1

48521 FUNDAMENTALS of ELECTRICAL ENGINEERING

LECTURE 11A

The BJT

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Eng: The BJT 1

The BJT(Bipolar Junction Transistor)

N-P-N Bipolar Junction Transistor

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The BJT 2

2

N-P-N Bipolar Junction Transistor

In normal operation, B-E junction is biased in In normal operation, B E junction is biased in forward and B-C junction is biased in reverse.

Emitter current iE is given by Shockley’s equation:

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The BJT 3

⎥⎦

⎤⎢⎣

⎡−⎟⎟⎠

⎞⎜⎜⎝

⎛= 1exp

T

BEESE V

vIi

N-P-N Bipolar Junction Transistor

The KCL requires that iE = iC + iBq E C B

Introducing the parameter α = iC /iE we can write:

⎥⎦

⎤⎢⎣

⎡−⎟⎟⎠

⎞⎜⎜⎝

⎛= 1exp

T

BEESC V

vIi αand:

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The BJT 4

and:

EB ii )1( α−= ⎥⎦

⎤⎢⎣

⎡−⎟⎟⎠

⎞⎜⎜⎝

⎛−= 1exp)1(

T

BEESB V

vIi α

3

N-P-N Bipolar Junction Transistor

Defining the parameter β = iC /iB = α/(1− α), we g p β C B ( ),have: iC = βiB

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The BJT 5

Common-Emitter Characteristics

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The BJT 6

4

Common-Emitter Characteristics

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The BJT 7

P-N-P Device

All equations are the same as for p-n-p d i if th l it fdevice if we reverse the polarity of vBEand vBC

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The BJT 8

5

BJT: Regions of Operation

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The BJT 9

Large-Signal Models

Normal Active Region: B-E - fwd, B-C - rev.o a ct e eg o d, C e

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The BJT 10

6

Large-Signal Models

Saturation Region: B-E - fwd, B-C - fwdSaturation Region: B E fwd, B C fwd

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The BJT 11

Large-Signal Models

Cut-off Region: B-E - rev., B-C – rev.Cut o eg o e , C e

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The BJT 12

7

DC Analysis of BJT Circuits

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The BJT 13

DC Analysis of BJT Circuits

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The BJT 14

8

DC Analysis of BJT Circuits

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The BJT 15

DC Analysis of BJT Circuits

KVL in a B-E loop gives:

EEBEBBB RIVRIV ++=

But IE = (β+1)IB , so:

[ ]EBBEBBB

IRRVRIVRIV

)1()1(

++++++=

ββ

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The BJT 16

[ ] BEBBE IRRV )1( +++ β

EB

BEBB RR

VVI)1( ++

−=βEECCCCCE IRIRVV −−=

9

( ) ( )B BQ bi t I i t= +

ib(t) denotes the signal current flowing into the base,

( ) ( )tvVtv beBEQBE +=

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The BJT 17

ib(t) denotes the signal current flowing into the base, IBQ is the dc current that flows when the signal is absent, and iB(t) is the total base current. Similar notation is used for the other currents and voltages.

BJT: Small-Signal Model (hybrid-π)

There are three mathematically identical models with diff t t l M d l 1 ( ith t d t )different topology. Model 1 (with transconductance gm):

gm vπ

rorπ

+

-

vπ

B C

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The BJT 18

E

10

BJT: Small-Signal Model

There are three mathematically identical models with diff t t l M d l 2 ( ith CCCS βi )different topology. Model 2 (with CCCS βib):

βib

rorπ

B Cib

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The BJT 19

E

BJT: Small-Signal Model

There are three mathematically identical models with diff t t l M d l 3 ( ith itt i t )different topology. Model 3 (with emitter resistance re):

βibroB

C

ib

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The BJT 20

re

E

11

BJT: Small-Signal Model (hybrid-π)

The values of the basic elements of the these models depend on the BJT parameters and the operating point.

T

CQm V

Ig =

mgr βπ =

CQ

Ao I

Vr =

current collector quiescent :Where −CQI

me g

r α=

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The BJT 21

)1/(gaincurrent s'transistorV) 100(~ ageEarly voltmV) 26(~ voltagethermal

+=−−−

ββαβ

A

T

VV

Basic BJT AmplifiersCommon Emitter

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The BJT 22

21

2121 ||

RRRRRRRB +

==

12

Basic BJT AmplifiersCommon Emitter

Small-signal mid-band equivalent circuit:

gmvπ

rorπ

+

-vπ

+RC RLRB

RS

VS

+

-

vi

+

-vo

Network functions:

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The BJT 23

LoC

m

i

oV GgG

gvvA

++−

==πgG

ZB

in += 1

oCout gG

Z+

= 1

Basic BJT AmplifiersCommon Collector (Emitter Follower)

21

2121 ||

RRRRRRRB +

==

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The BJT 24

21 RR +

13

Basic BJT AmplifiersCommon Collector (Emitter Follower)

Small-signal mid-band equivalent circuit:

Network functions: 1≈+== mo ggvA π

gmvπ

ro

rπ

+ -vπ+RE RL

RB

RS

VS

+

-

vi

+

-

Vo

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The BJT 25

1≈++++

==LoEm

m

i

oV GgGggv

Aπ

π

BVBin GAgG

Z 1)1(

1 ≈−+

=π

⎟⎟⎠

⎞⎜⎜⎝

⎛++

−+++=

BSmoE

out

GGgggggG

Z

π

ππ 1)(

1

Basic BJT AmplifiersCommon Base

CB

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The BJT 26

14

Basic BJT AmplifiersCommon Base

Small-signal mid-band equivalent circuit:

gmvπ

ro

rπ

-

+vπ

+ RCRLRE

RS

VS

+

-vi

+

-vo

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The BJT 27

LoC

om

i

oV GgG

ggvv

A++

+==

mVoEin gAggG

Z−−++

=)1(

1

π