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

 Page 1


Formula Sheet for Ampli?ers (Analog and Digital
Electronics) – GATE
1. Basic Concepts
• Ampli?er: Circuit that increases the power, voltage, or current of an input signal.
• Types: Voltage, current, transconductance, transresistance ampli?ers.
• Transistors Used: BJT (NPN, PNP), MOSFET (N-channel, P-channel).
• Con?gurations: CommonEmitter(CE),CommonCollector(CC),CommonBase
(CB) for BJT; Common Source (CS), Common Drain (CD), Common Gate (CG)
for MOSFET.
2. BJT Small-Signal Parameters
• Transconductance:
g
m
=
I
C
V
T
where V
T
˜ 25mV at 300 K, I
C
: Collector current.
• Input Resistance:
r
p
=
ßV
T
I
C
where ß: Current gain.
• Output Resistance:
r
o
=
V
A
I
C
where V
A
: Early voltage.
3. MOSFET Small-Signal Parameters
• Transconductance:
g
m
=k
n
(V
GS
-V
TH
) =
v
2k
n
I
D
where k
n
=µ n
C
ox
W
L
, V
TH
: Threshold voltage.
• Output Resistance:
r
o
=
1
?I
D
where ?: Channel-length modulation parameter.
• Input Resistance: R
in
˜8 (gate insulated).
1
Page 2


Formula Sheet for Ampli?ers (Analog and Digital
Electronics) – GATE
1. Basic Concepts
• Ampli?er: Circuit that increases the power, voltage, or current of an input signal.
• Types: Voltage, current, transconductance, transresistance ampli?ers.
• Transistors Used: BJT (NPN, PNP), MOSFET (N-channel, P-channel).
• Con?gurations: CommonEmitter(CE),CommonCollector(CC),CommonBase
(CB) for BJT; Common Source (CS), Common Drain (CD), Common Gate (CG)
for MOSFET.
2. BJT Small-Signal Parameters
• Transconductance:
g
m
=
I
C
V
T
where V
T
˜ 25mV at 300 K, I
C
: Collector current.
• Input Resistance:
r
p
=
ßV
T
I
C
where ß: Current gain.
• Output Resistance:
r
o
=
V
A
I
C
where V
A
: Early voltage.
3. MOSFET Small-Signal Parameters
• Transconductance:
g
m
=k
n
(V
GS
-V
TH
) =
v
2k
n
I
D
where k
n
=µ n
C
ox
W
L
, V
TH
: Threshold voltage.
• Output Resistance:
r
o
=
1
?I
D
where ?: Channel-length modulation parameter.
• Input Resistance: R
in
˜8 (gate insulated).
1
4. BJT Ampli?er Con?gurations
4.1 Common Emitter (CE)
• Voltage Gain:
A
v
=-g
m
(R
C
?R
L
?r
o
)
• Input Resistance: R
in
˜r
p
.
• Output Resistance: R
out
˜R
C
.
• Characteristics: High voltage and current gain, phase inversion.
4.2 Common Collector (CC)
• Voltage Gain:
A
v
˜ 1
• Input Resistance: R
in
˜r
p
+(ß +1)(R
E
?R
L
).
• Output Resistance: R
out
˜
rp
ß+1
?R
E
.
• Characteristics: High input impedance, low output impedance, no phase inver-
sion.
4.3 Common Base (CB)
• Voltage Gain:
A
v
=g
m
(R
C
?R
L
?r
o
)
• Input Resistance: R
in
˜
rp
ß+1
.
• Output Resistance: R
out
˜R
C
.
• Characteristics: High voltage gain, low input impedance, no phase inversion.
5. MOSFET Ampli?er Con?gurations
5.1 Common Source (CS)
5.2 Common Drain (CD, Source Follower)
• Voltage Gain:
A
v
˜ 1
• Input Resistance: R
in
˜8.
• Output Resistance: R
out
˜
1
gm
?R
S
.
• Characteristics: High input impedance, low output impedance, no phase inver-
sion.
2
Page 3


