Bipolar Small Signal Device Models

EE 434Lecture 24

Bipolar Small Signal Device Models

Quiz 16What is a “binning model” and what is the purpose of using “binning models”?

And the number is ….

631

24578

9

And the number is ….

631

24578

9

Quiz 16What is a “binning model” and what is the purpose of using “binning models”?

Solution:

A binning model is actually a set of models whereby the model derived for dimensions close to those of a specific device is used rather than using the same model for each device (the functional form of most binning models does not change, simply the parameters in the model)

A good binning model will more closely predict the actual characteristics of a device than a model that does not change with device dimensions.

Models for Computer Simulation

Simple dc Model

Small SignalModel

Frequency-Dependent Small Signal Model

Better Analytical dc Models

Sophisticated Model for Computer Simulations

Better Modelsfor Predicting

Device Operation

Review from Last Time

Concept in modeling is to partition model into two parts, one that characterizes the technology and the other that characterizes the geometric aspects of a device

Technology part of the model common to all devices in a process(Level 1, BSIM4 , PSP models – over 100 paramaters in BSIM 4 model)

Geometric information unique to each device{W,L,NRD, NRS, AD,AS,PD,PS}, (default values used in not specified)

Models based upon physical principles but emperically modified to either simplfy model or improve validity

Geometric description may not be unique

Anticipated parasitics often included at schematic level for design prior to layout

Hierarchy used in models

Review from Last Time

Bipolar Models

Simple dc Model

Small SignalModel

Frequency-Dependent Small Signal Model

Better Analytical dc Models

Sophisticated Model for Computer Simulations

Better Modelsfor Predicting

Device Operation

Small-Signal Model( )( )( )

⎪⎪

⎭

⎪⎪

⎬

⎫

=

=

=

32131

32122

32111

,,,,,,

VVVi

VVVi

VVVi

g

g

g

3232221212 Vyyy ++= VVi

3332321313 Vyyy ++= VVi

3132121111 Vyyy ++= VVi( )

QVVj

321iij V

V,,VVfy=

∂∂

=

• Small signal circuit model is linear (and unique at a Q-point)• Small signal equivalent circuits are not unique

Recall:


⎪⎪

⎭

⎪⎪

⎬

⎫

=

=

=

32131

32122

32111

,,,,,,

VVVi

VVVi

VVVi

g

g

g

Small signal model is that which represents the relationship between the small signal voltages and the small signal currents

For small signals, this relationship should be linear

Recall:


⎪⎪

⎭

⎪⎪

⎬

⎫

=

=

=

32131

32122

32111

,,,,,,

VVVi

VVVi

VVVi

g

g

g

3232221212 Vyyy ++= VVi

3332321313 Vyyy ++= VVi

3132121111 Vyyy ++= VVi( )

QVVj

321iij V

V,,VVfy=

∂∂

=

• Small signal circuit model is linear (and unique at a Q-point)• Small signal equivalent circuits are not unique

Recall:

3

Small-Signal Model

( )( ) ⎭

⎬⎫

==

2122

2111

,VVfI,VVfI

I1

I2

V1V2

3-TerminalDevice

Define

2Q22

1Q11

IIII−=

−=

i

i

2Q22

1Q11

VVVV−=

−=

v

v

Small signal model is that which represents the relationship between the small signal voltages and the small signal currents

Recall:

Small-Signal Model

( )( ) ⎪⎭

⎪⎬⎫

=

=

2122

2111

,,VVi

VVi

g

g

I1I2

V1V2

3-TerminalDevice

2221212 VVi yy +=2121111 VVi yy +=

( )

QVVj

21iij V

,VVfy=

∂∂

=

Recall:

A Small Signal Equivalent Circuit

⎟⎟⎠

⎞⎜⎜⎝

⎛=

2Q

1Q

VV

V

Small Signal BJT Model

B

E

C

Vbe

ic

12Vbe21Vce11 22 Vce

ib

πgdefn

PTQ

=∂∂

=−BE

B11 V

Iy

?defn

PTQ

=∂∂

=−CE

B12 V

Iy

m

defn

PTQ

g=∂∂

=−BE

C21 V

Iy

o

defn

PTQ

g=∂∂

=−CE

C22 V

Iy


⎟⎟⎠

⎞⎜⎜⎝

⎛+=

AF

CEBC V

V1βII

πgdefn

PTQ

=∂∂

=−BE

B11 V

Iy

?defn

PTQ

=∂∂

=−CE

B12 V

Iy

m

defn

PTQ

g=∂∂

=−BE

C21 V

Iy

o

defn

PTQ

g=∂∂

=−CE

C22 V

Iy

Region of Operation for Small Signal Model : Forward Active

t

BE

VV

ESB e

βAJI =“1”

