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Department of Electrical and Computer Engineering ECSE-330B Electronic Circuits I

MOSFETs 1

Biasing in MOSFET Amplifiers

• Biasing: Creating the circuit to establish the desired DC voltages and currents for the operation of the amplifier

• Four common ways:1. Biasing by fixing VGS

2. Biasing by fixing VG and connecting a resistance in the Source

3. Biasing using a Drain-to-Gate Feedback Resistor4. Biasing Using a Constant-Current Source


MOSFETs 2

Biasing in MOSFET Amplifiers• Biasing by fixing VGS

When the MOSFET device is changed (even using the same supplier), this method can result in a large variability in the value of ID. Devices 1 and 2 represent extremes among units of the same type.

( )221

tGSnD VVL

WkI −′=

oxnox

oxnn C

tk μεμ ==′

VDD

-VEE

VGG

RG

RD

RS

M1

VGVD

VS


MOSFETs 3

Biasing in MOSFET Amplifiers• Biasing by fixing VG and connecting a resistance in the Source

Degeneration Resistance


MOSFETs 4

Biasing in MOSFET Amplifiers• Biasing using a Drain-to-Gate Feedback Resistor

Large Resistor


MOSFETs 5

Biasing in MOSFET Amplifiers• Biasing Using a Constant-Current Source

Figure 4.33 (a) Biasing the MOSFET using a constant-current source I. (b) Implementation of the constant-current source Iusing a current mirror.

Current Mirror

Used in Integrated Circuits


MOSFETs 6

Current Mirror DC Analysis• The width and length (the W/L aspect

ratio) and the parameters of the two transistors can be different

• We can choose W/L freely• In this circuit, consider W/L of both

MOSFETs are the same and transistors are identical. The Gate-Source voltages are also the same, then

( )21

121

tGSnREF VVLWkI −′=

( )21

121

tGSn VVLWkI −′=

REF

REF

IIWL

LW

II

=

=⋅= 11

1

1

1

W1

L1

VGS VGS

+

--

+

W1

L1

I


MOSFETs 7

Current Mirror DC Analysis

• Designing IREF

RVVVI SSGSDD

REF+−

=

( )21

121


• It is often needed to find the value of R in order to achieve a desired IREF


MOSFETs 8

Biasing of MOSFET Amplifier

• 1- Intro to MOS Field Effect Transistor (MOSFET)• 2- NMOS FET• 3- PMOS FET• 4- DC Analysis of MOSFET Circuits• 5- MOSFET Amplifier• 6- MOSFET Small Signal Model• 7- MOSFET Integrated Circuits• 8- CSA, CGA, CDA• 9- CMOS Inverter & MOS Digital Logic


MOSFETs 9

MOSFET Design Space• Modern integrated circuits use MOSFETs

extensively– Very high densities of transistors – up to 109

transistors/cm2 in some ULSI memory arrays.– Off-chip discrete resistors and capacitors are NOT

commonly used– On-chip resistors and capacitors generally small– Multistage amplifiers are usually DC-coupled

• Transistors used wherever possible to implement current sources, resistors, capacitors,


MOSFETs 10

Using MOSFETs to implement R’s and C’s

• Resistors:Active Loads (large R’s)Diode-connected loads (small R’s)MOSFET Triode-Region (moderate R’s)

• CapacitorsMost obvious is the gate-body capacitorCan be used to have variable-capacitors as well

• Current Mirrors


MOSFETs 11

MOSFET Active Loads• MOSFETs used as an active load for high resistances:

– MOSFET is held in saturation with the source and gate held at a constant DC voltage

– Drain connected to circuit

vgs = 0gmvgs = 0

Do I

r⋅

=λ

1

– ro is inversely proportional to ID

Rin= ?

Rin=ro


MOSFETs 12

Diode-Connected MOSFETs• A Diode connected MOSFET can be used to achieve

small resistances:– The Drain is directly connected to Gate, and therefore it

can only be operated in saturation (or cutoff)

Source Absorption Theorem


MOSFETs 13

MOSFET Current Mirrors• Used extensively in

MOSFET IC applications

• Often ro,is neglected. Since there is no gate current, the drain currents of M1 and M2 are identical

• In practice, IREF ≠ I due to finite ro. (Not included in EC1)

VGS VGS

+

--

+

0 0

( ) )1(21 2

1

1XtXnREF VVV

LWkI λ+−′=

11 DSGSX VVV ==

VX

The current I will also depend on VDS2

I


MOSFETs 14

Current Mirror DC Analysis• The width and length (the W/L

aspect ratio) of MOSFETs can be designed almost freely

• Since the W/L of M1 and M2need not be the same, the size ratios can affect current ratios

( )21

121


( )22

221

tGSn VVLWkI −′=

1

1

2

2

WL

LW

II

REF⋅=

W1

L1

W2

L2

VGS VGS

+

--

+

I


MOSFETs 15

Current Scaling (Steering)• Ratio of

aspect ratios can be selected to achieve nearly any scale factor I/IREF

WL

WL

WL

WL

Note: All gates are connected


MOSFETs 16

Current Mirroring – Pushing and Pulling


MOSFETs 17

Small Signal• Transistor M1 is diode

connected and acts like a resistor to s.-s. ground.