Formula Sheet for Ampli?ers (Analog and Digital
Electronics) – GATE
1. Basic Concepts
• Ampli?er: Circuit that increases the power, voltage, or current of an input signal.
• Types: Voltage, current, transconductance, transresistance ampli?ers.
• Transistors Used: BJT (NPN, PNP), MOSFET (N-channel, P-channel).
• Con?gurations: CommonEmitter(CE),CommonCollector(CC),CommonBase
(CB) for BJT; Common Source (CS), Common Drain (CD), Common Gate (CG)
for MOSFET.
2. BJT Small-Signal Parameters
• Transconductance:
g
m
=
I
C
V
T
where V
T
˜ 25mV at 300 K, I
C
: Collector current.
• Input Resistance:
r
p
=
ßV
T
I
C
where ß: Current gain.
• Output Resistance:
r
o
=
V
A
I
C
where V
A
: Early voltage.
3. MOSFET Small-Signal Parameters
• Transconductance:
g
m
=k
n
(V
GS
-V
TH
) =
v
2k
n
I
D
where k
n
=µ n
C
ox
W
L
, V
TH
: Threshold voltage.
• Output Resistance:
r
o
=
1
?I
D
where ?: Channel-length modulation parameter.
• Input Resistance: R
in
˜8 (gate insulated).
1
4. BJT Ampli?er Con?gurations
4.1 Common Emitter (CE)
• Voltage Gain:
A
v
=-g
m
(R
C
?R
L
?r
o
)
• Input Resistance: R
in
˜r
p
.
• Output Resistance: R
out
˜R
C
.
• Characteristics: High voltage and current gain, phase inversion.
4.2 Common Collector (CC)
• Voltage Gain:
A
v
˜ 1
• Input Resistance: R
in
˜r
p
+(ß +1)(R
E
?R
L
).
• Output Resistance: R
out
˜
rp
ß+1
?R
E
.
• Characteristics: High input impedance, low output impedance, no phase inver-
sion.
4.3 Common Base (CB)
• Voltage Gain:
A
v
=g
m
(R
C
?R
L
?r
o
)
• Input Resistance: R
in
˜
rp
ß+1
.
• Output Resistance: R
out
˜R
C
.
• Characteristics: High voltage gain, low input impedance, no phase inversion.
5. MOSFET Ampli?er Con?gurations
5.1 Common Source (CS)
5.2 Common Drain (CD, Source Follower)
• Voltage Gain:
A
v
˜ 1
• Input Resistance: R
in
˜8.
• Output Resistance: R
out
˜
1
gm
?R
S
.
• Characteristics: High input impedance, low output impedance, no phase inver-
sion.
2
5.3 Common Gate (CG)
• Voltage Gain:
A
v
=g
m
(R
D
?R
L
?r
o
)
• Input Resistance: R
in
˜
1
gm
.
• Output Resistance: R
out
˜R
D
.
• Characteristics: High voltage gain, low input impedance, no phase inversion.
6. Frequency Response
• Low-Frequency Cut-o?: Due to coupling and bypass capacitors.
f
L
=
1
2pR
eq
C
where R
eq
: Equivalent resistance seen by capacitor.
• High-Frequency Cut-o?: Due to parasitic capacitances (e.g., C
p
, C
µ for BJT;
C
gs
, C
gd
for MOSFET).
f
H
=
1
2pR
eq
C
eq
• Bandwidth: BW =f
H
-f
L
.
7. Ampli?er E?ciency
• Class A (BJT/MOSFET):
? =
P
out
P
DC
= 25%
• Class B Push-Pull:
?
max
=
p
4
˜ 78.5%
• Class AB: E?ciency between Class A and B.
8. Power Dissipation
• BJT:
P =V
CE
I
C
• MOSFET:
P =V
DS
I
D
• Maximum Power: Limited by thermal constraints and safe operating area.
3
Page 4


