN
VBE>0+ +- -
WE WB WC
dCNholes
electrons
pxnxE-field
0
swept electrons
VCB=0
01'2
KT
qV
aB
iBp
BC
eNn
Wxn
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ECE 315 – Spring 2007 – Farhan Rana – Cornell University
dEN aBN
VBE>0+ +- -
WE WB WC
dCNholes
electrons
pxnxE-field
0
swept electrons
VCB=0NPN BJT: Electron-Hole Populations
• Ignore carrier recombination (i.e. assume Ln = ∞)
0
'2
2
x
xn
Boundaryconditions
xn'
Solution is:
B
pKT
qV
aB
i
B
pn W
xxe
Nn
W
xxxnxn
BE
111''2
1'
2KT
Vq
aB
ip
BE
eNn
xn
01'2
KT
qV
aB
iBp
BC
eNn
Wxn
ECE 315 – Spring 2007 – Farhan Rana – Cornell University
NPN BJT: Electron-Hole Populations
Consider the emitter now:
In the emitter, the hole population can be written as:
In the emitter, the excess hole population satisfies the differential equation:
xppxp no '
Equilibrium hole density Excess hole densitydE
ino N
np
2
1'
2KT
Vq
dE
in
BE
eNn
xp 0
''22
2
pL
xp
x
xpBoundaryconditions
0' En Wxp
dEN aBN
VBE>0+ +- -
WE WB WC
dCNholes
electrons
pxnxE-field
0
swept electrons xn'
VCB=0
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ECE 315 – Spring 2007 – Farhan Rana – Cornell University
dEN aBN
VBE>0+ +- -
WE WB WC
dCNholes
electrons
pxnxE-field
0
swept electrons
VCB=0NPN BJT: Electron-Hole Populations
• Ignore carrier recombination (i.e. assume Lp = ∞)
0
'2
2
x
xp
xn'
Solution is:
Boundaryconditions
E
nKT
qV
dE
i
E
nn W
xxe
Nn
Wxx
xpxpBE
111''2
xp'
1'
2KT
Vq
dE
in
BE
eNn
xp
0' En Wxp
ECE 315 – Spring 2007 – Farhan Rana – Cornell University
NPN BJT: Electron and Hole Current DensitiesVCB=0
+ +- -
WE WB WCpxnx
xJn
In the base:• The electron current is:
xxp
DqxJ pp
12 KT
qV
EdE
pi
BE
eWN
Dqn
In the emitter:• The hole current is:
xxn
DqxJ nn
12 KT
qV
BaB
ni
BE
eWN
Dqn
xJp
dEN aBN dCN
Area = A
0
VBE>0
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ECE 315 – Spring 2007 – Farhan Rana – Cornell University
NPN BJT: Terminal Currents
Emitter current:
• The current flowing out of the emitter is the sum of the total electron and total hole currents in the emitter:
12 KT
qV
BaB
n
EdE
piE
BE
eWN
DWN
DAqnI
VCB=0+ +- -
WE WB WCpxnx
xJn xJp
EI dEN aBN dCN
Area = A
0
VBE>0
ECE 315 – Spring 2007 – Farhan Rana – Cornell University
+ +- -
WE WB WCpxnx
xJn
Collector Current:• The current going into the collector is due to the electrons that got swept from the Base through the Base-Collector depletion region by the electric-fields:
xJp
EI dEN aBN dCN CI
Area = A
12 KT
qV
BaB
niC
BE
eWN
DAqnI
BI
Base Current:• The current going into the Base is due to the holes that got injected from the base into the emitter:
12 KT
qV
EdE
piB
BE
eWN
DAqnI
E-field
NPN BJT: Terminal Currents
0
VCB=0VBE>0
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ECE 315 – Spring 2007 – Farhan Rana – Cornell University
12 KT
qV
BaB
n
EdE
piE
BE
eWN
DWN
DAqnI
12 KT
qV
BaB
niC
BE
eWN
DAqnI
12 KT
qV
EdE
piB
BE
eWN
DAqnI
B
E
C
VCB=0
+-
+-
IC
IE
IB
CBE III
NPN BJT: Terminal Currents
VBE>0
+ +- -
WE WB WCpxnx
xJn xJp
EI dEN aBN dCN CI
Area = A BI
0
VCB=0VBE>0
ECE 315 – Spring 2007 – Farhan Rana – Cornell University
+ +- -
WE WB WCpxnx
EIdEN dCN
CI
Area = A BI
0
VCB=0VBE>0
aBN
Electrons
Holes
NPN BJT: Terminal Currents
12 KT
qV
BaB
n
EdE
piE
BE
eWN
DWN
DAqnI
12 KT
qV
BaB
niC
BE
eWN
DAqnI
12 KT
qV
EdE
piB
BE
eWN
DAqnI
B
E
C
VCB=0
+-
+-
IC
IE
IB
CBE III
VBE>0
Red curr
tBlue curre
t
n
enCF
B
I
I
