FALLSEM2014-15_CP0968_14-Oct-2014_RM02_smith-ch04a

8/10/2019 FALLSEM2014-15_CP0968_14-Oct-2014_RM02_smith-ch04a

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2S. C. Lin, EE National Chin-Yi University of Technology

Outline

4.1 Device Structure and Physical Operation

4.2 CurrentVoltage Characteristics

4.3 BJT Circuits at DC

4.4 Applying the BJT in Amplifier Design

4.5 Small-Signal Operation and Models

4.6 Basic BJT Amplifier Configurations

4.7 Biasing in BJT Amplifier Circuits

4.8 Discrete-Circuit BJT Amplifiers

4.9 Transistor Breakdown and Temperature Effects


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4.1 Device structure and physical operation

Emitter and collector regions having identical physical dimensions(C > E > B) and doping concentrations (E > C > B)


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ForwardForwardSaturation

ForwardReverseReverse active

ReverseForwardActive

ReverseReverseCutoff

CBJEBJMode

BJT modes operation


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Figure 5.3 Current flow in an npn transistor biased to operate inthe active mode. (Reverse current components due to drift of

thermally generated minority carriers are not shown.)


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Figure 5.4 Profiles of minority-carrier concentrations in the base and

in the emitter of an npn transistor operating in the active mode: vBE 0and vCB 0.

/ 3 0.7 / 0.025(0) 0 10 highly

BE TV Vp pn n e e

/ 3 1/ 0.025( ) 0 10 0CB TV Vp w pn n e e


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This electron diffusion current as foll

((

ows :

4.2) 0) )(

n

p p

n E n E ndn x nI A qD A q

dx W

I

D

/

0

/

0

According to the law of the junction (sec. p.61, eq.1.57)

the concentration (0) will be propotiona

(0)

l to

where is

(4.1)

BE T

BE T

v V

p p

p

p

v Vn

n

n

n e

e

the thermal- equilibrium value of the

minority-carrier (electron) concentration in the base regionis the thermal-voltage ( 25mV)TT VV

where is the cross-sectional area of B-E junction,

is the magnitude of the base,is the electron diffusivity in the base,

is the effectiv

e width of the base,

E

n

A

qD

W

flows from right to left(in the negtive dir ection of )nI x

(0)p

n

W

pn


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/

0

2

2

/

0

0

(0)

where ,subtituting

(4.

4 )

BE T

BE T

p is

v V

p p v VC n E

E n p

n E n s

is E n

A

A

n nI A qD n

n n ei I A qD A qD I e

W W

nI A qD

N W

w N

The Collector Current

12 18

The is inversely propotional to the base width W and is directly

propotional to the area of the EBJ.

Typically is in the range of 10 A to 10 A

(depending on the size of the dev

s

s

I

I

2

o

ice)The is propotional to , it is a strong function of temperature,

approximately doubling for every 5 rise in temperature.

s iI n

C


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The Base Current

1

2 2/ / /

is the hole diffusion length in the emitter

BE T BE T BE T

s

E p i p Av V v V v V n E i p A

s

D p

B

n

D p A D p n

A

n

p

n

I

A

i

L

D N WN W D

A qD n D N WD A qne e eN L

D N WIN LN L DN W D

2

2/

0 0

, is minority-carrier lifetime,

is replenished by electron injection from the emitter

subtituting (0) and

1

, give

(0) .

s

2

BE T

n E

nB b

b

n

v V i Ep p

p

p n

A

Qi

Q

n An n e n Q

Q

N

A q n W

2

2/

2/ /

2/

22 21

2

2

1

2

1

2

BE T

BE T BE T

s

BE Tv VE iB

A b

v Vi

A

v V v V E in n E i

A nb

I

n bA

qWneN

A qW nDA q D A qn W

N W D

Wni e e

NDe

N W


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1 2

2

/

/

2

1where

(4.6

1

2

The is called the common- emitter

2

c

1

)

BE

E

T

B T

B B B

p v VAs

n D p

v VC sB

n b

p A

n D p n b

i

i i i

D N W W

D N L D

D N W WI

i

e

D

e

D N L

i

urrent gain,For moden npn transistor, is in the range 50 to 200,

but it can be as high as1000 for special devices


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The Emitter current

/

/

(4.9)

(4.1

The

1 1

, =1 1

is co

mmon-base current gain, that is less than

2)

but very close

B

E

E

B

T

T

E B C

v V

C s

v Vs

E

i

i

i i i

i i e

e

to unity.


