1. MOSFET Equations
a) N-channel MOSFET
Cut Off
Linear
VGS " VT
VGS > VT , VDS " VGS # VT
!
Saturation
!
!
VGS > VT , VDS > VGS " VT
!
IDS = 0
IDS = µn Cox
W
L
#
VDS 2 &
V
"
V
V
"
(
)
% GS
((1+ )VDS )
T
DS
2 '
$
1
W
IDS = µn Cox (VGS " VT ) 2 (1+ #VDS )
2
L
!
!
!
!
The simplest model in SPICE (Level 1 or default model) uses the above equations.
Parameter
µnCox
VT0
λ
SPICE Parameter
KP
VTO
LAMBDA
Units
A/V2
V
V-1
Typical Values
200µ
0.5 – 1.0
0.05 – 0.005
b) P-channel MOSFET
Cut Off
Linear
VSG " VT
VSG > VT , VSD " VSG # VT
!
Saturation
!
!
VSG > VT , VSD > VSG " VT
!
!
!
!
!
ISD = 0
ISD
2
W#
VSD &
= µ p Cox %(VSG " VT )VSD "
((1+ )VSD )
L$
2 '
1
W
ISD = µ p Cox (VSG " VT ) 2 (1+ #VSD )
2
L
Example)
VS = 4 V, VG = 2 V, VD = 1 V
VT = -0.8 V, λ = 0, Kp = 100 µA/V2
W = 10 µm, L= 2 µm
Find MOSFET type, operation region, IDS.
- Solution
VDS > VGS " VT # saturation
100µ 10µ
(2 " "0.8 ) 2 (1+ 0) = 360µA
2 2µ
= "360µA
ISD =
IDS
!
2. MOSFET Circuits
Example) The PMOS transistor has VT = -2 V, Kp = 8 µA/V2,
L = 10 µm, λ = 0.
Find the values required for W and R in order to establish
a drain current of 0.1 mA and a voltage VD of 2 V.
- Solution
VD = VG " VSD > VSG # VT " saturation
1 W
8µ W
IDS = Kp (VSG # VT ) 2 (1+ $VSD ) =
(3 # 2) 2 (1+ 0) = 0.1mA
2
L
2 10µ
V
2
IR = D = = 0.1mA
R R
W = 250µm, R = 20k%
!
Example) The PMOS transistor has VT = -1 V, Kp = 8 µA/V2,
W/L = 25, λ = 0.
For I = 100 µA, find the VSD and VSG for R = 0, 10k, 30k, 100k.
- Solution
λ = 0 (no channel length modulation)
1) R = 0
VD = VG " VSD > VSG # VT " saturation
1 W
8µ
ISD = Kp (VSG # VT ) 2 =
$ 25 $ (VSG #1) 2 = 100µ
2
L
2
VSG = 2V VSD = 2V
2) R = 10k
VD # VG = IR = 100µ $10k = 1 " VSD = VSG # VT " saturation or linear
1 W
8µ
ISD = Kp (VSG # VT ) 2 =
$ 25 $ (VSG #1) 2 = 100µ
2
L
2
VSG = 2V VSD = 1V
3) R = 30k
VD # VG = IR = 100µ $ 30k = 3 " VSD < VSG # VT " linear
W
V 2
V 2
((VSG # VT )VSD # SD ) = 8µ $ 25 $ ((VSD + 3 #1)VSD # SD ) = 100µ
L
2
2
% 0.24V VSG = 3.24V
ISD = Kp
VSD
4) R = 100k
VD # VG = IR = 100µ $100k = 10 " VSD < VSG # VT " linear
W
V 2
V 2
((VSG # VT )VSD # SD ) = 8µ $ 25 $ ((VSD + 10 #1)VSD # SD ) = 100µ
L
2
2
% 0.06V VSG = 10.06V
ISD = Kp
VSD
!