Formula Sheets: Bipolar Junction Transistors | Analog and Digital Electronics - Electrical Engineering (EE) PDF Download

 Page 1


Formula Sheet for Bipolar Junction Transistors
(Analog and Digital Electronics) – GATE
1. Basic Concepts
• BJT Types: NPN, PNP.
• Structure: Emitter, Base, Collector.
• Operating Regions: Active, Saturation, Cut-o?.
• Function: Current-controlled device, used for ampli?cation and switching.
2. BJT Current Relationships
• Current Equation:
I
E
=I
B
+I
C
• Collector Current:
I
C
=ßI
B
, I
C
=aI
E
where:
– ß: Common-emitter current gain (I
C
/I
B
, typically 201000).
– a: Common-base current gain (I
C
/I
E
, a =
ß
ß+1
).
• Emitter Current:
I
E
=I
C
/a =(ß +1)I
B
3. BJT Characteristics
• Base-Emitter Voltage: V
BE
˜ 0.7V (silicon, forward bias in active/saturation).
• Shockley Equation:
I
C
=I
S
(
e
V
BE
V
T
-1
)
where:
– I
S
: Reverse saturation current.
– V
T
: Thermal voltage, V
T
=
kT
q
˜ 25mV at 300 K.
• Early E?ect: Accounts for I
C
increase with V
CE
.
I
C
=I
S
(
e
V
BE
V
T
)(
1+
V
CE
V
A
)
where V
A
: Early voltage (typically 50150 V).
4. Operating Regions
• Cut-o?: I
B
= 0, I
C
=0, V
BE
< 0.7V, V
CE
>V
CC
.
1
Page 2


Formula Sheet for Bipolar Junction Transistors
(Analog and Digital Electronics) – GATE
1. Basic Concepts
• BJT Types: NPN, PNP.
• Structure: Emitter, Base, Collector.
• Operating Regions: Active, Saturation, Cut-o?.
• Function: Current-controlled device, used for ampli?cation and switching.
2. BJT Current Relationships
• Current Equation:
I
E
=I
B
+I
C
• Collector Current:
I
C
=ßI
B
, I
C
=aI
E
where:
– ß: Common-emitter current gain (I
C
/I
B
, typically 201000).
– a: Common-base current gain (I
C
/I
E
, a =
ß
ß+1
).
• Emitter Current:
I
E
=I
C
/a =(ß +1)I
B
3. BJT Characteristics
• Base-Emitter Voltage: V
BE
˜ 0.7V (silicon, forward bias in active/saturation).
• Shockley Equation:
I
C
=I
S
(
e
V
BE
V
T
-1
)
where:
– I
S
: Reverse saturation current.
– V
T
: Thermal voltage, V
T
=
kT
q
˜ 25mV at 300 K.
• Early E?ect: Accounts for I
C
increase with V
CE
.
I
C
=I
S
(
e
V
BE
V
T
)(
1+
V
CE
V
A
)
where V
A
: Early voltage (typically 50150 V).
4. Operating Regions
• Cut-o?: I
B
= 0, I
C
=0, V
BE
< 0.7V, V
CE
>V
CC
.
1
• Active: V
BE
˜ 0.7V, V
CE
> 0.2V, I
C
=ßI
B
.
• Saturation: V
BE
˜ 0.7V, V
CE
˜ 0.2V, I
C
<ßI
B
.
5. BJT Biasing
• Fixed Bias:
I
B
=
V
CC
-V
BE
R
B
I
C
=ßI
B
• Voltage Divider Bias:
V
B
=V
CC
·
R
2
R
1
+R
2
V
E
=V
B
-V
BE
, I
E
=
V
E
R
E
I
C
˜I
E
, V
CE
=V
CC
-I
C
R
C
-I
E
R
E
• Collector-to-Base Bias:
I
B
=
V
CC
-V
BE
-V
CE
R
B
• Stability Factor (S):
S =
? I
C
? I
CBO
˜ 1+ß·
R
B
R
B
+(ß +1)R
E
6. Small-Signal Parameters
• Transconductance:
g
m
=
I
C
V
T
• Input Resistance:
r
p
=
ßV
T
I
C
• Output Resistance:
r
o
=
V
A
I
C
7. Ampli?er Con?gurations
• Common Emitter (CE):
A
v
=-g
m
(R
C
?R
L
), R
in
˜r
p
, R
out
˜R
C
• Common Collector (CC):
A
v
˜ 1, R
in
˜r
p
+(ß +1)R
E
, R
out
˜
r
p
ß +1
2
Page 3