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Figure 5.5 Large-signal equivalent-circuit models of the npn BJT

operating in the forward active mode.


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Figure 5.7 Model for the npn transistor when operated in the reverseactive mode (i.e., with the CBJ forward biased and the EBJ reverse

biased).


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Figure The Ebers-Moll (EM) model of the npn transistor.

Ebers-Moll (EM) Model

E DE R DC

C DC F DE

B E C

i i i

i i i

i i i

E

i

Bi

Ci

DEi DCi

R DCi F DEi


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CD collector-base junctionThe diode represents the

the scale current

,

is SCI

ED mitter-base junctioThe diode represents the e

the scale current is

n,

SEI

SC SE I I

is in the range of 0.01 to 0.5R

Ris in the range of 0.01 to 0.1

F SE R SC S I I I


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/ /

/ /

The transistor terminal current equtions:

1 1 (a)

(c

1 1

)

( )

b

BE T BE T

BE T BE T

v V v V S

DE SE

E DE R DC

C DC F D

F

v V v V SDC

R

E

SC

I

i I e e

Ii I e

i i i

i

e

i i

(d)

(1 ) (1 )

Subtituting (a) and (b) into (c),(d)and

(e)

(e), we have

B E C F DE R DCi i i i i


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//

//

//

1 1

1 1

1 1

where ,1 1

BC TBE T

BC TBE T

BC TBE T

v Vv VSE S

F

v Vv V

F RF

SC S

R

v Vv VS SB

F

F R

R

R

Ii e I e

I

i I e e

I Ii e e

+


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Application of the EM model

/

/

0

/

/

0

/

/

/

/

(A) Opoerating in the forard avtive mode

1 11

1

1

1

111

BE T

BE T

BC T

BC T

B

BE T

BE T

B TE CT

v VS

E SF

v V SC S

v V

v V

R

v VS

v VS

SF

S

F

v VS

R

v VB

F

S

R

Ii e I

Ii I e

I I

e

i

e

e

I

I I

e

e I

e

0

/ 1 11 BE Tv VS SF F R

Ie I


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4.1.4 Operation in the Saturation Mode

BI forced BI

BCV

BEV

satCE

V

CCV

/

/

forced

1

1

1

BE T

BC T

v V

v V

C B

RR

R

e

e

i I


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/ /

forced f

//

//

fo

o

rced

rced

11 1

The EM expression for

T

1

1 1 (a

he EM expres

)

sion

BC TBE T

BC TB

v V v

E T

VBE T BC TS S

RB

I

R

v V

X Y

v V

C S S

R

v Vv V RC S S

R

R

I

B

e

C

e

R

i I e I e

i I

Xi Y

e I e

i X

i

Y

fo r (b)BF

B

Ri

X Y

i


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( )1

ln R forced F CE sat T v V

F forced R

1

F 1

R

F R

( )

1 (1 ) / ln

1 (

/

)

forced R

CE sat T

forced F

v V

The for the case( ) 50, 0.and 1CE F RV sat

60123147166191211235

010203040454850

( )CE satv

forced


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Figure 4.8 The iCvCB characteristic of an npn transistor fed with aconstant emitter current IE. The transistor enters the saturation mode of

operation for vCB0.4 V, and the collector current diminishes.


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Figure 4.10 Current flow in a pnp transistor biased to operate in the

active mode.


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Figure 4.13 Voltage polarities and current flow in transistors biased in

the active mode.

4.2 CurrentVoltage Characteristics

4.2.1 Circuit symbols and Conventions


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The constantn

The constant , its value is between 1 and 2.

For modern BJT the constant is close to unity except in special cases:

At high currents, the relationship exhibits a value for

that is cl

-

s

o

C BE

n

n

n

i v

e to 2 .

At low currents, the relationship shows a value for

approxima

-

tely 2 .

B BEi v

n

0

The current is the reverse current flowing from collector

to base with the emitter open-circuited.

The current depends strongly on temperature,

approximately doubling for

10 rise

CBO

CBO

I

I

C

2 1( ) /10

2 1

.

2T T

CBO CBOI I

( )CBOIThe Collector-Base Reverse Current


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The transistor in the circuit of Fig (a) has 100 and

exhibits of 0.7V at 1mA. Design the circuit so that a current

of 2mA flows through the collector and a voltage of +5V

BE Cv i

appear at

the collector.

