Lect. 21: MOSFET Small-signal Model(R i 6 3 1)

vD

(Razavi 6.3.1)

vGS

Prof. Woo-Young ChoiElectronic Circuits 1 (09/2)

Lect. 21: MOSFET Small-signal Model(R i 6 3 1)

Decompose all signals into Large Signals and Small Signals

(Razavi 6.3.1)

vGS= VGS + vgs

iD = ID + idvD = VD + vd

vD

vD VD vd

L i l id biLarge signals provide biases.

Small signals are amplified. ( v = A v )( vd = Av vgs).

What is Av=vd/vgs?vGS

Prof. Woo-Young ChoiElectronic Circuits 1 (09/2)

Lect. 21: MOSFET Small-signal Model

Small signal model for NMOS in saturation

vGS=VGS + vgs, vDS=VDS + vds

iG = IG + ig, iD=ID + id

ig, id as functions of vgs, dvs

0gi =

21From ( ) withWi C v V v V vμ= − = +From ( ) with 2D n ox GS T GS GS gsi C v V v V v

Lμ= = +

=i ( )WC V V vμ= − ⋅|Ddi v⋅di

= m gsg v⋅

( )n ox GS T gsC V V vL

μ= ⋅|GSV gs

GS

vdv

Prof. Woo-Young ChoiElectronic Circuits 1 (09/2)

g

Lect. 21: MOSFET Small-signal Model

Small signal circuit

= - d m gs Dv g v R

Prof. Woo-Young ChoiElectronic Circuits 1 (09/2)

Lect. 21: MOSFET Small-signal Model

Various expressions for gmp gm

21From ( )D n ox GS TWi C v Vμ= −( )

2D n ox GS TLμ

| ( )GS

Dm V n ox GS T

di Wg C V Vd L

μ= = −GS

GSdv L2= DI

V V−

= 2 n ox DWC IL

μ ⋅ ⋅

GS TV V

L

Prof. Woo-Young ChoiElectronic Circuits 1 (09/2)

Lect. 21: MOSFET Small-signal Model

No change in id with vds

21 ( )2D n ox GS T

Wi C v VL

μ= −

But in real MOSFET devices iD increases due to channel length modulation

21 ' (1 )( )2 DSD GS t

Wk v VL

vi λ ⋅= + −

i i∂ ∂ 2i iW∂D DD GS DS

GS DS

i ii v vv v

∂ ∂Δ = ⋅Δ + ⋅Δ

∂ ∂2' (1 )( )D D

DS GS t mGS GS t

i iWk v v V gv L v V

λ∂= + ⋅ − = =

∂ −

1i W∂ 121 ' ( )2

DGS t

DS

i Wk v Vv L

λ∂= −

∂

0

dsd m gs

vi g vr

= ⋅ + 0

1r

=

Prof. Woo-Young ChoiElectronic Circuits 1 (09/2)

Lect. 21: MOSFET Small-signal Model

Small signal model for NMOS with channel-length modulation

NMOS I-V with λ=0 to 0.1 by 0.01 increment.y

vGS=5.0V

21 ' (1 )( )2 DSD GS t

Wk v VL

vi λ ⋅= + −

vGS=2.5V

2 L

Prof. Woo-Young ChoiElectronic Circuits 1 (09/2)

Lect. 21: MOSFET Small-signal Model

Ex 4 10Ex. 4.10

Vt=1.5V, k’ (W/L)=0.25mA/V2

1. Determine bias conditions.2. Derive small signal circuit model.3. Voltage gain?g g4. Input resistance?5. Max. vi?

Prof. Woo-Young ChoiElectronic Circuits 1 (09/2)

Lect. 21: MOSFET Small-signal Model

1. Determine bias conditions.

Vt=1.5V, k’ (W/L)=0.25mA/V2

ID=0.5X0.25 (VD-1.5)2

VD=15-RDID

ID=1.06mA, VD=4.4V

In saturation?

gm= k’ (W/L) (VGS-Vt) = 0.725mA/V

In saturation?

Prof. Woo-Young ChoiElectronic Circuits 1 (09/2)

Lect. 21: MOSFET Small-signal Model

Voltage Gain

Small-Signal model

0( || || )

( || || ) 3 3

o m i D L

o

v g v R R rvA g R R r

= − ⋅ ⋅

= = =0( || || ) 3.3v m D Li

A g R R rv

= = − ⋅ = −

RD=10KΩ, RL=10KΩ, RG=10MΩ, ro = 47kΩ

Prof. Woo-Young ChoiElectronic Circuits 1 (09/2)

Lect. 21: MOSFET Small-signal Model

R =10KΩ R =10KΩ R =10MΩRD=10KΩ, RL=10KΩ, RG=10MΩ

v

Input Resistance

(1 )

iin

i

i i

vRi

v v v v

=

− (1 )

2 33 M

i o i oi

G G i

i G

v v v viR R v

v RR

= = −

∴ = = = Ω2.33 M1in

i v

Ri A

∴ = = = Ω−

Prof. Woo-Young ChoiElectronic Circuits 1 (09/2)

Lect. 21: MOSFET Small-signal Model

For Max. vi, vDS>vGS-Vt (saturation)

,max ,maxDS V i GS i tV A v V v V− = + −

,max 0.34Viv =

Prof. Woo-Young ChoiElectronic Circuits 1 (09/2)

Lect. 21: MOSFET Small-signal Model

S ll i l d l f PMOS ?Small signal model for PMOS ?

Identical to NMOS small signal model!

Homework: Due before Tutorial on 11/9

Determine small-signal resistance Rx and Ry in the following circuits. Assuming M1 and M2 are in saturation. Consider the channel length modulation but not body effect.

Prof. Woo-Young ChoiElectronic Circuits 1 (09/2)