Formula Sheet for Bipolar Junction Transistors
(Analog and Digital Electronics) – GATE
1. Basic Concepts
• BJT Types: NPN, PNP.
• Structure: Emitter, Base, Collector.
• Operating Regions: Active, Saturation, Cut-o?.
• Function: Current-controlled device, used for ampli?cation and switching.
2. BJT Current Relationships
• Current Equation:
I
E
=I
B
+I
C
• Collector Current:
I
C
=ßI
B
, I
C
=aI
E
where:
– ß: Common-emitter current gain (I
C
/I
B
, typically 201000).
– a: Common-base current gain (I
C
/I
E
, a =
ß
ß+1
).
• Emitter Current:
I
E
=I
C
/a =(ß +1)I
B
3. BJT Characteristics
• Base-Emitter Voltage: V
BE
˜ 0.7V (silicon, forward bias in active/saturation).
• Shockley Equation:
I
C
=I
S
(
e
V
BE
V
T
-1
)
where:
– I
S
: Reverse saturation current.
– V
T
: Thermal voltage, V
T
=
kT
q
˜ 25mV at 300 K.
• Early E?ect: Accounts for I
C
increase with V
CE
.
I
C
=I
S
(
e
V
BE
V
T
)(
1+
V
CE
V
A
)
where V
A
: Early voltage (typically 50150 V).
4. Operating Regions
• Cut-o?: I
B
= 0, I
C
=0, V
BE
< 0.7V, V
CE
>V
CC
.
1
• Active: V
BE
˜ 0.7V, V
CE
> 0.2V, I
C
=ßI
B
.
• Saturation: V
BE
˜ 0.7V, V
CE
˜ 0.2V, I
C
<ßI
B
.
5. BJT Biasing
• Fixed Bias:
I
B
=
V
CC
-V
BE
R
B
I
C
=ßI
B
• Voltage Divider Bias:
V
B
=V
CC
·
R
2
R
1
+R
2
V
E
=V
B
-V
BE
, I
E
=
V
E
R
E
I
C
˜I
E
, V
CE
=V
CC
-I
C
R
C
-I
E
R
E
• Collector-to-Base Bias:
I
B
=
V
CC
-V
BE
-V
CE
R
B
• Stability Factor (S):
S =
? I
C
? I
CBO
˜ 1+ß·
R
B
R
B
+(ß +1)R
E
6. Small-Signal Parameters
• Transconductance:
g
m
=
I
C
V
T
• Input Resistance:
r
p
=
ßV
T
I
C
• Output Resistance:
r
o
=
V
A
I
C
7. Ampli?er Con?gurations
• Common Emitter (CE):
A
v
=-g
m
(R
C
?R
L
), R
in
˜r
p
, R
out
˜R
C
• Common Collector (CC):
A
v
˜ 1, R
in
˜r
p
+(ß +1)R
E
, R
out
˜
r
p
ß +1
2
• Common Base (CB):
A
v
=g
m
(R
C
?R
L
), R
in
˜
r
p
ß +1
, R
out
˜R
C
8. BJT as a Switch
• Cut-o?: Open switch (I
C
=0).
• Saturation: Closed switch (V
CE
˜ 0.2V).
• Collector Current in Saturation:
I
C,sat
=
V
CC
-V
CE,sat
R
C
9. Power Dissipation
• Power:
P =V
CE
I
C
+V
BE
I
B
˜V
CE
I
C
• Maximum Power: Occurs in active region, limited by thermal constraints.
10. Design Considerations
• Thermal Stability: Use R
E
to prevent thermal runaway.
• Biasing: Ensure stable Q-point in active region for ampli?ers.
• Applications: Ampli?ers (CE, CC, CB), switches, oscillators, digital logic.
• Load Line Analysis:
V
CE
=V
CC
-I
C
R
C
• Beta Variation: Design for minimum ß to ensure reliability.
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