Applications of the Small-signal Model

EE 330

Lecture 28

Small-Signal Model Extension

Applications of the Small-signal Model

Small Signal Model of BJT

CQ

t

I

βVg

CQ

t

I

Vm

g CQ

AF

I

VO

g

21 22C BE CEy y i V V

11 12B BE CEy y i V V

C m BE O CEg g i V V

B BEg

i V

gOgmVBE

VBEgπ

B

E

C

An equivalent circuit

Review from Last Lecture

Small Signal BJT Model

B

E

C

Vbe

ic

gmVbego Vce

ib

gπ

t

CQm

V

Ig

t

CQ

βV

Ig

AF

CQ

V

Ig o

t

CQ

βV

Ig

AF

CQ

V

Ig o

B

E

C

Vbe

ic

go Vce

ib

gπbiβ

Alternate equivalent small signal model


Bi-Linear Relationship between

i1 ,i2, v1, v2

i1

Linear Two Port

v1

i2

v2

Small-Signal Model Representations

The good, the bad, and the unnecessary !!

i1

Linear Two Port

v1

i2

v2

y-parameters

1 11 1 12 2y y i V V

2 21 1 22 2y y i V V

i1

Linear Two Port

v1

i2

v2

y-parameters

1 1 2mrg g i V V

2 1 2m og g i V V

i1

Linear Two Port

v1

i2

v2

H-parameters

(Hybrid Parameters)

1 11 1 12 2h h V i v

2 21 1 22 2h h i i v

i1

Linear Two Port

v1

i2

v2

H-parameters

(Hybrid Parameters)

1 1 2ie reh h V i v

2 1 2fe oeh h i i v

what we have developed:

The hybrid parameters:


Bi-Linear Relationship between

i1 ,i2, v1, v2

i1

Linear Two Port

v1

i2

v2

Small-Signal Model Representations

The good, the bad, and the unnecessary !!

i1

Linear Two Port

v1

i2

v2

y-parameters

1 11 1 12 2y y i V V

2 21 1 22 2y y i V V

i1

Linear Two Port

v1

i2

v2

y-parameters

1 1 2mrg g i V V

2 1 2m og g i V V

i1

Linear Two Port

v1

i2

v2

H-parameters

(Hybrid Parameters)

1 11 1 12 2h h V i v

2 21 1 22 2h h i i v

i1

Linear Two Port

v1

i2

v2

H-parameters

(Hybrid Parameters)

1 1 2ie reh h V i v

2 1 2fe oeh h i i v

i1

Linear Two Port

v1

i2

v2

z-parameters

1 11 1 12 2z z V i i

2 21 1 22 2z z V i i

i1

Linear Two Port

v1

i2

v2

ABCD-parameters

1 2 2A Bv V i

1 2 2C D i v i

i1

Linear Two Port

i2

v2

S-parameters

v1

i1

Linear Two Port

i2

v2

T-parameters

v1

• Equivalent circuits often given for each representation

• All provide identical characterization

• Easy to move from any one to another


Active Device Model Summary What are the simplified dc equivalent models?

Simplified

Simplified

Simplified

Simplified

Simplified

0.6V

dc equivalent

G D

S

VGSQ 2OX

GSQ TnμC W

V -V2L

G D

S

VGSQ 2OX

GSQ TpμC W

V -V2L

B C

E

BQβI0.6V

IBQ

B C

E

BQβI0.6V

IBQ


Engineering Trends and

Study Abroad Options

Engineers educated today will be under increasing pressure to be able to

communicate with, supervise, work with, and work for Asian engineers

that may or may not have good English communication skills and must

understand the culture of engineers around the world to be effective

This is not something that may happen in the future but rather is something that

is already occurring and WILL become increasingly critical in the next decade

The increasing role Asia is playing in both the engineering field and the world’s economy is unlike anything we have seen in many decades

All indicators suggest that this role will become even more significant in the future

Both opportunities and expectations in the field will invariable show increased alignment with business and engineering in a global economy

Understanding the culture and the environment of engineers working in Asia will offer substantial benefits for many/most engineers in the short-term and will likely be expected of many/most engineers within a decade

Study Abroad Opportunities

in Asia

Two Opportunities in Taiwan

Taipei 101 – The tallest building in the world !

