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

 Page 1


Formula Sheet for Transistors (Analog and Digital
Electronics) – GATE
1. Basic Concepts
• Transistor Types: Bipolar Junction Transistor (BJT), Field-E?ect Transistor
(FET: JFET, MOSFET).
• BJT Types: NPN, PNP.
• MOSFET Types: N-channel, P-channel; Enhancement, Depletion.
• Operating Regions:
– BJT: Active, Saturation, Cut-o?.
– MOSFET: Cut-o?, Triode (Linear), Saturation.
2. BJT Characteristics
• Current Relationships (NPN):
I
E
=I
B
+I
C
I
C
=ßI
B
, I
C
=aI
E
where ß: Current gain (I
C
/I
B
), a =
ß
ß+1
.
• Base-Emitter Voltage: V
BE
˜ 0.7V (silicon, forward bias).
• Early E?ect: I
C
increases with V
CE
in active region.
I
C
=I
S
(
e
V
BE
V
T
)(
1+
V
CE
V
A
)
where V
A
: Early voltage, V
T
˜ 25mV at 300 K.
3. BJT Operating Regions
• Cut-o?: I
B
= 0, I
C
=0, V
BE
< 0.7V.
• Active: V
BE
˜ 0.7V, V
CE
> 0.2V, I
C
=ßI
B
.
• Saturation: V
BE
˜ 0.7V, V
CE
˜ 0.2V.
4. BJT Biasing
• 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
1
Page 2


Formula Sheet for Transistors (Analog and Digital
Electronics) – GATE
1. Basic Concepts
• Transistor Types: Bipolar Junction Transistor (BJT), Field-E?ect Transistor
(FET: JFET, MOSFET).
• BJT Types: NPN, PNP.
• MOSFET Types: N-channel, P-channel; Enhancement, Depletion.
• Operating Regions:
– BJT: Active, Saturation, Cut-o?.
– MOSFET: Cut-o?, Triode (Linear), Saturation.
2. BJT Characteristics
• Current Relationships (NPN):
I
E
=I
B
+I
C
I
C
=ßI
B
, I
C
=aI
E
where ß: Current gain (I
C
/I
B
), a =
ß
ß+1
.
• Base-Emitter Voltage: V
BE
˜ 0.7V (silicon, forward bias).
• Early E?ect: I
C
increases with V
CE
in active region.
I
C
=I
S
(
e
V
BE
V
T
)(
1+
V
CE
V
A
)
where V
A
: Early voltage, V
T
˜ 25mV at 300 K.
3. BJT Operating Regions
• Cut-o?: I
B
= 0, I
C
=0, V
BE
< 0.7V.
• Active: V
BE
˜ 0.7V, V
CE
> 0.2V, I
C
=ßI
B
.
• Saturation: V
BE
˜ 0.7V, V
CE
˜ 0.2V.
4. BJT Biasing
• 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
1
• Collector-to-Base Bias:
I
B
=
V
CC
-V
BE
R
B
+(ß +1)R
E
• Stability Factor (S):
S =
? I
C
? I
CBO
˜ 1+ß·
R
B
R
B
+(ß +1)R
E
5. MOSFET Characteristics
• Drain Current (N-channel Enhancement, Saturation):
I
D
=
k
n
2
(V
GS
-V
TH
)
2
where k
n
=µ n
C
ox
W
L
, V
TH
: Threshold voltage.
• Triode Region:
I
D
=k
n
[
(V
GS
-V
TH
)V
DS
-
V
2
DS
2
]
• Cut-o?: V
GS
<V
TH
, I
D
=0.
6. MOSFET Operating Regions
• Cut-o?: V
GS
<V
TH
.
• Triode: V
GS
>V
TH
, V
DS
<V
GS
-V
TH
.
• Saturation: V
GS
>V
TH
, V
DS
=V
GS
-V
TH
.
7. Small-Signal Parameters (BJT)
• Transconductance:
g
m
=
I
C
V
T
• Input Resistance:
r
p
=
ßV
T
I
C
• Output Resistance:
r
o
=
V
A
I
C
8. Small-Signal Parameters (MOSFET)
• Transconductance:
g
m
=k
n
(V
GS
-V
TH
)=
v
2k
n
I
D
2
Page 3


