Lecture 18 Bipolar Junction Transistors (BJTs) › ece315 › Lectures › handout18a.pdfNPN BJT:...

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ECE 315 – Spring 2007 – Farhan Rana – Cornell University

Lecture 18

Bipolar Junction Transistors (BJTs)

In this lecture you will learn:

• The operation of bipolar junction transistors

• Forward and reverse active operations, saturation, cutoff

• Ebers-Moll model

• Small signal models


Bipolar Transistors

First Bipolar Transistor (AT&T Bell Labs)

First Bipolar Transistor (AT&T Bell Labs)

William Shockley, John Bardeen, Walter Brattain(Nobel Prize for the Transistor, AT&T Bell Labs)

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Emitter

N-doped

Collector

N-doped

aBNdEN

Base

P-doped

dCN

VBE VCB+ +- -

NPN Bipolar Junction Transistor

B

E

C

VBE

VCB

+-

+-

VGS+-

VDG+-


Emitter

P-doped

Collector

P-dopedaEN dBN

Base

N-doped

VBE VCB+ +- -

PNP Bipolar Junction Transistor

B

E

C

VBE

VCB

+-

+-

aCN

VGS+-

VDG+-

3


Metal base contact Metal emitter contact Metal collector contact

P (base)N+ (emitter)

N (collector)

N+ (contact layer)

N (substrate)

Insulator (SiO2)

Insulator (SiO2)

Insulator (SiO2)

A Silicon NPN BJT

P+ (contact)


NPN BJT: Basic Operation

Emitter

N-doped

Collector

N-dopeddEN aBN

Base

P-doped

VBE > 0 VCB=0+ +- -

WE WB WC

dCN

Suppose:

The base-emitter junction is forward biased

The base-collector junction is zero biased

0BEV

0CBV

This biasing scheme will put the device in the “forward active” operation (to be discussed fully later)

pxnx 0

4


NPN BJT: Basic Operation

dEN aBN

VBE>0+ +- -

WE WB WC

dCN

Consider the action in the base first (VBE > 0 and VCB = 0)

• The electrons diffuse from the emitter, cross the depletion region, and enter the base

• In the base, the electrons are the minority carriers

• In the base, the electrons diffuse towards the collector

• As soon as the electrons reach the base-collector depletion region they are immediately swept away into the collector by the strong electric fields in the depletion region

holes

electrons

pxnxE-field

0

swept electrons

VCB=0


NPN BJT: Electron-Hole Populations

Consider the base first:

In the base, the electron population can be written as:

In the base, the excess electron population satisfies the differential equation:

xnnxn po '

Equilibrium electron density Excess electron densityaB

ipo N

nn

2

1'

2KT

Vq

aB

ip

BE

eNn

xn 0

''22

2

nL

xn

x

xn

Boundaryconditions

dEN aBN

VBE>0+ +- -

WE WB WC

dCNholes

electrons

pxnxE-field

0

swept electrons

VCB=0

01'2

KT

qV

aB

iBp

BC

eNn

Wxn

5


dEN aBN

VBE>0+ +- -

WE WB WC

dCNholes

electrons

pxnxE-field

0

swept electrons

VCB=0NPN BJT: Electron-Hole Populations

• Ignore carrier recombination (i.e. assume Ln = ∞)

0

'2

2

x

xn

Boundaryconditions

xn'

Solution is:

B

pKT

qV

aB

i

B

pn W

xxe

Nn

W

xxxnxn

BE

111''2

1'

2KT

Vq

aB

ip

BE

eNn

xn

01'2

KT

qV

aB

iBp

BC

eNn

Wxn


NPN BJT: Electron-Hole Populations

Consider the emitter now:

In the emitter, the hole population can be written as:

In the emitter, the excess hole population satisfies the differential equation:

xppxp no '

Equilibrium hole density Excess hole densitydE

ino N

np

2

1'

2KT

Vq

dE

in

BE

eNn

xp 0

''22

2

pL

xp

x

xpBoundaryconditions

0' En Wxp

dEN aBN

VBE>0+ +- -

WE WB WC

dCNholes

electrons

pxnxE-field

0

swept electrons xn'

VCB=0

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dEN aBN

VBE>0+ +- -

WE WB WC

dCNholes

electrons

pxnxE-field

0

swept electrons

VCB=0NPN BJT: Electron-Hole Populations

• Ignore carrier recombination (i.e. assume Lp = ∞)

0

'2

2

x

xp

xn'

Solution is:

Boundaryconditions

E

nKT

qV

dE

i

E

nn W

xxe

Nn

Wxx

xpxpBE

111''2

xp'

1'

