Chapter 5
Bipolar Junction Transistors
Chapter Goals
•
Explore the physical structure of bipolar transistor
•
Study terminal characteristics of BJT.
•
Explore differences between
npn
and
pnp
transistors.
•
Develop the Transport Model for bipolar devices.
•
Define four operation regions of the BJT.
•
Explore model simplifications for the forward active
region.
•
Understand the origin and modeling of the Early effect.
•
Present a PSPICE model for the bipolar transistor. Discuss
bipolar current sources and the current mirror.
Physical Structure
•
The BJT consists of 3 alternating layers
of
n

and
p

type semiconductor called
emitter
(
E
),
base
(
B
) and
collector
(
C
).
•
The majority of current enters collector,
crosses the base region and exits through
the emitter. A small current also enters
the base terminal, crosses the base

emitter junction and exits through the
emitter.
•
Carrier transport in the active base
region directly beneath the heavily
doped (
n
+
) emitter dominates the
i

v
characteristics of the BJT.
Transport Model for the
npn
Transistor
•
The narrow width of the base
region causes a coupling between
the two back to back
pn
junctions.
•
The emitter injects electrons into
base region; almost all of them
travel across narrow base and are
removed by collector.
•
Base

emitter voltage
v
BE
and
base

collector voltage
v
BC
determine the currents in the
transistor and are said to be
positive when they forward

bias
their respective
pn
junctions.
•
The terminal currents are the
collector current(
i
C
), the base
current (
i
B
) and the emitter
current (
i
E
).
•
The primary difference between
the BJT and the FET is that
i
B
is
significant, while
i
G
= 0.
npn
Transistor: Forward Characteristics
Forward transport current is
I
S
is saturation current
V
T
=
kT/q
=0.025 V at room temperature
Base current is given by
Emitter current is given by
In this forward active operation region,
npn
Transistor: Reverse Characteristics
Reverse transport current is
Emitter current is given by
is
reverse current gain
Base current is given by
Base currents in forward and reverse modes
are different due to asymmetric doping levels
in the emitter and collector regions.
npn
Transistor: Complete Transport
Model Equations for Any Bias
The first term in both the emitter and collector current expressions gives
the current transported completely across the base region.
Symmetry exists between base

emitter and base

collector voltages in
establishing the dominant current in the bipolar transistor.
pnp
Transistor: Operation
•
The voltages
v
EB
and
v
CB
are positive when they forward bias
their respective
pn
junctions.
•
Collector current and base current exit the transistor terminals
and emitter current enters the device.
pnp
Transistor: Forward Characteristics
Forward transport current is:
Base current is given by:
Emitter current is given by:
pnp
Transistor: Reverse Characteristics
Reverse transport current is:
Base current is given by:
Emitter current is given by:
pnp
Transistor: Complete Transport
Model Equations for Any Bias
Circuit Representation for Transport
Models
In the
npn
transistor (expressions analogous for the
pnp
transistors), total
current traversing the base is modeled by a current source given by:
Diode currents correspond directly to the 2 components of base current.
Operation Regions of the Bipolar
Transistor
Base

emitter junction
Base

collector junction
i

v
Characteristics Bipolar Transistor:
Common

Emitter Output Characteristics
For
i
B
=0, the transistor is cutoff. If
i
B
>0,
i
C
also increases.
For
v
CE
>
v
BE
, the
npn
transistor is in the
forward active region,
i
C
=
F
i
B
is independent
of
v
CE.
.
For
v
CE
<
v
BE
, the transistor is in saturation.
For
v
CE
< 0, the roles of collector and emitter
are reversed.
i

v
Characteristics of Bipolar Transistor:
Common

Emitter Transfer Characteristic
This characteristic defines the relation
between collector current and base

emitter
voltage of the transistor.
It is almost identical to the transfer
characteristic of a
pn
junction diode.
Setting
v
BC
=0 in the collector

current
expression:
Junction Breakdown Voltages
•
If reverse voltage across either of the two
pn
junctions in the transistor
is too large, the corresponding diode will break down.
•
The emitter is the most heavily doped region, and the collector is the
most lightly doped region.
•
Due to these doping differences, the base

emitter diode has a relatively
low breakdown voltage (3 to 10 V). The collector

base diode is
typically designed to break down at much larger voltages.
•
Transistors must therefore be selected in accordance with the possible
reverse voltages in circuit.
Simplified Forward