“2”t

CQVV

EStBE

C21 V

IeAJV1

VIy t

BE

=⎟⎟

⎠

⎞

⎜⎜

⎝

⎛=

∂∂

==− PTQPTQ

t

CQ

t

BQVV

ES

tBE

B11 βV

IVIeAJ

V1

VIy t

BE

==⎟⎟

⎠

⎞

⎜⎜

⎝

⎛=

∂∂

==− PTQPTQ β

0=∂∂

=−PTQCE

B12 V

Iy

AF

CQ

oPTQ

VV

ESAFCE

C22 V

IeAJV1

VIy t

BE

≅⎥⎥

⎦

⎤

⎢⎢

⎣

⎡=

∂∂

=−−PTQ


t

CQm V

Ig =

t

CQ

βVIg =π

AF

CQ

VIg ≅o


t

CQm V

Ig =t

CQ

βVIg =π

AF

CQ

VIg ≅o

bbe iv =πg

π

mm g

gg bbe iv =

β

βVIVI

gg

t

Q

t

Q

π

m =

⎥⎦

⎤⎢⎣

⎡

⎥⎦

⎤⎢⎣

⎡

=

bbe iv βgm =

Observe :


t

CQm V

Ig =t

CQ

βVIg =π

AF

CQ

VIg ≅o

t

CQ

βVIg =π

AF

CQ

VIg ≅o

B

E

C

Vbe

ic

o Vce

ib

π biβ

Alternate equivalent small signal model

Properties of the BJT

• Alternate Equivalent Small Signal Model• Relative magnitude of small signal

parameters– Simplified small signal model


t

CQm V

Ig =t

CQ

βVIg =π

AF

CQ

VIg ≅o

bbe iv =πg

π

mm g

gg bbe iv =

β

βVIVI

gg

t

Q

t

Q

π

m =

⎥⎦

⎤⎢⎣

⎡

⎥⎦

⎤⎢⎣

⎡

=

bbe iv βgm =

Observe :


t

CQm V

Ig =t

CQ

βVIg =π

AF

CQ

VIg ≅o

t

CQ

βVIg =π

AF

CQ

VIg ≅o

B

E

C

Vbe

ic

o Vce

ib

π biβ

Alternate equivalent small signal model

Properties of the BJT

• Alternate Equivalent Small Signal Model• Magnitude of small signal parameters

Relative Magnitude of Small Signal Parameters

t

CQm V

Ig =t

CQ

βVIg =π

AF

CQ

VIg ≅o

β

βVIVI

gg

t

Q

t

Q

π

m =

⎥⎦

⎤⎢⎣

⎡

⎥⎦

⎤⎢⎣

⎡

=

7726mV100

200VVβ

V

VIVβ

I

gg

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

βVIg =π

AF

CQ

VIg ≅o

β

βVIVI

gg

t

Q

t

Q

π

m =

⎥⎦

⎤⎢⎣

⎡

⎥⎦

⎤⎢⎣

⎡

=

7726mV100

200VVβ

V

VIVβ

I

gg

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

Simplified small signal model

Vbe

ic

mVbe Vce

ib

π

Comparison of BJT and MOSFET

Comparison of MOSFET and BJT

t

CQm V

Ig =

EBVL

WµCg OXm =

DQOX

m IL

WC2µg =

EBQ

DQm V

2Ig =

BJT MOSFET

⎪⎪⎩

⎪⎪⎨

⎧

==>

==>===

2VVif50mV

2V50mV

V

100mVV if250mV

100mV50mV

V

2VV

V2IVI

gg

EBEB

EBEB

t

EB

EB

DQ

t

CQ

mMOS

mBJT

40

The transconductance of the BJT is typically much larger than that of the MOSFET (and larger is better!) This is due to the exponential rather than quadratic output/input relationship


t

CQm V

Ig =

EBVL

WµCg OXm =

DQOX

m IL

WC2µg =

EBQ

DQm V

2Ig =

BJT MOSFET

⎪⎪⎩

⎪⎪⎨

⎧

==>

==>===

2VVif50mV

2V50mV

V

100mVV if250mV

100mV50mV

V

2VV

V2IVI

gg

EBEB

EBEB

t

EB

EB

DQ

t

CQ

mMOS

mBJT

40

The transconductance of the BJT is typically much larger than that of the MOSFET (and larger is better)This is due to the exponential rather than quadratic output/input relationship


AF

CQ

VIg ≅o DQIλ=og

BJT MOSFET

5.020001.