Landmark Architecture – The Grand Hotel in Taipei

The two schools in Taipei Taiwan with exchange

programs with ISU College of Engineering

• Both good schools with strong engineering programs

• Ongoing interactions between faculty and students

• Strong ties with industry in Taiwan

• Interactions expected to expand in years to come

Tatung University

National Taiwan University of Science and

Technology (NTUST)

• Both schools will offer selected courses to ISU students in English

• Courses pre-approved so that progress towards graduation is not delayed

• Approximately revenue neutral exchange (often costs less than spending the time in Ames)

• Internship opportunity often provided

Exchange program principles:

13 Departments

21 Graduate Institutes

College

Department

Graduate

Institute

Engineering Elec. Eng. &

Comp. Sci. Management Design

Liberal Arts

& Soc. Sci.

Mech.

Polymer

Construction

Chemical

Automation & Control

Materials Science &

Technology

Electronic

Electrical

Computer

Science &

Information

Electro-

Optical

Industrial

Business

Information

MBA

EMBA

Management

Finance

Technology

Management

Architecture

Industrial &

Commercial

Design

Design

Applied

Foreign Lang.

Humanities

General

Education

Technological & Vocational

Education

Honors

University

Inter-discipline

Engineering

Current Status / Academics

Introduction to

College of Electrical Engineering and

Computer Science (CEECS) College of Electrical

Engineering &

Computer Science

Department of

Electronic Engineering

Department of

Electrical Engineering

Deptartment of Computer

Science & Information

Graduate Institute of

Opto-Electronic Engineering

120 full-time

faculty members: 42 Professors,

35 Associate Professors,

38 Assistant Professors,

5 Instructors.

2,645 students: (1,386 undergraduates,

1,020 Master candidates,

239 Doctoral candidates).

Founded in 1998

Introduction to Electronic Engineering Dept.

Founded in 1974.

Faculty Members: 54 active members.

Teaching and research are categorized into three major groups:

features parallel and

distributed processing,

multimedia processing,

embedded system and

FPGA design, computer

architecture, and VLSI

design.

The Computer

Engineering Group

The Electronic

System Group focuses on broadband

networks, communication

systems, digital signal and

image processing,

microwave engineering,

and power electronics.

The Optoelectronics

and Semiconductor

Group emphasizes on

semiconductor materials

and devices,

optoelectronics, fiber-optic

modules and systems,

display technology, lighting,

solar cells, and bio-

photonics.

Faculty

Members Prof.

Associa

te Prof.

Assistant

Prof.

Lect

urer

Tot

al

17 15 19 3 54

Joint

Appointment

included

Research Achievements of Electronic Engineering Dept.

Journal Paper Conference

Paper

Patent

2005 77 156 9

2006 117 148 8

2007 123 205 32

2008 156 185 31

Industry and Academia Cooperation ■To realize the advanced technologies for industrial applications.

■ The industry and academia cooperation is strongly encouraged.

■ The department seeks to build up strong links with the industry.

■ This elegantly balances the focus between theory and practice.

■ In the past few years, the department has achieved excellence in the

fields of embedded systems, IC chip design, wireless and

broadband networks, optical communications, image display, nano-

photonic materials and devices, bio-medical technologies and

solid-state lighting.

Research Areas of

Electrical Engineering Dept. Power and Energy

Power Electronics

System Engineering

Integrated Circuits and Systems

Computer and Network

Communication and Electromagnetic Engineering

Communication and Electromagnetic

Technology Center

Power Electronics Technology Center

Building Energy Efficiency and Renewable

Energy Center

Introduction to Computer Science and

Information Engineering Dept. (CSIE)

Founded in 1999

22 full-time faculty members:

Research in fields such as : (1) Multi-media Systems (2) Information security

(3) Artificial intelligence (4) Communication network

Research areas in Multi-media Systems include:

Image processing, video and data compression

Machine vision

Augmented reality

Voice synthesis, song synthesis, and related machine audio processing

Faculty

Members Prof.

Associ

ate

Prof.

Assistan

t Prof.

Lec

ture

r

Total

8 6 7 1 22

Research Areas of CSIE Dept.