2KT

Vq

dE

in

BE

eNn

xp

0' En Wxp


NPN BJT: Electron and Hole Current DensitiesVCB=0

+ +- -

WE WB WCpxnx

xJn

In the base:• The electron current is:

xxp

DqxJ pp

12 KT

qV

EdE

pi

BE

eWN

Dqn

In the emitter:• The hole current is:

xxn

DqxJ nn

12 KT

qV

BaB

ni

BE

eWN

Dqn

xJp

dEN aBN dCN

Area = A

0

VBE>0

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NPN BJT: Terminal Currents

Emitter current:

• The current flowing out of the emitter is the sum of the total electron and total hole currents in the emitter:

12 KT

qV

BaB

n

EdE

piE

BE

eWN

DWN

DAqnI

VCB=0+ +- -

WE WB WCpxnx

xJn xJp

EI dEN aBN dCN

Area = A

0

VBE>0


+ +- -

WE WB WCpxnx

xJn

Collector Current:• The current going into the collector is due to the electrons that got swept from the Base through the Base-Collector depletion region by the electric-fields:

xJp

EI dEN aBN dCN CI

Area = A

12 KT

qV

BaB

niC

BE

eWN

DAqnI

BI

Base Current:• The current going into the Base is due to the holes that got injected from the base into the emitter:

12 KT

qV

EdE

piB

BE

eWN

DAqnI

E-field


0

VCB=0VBE>0

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12 KT

qV

BaB

n

EdE

piE

BE

eWN

DWN

DAqnI

12 KT

qV

BaB

niC

BE

eWN

DAqnI

12 KT

qV

EdE

piB

BE

eWN

DAqnI

B

E

C

VCB=0

+-

+-

IC

IE

IB

CBE III


VBE>0

+ +- -

WE WB WCpxnx

xJn xJp

EI dEN aBN dCN CI

Area = A BI

0

VCB=0VBE>0


+ +- -

WE WB WCpxnx

EIdEN dCN

CI

Area = A BI

0

VCB=0VBE>0

aBN

Electrons

Holes


12 KT

qV

BaB

n

EdE

piE

BE

eWN

DWN

DAqnI

12 KT

qV

BaB

niC

BE

eWN

DAqnI

12 KT

qV

EdE

piB

BE

eWN

DAqnI

B

E

C

VCB=0

+-

+-

IC

IE

IB

CBE III

VBE>0

Red curr

tBlue curre

t

n

enCF

B

I

I

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NPN BJT: Circuit Level Parameters

B

E

C

VCB=0

+-

+-

IC = FIE = FIB

IE

IB

Current gain F :Current gain of the BJT in the forward active operation is defined as the ratio of the collector and base currents:

BFCp

EdE

BaB

n

B

CF II

DWN

WND

II

Typical values of F are between 20-200 and:

F :In the forward active operation F is defined as the ratio of the collector and emitter currents:

E

CF I

I EFC

BaB

n

EdE

p

BaB

n

II

WND

WN

DWN

D

Transistor relation:F and F are related:

F

FF

1

VBE>0

dCaBdE NNN

CBE III


NPN BJT: Ebers-Moll Model for Forward Active Operation

Suppose:

B

E

C

1

12

KTqV

ES

KTqV

BaB

n

EdE

piF

BE

BE

eI

eWN

DWN

DAqnI

FI

FF IBV

EV

CV

BV

EV

CV

ESI

The circuit level simplified model with an ideal diode and a current-controlled current source models the NPN transistor in the forward active operation

0BEV

0CBV

IB

IE

IC

IB

IE

IC

1B F FI I

C F FI I

E FI I

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NPN BJT: Forward Active Operation

B

E

C

VBE+-

+-

IC

IE

IB

0BEV

0CBV

Forward active operation

B

CF I

I

E

CF I

I

F

FF

1

VCB


NPN BJT: Forward and Reverse Active Operations

B

E

C

VBE+-

+-

IC

IE

IB

B

E

C

VBE

VCB

+-

+-

IC

IE

IB

0BEV

0CBV 0BEV

0CBV

Forward active operation Reverse active operation

B

ER I

I

C

ER I

I

B

CF I

I

E

CF I

I

F

FF

1 R

RR

1

p

CdC

BaB

n

D

WN

WND

RF In a well designed transistor:

VCB( )

( )

Actual

Actual

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Suppose:

B

E

C

2 1

1

BC

BC

qVp n KT

R idC C aB B

qV

KTCS

D DI qn A e

N W N W

I e

RI

RRI

BV

EV

CV

BV

EV

CV CSI

The circuit level simplified model with an ideal diode and a current-controlled current source models the NPN transistor in the reverse active operation