2

1

10V 2mA

0.7 ln 0.717V

0.717V

100 0.99

/ 2mA / 0.99 2.02mA( 15

5k

7.07

k )

Sol :

C

BE T

E

E C

EE

E

R

IV V

IV

I IV V

RI

Example 4.2


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Figure (a) The iCvBEcharacteristic for an npn transistor.(b) Effect of temperature on the iCvBEcharacteristic. At a constant

emitter current (broken line), vBE changes by 2 mV/C.

/BE Tv V

C S

T T C

i I e

V T T V i

4.4.2 Graphical Representation of Transistor Characteristic


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1

5

4

3

2

0 2 4 6 8 10 12

1mAEi

2mA

3mA

4mA

5mA

(V)CBv

(mA)C

i

/BE Tv VC Si I e

4.2.3 Dependence of on the Collector VoltageThe Early effectci


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(1) increases with increasing

(2) increases with increasing re

Early ef

verse co

fect has three con

llector voltage.

(3) punch through

sequences:

CB

C

V

I

o EBV V

EBV

CBV

oV

'B

W W

BW


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'Ci

=C C CA CE CE

C CE C CE

i i iV v v

i v i v

C A C CE i V i v

CEC C

A

vi i

V

CEv

Ci


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/'

' ' '

The collector current ( operation in the active mode)

neglected the Early effect:

includ

=

ing the Early e

ff

=

ect

:

BE T

v V

C S

CEC C C C C

A

v

S

i I ev

i i i i iV

I e

/1+BE T

V CE

A

v

V

1

tan

The nonzero slopeof the straight line indicatesthat the output resistance looking into the collector

is not infinite. Rather, it is finite and defined by

BE

C C

C A Co

CE v o s

E

c n t

i

V

v

v

i Vr

'

E A

C C

V

I I


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Figure 4.18 Large-signal equivalent-circuit models of an npn BJT

operating in the active mode in the common-emitter configuration.

4 2 4 A Alt ti F f Th C E itt Ch t i ti


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Figure 4.19(a)(b) Common-emitter characteristics. Note that the

horizontal scale is expanded around the origin to show the saturation

region in some detail.

4.2.4 An Alternative Form of The Common-Emitter Characteristics

( ),

( )

CQ

dc FE

BQ

Cac fe

B

I

hI

ih

i

Common-emitter Current Gain

Th t ti lt V d t ti i t R


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Figure 4.19(c) An expanded view of the common-emitter

characteristics in the saturation region.

sat

sat

sat

B B

C Csat

C F B

C

forced

B

forced F

CE

CEi I

Ci I

I I

I

I

V

R i

The saturation voltage VCEsat

and saturation resistance RCEsat


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Typically, 0.1 to 0.3

CE sat CEoff Csat CEsat

CEsat

V V I R

V V V

Example 4 3 For the circuit in Fig 4 21 has 10k and 1kR R


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Example 4.3

BI

CI

BCV

BEV

CEV

10VCCV

BBV

BR

CR

For the circuit in Fig.4.21 has 10k and 1k ,

it is required to determine the value of the voltage that results the

transistor operating (a) in the active mode with

B C

BB

C

R R

V

V

forced

5V, (b) at the edge

of saturation, (c) deep in saturation with 10

For simplicity, assume that 0.7V. The transistor 50

E

BEV

Solution:

CCC

10 5 V 5mA1k

/ 5mA / 50 0.1mA

0.1 1 1.7V0 0.7

CEC

B C

BB B B BE

V VIR

I I

V I R V

10 0 3 VV V


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CC

C

10 0.3 V( ) 9.7mA

1k

/ 9.7mA / 50 0.194mA

0.194 10 0. 2 4V7 .6

satCE

C

B C

BB B B BE

V Vb I

R

I I

V I R V

CC

C

( ) 0.2V

10 0.2 V

9.8mA1k

9.8mA 0.98mA

10 the requred can now be found as

0.98 10 0.7 10 5V .

sat

sat

CE CE

CE

C

CB

forced

BB

BB B B BE

c V V

V V

I R

II

V

V I R V

4 3 BJT i it t DC


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4.3 BJT circuits at DC

Consider the circuit shown in below Fig. We wish toanalyze this circuit t node voltages branch

currents

o determine all and

We will assume that is speci

fied to b. e 100

Example 4.4


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We wish to analyze this circuit below Fig. to determineExample 4.5


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W y g

all node voltages and branch currents.We will assume that is

specified to be at least 50.

Example 4.5


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0.96 1.50.64

CforcedB

I

I


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We wish to analyze this circuit below Fig., to determine

all node voltages and branch currents.

