Điện tử cơ bản - Công thức tính phân cực tranzitor P2

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
48 Discrete
Circuit BJT Amplifiers
NTUEE Electronics – L. H. Lu 4-1
4
.
8

Discrete
-
Circuit

BJT

Amplifiers
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.
NTUEE Electronics – L. H. Lu 4-2
Mode EBJ CBJ
Cutoff Reverse Reverse
Active Forward Reverse
Saturation Forward Forward
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 (

) = i
En
/ ( i
En
+ i
Ep
)
Base transport factor (

T
) = i
Cn
/ i
En
Common-base current gain (


) = i
Cn
/ i
E
=

T
< 1
Terminal currents of BJT in active mode:
i
E
(emitter current) = i
En
(electron injection from E to B) + i
Ep
(hole injection from B to E)
i
C
(collector current) = i
Cn
(electron drift) + i
CBO
(CBJ reverse saturation current with emitter open)
i
B
(base current) = i
B1
(hole injection from B to E) + i
B2
(recombination in base region)

NTUEE Electronics – L. H. Lu 4-3
Terminal currents:
Collector current:
Base current:
 Hole injection into emitter due to forward bias:
 Eelectron-hole recombination in base:
 Total base current:
Emitter current:
TBETBE
Vv
S
Vv
B
inBE
BnBEBnBECnC
eIe
WN
nqDA
WnqDAdxxdnqDAii
//
2
/)0(/)( 
TBE
Vv
pEE
ipEE
EpEEB
e
LN
nqDA

dxxdpqDAi
/
2
1
/)( 
TBE
Vv
SC
CBCE
e
Ii
iiii
/
1







TBE
Vv
nB
iE
nBEnnB
e
N
qWnA
WnqAQi

/
2
2
2
/)0(
2
1
/











C
Vv
nnBpEE
B
nB
pE
SBBB
i
e
D
W

L
W
N
N
D
D
Iiii
TBE

/
2
21
)
2
1
(
NTUEE Electronics – L. H. Lu 4-4



Large-signal model and current gain for BJT in active region
Common-emitter current gain:
)1/()
2
1
(
1
2






nnBpEE
B
nB
pE
B
C
D
W
L
W
N
N
D
D
i
i
Common-base current gain
i
B
i
C
i
E
1

(


+1)
1
Common-emitter
current gain
i
B
i
E
i
C

(1

)
Common-base current gain:
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.
NTUEE Electronics – L. H. Lu 4-5
)1/(





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 v
BC
increases
Collector current drops from the value in active mode for negative v
CB
For a given v
BE
, i
C
drops sharply to zero at v
CB
around 0.5 V and v
CE
around 0.2 V.
BJT in saturation: V
CEsat
= 0.2 V
Current gain reduces from

to

forced
:


saturation
B
C

forced
i
i
NTUEE Electronics – L. H. Lu 4-6
n
p0
n
p0
exp(v
BE
/V
T
)
n
p0
exp(v
BC
/V
T
)
v
BC
increases
Ebers-Moll model
In EM model, the EBJ and CBJ are represented by two back to back diodes i
DE
and i
DC
.
The 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 which can not be performed by the simplified models.
The diode currents:
The terminal currents:
Application of the EM model
The forward active mode:
i
i
CEB
iii


SSCRSEF
III








1
1

/
V
v
I
I
)1(
/

TBE
Vv
SEDE
eIi )1(
/

TBC
Vv
SCDC
eIi
DEFDCC
iii




DCRDEE
iii



The saturation mode:

NTUEE Electronics – L. H. Lu 4-7
i
DE
i
DC

F
i
DE

R
i
DC
i
C
i
E
i
B









F
S

Vv
F
S
E
Ie
I
i
TBE

1
1
/










1
1
/
R
S
V
v
SC

I
e
I
i
T
B
E










RF
S
Vv
F
S
B
Ie
I
i
TBE

11
/

TBC
TBE
Vv
S
Vv
SEE
eIeIi
/
/

TBC
TBE
Vv
SC
Vv
SC
eIeIi
/
/

TBC
TBE
Vv
RSC
Vv
FSEB
eIeIi
/
/
)1()1(



The cutoff mode
 I
CBO
(CBJ reverse current with emitter open-circuited)
I
CBO
= (1

R

F
)I
SC
Both EBJ and CBJ are reverse-biased.
In real case, reverse current depends on v
CB
.
 I
CEO
(CBJ reverse current with base open-circuited)
I
CEO
= I
CBO
/(1

F
)



F
is always smaller than unity such that I
CEO
> I
CBO
.
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.

