Chapter 5 Bipolar Junction Transistors

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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


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.