Example 4.6


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We want to analyze the circuit in below Fig to determineE l 4 8


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We want to analyze the circuit in below Fig., to determine

the voltages at all nodes and the currents in all branchs .Assume 100Example 4.8

We want to analyze the circuit in below Fig., to determineExample 4.9


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the voltages at all nodes and the currents in all branchs .The minimum

value of is specified to be 30.

p

We want to analyze the circuit in below Fig., toExample 4.10


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determine the voltages at all nodes and the currents though all branchs .

Assume 100


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We desire to evaluate the voltages at all nodes and theExample 4.12


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We desire to evaluate the voltages at all nodes and the

currents though all branchs in the circuit of below Fig., Assume 100

Example 4.12



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BE

v

CRCi

o CEv v

CCV

X Y

Z

CEv

CCV

BEv

Active

mode SaturationCut Off

Edge ofSaturation

0 0.5V

0.3V

4.4.1 Obtaining a Voltage Amplifier

4.4.2 The Voltage Transfer Characteristic (VTC)


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g ( )

X Y

Z

CEv

CCV

BEv

Activemode SaturationCut Off

Edge ofSaturation

0 0.5V

0.3V

/

/

BE T

BE T

v V

C S

CE CC C C

v V

CC C S

i I e

v V i R

V R I e

4.4.3 Biasing the BJT to Obtain Linear Amplification


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BE

v

CRCi

o CEv v

CCV

X Y

Z

CEV

CEv

CCV

BEV BEv

Q

g J p

CEv


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X Y

Z

CCV

BEv

SaturationCut Off

0 0.5V

0.3V

BEV

Time

Time

Slop Av

Q

Active

mode

/

/

( ) ( )

BE T

BE T

v V

C S

v VCE CC C S

BE BE be

I I e

v V R I e

v t V v t

Figure 4.33(a)

4.4.4 The Small-Signal Voltage Gain


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/

(4.29)

,where

(4.30)

(4.32)

BE BE

BE T

C

C

CEv

BE v V

v VCE C C

S v CBE T T

RC Cv R CC CE

T T

dVAdV

dV R I

I e A RdV V V

VI RA V V V

V V

o

The observations on this expression for the voltage gain:

The gain is negative, which signifies that the amplifier is inverting

; that is, there is a 180 phase shift between the input and the out

put.

The gain is propotional to the collector bias current and to the load

resistance .

C

C

I

R

Example 4.1315

Consider an amplifier circuit using a BJT having


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1510 A, a collector resistance 6.8k , and a power supply

10V.(a) Find ,and , such that the BJT operate at 3.2V

s C

CC BE C CE

I R

V V I V

(b)Find the voltage gain at this bias point. If 5sin (mV)

find .(c)Find the positive increment in that drive the transistor to

the edge of saturation( 0.3V).(d)Find the negative insat

v i be

o BE

CE

A v v t

v v

v

crement in

that drive the transistor to the within 1% of cut-off.BEv

Solution:

CC

C

/

CC

10 3.2 V( )6.8k

ln /

10 3.2 V( )

0.025V

272V/V

1.36sin (V 272 0

1mA

690.

.005si

8 mV

) n

BE T

CEC

v VC S BE T C S

CEv

T

o ce

V Va IR

I I e v V I I

V Vb

V

v V t t

A

( ) For 0.3VsatCE

c v


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CCC

2

1

10 0.3 V 1.617mA6.8k

To increase from 1mA to 1.617mA, must be increase by

1.617 ln 0.025ln

112mV

sat

CEC

C BE

CBE T

C

V ViR

i v

Iv V

I

CCC

( ) For 0.99 9.9V10 9.9 V

0.0147mA6.8k

To decrease from 1mA to 0.0147mA, must be change by

0.0147 0.025ln 105.5mV

1

CE CC

CEC

C BE

BE

d v V

V vi

R

i v

v

4.4.5 Determining The VTC by Graphical Analysis


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Figure Graphical construction for the determination of the dc base

current in the circuit of Fig.4.33(a).

Figure 4.33(a)


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Figure 4.34 Graphical construction for determining the dccollector current IC and the collector-to-emitter voltage VCE in the

circuit of Fig.4.33(a).

CE CC C C

CC CE C

C C

v V i R

V Vi R R

4.4.6 Locating the Bias Point Q


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Figure 4.35 Effect of bias-point location on allowable signal swing: Load-line A resultsin bias point QA with a corresponding VCEwhich is too close to VCCand thus limits the

positive swing of vCE. At the other extreme, load-line B results in an operating point too

close to the saturation region, thus limiting the negative swing of vCE.


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