0BCV

0BEV

NPN BJT: Ebers-Moll Model for Reverse Active Operation

IB

IE

IC

IB

IE

IC ( )

( )

1B R RI I

C RI I

E R RI I


NPN BJT: Ebers-Moll Model and Terminal Currents

Terminal currents:

B

E

C

BV

EV

CV

FI

FF IBV

EV

CV

ESI

RI

RRI

CSI

IC

IE

IB IB

IE

IC

1KT

qV

CSR

BC

eII

1KT

qV

ESF

BE

eII

RRFFB III 11

RFFC III

RRFE III

And

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B

E

C

IC

IE

IB

0BEV 0CBV

In forward active operation:

NPN BJT: Regimes of Operation - I

VCE+-

BECBCE VVV

BFKT

qV

BaB

niC Ie

WND

AqnIBE

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Independent of VCE

Since:

In forward active operation: BECE VV

CEVBEV

CIForward active IB >0 & IC = F IBVCE > VBE

SaturationIB >0VCE < VBE

0BI

Forward active:Base-emitter junction forward biasedBase-collector junction reversed biased

000 CBBEB VVI

Saturation:Base-emitter junction forward biasedBase-collector junction forward biased

000 CBBEB VVIF

R

F

F

VBE+-


dEN aBN

VBE > 0+ +- -

WE WB WC

dCNholes

electrons

pxnx 0

VCB ≥ 0

xn' xp'

Carrier Densities in Different Regimes of Operation

Forward active:

Saturation:

dEN aBN

VBE > 0+ +- -

WE WB WC

dCNholes

electrons

pxnx 0

VCB < 0

xn' xp'

xp'

xp'

electrons

holes

electrons

holes

dCaBdE NNN

The forward biased base-collector junction reduces the collector current!

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B

E

C

IC

IE

IB

NPN-BJT: Regimes of Operation - II

VCE+-

BI

Forward active:Base-emitter junction forward biasedBase-collector junction reversed biased

000 CBBEB VVI

Saturation:Base-emitter junction forward biasedBase-collector junction forward biased

000 CBBEB VVI

Cutoff:Base current zero

0BI

Reverse active:Base-emitter junction reverse biasedBase-collector junction forward biased

000 CBBEB VVI

CEV

CI

Curves for increasing IB

IB = 0 (cutoff)

Forward active IB >0 & IC = F IBVCE ≥VBE

SaturationIB >0VCE <VBE

BECE VV

C F BI I

E R BI I


NPN BJT: Different Regimes of Operation

FI

FF IBV

EV

CV

ESI

RI

RRI

CSI

IB

IE

IC

Reversed biased

Forward biased

0BEV

0CBV

Forward Active Saturation Reverse Active

FI

FFIBV

EV

CV

ESI

RI

RRI

CSI

IB

IE

IC

Forward biased

Forward biased

0CBV

0BEV

FI

FFIBV

EV

CV

ESI

RI

RRI

CSI

IB

IE

IC

Forward biased

Reversed biased

0CBV

0BEV

( )

( )

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NPN BJT: A Simple Amplifier Circuit

B

E

C IC

IE

IB

DDV

R

IIN

FB

C

IN

OUT

II

II

Current gain (in forward active regime):

CEC VV

RVV

I

RIVV

CEDDC

CDDCE

Load line equation:

Lesson: Don’t let the base-collector junction become forward biased

CEV

CI

Curves for increasing IB

IB = 0 (cutoff)



BECE VV

DDV

Load line

RVDD


NPN BJT

CEV

CI

Curves for increasing IB(And increasing VBE)

IB = 0 (cutoff)



VCE-SAT

BECE VV Better/easier definition:In saturationIB >0VCE <VCE-SAT

Better/easier definition:In forward activeIB >0VCE >VCE-SAT

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NPN BJT: Voltage Biasing of a Simple Amplifier Circuit

Approximate analysis of transistor DC biasing:

S

ONBEINB

ONBESBIN

RVV

I

VRIV

0BONBEIN IVV Transistor in cut-off

If: ONBEIN VV

Assume forward active operation (VCE > VCE-SAT):

BFC II

RR

VVVRIVV

s

ONBEINFDDCDDOUT

Final Step - confirm if the assumption of forward active operation was valid:

SATCEs

ONBEINFDDCDDOUTCE

SATCECE

VRRVV

VRIVVV

VV

If:

B

E

C IC

IE

IB

DDV

R

VIN

OUTV

SR

+

-VON+

-

Acting as a current source

V2.0~

V6.0~

SATCE

ONBE

V

V


NPN BJT Amplifier Circuit: Transfer Curve

00

OUTV

INVONBEV

DDV

Cu

t-o

ff

Forward active

Saturation

ONBEINs

FDDCDDOUT VVRR

VRIVV

B

E

C IC

IE

IB

DDV

R

VIN

OUTV

SR

+

-VON+

-

Acting as a current source

SATCEV

S

ONBEINB R

VVI

DDOUTBONBEIN VVIVV 0 Transistor in cut-off

If: ONBEIN VV

If:

Transistor in forward active

If: SATCEOUTCEB VVVI & 0

V2.0~

V6.0~

SATCE

ONBE

V

V

Transistor in saturation

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00

OUTV

INVONBEV

DDV

Cu

t-o

ff

Forward active

SaturationSATCEV

B

E

C IC + ic

IE + ie

IB + ib

DDV

R

VBIAS

outOUT vV

SR

+

-

vs

+

-

vVBE +

-

NPN BJT Common Emitter (CE) Voltage Amplifier

V2.0~

V6.0~

SATCE

ONBE

V

V

Bias point

We need better techniques to calculate the voltage gain of such amplifier circuits

We need small signal models of the BJTs!


NPN BJT: Small Signal Circuit Model

KTqI

g

vgvKTqI

vKT

IIqv

VI

i

eIiI

eI

eWN

DAqnI

B

BBSB

BE

Bb

KT

vVq

BSbB

KT

qV

BS

KTqV

EdE

piB

BE

BE

BE

1

1

12

B

E

C IC + ic

IE + ie

IB + ib

DDV

R

VBIAS

outOUT vV

SR

+

-

vs

+

-

KT

qI

KTqI

gg

vgvgii

iIiI

CBFFm

mFbFc

bBFcC

Collector current:

Base current:

Increases linearly with the collector current

vVBE +

-

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BaseCollectorci

vgm+v

- r

g1

bi

Emitter

ei

B

E

C IC + ic

IE + ie

IB + ib

DDV

R

VBIAS

outOUT vV

SR

+

-

vs

+

-

NPN BJT: Small Signal Circuit Model

KTqI

g BKT

qIgg C

Fm


NPN BJT: Forward Active Current vs VCE

As VCE becomes more positive, the base-collector junction becomes more reverse biased, and the thickness of the depletion increases thereby reducing the thickness WBof the base

Consequently, the collector current increases

The output conductance go is not zero!

Depletion region width

CEV

CI

IB = 0 (cutoff)



oCE

C gdV

dI

BECE VV

VCE-SAT

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CnA

Co

CE

C IV

Ig

dV

dI

CI

CEV

NPN BJT: Output Conductance and the Early Voltage

AV

The slope of the IC vs VCE curves are modeled using the early voltage VA:

The early voltage is usually in the 50-200 V range


NPN BJT: Output Conductance

BaseCollectorci

vgm+v

- r

g1

bi

Emitter

ei

oo r

g1

CE

C

oo V

I

rg

1

Output conductance:

CEV

CI

IB = 0 (cutoff)



BECE VV

VCE-SAT

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NPN BJT Common Emitter (CE) Voltage Amplifier

B

E

C IC + ic

IE + ie

IB + ib

DDV

R

VBIAS

outOUT vV

SR

+

-

vs+

-

Base Collector ci

vgm+v

- r

g1

bi

Emitter ei

oo r

g1

R outv+

-SR

vs+

-

ss

omout

omout

cout

o

outmc

ss

vRr

rRrgv

vRrgv

Riv

rv

vgi

Rr

rvv

||

||

Voltage gain:

s

oms

outv Rr

rRrg

v

vA

||


00

OUTV

INVONBEV

DDV

Cu

t-o

ff

Forward active

SaturationSATCEV

V2.0~

V6.0~

SATCE

ONBE

V

V

Output voltage swing

Input voltage swing

NPN BJT CE Amplifier: Limits of Output Voltage Swing

Bias point

Minimum output voltage and maximum input voltage:If the output voltage becomes too small (happens when the input voltage becomes too large), the BJT will go into the saturation region (in the saturation region the gain is small)

Maximum output voltage and minimum input voltage:If the input voltage becomes too small the BJT will go into cut-off

B

E

C IC + ic

IE + ie

IB + ib

DDV

R

VBIAS

outOUT vV

SR

+

-

vs+

-

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Lecture 18 Bipolar Junction Transistors (BJTs) › ece315 › Lectures › handout18a.pdfNPN BJT:...

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Transcript of Lecture 18 Bipolar Junction Transistors (BJTs) › ece315 › Lectures › handout18a.pdfNPN BJT:...