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

 Page 1


Formula Sheet for MOSFET (Analog and Digital
Electronics) – GATE
1. Basic Concepts
• MOSFET Types: N-channel, P-channel; Enhancement, Depletion.
• Structure: Gate, Drain, Source, Body (Substrate).
• Operating Regions: Cut-o?, Triode (Linear), Saturation.
• Function: Voltage-controlled device, used for ampli?cation and switching.
2. MOSFET Characteristics
• Drain Current (N-channel Enhancement, Saturation):
I
D
=
k
n
2
(V
GS
-V
TH
)
2
(1+?V
DS
)
where:
– k
n
=µ n
C
ox
W
L
: Process transconductance parameter.
– µ n
: Electron mobility.
– C
ox
: Oxide capacitance per unit area.
– W/L: Channel width-to-length ratio.
– V
TH
: Threshold voltage.
– ?: Channel-length modulation parameter.
• 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.
• Depletion Mode (N-channel):
I
D
=
k
n
2
(V
GS
-V
TH
)
2
(conducts at V
GS
= 0)
3. Operating Regions
• Cut-o?: V
GS
<V
TH
, I
D
= 0.
• Triode (Linear): V
GS
>V
TH
, V
DS
<V
GS
-V
TH
.
• Saturation: V
GS
>V
TH
, V
DS
=V
GS
-V
TH
.
1
Page 2


Formula Sheet for MOSFET (Analog and Digital
Electronics) – GATE
1. Basic Concepts
• MOSFET Types: N-channel, P-channel; Enhancement, Depletion.
• Structure: Gate, Drain, Source, Body (Substrate).
• Operating Regions: Cut-o?, Triode (Linear), Saturation.
• Function: Voltage-controlled device, used for ampli?cation and switching.
2. MOSFET Characteristics
• Drain Current (N-channel Enhancement, Saturation):
I
D
=
k
n
2
(V
GS
-V
TH
)
2
(1+?V
DS
)
where:
– k
n
=µ n
C
ox
W
L
: Process transconductance parameter.
– µ n
: Electron mobility.
– C
ox
: Oxide capacitance per unit area.
– W/L: Channel width-to-length ratio.
– V
TH
: Threshold voltage.
– ?: Channel-length modulation parameter.
• 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.
• Depletion Mode (N-channel):
I
D
=
k
n
2
(V
GS
-V
TH
)
2
(conducts at V
GS
= 0)
3. Operating Regions
• Cut-o?: V
GS
<V
TH
, I
D
= 0.
• Triode (Linear): V
GS
>V
TH
, V
DS
<V
GS
-V
TH
.
• Saturation: V
GS
>V
TH
, V
DS
=V
GS
-V
TH
.
1
4. Small-Signal Parameters
• Transconductance:
g
m
=k
n
(V
GS
-V
TH
) =
v
2k
n
I
D
• Output Resistance:
r
o
=
1
?I
D
• Input Resistance: R
in
˜8 (gate is insulated).
5. MOSFET Biasing
• Voltage Divider Bias:
V
G
=V
DD
·
R
2
R
1
+R
2
V
GS
=V
G
-V
S
, V
S
=I
D
R
S
• Drain Current:
I
D
=
V
DD
-V
D
R
D
+R
S
• Q-point Stability: Adjust R
S
and R
D
to set V
GS
>V
TH
.
6. MOSFET as a Switch
• Cut-o?: Open switch (V
GS
<V
TH
, I
D
= 0).
• Triode: Closed switch (V
GS
»V
TH
).
• On-Resistance:
R
DS(on)
˜
1
k
n
(V
GS
-V
TH
)
• Drain-Source Voltage (On):
V
DS(on)
=I
D
R
DS(on)
7. Ampli?er Con?gurations
• Common Source (CS):
A
v
=-g
m
(R
D
?R
L
), R
in
˜8, R
out
˜R
D
• Common Drain (CD, Source Follower):
A
v
˜ 1, R
in
˜8, R
out
˜
1
g
m
• Common Gate (CG):
A
v
=g
m
(R
D
?R
L
), R
in
˜
1
g
m
, R
out
˜R
D
2
Page 3