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ECE 315 – Spring 2007 – Farhan Rana – Cornell University
NPN BJT: Circuit Level Parameters
B
E
C
VCB=0
+-
+-
IC = FIE = FIB
IE
IB
Current gain F :Current gain of the BJT in the forward active operation is defined as the ratio of the collector and base currents:
BFCp
EdE
BaB
n
B
CF II
DWN
WND
II
Typical values of F are between 20-200 and:
F :In the forward active operation F is defined as the ratio of the collector and emitter currents:
E
CF I
I EFC
BaB
n
EdE
p
BaB
n
II
WND
WN
DWN
D
Transistor relation:F and F are related:
F
FF
1
VBE>0
dCaBdE NNN
CBE III
ECE 315 – Spring 2007 – Farhan Rana – Cornell University
NPN BJT: Ebers-Moll Model for Forward Active Operation
Suppose:
B
E
C
1
12
KTqV
ES
KTqV
BaB
n
EdE
piF
BE
BE
eI
eWN
DWN
DAqnI
FI
FF IBV
EV
CV
BV
EV
CV
ESI
The circuit level simplified model with an ideal diode and a current-controlled current source models the NPN transistor in the forward active operation
0BEV
0CBV
IB
IE
IC
IB
IE
IC
1B F FI I
C F FI I
E FI I
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ECE 315 – Spring 2007 – Farhan Rana – Cornell University
NPN BJT: Forward Active Operation
B
E
C
VBE+-
+-
IC
IE
IB
0BEV
0CBV
Forward active operation
B
CF I
I
E
CF I
I
F
FF
1
VCB
ECE 315 – Spring 2007 – Farhan Rana – Cornell University
NPN BJT: Forward and Reverse Active Operations
B
E
C
VBE+-
+-
IC
IE
IB
B
E
C
VBE
VCB
+-
+-
IC
IE
IB
0BEV
0CBV 0BEV
0CBV
Forward active operation Reverse active operation
B
ER I
I
C
ER I
I
B
CF I
I
E
CF I
I
F
FF
1 R
RR
1
p
CdC
BaB
n
D
WN
WND
RF In a well designed transistor:
VCB( )
( )
Actual
Actual
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ECE 315 – Spring 2007 – Farhan Rana – Cornell University
Suppose:
B
E
C
2 1
1
BC
BC
qVp n KT
R idC C aB B
qV
KTCS
D DI qn A e
N W N W
I e
RI
RRI
BV
EV
CV
BV
EV
CV CSI
The circuit level simplified model with an ideal diode and a current-controlled current source models the NPN transistor in the reverse active operation
0BCV
0BEV
NPN BJT: Ebers-Moll Model for Reverse Active Operation
IB
IE
IC
IB
IE
IC ( )
( )
1B R RI I
C RI I
E R RI I
ECE 315 – Spring 2007 – Farhan Rana – Cornell University
NPN BJT: Ebers-Moll Model and Terminal Currents
Terminal currents:
B
E
C
BV
EV
CV
FI
FF IBV
EV
CV
ESI
RI
RRI
CSI
IC
IE
IB IB
IE
IC
1KT
qV
CSR
BC
eII
1KT
qV
ESF
BE
eII
RRFFB III 11
RFFC III
RRFE III
And
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ECE 315 – Spring 2007 – Farhan Rana – Cornell University
B
E
C
IC
IE
IB
0BEV 0CBV
In forward active operation:
NPN BJT: Regimes of Operation - I
VCE+-
BECBCE VVV
BFKT
qV
BaB
niC Ie
WND
AqnIBE
12
Independent of VCE
Since:
In forward active operation: BECE VV
CEVBEV
CIForward active IB >0 & IC = F IBVCE > VBE
SaturationIB >0VCE < VBE
0BI
Forward active:Base-emitter junction forward biasedBase-collector junction reversed biased
000 CBBEB VVI
Saturation:Base-emitter junction forward biasedBase-collector junction forward biased
000 CBBEB VVIF
R
F
F
VBE+-
ECE 315 – Spring 2007 – Farhan Rana – Cornell University
dEN aBN
VBE > 0+ +- -
WE WB WC
dCNholes
electrons
pxnx 0
VCB ≥ 0
xn' xp'
Carrier Densities in Different Regimes of Operation
Forward active:
Saturation:
dEN aBN
VBE > 0+ +- -
WE WB WC
dCNholes
electrons
pxnx 0
VCB < 0
xn' xp'
xp'
xp'
electrons
holes
electrons
holes
dCaBdE NNN
The forward biased base-collector junction reduces the collector current!