Formula Sheet for Transistors (Analog and Digital
Electronics) – GATE
1. Basic Concepts
• Transistor Types: Bipolar Junction Transistor (BJT), Field-E?ect Transistor
(FET: JFET, MOSFET).
• BJT Types: NPN, PNP.
• MOSFET Types: N-channel, P-channel; Enhancement, Depletion.
• Operating Regions:
– BJT: Active, Saturation, Cut-o?.
– MOSFET: Cut-o?, Triode (Linear), Saturation.
2. BJT Characteristics
• Current Relationships (NPN):
I
E
=I
B
+I
C
I
C
=ßI
B
, I
C
=aI
E
where ß: Current gain (I
C
/I
B
), a =
ß
ß+1
.
• Base-Emitter Voltage: V
BE
˜ 0.7V (silicon, forward bias).
• Early E?ect: I
C
increases with V
CE
in active region.
I
C
=I
S
(
e
V
BE
V
T
)(
1+
V
CE
V
A
)
where V
A
: Early voltage, V
T
˜ 25mV at 300 K.
3. BJT Operating Regions
• Cut-o?: I
B
= 0, I
C
=0, V
BE
< 0.7V.
• Active: V
BE
˜ 0.7V, V
CE
> 0.2V, I
C
=ßI
B
.
• Saturation: V
BE
˜ 0.7V, V
CE
˜ 0.2V.
4. BJT Biasing
• 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
1
• Collector-to-Base Bias:
I
B
=
V
CC
-V
BE
R
B
+(ß +1)R
E
• Stability Factor (S):
S =
? I
C
? I
CBO
˜ 1+ß·
R
B
R
B
+(ß +1)R
E
5. MOSFET Characteristics
• Drain Current (N-channel Enhancement, Saturation):
I
D
=
k
n
2
(V
GS
-V
TH
)
2
where k
n
=µ n
C
ox
W
L
, V
TH
: Threshold voltage.
• Triode Region:
I
D
=k
n
[
(V
GS
-V
TH
)V
DS
-
V
2
DS
2
]
• Cut-o?: V
GS
<V
TH
, I
D
=0.
6. MOSFET Operating Regions
• Cut-o?: V
GS
<V
TH
.
• Triode: V
GS
>V
TH
, V
DS
<V
GS
-V
TH
.
• Saturation: V
GS
>V
TH
, V
DS
=V
GS
-V
TH
.
7. Small-Signal Parameters (BJT)
• Transconductance:
g
m
=
I
C
V
T
• Input Resistance:
r
p
=
ßV
T
I
C
• Output Resistance:
r
o
=
V
A
I
C
8. Small-Signal Parameters (MOSFET)
• Transconductance:
g
m
=k
n
(V
GS
-V
TH
)=
v
2k
n
I
D
2
• Output Resistance:
r
o
=
1
?I
D
where ?: Channel-length modulation parameter.
9. Transistor Applications
• BJT as Switch:
– Cut-o?: Open switch.
– Saturation: Closed switch.
• MOSFET as Switch:
R
DS(on)
˜ low resistance in triode region
• Ampli?er Con?gurations (BJT):
– Common Emitter: High gain, A
v
=-g
m
R
C
.
– Common Collector: Voltage gain ˜ 1, high current gain.
– Common Base: High voltage gain, low input impedance.
• MOSFET Ampli?er:
A
v
=-g
m
R
D
(Common Source, saturation region)
10. Design Considerations
• Biasing Stability: Minimize S for BJT, ensure V
GS
>V
TH
for MOSFET.
• Thermal Runaway (BJT): Prevent with proper R
E
.
• Power Dissipation:
P =V
CE
I
C
(BJT), P =V
DS
I
D
(MOSFET)
• Applications: Ampli?ers, switches, oscillators, digital logic (e.g., CMOS).
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