EEE 51: Second Semester 2014 - 2015 Lecture 2

Transistor Models

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Today

Transistor Models Large Signal Small Signal

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From Transistors to Transistor Circuits

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transistors

[wikipedia]

transistor circuits

?

Transistor Models

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transistor operaGon

device characterizaGon

IC = IS eVBEVT 1( ) 1+VCEVA

"

#$

%

&' IB =

1IC

[wikipedia]

device models

I-V models (large signal approximaGon)

large signal terminal behavior (I-V curves)

transistor circuits

?

EEE 41

EEE 41 EEE 51

Large Signal Models

V and I over dierent transistor opera:ng regions BJT: Forward-acGve, saturaGon, cut-o MOSFET: SaturaGon, linear (ohmic), subthreshold (cut-o)

Large signal model reference largest gain topology Transfer CharacterisGc Output CharacterisGc Input CharacterisGc Unilateral Low frequency

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gain input output

How many ways can you congure a 3-terminal device?

C

E

B

BJT Transfer CharacterisGcs (IC vs. VBE)

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Common-Emi^er topology

IC = IS eVBEVT 1( ) 1+VCEVA

"

#$

%

&'

IS eVBEVT

MOSFET Transfer CharacterisGcs (ID vs. VGS)

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Common-Source topology

ID = k VGS VTH( )2 1+ VDS( )

k VGS VTH( )2

Output CharacterisGcs

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2N2222A

ZVN3306A

IB =10A

IB = 50A VGS = 9V

VGS =1V

IC = IS eVBEVT 1( ) 1+VCEVA

"

#$

%

&'

ID = k VGS VTH( )2 1+ VDS( )

(forward acGve)

(saturaGon)

ID = 2k VGS VTH( )VDS 12VDS2#$ %&(linear/ohmic)

Input CharacterisGcs

BJT MOSFET

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IB =IC

1IS e

VBEVT IG = 0

Two Ways to Bridge the Gap

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IC = IS eVBEVT 1( ) 1+VCEVA

"

#$

%

&'

IB =1IC

I-V models (large signal transfer, input and output characterisGcs)

transistor circuits

EEE 51 way ( aka the fun way J ) Allows us to use our EEE 31, 33 skills Allows us to break up large circuits into smaller ones Gives us more intuiGon in terms of circuit operaGon

direct applicaGon of KCL and KVL

linearizaGon + two-port network

reducGon

The complex, non-intuiGve, non-extendable way

LinearizaGon (1)

Consider an amplier with large gain:

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gain input output

5V

voltage gain = 1,000

input voltage levels?

In most amplier applicaGons, we are interested in the transistor behavior when we apply small signals

LinearizaGon (2) Consider a BJT in the forward acGve region:

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IC = IS eVBEVT

A is known as the quiescent DC operaGng point

LinearizaGon (3)

So what if the signals are small? Recall: Taylor Series expansion

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f x( ) = f a( )+f ' a( )1! x a( )+

f '' a( )2! x a( )

2+f ''' a( )3! x a( )

3+

ex = e0 + e0

1! x +e02! x

2 +e03! x

3 +

=1+ x + x2

2! +x33! +

Example:

Linearizing the BJT Transfer CharacterisGc (1)

Expanding the transfer characterisGc

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iC = IC,Q + ic = IS eVBE ,Q+vbe

VT

IC,Q + ic = IS eVBE ,QVT e

vbeVT = IC,Q e

vbeVT

= IC,Q 1+vbeVT

+v2be2V 2T

+v3be6V 3T

+"

#$

%

&'

IC,Q + ic = IC,Q + IC,QvbeVT

+IC,Q2

vbeVT

"

#$

%

&'

2

+IC,Q6

vbeVT

"

#$

%

&'

3

+

ic = IC,QvbeVT

+IC,Q2

vbeVT

"

#$

%

&'

2

+IC,Q6

vbeVT

"

#$

%

&'

3

+

(VBE,Q, IC,Q )

vbe

ic

vBE =VBE,Q + vbeiC = IC,Q + ic nonlinear!

Linearizing the BJT Transfer CharacterisGc (2)

If vbe is small

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ic = IC,QvbeVT

+IC,Q2

vbeVT

!

"#

$

%&

2

+IC,Q6

vbeVT

!