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ECE 315 – Spring 2007 – Farhan Rana – Cornell University
B
E
C
IC
IE
IB
NPN-BJT: Regimes of Operation - II
VCE+-
BI
Forward active:Base-emitter junction forward biasedBase-collector junction reversed biased
000 CBBEB VVI
Saturation:Base-emitter junction forward biasedBase-collector junction forward biased
000 CBBEB VVI
Cutoff:Base current zero
0BI
Reverse active:Base-emitter junction reverse biasedBase-collector junction forward biased
000 CBBEB VVI
CEV
CI
Curves for increasing IB
IB = 0 (cutoff)
Forward active IB >0 & IC = F IBVCE ≥VBE
SaturationIB >0VCE <VBE
BECE VV
C F BI I
E R BI I
ECE 315 – Spring 2007 – Farhan Rana – Cornell University
NPN BJT: Different Regimes of Operation
FI
FF IBV
EV
CV
ESI
RI
RRI
CSI
IB
IE
IC
Reversed biased
Forward biased
0BEV
0CBV
Forward Active Saturation Reverse Active
FI
FFIBV
EV
CV
ESI
RI
RRI
CSI
IB
IE
IC
Forward biased
Forward biased
0CBV
0BEV
FI
FFIBV
EV
CV
ESI
RI
RRI
CSI
IB
IE
IC
Forward biased
Reversed biased
0CBV
0BEV
( )
( )
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ECE 315 – Spring 2007 – Farhan Rana – Cornell University
NPN BJT: A Simple Amplifier Circuit
B
E
C IC
IE
IB
DDV
R
IIN
FB
C
IN
OUT
II
II
Current gain (in forward active regime):
CEC VV
RVV
I
RIVV
CEDDC
CDDCE
Load line equation:
Lesson: Don’t let the base-collector junction become forward biased
CEV
CI
Curves for increasing IB
IB = 0 (cutoff)
Forward active IB >0 & IC = F IBVCE ≥VBE
SaturationIB >0VCE <VBE
BECE VV
DDV
Load line
RVDD
ECE 315 – Spring 2007 – Farhan Rana – Cornell University
NPN BJT
CEV
CI
Curves for increasing IB(And increasing VBE)
IB = 0 (cutoff)
Forward active IB >0 & IC = F IBVCE ≥VBE
SaturationIB >0VCE <VBE
VCE-SAT
BECE VV Better/easier definition:In saturationIB >0VCE <VCE-SAT
Better/easier definition:In forward activeIB >0VCE >VCE-SAT
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ECE 315 – Spring 2007 – Farhan Rana – Cornell University
NPN BJT: Voltage Biasing of a Simple Amplifier Circuit
Approximate analysis of transistor DC biasing:
S
ONBEINB
ONBESBIN
RVV
I
VRIV
0BONBEIN IVV Transistor in cut-off
If: ONBEIN VV
Assume forward active operation (VCE > VCE-SAT):
BFC II
RR
VVVRIVV
s
ONBEINFDDCDDOUT
Final Step - confirm if the assumption of forward active operation was valid:
SATCEs
ONBEINFDDCDDOUTCE
SATCECE
VRRVV
VRIVVV
VV
If:
B
E
C IC
IE
IB
DDV
R
VIN
OUTV
SR
+
-VON+
-
Acting as a current source
V2.0~
V6.0~
SATCE
ONBE
V
V
ECE 315 – Spring 2007 – Farhan Rana – Cornell University
NPN BJT Amplifier Circuit: Transfer Curve
00
OUTV
INVONBEV
DDV
Cu
t-o
ff
Forward active
Saturation
ONBEINs
FDDCDDOUT VVRR
VRIVV
B
E
C IC
IE
IB
DDV
R
VIN
OUTV
SR
+
-VON+
-
Acting as a current source
SATCEV
S
ONBEINB R
VVI
DDOUTBONBEIN VVIVV 0 Transistor in cut-off
If: ONBEIN VV
If:
Transistor in forward active
If: SATCEOUTCEB VVVI & 0
V2.0~
V6.0~
SATCE
ONBE
V
V
Transistor in saturation
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ECE 315 – Spring 2007 – Farhan Rana – Cornell University
00
OUTV
INVONBEV
DDV
Cu
t-o
ff
Forward active
SaturationSATCEV
B
E
C IC + ic
IE + ie
IB + ib
DDV
R
VBIAS
outOUT vV
SR
+
-
vs
+
-
vVBE +
-
NPN BJT Common Emitter (CE) Voltage Amplifier
V2.0~
V6.0~
SATCE
ONBE
V
V
Bias point
We need better techniques to calculate the voltage gain of such amplifier circuits
We need small signal models of the BJTs!