11 =≈== − VVAFDQ

AF

CQ

oMOS

oBJT

V1

IVI

gg

λλ

The output conductances are comparable but that of the BJT is usually modestly smaller (and smaller is better!)


t

CQ

βVIg =π

BJT MOSFET

0=πg

gπ of a MOSFET is much smaller than that of a BJT (and smaller is better!)

gπ is the reciprocal of the input impedance

Comparison of MOSFET and BJTBJT MOSFET

Assume BJT operating in FA region, MOSFET operating in Saturation

Assume same quiescent output voltage and same resistor R1One of the most widely used amplifier architectures


R1

Q1

VIN(t)

VOUT

VCC

VEE

BJT MOSFET

1

VIN

VOUT

1

VIN

VOUT


1

VIN

VOUT

1

VIN

VOUT

assume go can be neglected assume go can be neglected


m 1g R

OUT gsv v= −

IN gsv v=

m 1g R

OUT bev v= −

IN bev v=

1OUT

V m

IN

vA g Rv

= = −

The functional form of the gain is the same for both circuits !


1OUT

V m

IN

vA g Rv

= = − 1OUT

V m

IN

vA g Rv

= = −

CQ 1VBJT

t

I RAV

= − DQ 1VMOS

EB

2I RAV

= −

For the same power level and the same quiescent voltage drop across R1, the BJT will generally have a much larger gain since usually Vt<<VEB


Assume BJT operating in FA region, MOSFET operating in SaturationAssume same bias current

One of the most widely used amplifier architectures in integrated applications

Special Case of Previous Architecture



assume go can be neglected assume go can be neglected

OUTV

IN

vAv

= = −∞

• AV is unrealistically large• Must include more accurate small-signal model !


include go effects include go effects

OUT mV

IN o

v gAv g

= = −

Functional form of gain is the same for both circuits


OUT mV

IN o

v gAv g

= = −

• BJT Gain is Very Large and Independent of Operating Point• MOS Gain is dependent upon operating conditions (VEB)• VAF and 2/λ are comparable for large MOS devices, VAF considerably

larger than 2/λ for short devices• Practically, Vt<<VEB• BJT gain typically much larger than MOS gain for this configuration too

OUT mV

IN o

v gAv g

= = −

CQ t AFVBJT

CQ AF t

I / V VA = - I / V V

= − DQ EBVMOS

DQ EB

2I / V 2A =- =-λI λV

Student Question

IOUT

Can a single transistor be used to realize the current source?

Yes – it provides reasonable performance but there are some limitations

( )2EBOXOUT V2LWµCI ≅

Current sources often characterized by their nominal output current, their small signal output impedance, and their output signal swing

Nominal output current:

Student QuestionCan a single transistor be used to realize the current source?

Output impedance:

i

V

iv

=outR

Student QuestionCan a single transistor be used to realize the current source?

Output signal swing:

To maintain saturation region operation

VDS>VGS-VT

VOUT>VXX-VT

OUT

XX

OUT

Student Question

1

2

XX

YY

OUT

Are there better current source circuits?

High output impedance current source:

Yes – and most focus on improving either the signal swing or the output impedance

( )2EB11

1OXOUT V

2LWµCI ≅

Student Question

M1

M2

VXX

VYY

IOUT

Are there better current source circuits?

Output Impedance:

i

V

iv

=outR

Student QuestionAre there better current source circuits?

Output Impedance:

iv

=outR

( )( )

⎪⎭

⎪⎬

⎫

−=

+=+

+−=

21

222211

2221

gs

ogsmoo

gsmo

vv

vgvgggv

vggvvi

⎥⎦

⎤⎢⎣

⎡>>⎥

⎦

⎤⎢⎣

⎡≅

+++

==12

2

121

212 11

oo

m

ooo

oomout gg

gggg

gggivR

Documents

Bipolar Small Signal Device Models