Active Region
Model
In the forward

active region, the base

emitter junction is forward

biased
and the base

collector junction is reverse

biased.
v
BE
> 0,
v
BC
< 0
If we assume that
then the transport model terminal current equations simplify to:
The BJT is often considered a current

controlled current source, although
fundamental forward active behavior suggests a voltage

controlled current
source.
Simplified Circuit Model for Forward

Active Region
•
Current in the base

emitter diode is amplified by the common

emitter
current gain
F
and appears at the collector
•
The base and collector currents are exponentially related to the base

emitter
voltage.
•
The base

emitter diode is often replaced by a constant voltage drop model
(
V
BE
= 0.7 V), since it is forward

biased in the forward

active region.
Simplified Forward

Active Region
Model (Analysis Example)
•
Problem:
Find Q

point
•
Given data:
F
=
50,
V
BC
=
V
B

V
C
=

9 V
•
Assumptions:
Forward

active region of operation,
V
BE
= 0.7 V
•
Analysis:
Biasing for BJT
•
The goal of biasing is to establish a known Q

point, which
in turn establishes the initial operating region of transistor.
•
In BJT circuits, the Q

point is represented by (
V
CE
,
I
C
) for
the
npn
transistor or (
V
EC
,
I
C
) for the
pnp
transistor.
•
In general, during circuit analysis, we use a simplified
mathematical relationships derived for the specified
operation region of the transistor.
•
The practical biasing circuits used with BJTs are:
–
The Four

Resistor Bias network
–
The Two

Resistor Bias network
Four

Resistor Bias Network for BJT
Q

point is (4.32 V, 201
m
䄩
BE Loop
CE Loop
Four

Resistor Bias Network for BJT
(Check Analysis)
•
All calculated currents > 0,
V
BC
=
V
BE

V
CE
= 0.7

4.32 =

3.62 V
•
Hence, the base

collector junction is reverse

biased and the assumption
of forward

active region operation is correct.
•
The load

line for the circuit is:
The two points needed to plot the load
line are (0, 12 V) and (314
m
A, 0). The
resulting load line is plotted on the
common

emitter output characteristics
for
I
B
= 2.7
m
A.
The intersection of the corresponding
characteristic with the load line
determines the Q

point.
Four

Resistor Bias Network for BJT:
Design Objectives
•
From the BE loop analysis, we know that
•
This will imply that
I
B
<<
I
2
so that
I
1
=
I
2
to good approximation in
the base voltage divider. Then the base current doesn’t disturb the
voltage divider action, and the Q

point will be approximately
independent of base voltage divider current.
•
Also,
V
EQ
is designed to be large enough that small variations in the
assumed value of
V
BE
won’t have a significant effect on
I
B
.
•
Base voltage divider current is limited by choosing
This ensures that power dissipation in base bias resistors is < 17 % of
the total quiescent power consumed by the circuit, while
I
2
>>
I
B
.
for
Four

Resistor Bias Network for BJT:
Design Guidelines
•
Choose
I
2
= I
C
/5.
This means that (
R
1
+R
2
) =
5V
CC
/I
C
.
•
Let
I
C
R
C
=I
E
R
E
=
(
V
CC

V
CE
)/
2
. Then
R
C
=
(
V
CC

V
CE
)/
2I
C
;
R
E
=
F
R
C
•
If
R
EQ
<<
(
F
+1
)
R
E
, then
I
E
R
E
= V
EQ

V
BE
.
•
Then (
V
CC

V
CE
)/
2 = V
EQ

V
BE
, or
V
EQ
=
(
V
CC

V
CE
+ V
BE
)/
2
.
•
Since
V
EQ
= V
CC
R
1
/
(
R
1
+R
2
) and (
R
1
+R
2
) =
5V
CC
/I
C
,
•
Then
R
2
=
5V
CC
/I
C

R
1
.
•
Check that
R
EQ
<<
(
F
+1
)
R
E
. If not, adjust bullets 1 and 2 above.
•
Note:
In the LabVIEW bias circuit design VI (NPNBias.vi), bullet 1
is called the “Base Margin” and bullet 2 is called the “C