Research areas in Communication network include:

Mobile computing

Wireless network

Wireless sensor network

Multi-media network

Voice over Internet Protocol (VoIP)

High-speed network

Network performance analysis

Queuing theory

Network communication protocol

Study Abroad Opportunities in Asia

Both are good schools and both should provide a good study abroad opportunity

If interested in either program contact:

Tatung University

Prof. Morris Chang (ISU coordinator) or

Prof. Randy Geiger

National Taiwan University of Science and Technology

Prof. Randy Geiger (ISU coordinator)

R1

VIN(t)

VOUT

VDD

VSS

M1

OUT DD DV =V -I R

2

OX

DQ SS T

μ C WI V V

2L

2OX

D IN SS T

μC WI V -V -V

2L

2

TSSOX

DQ VV2L

WC μI

Graphical Analysis and Interpretation Consider Again

ID

VDS

VGS1

VGS6

VGS5

VGS4

VGS3

VGS2

R1

VIN(t)

VOUT

VDD

VSS

M1

OUT DD DV =V -I R

2

OX

DQ SS T

μ C WI V V

2L

Graphical Analysis and Interpretation

Device Model (family of curves) 2

1 OX

DQ GS T DS

μ C WI V -V V

2L

Load Line

Device Model at Operating Point

ID

VDS

VGS1

VGS6

VGS5

VGS4

VGS3

VGS2

Load LineQ-Point

R1

VIN(t)

VOUT

VDD

VSS

M1

OUT DD DV =V -I R

2

OX

DQ SS T

μ C WI V V

2L

2

OX

D IN SS T

μC WI V -V -V

2L

2

TSSOX

DQ VV2L

WC μI


VGSQ=-VSS


1 OX

DQ GS T DS

μ C WI V -V V

2L

ID

VDS

VGS1

VGS6

VGS5

VGS4

VGS3

VGS2

Load LineQ-Point

R1

VIN(t)

VOUT

VDD

VSS

M1


VGSQ=-VSS


1 OX

DQ GS T DS

μ C WI V -V V

2L

Saturation region

ID

VDS

VGS1

VGS6

VGS5

VGS4

VGS3

VGS2

Load LineQ-Point

R1

VIN(t)

VOUT

VDD

VSS

M1


VGSQ=-VSS


1 OX

DQ GS T DS

μ C WI V -V V

2L

Saturation region

• Linear signal swing region smaller than saturation region

• Modest nonlinear distortion provided saturation region operation maintained

• Symmetric swing about Q-point

• Signal swing can be maximized by judicious location of Q-point

ID

VDS

VGS1

VGS6

VGS5

VGS4

VGS3

VGS2

Load LineQ-Point

R1

VIN(t)

VOUT

VDD

VSS

M1


VGSQ=-VSS


1 OX

DQ GS T DS

μ C WI V -V V

2L

Saturation region

Very limited signal swing with non-optimal Q-point location

ID

VDS

VGS1

VGS6

VGS5

VGS4

VGS3

VGS2

Load LineQ-Point

R1

VIN(t)

VOUT

VDD

VSS

M1


VGSQ=-VSS


1 OX

DQ GS T DS

μ C WI V -V V

2L

Saturation region

• Signal swing can be maximized by judicious location of Q-point

• Often selected to be at middle of load line in saturation region

Small-Signal MOSFET Model Extension

Existing model does not depend upon the bulk voltage !

Observe that changing the bulk voltage will change the electric field in the

channel region !

VBS

VGS

VDS

IDIG

IB

(VBS small)

E

Further Model Extensions Existing model does not depend upon the bulk voltage !

Observe that changing the bulk voltage will change the electric field in the

channel region !

VBS

VGS

VDS

IDIG

IB

(VBS small)

E

Changing the bulk voltage will change the thickness of the inversion layer

Changing the bulk voltage will change the threshold voltage of the device

BST0T VVV

VT

VT0

VBS

~ -5V

BST0T VVV

Typical Effects of Bulk on Threshold Voltage for n-channel Device

1-20.4V 0.6V

Bulk-Diffusion Generally Reverse Biased (VBS< 0 or at least less than 0.3V) for n-

channel

Shift in threshold voltage with bulk voltage can be substantial

Often VBS=0

T T0 BSV V V

Typical Effects of Bulk on Threshold Voltage for p-channel Device

1-20.4V 0.6V

Bulk-Diffusion Generally Reverse Biased (VBS > 0 or at least greater than -0.3V)

