1. MOSFET Equations a) N-channel MOSFET Cut Off

!

VGS"V

T

!

IDS

= 0

Linear

!

VGS

>VT

,

!

VDS"V

GS#V

T

!

IDS

= µnCox

W

LVGS"V

T( )VDS"VDS

2

2

#

$ %

&

' ( (1+ )V

DS)

Saturation

!

VGS

>VT

,

!

VDS

>VGS"V

T

!

IDS

=1

2µnCox

W

L(V

GS"V

T)2(1+ #V

DS)

The simplest model in SPICE (Level 1 or default model) uses the above equations.

Parameter SPICE Parameter Units Typical Values µnCox KP A/V2 200µ VT0 VTO V 0.5 – 1.0 λ LAMBDA V-1 0.05 – 0.005

b) P-channel MOSFET Cut Off

!

VSG" V

T

!

ISD

= 0

Linear

!

VSG

> VT

,

!

VSD"V

SG# V

T

!

ISD = µpCox

W

LVSG " VT( )VSD "

VSD

2

2

#

$ %

&

' ( (1+ )VSD )

Saturation

!

VSG

> VT

,

!

VSD

>VSG" V

T

!

ISD =1

2µpCox

W

L(VSG " VT )

2(1+ #VSD )

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" V

T# saturation

ISD

=100µ

2

10µ

2µ(2 " "0.8)

2(1+ 0) = 360µA

IDS

= "360µA

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

IDS =1

2Kp

W

L(VSG # VT )

2(1+ $VSD ) =

8µ

2

W

10µ(3# 2)

2(1+ 0) = 0.1mA

IR =VD

R=2

R= 0.1mA

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

ISD =1

2Kp

W

L(VSG # VT )

2 =8µ

2$ 25 $ (VSG #1)

2 =100µ

VSG = 2V VSD = 2V

2) R =10k

VD #VG = IR =100µ $10k =1"VSD =VSG # VT " saturation or linear

ISD =1

2Kp

W

L(VSG # VT )

2 =8µ

2$ 25 $ (VSG #1)

2 =100µ

VSG = 2V VSD =1V

3) R = 30k

VD #VG = IR =100µ $ 30k = 3"VSD <VSG # VT " linear

ISD = KpW

L((VSG # VT )VSD #

VSD

2

2) = 8µ $ 25 $ ((VSD + 3#1)VSD #

VSD

2

2) =100µ

VSD % 0.24V VSG = 3.24V

4) R =100k

VD #VG = IR =100µ $100k =10"VSD <VSG # VT " linear

ISD = KpW

L((VSG # VT )VSD #

VSD

2

2) = 8µ $ 25 $ ((VSD +10 #1)VSD #

VSD

2

2) =100µ

VSD % 0.06V VSG =10.06V