ECE 315 – Spring 2007 – Farhan Rana – Cornell University
NPN BJT: Small Signal Circuit Model
KTqI
g
vgvKTqI
vKT
IIqv
VI
i
eIiI
eI
eWN
DAqnI
B
BBSB
BE
Bb
KT
vVq
BSbB
KT
qV
BS
KTqV
EdE
piB
BE
BE
BE
1
1
12
B
E
C IC + ic
IE + ie
IB + ib
DDV
R
VBIAS
outOUT vV
SR
+
-
vs
+
-
KT
qI
KTqI
gg
vgvgii
iIiI
CBFFm
mFbFc
bBFcC
Collector current:
Base current:
Increases linearly with the collector current
vVBE +
-
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ECE 315 – Spring 2007 – Farhan Rana – Cornell University
BaseCollectorci
vgm+v
- r
g1
bi
Emitter
ei
B
E
C IC + ic
IE + ie
IB + ib
DDV
R
VBIAS
outOUT vV
SR
+
-
vs
+
-
NPN BJT: Small Signal Circuit Model
KTqI
g BKT
qIgg C
Fm
ECE 315 – Spring 2007 – Farhan Rana – Cornell University
NPN BJT: Forward Active Current vs VCE
As VCE becomes more positive, the base-collector junction becomes more reverse biased, and the thickness of the depletion increases thereby reducing the thickness WBof the base
Consequently, the collector current increases
The output conductance go is not zero!
Depletion region width
CEV
CI
IB = 0 (cutoff)
Forward active IB >0 & IC = F IBVCE ≥VBE
SaturationIB >0VCE <VBE
oCE
C gdV
dI
BECE VV
VCE-SAT
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ECE 315 – Spring 2007 – Farhan Rana – Cornell University
CnA
Co
CE
C IV
Ig
dV
dI
CI
CEV
NPN BJT: Output Conductance and the Early Voltage
AV
The slope of the IC vs VCE curves are modeled using the early voltage VA:
The early voltage is usually in the 50-200 V range
ECE 315 – Spring 2007 – Farhan Rana – Cornell University
NPN BJT: Output Conductance
BaseCollectorci
vgm+v
- r
g1
bi
Emitter
ei
oo r
g1
CE
C
oo V
I
rg
1
Output conductance:
CEV
CI
IB = 0 (cutoff)
Forward active IB >0 & IC = F IBVCE ≥VBE
SaturationIB >0VCE <VBE
BECE VV
VCE-SAT
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ECE 315 – Spring 2007 – Farhan Rana – Cornell University
NPN BJT Common Emitter (CE) Voltage Amplifier
B
E
C IC + ic
IE + ie
IB + ib
DDV
R
VBIAS
outOUT vV
SR
+
-
vs+
-
Base Collector ci
vgm+v
- r
g1
bi
Emitter ei
oo r
g1
R outv+
-SR
vs+
-
ss
omout
omout
cout
o
outmc
ss
vRr
rRrgv
vRrgv
Riv
rv
vgi
Rr
rvv
||
||
Voltage gain:
s
oms
outv Rr
rRrg
v
vA
||
ECE 315 – Spring 2007 – Farhan Rana – Cornell University
00
OUTV
INVONBEV
DDV
Cu
t-o
ff
Forward active
SaturationSATCEV
V2.0~
V6.0~
SATCE
ONBE
V
V
Output voltage swing
Input voltage swing
NPN BJT CE Amplifier: Limits of Output Voltage Swing
Bias point
Minimum output voltage and maximum input voltage:If the output voltage becomes too small (happens when the input voltage becomes too large), the BJT will go into the saturation region (in the saturation region the gain is small)
Maximum output voltage and minimum input voltage:If the input voltage becomes too small the BJT will go into cut-off
B
E
C IC + ic
IE + ie
IB + ib
DDV
R
VBIAS
outOUT vV
SR
+
-
vs+
-
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ECE 315 – Spring 2007 – Farhan Rana – Cornell University
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