for n-channel

VT

VT0

VBS

Same functional form as for n-channel devices but VT0 is now negative and

the magnitude of VT still increases with the magnitude of the reverse bias

Model Extension Summary

1

GS T

DS

D OX GS T DS GS DS GS T

2

OX GS T DS GS T DS GS T

0 V V

VWI μC V V V V V V V V

L 2

WμC V V V V V V V V

2L

T

BST0T VVV

Model Parameters : {μ,COX,VT0,φ,γ,λ}

Design Parameters : {W,L} but only one degree of freedom W/L

0I

0I

B

G

Small-Signal Model Extension

1

GS T

DS


2


0 V V


L 2


2L

T

BST0T VVV

000

QQQ VVGS

G13

VVDS

G12

VVGS

G11

V

Iy

V

Iy

V

Iy

000

QQQ VVGS

B33

VVDS

B32

VVGS

B31

V

Iy

V

Iy

V

Iy

Q Q Q

D D D

21 12 13

GS DS GSV V V V V V

I I Iy y y

V V Vm o mb

g g g

GI =0

BI =0

DS

2

TGSOXD VVV2L

WμCI 1

BST0T VVV

11

OX GS T DS OX EBQ

W WμC 2 V V V μC V

2L LQ

Q

D

m

V VGS V V

Ig

V

2

OX GS T DQ

WμC 2 V V λ λI

2LQ

Q

D

o

V VDS V V

Ig

V

1

OX GS T DS

WμC 2 V V 1+λV

2LQ Q

D T

mb

BS BSV V V V

I Vg

V V

1

21

1 12 Q

Q Q

D T

mb BS

V VBS BSV V V V

I Vg V

V V

OX EBQ OX EBQ

W WμC V μC V

L L

2m

BSQ

g-V

mbg

Small Signal Model Summary

OX

m EBQ

μC Wg V

L

DQo λIg

BSQ

mmbV

gg

2

G

S

Vgs

Vbs

Vds

id

ig

ibB

D

Small

Signal

Network

dsobsmbgsmd

b

g

vgvgvgi

i

i

0

0

Relative Magnitude of Small Signal MOS

Parameters

OX

m EBQ

μC Wg V

L

o DQg λI 5E-7

2mb m m

BSQ

g g .26gV

d m gs mb bs o dsi g v g v g v

DQOX

m IL

WC2μg

DQ

m

EBQ

2Ig

V

Consider:

3 alternate equivalent expressions for gm

If μCOX=100μA/V2 , λ=.01V-1, γ = 0.4V0.5, VEBQ=1V, W/L=1, VBSQ=0V

-4

22OX

DQ EBQ

μC W 10 WI V 1V =5E-5

2L 2L

OX

m EBQ

μC Wg V 1E-4

L

0 m mbg <<g ,g

mb mg < g

In this example

This relationship is

common

In many circuits,

VBS=0 as well

Large and Small Signal Model Summary

dsobsmbgsmd

b

g

vgvgvgi

i

i

0

0

1

GS T

DS


2


0 V V


L 2


2L

T

BST0T VVV

Large Signal Model Small Signal Model

OX

m EBQ

μC Wg V

L

DQo λIg

BSQ

mmbV

gg

2

where

saturation

saturation

Example: Obtain the small signal model of the following circuit. Assume

MOSFET is operating in the saturation region

Example Obtain the small signal model of the following circuit. Assume

MOSFET is operating in the saturation region

Solution:

gmvgsvgsg0

G D

V

I

0mV g g I

0

1 1EQ

m m

Rg g g

Relative Magnitude of Small Signal BJT Parameters

t

CQm

V

Ig

t

CQ

βV

Ig

AF

CQ

V

Ig o

β

βV

I

V

I

g

g

t

Q

t

Q

π

m

7726mV100

200V

Vβ

V

V

I

Vβ

I

g

g

t

AF

AF

Q

t

Q

o

π

oπm ggg

Often the go term can be neglected in the small signal model because it is so small

Relative Magnitude of Small Signal Parameters

t

CQm

V

Ig

t

CQ

βV

Ig

AF

CQ

V

Ig o

β

βV

I

V

I

g

g

t

Q

t

Q

π

m

7726mV100

200V

Vβ

V

V

I

Vβ

I

g

g

t

AF

AF

Q

t

Q

o

π

oπm ggg

Often the go term can be neglected in the small signal model because it is so small

End of Lecture 28

Documents

Applications of the Small-signal Model