ro2


MOSFETs 18

Outline of Chapter 5

• 1- Intro to MOS Field Effect Transistor (MOSFET)• 2- NMOS FET• 3- PMOS FET• 4- DC Analysis of MOSFET Circuits• 5- MOSFET Amplifier• 6- MOSFET Small Signal Model• 7- MOSFET Integrated Circuits• 8- CSA, CGA, CDA• 9- CMOS Inverter & MOS Digital Logic


MOSFETs 19

DC and AC - Body-Effect / CLM

Three types of analysis:Neglect AC Body-Effect & AC CLM

/ Neglect AC CLMUse AC Body-Effect

Use AC Body-Effect / Use CLM

Three types of analysis:Neglect DC Body-Effect & DC CLM

/ Neglect DC CLMUse DC Body-Effect

Use DC Body-Effect / Use DC CLM

DC Analysis

AC Analysis(small-signal)

Use whatever DC values for V and I in the small-signal

analysis


MOSFETs 20

Common Source Amplifier (CSA)• Current source I implemented

with current mirror.• Current mirror provides

active load at drain• Source terminal grounded –

no DC or AC Body effect


MOSFETs 21

CSA with Current Mirror

CSA

ro2


MOSFETs 22

CSA Small Signal Analysis• From MOSFET

Current-Mirror: only ro2 appears in analysis

igs vv =1

( ) 1211 gsoomout vrrgv −=

( )211 oomi

outV rrg

vvA −==


MOSFETs 23

CSA Input/Output Resistance

• Input Resistance

• Output resistance

21 ooOUT rrR =

vgs1 = 0

gm1vgs1 = 0

∞⇒INR


MOSFETs 24

CSA Calculations• In practice, difficult to keep all

transistors operating in saturation VOUT is hard to control, and

sensitive to: W/L, VG, and CLM

Ω=−==

==

=′

=′

==

== −

kRVVVV

LW

LWk

kVVV

V

REF

SSDD

VA

n

VA

p

tt

12,5

40,50

125

501

01.0

1

1

2

2

21

121

μ

μ

λλ

VV

V

o

VA

m

OUT

G

Akr

mgVV

mAIVV

10052.38192.5855.3

596.2567.2

1

−=Ω=

==

==Hand: SPICE:

VV

V

OUT

G

AVV

mAIVV

4.102895.2

57.258.2

−==

==


MOSFETs 25

Common Gate Amplifier (CGA)• A pMOS current mirror is used

as IREF including the output resistance.

• Since source terminal not at signal ground, the body effect is present.

• The gate terminal held at a DC voltage. (AC Ground)

Typically used as second stage of a multi-stage amplifier circuit


MOSFETs 26

CGA – DC Analysis• Current mirror is assumed to be ideal

during the DC analysis, thus IREF=I• DC voltage at the source terminal (VS)

must be obtained from driving the current IREF through the transistor.

• This assumes that the input voltage source VI is set to zero

• RI is part of the source voltage• Solve for VO, with VS and VG known,

and including CLM

( ) ( )[ ]SOtSGn VVVVVL

WkI −⋅+−−′= λ1221


MOSFETs 27

CGA

• Replace with a current source including output resistance ro2

Choice of analysis:

Neglect AC Body-Effect & CLM

/ Neglect CLMUse AC Body-Effect

Use AC Body-Effect / Use CLM

ro2


MOSFETs 28

CGA – No Body Effect or CLM

2ogsmo rvgv ⋅−=

I

Im

mgs v

Rg

gv+

−=

1

11

1

Im

o

I

oV

Rg

rvvA

+== 1

2

i=0

Non Inverting


MOSFETs 29

CGA – RIN & ROUT, No Body Effect or CLM

1

1

mIN g

R =

RIN

ROUT

2oOUT rR =

vI = 0


MOSFETs 30

CGA – With Body Effect & no CLM

( ) 211 oxmbxmo rvgvgv +−=

( ) 211 ombmx

oV rgg

vvA +==

xgsbs vvv −== 11

( ) 21111 obsmbgsmo rvgvgv +−=

( )IIN

INombm

i

x

x

o

i

ototalV RR

Rrggvv

vv

vvA

+⋅+=⋅==− 2

Include RI and solve for total voltage gain in term of RIN

RIN

Solve at vx first:

vX


MOSFETs 31

CGA – RIN With Body Effect & no CLM

xmbmx vggi )( 11 +=

xgsbs vvv −== 11

11

1

mbmIN gg

R+

=

RINiIN

vX

Neglect InputVoltage Source

xmbmin vggi )( 11 +=

iX


MOSFETs 32

CGA - With Body Effect & CLM

Neglect InputVoltage Source

gsx vv −=

2oxo riv ⋅=

( )1

11o

oxxmbmx r

vvvggi −++=

vXiX

iX

( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛++⋅== 11

121

1mbm

ooo

x

oV gg

rrr

vvA


MOSFETs 33

CGA – RIN With Body Effect & CLM

Neglect Input Voltage Source

2oxo riv ⋅=

( )1

11o

oxxmbmx r

vvvggi −++=

111

1

2

1

1

mbmo

o

o

x

xIN

ggr

rr

ivR

++

+==

RIN

iX

vX

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Department of Electrical and ECSE-330B Electronic Circuits ...simonfoucher.com/McGill/ECSE330 Electronics/Notes/4.4 MOSFETS in I… · Department of Electrical and Computer Engineering