"#

$

%&

3

+

IC,QvbeVT

(VBE,Q, IC,Q )

vbe

ic

vBE =VBE,Q + vbeiC = IC,Q + ic

linear!

small means vbeVT

Linearizing the BJT Transfer CharacterisGc (3)

Another way to think about linearizaGon

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(VBE,Q, IC,Q )

vbe

ic

vBE =VBE,Q + vbeiC = IC,Q + ic

If we make vbe 0

m = limvbe0

iC VBE,Q + vbe( ) iC VBE,Q( )VBE,Q + vbe VBE,Q

=ICVBE VBE=VBE ,Q

We can make the approximaGon:

ic =m vbe =ICVBE VBE=VBE ,Q

vbe

Linearizing the BJT Transfer CharacterisGc (4)

Transconductance

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(VBE,Q, IC,Q )

vbe

ic

vBE =VBE,Q + vbeiC = IC,Q + ic

Dene transconductance as

ic = gm vbe

gm =ICVBE VBE=VBE ,Q

For small signals

Linearizing the BJT Transfer CharacterisGc (5)

BJT transconductance

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(VBE,Q, IC,Q )

vbe

ic

vBE =VBE,Q + vbeiC = IC,Q + ic

gm =ICVBE VBE=VBE ,Q

=

VBEIS e

VBEVT

#

$%%

&

'((VBE=VBE ,Q

=IS e

VBE ,QVT

VT=IC,QVT

Again, we get: ic = gm vbe =IC,QVT

vbe

slope: gm

Linearizing the MOSFET Transfer CharacterisGc

MOSFET transconductance

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gm =IDVGS VGS=VGS ,Q

=

VGSk VGS VTH( )

2( )VGS=VGS ,Q

= 2k VGS,Q VTH( )(VGS,Q, ID,Q )

vgs

id

vGS =VGS,Q + vgsiD = ID,Q + id

slope: gm

We get the linear relaGonship:

id = gm vgs = 2k VGS,Q VTH( ) vbe

Does gm give us the complete picture?

What else changes ic or id?

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2N2222A

ZVN3306A

IB =10A

IB = 50A VGS = 9V

VGS =1V

IC = IS eVBEVT 1( ) 1+VCEVA

"

#$

%

&' ID = k VGS VTH( )

2 1+ VDS( )

BJT Transistor Output Resistance

What happens when there are small changes in VCE?

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2N2222A IB =10A

IB = 50A

ic =ICVCE VCE=VCE ,Q

vce

=

VCEIS e

VBEVT 1( ) 1+VCEVA

$

%&

'

()

$

%&&

'

())VCE=VCE ,Q

vce

=IS e

VBE ,QVT 1$

%&

'()

VA vce =

IC,QVA

vce = go vce =vcero

Output resistance: ro =VAIC,Q

MOSFET Transistor Output Resistance

What happens when there are small changes in VDS?

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id =IDVDS VDS=VDS ,Q

vds

=

VDSk VGS VTH( )

2 1+ VDS( )( )VDS=VDS ,Q

vds

= k VGS VTH( )2 vds = IDS,Q vds

= go vds =vdsro

Output resistance: ro =1

IC,Q

ZVN3306A VGS = 9V

VGS =1V

CompleGng the Picture: Transistor Input Resistance BJT Small signal base current

due to vbe

MOSFET Small signal gate current

due to vgs

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g =IBVBE VBE=VBE ,Q

=

VBEIC

"

#$

%

&'VBE=VBE ,Q

=1

ICVBE VBE=VBE ,Q

=gm

g =IGVGS VGS=VGS ,Q

= 0

r =1g

=gm

= VTIC,Q

r =1g

LinearizaGon Result: The Small Signal Model

BJT Total ic:

Total ib:

MOSFET Total id:

Total ig:

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ic =ICVBE VBE=VBE ,Q

vbe#

$

%%

&

'

((+

ICVCE VCE=VCE ,Q

vce#

$

%%

&

'

((

= gmvbe +vcero

id =IDVGS VGS=VGS ,Q

vgs#

$

%%

&

'

((+

IDVDS VDS=VDS ,Q

vds#

$

%%

&

'

((

= gmvgs +vdsro

ib =IBVBE VBE=VBE ,Q

vbe =vber

ig = 0

The BJT Small Signal Equivalent Circuit

KCL / KVL results in the small signal model

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ic = gmvbe +vcero

ib =vber

Linear! Fully describes the response of the BJT to small signal disturbances

about the quiescent point (no DC informaGon!) Dependent on the quiescent DC operaGng point

The MOSFET Small Signal Equivalent Circuit

KCL / KVL results in the small signal model

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id = gmvgs +vdsro

ig = 0

Large Signal vs. Small Signal

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IC,Q = IS eVBE ,QVT 1"

#$

%&' 1+VCE,QVA"

#$

%

&'

IB,Q =IC,Q

ic = gmvbe +vcero

ib =vber

IC,QVBE,Q ic

vbe

Small Signal Model ImplicaGons

Linear relaGonships! For small signals

Linear circuit analysis works! EEE 31 and 33 is useful amer all J Can use two-port network concepts

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gain input output

5V

voltage gain = 1,000

5mV input

Next MeeGng

Review of Two-Port Networks Single-Stage Ampliers

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