EBJ

current

flows

from

(E

to

B)

so

EBJ

is

slightly

forward
biased.
NTUEE Electronics – L. H. Lu 4-8
 +
EC
B
(2)

R
I
SC
I
SC
(1)
i
C
i
E
= 0
i
B
(3)

R

I
SC

R

F
I
SC
(4)
i
C
= I
CBO
= (1

R

F
)I
SC
(5)
i
B
= (

R
)I
SC
+ (


F
)i
DE
= 0  i
DE
= I
SC
(

R
) / (

F
) (5)
E
C
B
(2)

R
I
SC
I
SC
(1)
i
C
i
B
= 0

i
E
 +
(3) i
DE

F
i
DE
(4)
i
C
= I
SC
+

F
i
DE
= I
SC
(1

R

F
)/ (1

F
)  I

CEO
= I
CBO
/ (

F
) (6)
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:
Base current:
Emitter current:
L
ildld tifBJTi ti i
TEB
Vv
SC
eIi
/


/
CB
ii 
BCE
iii



L
ar
g
e-s
ig
na
l
mo
d
e
l
an
d
curren
t

g
a
i
n
f
or
BJT

i
n ac
ti
ve re

gi
on
NTUEE Electronics – L. H. Lu 4-9
Common-base current gain
i
B
i
C
i
E
1

(

+1)
1
Common-emitter
current gain
i
B
i
E
i
C

(1

)
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 values of 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.
NTUEE Electronics – L. H. Lu 4-10
TBE
Vv
SC
eIi
/

TBE
Vv
SC
B
e
Ii
i
/


TBE
Vv
SC
E
e
Ii
i

/


TEB
Vv
SC
eIi
/

TEB
Vv
SC
B
e
Ii
i
/


TEB
Vv
SC
E
e
Ii
i
/


BCE

iii


1









1
pnp transistornpn transistor
Current-voltage characteristics of BJT
The i
C
-v
CB
characteristics The i
C
-v
CE
characteristics
The Early effect
As CBJ reverse bias increases, the effective base width W
eff
reduces due to the increasing CBJ depletion.
For a constant junction voltage v

BE
:
 The slope of n
B
(x) increases  i
C
increases
 Charge storage Q
n
reduces  i
B
decreases
 Current gain

and

increases
Early voltage (V
A
) is used for the linear approximation of Early Effect.
Linear dependence of i
C
on v
CE
:
Exhibit finite output resistance:
NTUEE Electronics – L. H. Lu 4-11
n
B
(0)

n
B0
0 W
X
W
Y
W
Z
V
Y
V
Z
V
X
)/1(
/
ACE
Vv
SC
VveIi
TBE

C
A
constantv
CE
C
o
I
V

v
i
r
BE












1
Common-base output characteristics
breakdownEarly effect
i
C
versus v
CB
plot with various i
E
as parameter is known as common-base output characteristics
The slope indicates that i
C
depends to a small extent on v
CB

 Early effect
i
C
increases rapidly at high v
CB
 breakdown
BCJ is slightly forward-biased for 0.4V < v
CB
< 0
No significant change is observed in i
C
The BJT still exhibits I-V characteristics as in the active mode
BCJ turns on strongly and the i
C
starts to decrease for v
BC
< 0.4V
 I-V characteristics in the saturation mode and v
CEsat
is considered a constant ( 0.2 V)
Current gain (

): large-signal

 i
C
/i
E
and small-signal (incremental)


i
C
/i
E
NTUEE Electronics – L. H. Lu 4-12
Common-emitter output characteristics (I)
i
C
versus v
CE
plot with various v
BE
as parameter.
Common-emitter current gain is defined as

= i
C
/ i
B
The BCJ turns on with a positive v
BC
at low v
CE
BJT operates in saturation mode
The i
C
curve has a finite slope due to Early effect
The characteristics lines meet at v
CE
= V

A
V
A
is called the Early Voltage (~ 50 to 100 V)
Common-emitter output characteristics (II)
Plot of i
C
versus v
CE
with various i
B
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 i
B
= 0
Current gain: large-signal

dc
 i
C
/i
B
and

ac
i
C

/i
B
NTUEE Electronics – L. H. Lu 4-13
breakdownEarly effect
Saturation of common-emitter configuration
In saturation region, it behaves as a closed switch with a small resistance R
CEsat
The saturation IV curve can be approximated by a straight line intersecting the v
CE
axis at V
CEoff
The saturation voltage V
CEsat
 V
CEoff
+ I
Csat
R
CEsat
V
CEsat
is normally treated as a constant of 0.2 V for simplicity regardless the value of i
C
Incremental

in saturation is lower than that in active region:

forced
 I
Csat

/ I
B
<

Overdrive factor 

/

forced
NTUEE Electronics – L. H. Lu 4-14
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, BV
CBO
is defined at i
E
= 0.
The breakdown voltage is smaller than BV
CBO
for i
E
> 0.
In CE configuration, BV
CEO
is defined at i
B
=0.
The breakdown voltage is smaller than BV

CEO
for i
B
> 0.
Typically, BV
CEO
is about half of BV
CBO
.