Formula Sheet for Ampli?ers (Analog and Digital
Electronics) – GATE
1. Basic Concepts
• Ampli?er: Circuit that increases the power, voltage, or current of an input signal.
• Types: Voltage, current, transconductance, transresistance ampli?ers.
• Transistors Used: BJT (NPN, PNP), MOSFET (N-channel, P-channel).
• Con?gurations: CommonEmitter(CE),CommonCollector(CC),CommonBase
(CB) for BJT; Common Source (CS), Common Drain (CD), Common Gate (CG)
for MOSFET.
2. BJT Small-Signal Parameters
• Transconductance:
g
m
=
I
C
V
T
where V
T
˜ 25mV at 300 K, I
C
: Collector current.
• Input Resistance:
r
p
=
ßV
T
I
C
where ß: Current gain.
• Output Resistance:
r
o
=
V
A
I
C
where V
A
: Early voltage.
3. MOSFET Small-Signal Parameters
• Transconductance:
g
m
=k
n
(V
GS
-V
TH
) =
v
2k
n
I
D
where k
n
=µ n
C
ox
W
L
, V
TH
: Threshold voltage.
• Output Resistance:
r
o
=
1
?I
D
where ?: Channel-length modulation parameter.
• Input Resistance: R
in
˜8 (gate insulated).
1
4. BJT Ampli?er Con?gurations
4.1 Common Emitter (CE)
• Voltage Gain:
A
v
=-g
m
(R
C
?R
L
?r
o
)
• Input Resistance: R
in
˜r
p
.
• Output Resistance: R
out
˜R
C
.
• Characteristics: High voltage and current gain, phase inversion.
4.2 Common Collector (CC)
• Voltage Gain:
A
v
˜ 1
• Input Resistance: R
in
˜r
p
+(ß +1)(R
E
?R
L
).
• Output Resistance: R
out
˜
rp
ß+1
?R
E
.
• Characteristics: High input impedance, low output impedance, no phase inver-
sion.
4.3 Common Base (CB)
• Voltage Gain:
A
v
=g
m
(R
C
?R
L
?r
o
)
• Input Resistance: R
in
˜
rp
ß+1
.
• Output Resistance: R
out
˜R
C
.
• Characteristics: High voltage gain, low input impedance, no phase inversion.
5. MOSFET Ampli?er Con?gurations
5.1 Common Source (CS)
5.2 Common Drain (CD, Source Follower)
• Voltage Gain:
A
v
˜ 1
• Input Resistance: R
in
˜8.
• Output Resistance: R
out
˜
1
gm
?R
S
.
• Characteristics: High input impedance, low output impedance, no phase inver-
sion.
2
5.3 Common Gate (CG)
• Voltage Gain:
A
v
=g
m
(R
D
?R
L
?r
o
)
• Input Resistance: R
in
˜
1
gm
.
• Output Resistance: R
out
˜R
D
.
• Characteristics: High voltage gain, low input impedance, no phase inversion.
6. Frequency Response
• Low-Frequency Cut-o?: Due to coupling and bypass capacitors.
f
L
=
1
2pR
eq
C
where R
eq
: Equivalent resistance seen by capacitor.
• High-Frequency Cut-o?: Due to parasitic capacitances (e.g., C
p
, C
µ for BJT;
C
gs
, C
gd
for MOSFET).
f
H
=
1
2pR
eq
C
eq
• Bandwidth: BW =f
H
-f
L
.
7. Ampli?er E?ciency
• Class A (BJT/MOSFET):
? =
P
out
P
DC
= 25%
• Class B Push-Pull:
?
max
=
p
4
˜ 78.5%
• Class AB: E?ciency between Class A and B.
8. Power Dissipation
• BJT:
P =V
CE
I
C
• MOSFET:
P =V
DS
I
D
• Maximum Power: Limited by thermal constraints and safe operating area.
3
9. Multistage Ampli?ers
• Total Voltage Gain:
A
v,total
=A
v1
·A
v2
·...·A
vn
• Input Resistance: R
in
=R
in1
.
• Output Resistance: R
out
=R
out,n
.
• Cascading: CE-CS for high gain, CC-CD for bu?ering.
10. Design Considerations
• Biasing: Ensure active/saturation region for BJT/MOSFET.
• Gainvs. Bandwidth: Highergainreducesbandwidth(gain-bandwidthproduct).
• Applications: Audio ampli?ers, RF ampli?ers, operational ampli?ers, digital
bu?ers.
• Load Line Analysis:
V
CE
=V
CC
-I
C
R
C
(BJT), V
DS
=V
DD
-I
D
R
D
(MOSFET)
4