E V(oltage)
Drops”.
Problem 5.87 4

R Bias Circuit Design
Two

Resistor Bias Network for BJT:
Example
•
Problem:
Find the Q

point for the
pnp
transistor in the 2

resistor bias
circuit shown below.
•
Given data:
F
=
50,
V
CC
= 9 V
•
Assumptions:
Forward

active region operation with
V
EB
= 0.7 V
•
Analysis:
Q

point is : (6.01 mA, 2.87 V)
PNP Transistor Switch Circuit Design
Emitter Current for PNP Switch Design
BJT PSPICE Model
•
Besides the capacitances which are
associated with the physical structure,
additional model components are: diode
current
i
S
, capacitance
C
JS
, related to the
large area
pn
junction that isolates the
collector from the substrate and one
transistor from the next.
•
R
B
is the resistance between external
base contact and intrinsic base region.
•
Collector current must pass through
R
C
on its way to the active region of the
collector

base junction.
•
R
E
models any extrinsic emitter
resistance in the device.
BJT PSPICE Model

Typical Values
Saturation Current = 3 e

17 A
Forward current gain = 100
Reverse current gain = 0.5
Forward Early voltage = 75 V
Base resistance = 250
W
Collector Resistance = 50
W
Emitter Resistance = 1
W
Forward transit time = 0.15 ns
Reverse transit time = 15 ns
Minority Carrier Transport in Base
Region
•
With a narrow base region, minority carrier density decreases linearly
across the base, and the Saturation Current (NPN) is:
where
N
AB
= the doping concentration in the base
n
i
2
= the intrinsic carrier concentration (10
10
/cm
3
)
n
bo
=
n
i
2
/
N
AB
D
n
=
the diffusivity = (kT/q)
m
n
•
Saturation current for the PNP transistor is:
•
Due to the higher mobility (
m
) of electrons compared to holes, the
npn
transistor conducts higher current than the
pnp
for equivalent doping
and applied voltages.
Diffusion Capacitance
•
For
v
BE
and hence
i
C
to change, charge stored in the base region must
also change.
•
Diffusion capacitance in parallel with the forward

biased base

emitter
diode produces a good model for the change in charge with
v
BE
.
•
Since transport current normally represents collector current in the
forward

active region,
Early Effect and Early Voltage
•
As reverse

bias across the collector

base junction increases, the width of
the collector

base depletion layer increases and the effective width of base
decreases. This is called “base

width modulation”.
•
In a practical BJT, the output characteristics have a positive slope in the
forward

active region, so that collector current is not independent of
v
CE
.
•
“Early” effect: When the output characteristics are extrapolated back to
where the
i
C
curves intersect at common point,
v
CE
=

V
A
(Early voltage),
which lies between 15 V and 150 V.
•
Simplified F.A.R. equations, which include the Early effect, are:
BJT Current Mirror
•
The collector terminal of a BJT in the
forward

active region mimics the
behavior of a current source.
•
Output current is independent of
V
CC
as
long as
V
CC
≥ 0.8 V. This puts the BJT
in the forward

active region, since
V
BC
≤

0.1 V.
•
Q
1
and
Q
2
are assumed to be a
“matched” pair with identical
I
S,
FO,
and
V
A,
.
BJT Current Mirror (continued)
With an infinite
FO
and
V
A
(ideal device), the mirror ratio is unity. Finite
current gain and Early voltage introduce a mismatch between the output
and reference currents of the mirror.
BJT Current Mirror: Example
•
Problem:
Find output current for given current mirror
•
Given data:
FO
= 75
,
V
A
= 50 V
•
Assumptions:
Forward

active operation region,
V
BE
= 0.7 V
•
Analysis:
VBE =
6.7333e

01
IC2 =
5.3317e

04
IC21 =
5.3317e

04
BJT Current Mirror: Altering the Mirror Ratio
The Mirror Ratio of a BJT current mirror can be changed by simply
changing the relative sizes of the emitters in the transistors. For the
“ideal” case, the Mirror Ratio is determined only by the ratio of the
two emitter areas.
where
I
SO
is the saturation current of a BJT
with one unit of emitter area:
A
E
=1(A). The
actual dimensions of A are technology

dependent.
BJT Current Mirror: Output Resistance
•
A current source using BJTs doesn’t have an output current that is
completely independent of the terminal voltage across it, due to the
finite value of Early voltage. The current source seems to have a
resistive component in series with it.
•
R
o
is defined as the “small signal” output resistance of the current
mirror.
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