Formula Sheet for MOSFET (Analog and Digital
Electronics) – GATE
1. Basic Concepts
• MOSFET Types: N-channel, P-channel; Enhancement, Depletion.
• Structure: Gate, Drain, Source, Body (Substrate).
• Operating Regions: Cut-o?, Triode (Linear), Saturation.
• Function: Voltage-controlled device, used for ampli?cation and switching.
2. MOSFET Characteristics
• Drain Current (N-channel Enhancement, Saturation):
I
D
=
k
n
2
(V
GS
-V
TH
)
2
(1+?V
DS
)
where:
– k
n
=µ n
C
ox
W
L
: Process transconductance parameter.
– µ n
: Electron mobility.
– C
ox
: Oxide capacitance per unit area.
– W/L: Channel width-to-length ratio.
– V
TH
: Threshold voltage.
– ?: Channel-length modulation parameter.
• 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.
• Depletion Mode (N-channel):
I
D
=
k
n
2
(V
GS
-V
TH
)
2
(conducts at V
GS
= 0)
3. Operating Regions
• Cut-o?: V
GS
<V
TH
, I
D
= 0.
• Triode (Linear): V
GS
>V
TH
, V
DS
<V
GS
-V
TH
.
• Saturation: V
GS
>V
TH
, V
DS
=V
GS
-V
TH
.
1
4. Small-Signal Parameters
• Transconductance:
g
m
=k
n
(V
GS
-V
TH
) =
v
2k
n
I
D
• Output Resistance:
r
o
=
1
?I
D
• Input Resistance: R
in
˜8 (gate is insulated).
5. MOSFET Biasing
• Voltage Divider Bias:
V
G
=V
DD
·
R
2
R
1
+R
2
V
GS
=V
G
-V
S
, V
S
=I
D
R
S
• Drain Current:
I
D
=
V
DD
-V
D
R
D
+R
S
• Q-point Stability: Adjust R
S
and R
D
to set V
GS
>V
TH
.
6. MOSFET as a Switch
• Cut-o?: Open switch (V
GS
<V
TH
, I
D
= 0).
• Triode: Closed switch (V
GS
»V
TH
).
• On-Resistance:
R
DS(on)
˜
1
k
n
(V
GS
-V
TH
)
• Drain-Source Voltage (On):
V
DS(on)
=I
D
R
DS(on)
7. Ampli?er Con?gurations
• Common Source (CS):
A
v
=-g
m
(R
D
?R
L
), R
in
˜8, R
out
˜R
D
• Common Drain (CD, Source Follower):
A
v
˜ 1, R
in
˜8, R
out
˜
1
g
m
• Common Gate (CG):
A
v
=g
m
(R
D
?R
L
), R
in
˜
1
g
m
, R
out
˜R
D
2
8. Power Dissipation
• Power:
P =V
DS
I
D
• MaximumPower: Limitedbythermalconstraintsandsafeoperatingarea(SOA).
9. CMOS Logic
• Inverter (N-MOS + P-MOS):
V
out
=V
DD
(when N-MOS o?, P-MOS on), V
out
= 0 (when N-MOS on, P-MOS o?)
• Power Consumption:
P
static
˜ 0, P
dynamic
=C
L
V
2
DD
f
where C
L
: Load capacitance, f: Switching frequency.
10. Design Considerations
• Threshold Voltage: Ensure V
GS
>V
TH
for enhancement mode.
• Channel Sizing: Optimize W/L for desired I
D
and speed.
• Applications: Ampli?ers (CS, CD, CG), switches, CMOS digital circuits (NAND,
NOR).
• Load Line Analysis:
V
DS
=V
DD
-I
D
R
D
• Body E?ect: V
TH
increases with V
SB
:
V
TH
=V
TH0
+?
(
v
|V
SB
+2? F
|-
v
|2? F
|
)
where ?: Body e?ect parameter, ? F
: Fermi potential.
3