Breakdown of the BCJ is not destructive as long as the power dissipation is kept within safe limits

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


NTUEE Electronics – L. H. Lu 4-15
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
v
BE
v
BC
Active Mode
v
BE
 0, v
BC
 0
Saturation Mode
v
BE
 0, v
BC
 0
Inverse Mode
v
BE
 0, v
BC
 0
Cutoff Mode
v
BE
 0, v
BC
 0

npn transistor
v
EB
v
CB
Active Mode
v
EB
 0, v
CB
 0
Saturation Mode
v
EB
 0, v
CB
 0
Inverse Mode
v
EB
 0, v
CB
 0
Cutoff Mode
v
EB
 0, v
CB
 0
pnp transistor

Simplified models and classifications for the operation of the npn BJT
Cut-off mode:
 i
E
= i
C
= i
B
= 0
 v
BE
< 0.5 V and v
BC
< 0.4 V
Active mode:
 v
BE
= 0.7 V and i
B
: i
C
: i
E
= 1:

: (1+

)
 v
CE

> 0.3 V
Saturation mode:
 v
BE
= 0.7 V and v
CE
= 0.2 V
 i
C
/i
B
=

forced
<

NTUEE Electronics – L. H. Lu 4-16
Equivalent circuit models
NTUEE Electronics – L. H. Lu 4-17
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
Example 4.5
NTUEE Electronics – L. H. Lu 4-18
Example 4.9
Example 4 11
Example

4
.
11
NTUEE Electronics – L. H. Lu 4-19
4.4 Applying the BJT in Amplifier Design
BJT voltage amplifier
A BJT circuit with a collector resistor R
C
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 v
BE
 Cutoff mode:
0 V  v
BE
< 0.5 V and i
C
= 0
v
O
= v
CE
= V
CC
 Active mode:
v
BE
> 0.5 V and i
C

= I
S
exp(v
BE
/V
T
)

v
O
=
V
CC

i
C
R
C
=
V
CC

R
C
I
S
exp
(
v
BE

/
V
T
)

v
O

V
CC
i
C
R
C

V
CC
R
C
I
S
exp
(
v
BE
/
V
T
)
 Saturation:

v
BE
further increases
v
CE
= v
CEsat
= 0.2 V
v
O
= 0.2 V
NTUEE Electronics – L. H. Lu 4-20
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
I
C
= I
S
exp(V
BE
/V
T
)
The signal to be amplified is superimposed on V
BE
v
BE
(t) = V

BE
+ v
be
(t)
The time-varying part in v
CE
(t) is the amplified signal
The circuit can be used as a linear amplifier if:

A proper bias point is chosen for gain

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:
Voltage gain depends on I

C
and R
C
Maximum voltage gain of the amplifier
NTUEE Electronics – L. H. Lu 4-21
C
T
C
Vv
BE
CE
v
R
V
I
dv
dv
A
BEBE


||
maxv
T
CC
T
CECC
C
T
C

v
A
V
V
V
VV
R
V
I
A 


Determining the VTC by graphical analysis
Provides more insight into the circuit operation
Load line: the straight line represents in effect the load
i
C
= (V
CC
V
CE
)/R
C
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 V
CC
(upper bound) and V
CEsat

(lower bound)
The load line determines the voltage gain

The bias point determines the headroom or maximum upper/lower voltage swing of the amplifier

The

bias

point

determines

the

headroom

or

maximum

upper/lower

voltage

swing

of

the

amplifier

NTUEE Electronics – L. H. Lu 4-22
4.5 Small-Signal Operation and Models
The collector current and the transconductance
The total quantities (ac + dc) of the collector current:
Small-signal approximation: v
be
<< V
T
The transconductance indicates the incremental change of i
C
versus change of v
BE

Th
tdt
idt i dbitd ll t t
I
TbeTbeTBETBE
Vv
C
Vv
VV
S
Vv
SC
beBEBE
eIeeIeIi

vVv
//
//
)( 

be
T
C
C
T
be
CcCC
v
V
I
I
V
v
IiIi 









1
T

C
Ii
BE
C
m
V
I
v
i
g
CC






Th
e
t
ranscon
d
uc
t
ance
g
m
i
s
d

e
t
erm
i
ne
d

b
y
it
s
d
c co
ll
ec
t
or curren
t

I
C
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:
Small-signal approximation:
Resistance r

is the small-signal input resistance between base and emitter (looking into the base)
NTUEE Electronics – L. H. Lu 4-23
TbeTbe

TBETBE
Vv
B
VvVV
S
Vv
SC
B
eIee
I
e
II
i
////


be
T
B
B
T
be
BbBB
v
V
I
I
V
v
IiIi










 1
B
T
mb
be
I
V
gi
v
r 


The emitter current and the input resistance at the emitter
The total quantities (ac + dc) of the emitter current:
Small-signal approximation:
Relation between r

and r
e
:


cCC
eEE
iII
iIi 
mmE
T
e
be
e
ggI
V
i
v
r
1


be
T
E
be
T
C
be
mc
e
v
V
I
v

V
I
v
gi
i 

e
r


Output resistance accounting for Early effect
Use the collector current equation with linear v
CE
dependence:
The output resistance r
o
is included to represent Early Effect of the BJT
The resulting r
o
is typically a large resistance and can be neglected to simplify the analysis
NTUEE Electronics – L. H. Lu 4-24
e
rr )1(



m
m
e
g

r
g












A
CE
Vv
SC
V
v
eIi
TBE
1
/
C
A
constantv
CE
C
o

I
V
v
i
r
BE












1
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 r
o
The T model
 Typically used as the emitter is not grounded
NTUEE Electronics – L. H. Lu 4-25
Neglect r
o