© REP 8/25/2015 ENGR224 Bipolar Junction Transistors Page BJT 4.1-1 Physical Structure and Modes of...

© REP 04/19/23 ENGR224

Bipolar Junction Transistors

Page BJT 4.1-1

Physical Structure and Modes of Operation

n-type

Emitterregion

p-type

Baseregion

n-type

Collecterregion

Base(B)

Emitter(E)

Collecter(C)

Emitter-basejunction

(EBJ)

Collecter-basejunction

(CBJ)

Metalcontact

Mode EBJ CBJ

Cutoff Reverse ReverseActive Forward ReverseSaturation Forward Forward

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Page BJT 4.1-2

Injected Diffusing Collected electrons electrons electrons

Operation of the npn Transistor in the Active Mode

n p n

E C

B

EiBi

CiEiEi

Bi

Ci

CiInjected holes (iB1)

BEV CBV

BEv CBv

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Page BJT 4.1-3

Current Flow

Only diffusion-current components are considered Profiles of minority-carrier concentrations in the base and in the emitter of an npn

transistor operating in the active mode; vBE > 0 and vCB 0.

Collector(n)

Effective base width W

Ca

rrie

r c

on

ce

ntr

ati

on

Emitter(n)

EBJdepletion

region

Base(p)

CBJdepletion

region

Holeconcentration

Electronconcentration

np (ideal)

np (withrecombination)

np(0)

pn(0)pn0Distance (x)

T

BEV

v

pp enn 0)0(

W

nqDA

dx

xdnqDAI

pnE

pnEn

0

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Page BJT 4.1-4

The Collector Current

WN

nqDAI

A

inES

2

Most of the diffusing electrons will reach the boundary of the collector-base depletion region

These successful electrons will be swept across the CBJ depletion region into the collector

By convention, the direction of iC is opposite to that of electron flow

WnqDAI pnES 0

TBE

TBE

VvSC

VvppnC

eIi

ennIi

00 and

saturation current

Aip Nnn 20

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Page BJT 4.1-5

The Base Current

TBE Vv

pD

ipEB e

LN

nqDAi

2

1

Two components of base current, iB1 and iB2.

Hole diffusivityin the emitter

Hole diffusion lengthin the emitter

Doping concentration of the emitter

TBE Vv

Ab

iEB e

N

qWnAi

2

2 2

1

TBE Vv

A

iEn e

N

qWnAQ

2

2

b

nB

Qi

2

WnqAQ pEn 02

1

minority-carrierlifetime

TBE Vv

bnpD

A

n

pSB e

D

W

L

W

N

N

D

DIi

2

2

1

TBE VvSB

CB

eI

i

ii

bnpD

A

n

p

DW

LW

NN

D

D

2

21

1

common-emittercurrent gain

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Page BJT 4.1-6

The Emitter Current

EC

VvSE

CE

BCE

ii

Ii

ii

iii

TBE

1

1

1

1TBE Vv

SE eIi

common-basecurrent gain

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Page BJT 4.1-7

First Order Equivalent Circuit Models

The externally controlled signals for this model are the three currents shown outside the gray box.

The voltage VBE, exists internally as a result of the currents and can be externally measured. We can force a current and measure a voltage.

The diode in the model is designated as DE since the current flowing through the diode is the same as the emitter current. The collector current is dependent on the base-emitter voltage VBE.

The model is a non-linear voltage controlled current source Bi

Ci

Ei

T

BE

V

V

SeI

BEv

B

C

E

DE

Current Controlled Current Source

Voltage Controlled Current Source Model

Bi

Ci

Ei

Ei

BEv

B

C

E

DE

The externally controlled signals for this model are two currents and the voltage VBE shown outside the gray box.

The current iE exists internally as a result of the voltage VBE and can be externally measured.

The collector current is dependent on the emitter current iE.

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Page BJT 4.1-8

Equivalent Circuit Models, cont’d

In this version of the model the diode conducts the BASE current which is beta times smaller. In one version the dependent current source is voltage controlled (vBE), in the other version the dependent current source

is current controlled ().

BEv

Ci

Ei

Bi

TBE VvSeIBD

SI

E

B C

BEv

Ci

Ei

Bi

BIBD SI

E

B C

Current Controlled Current SourceVoltage Controlled Current Source Model

Note connection point is now on the opposite side of the diode

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Page BJT 4.1-9

Two Port Model of the Common-Base Configuration

Bi

Ci

Ei

T

BE

V

V

SeI

BEv

B

E

DE

B

C

B

B

E

C

BB

E C

Two portNetwork

If we switch the leads within the networkthe common base aspect is more apparent

The base lead is common to both ports

B

C

B

E

Two-Port representation of a BJT Transistor symbol in a common-base configuration

Ei Ci

cout

Ein

ii

ii

E

C

in

outi i

i

i

iA

iniouti

The common-base current gain is

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Page BJT 4.1-10

Two Port Model of the Common-Emitter Configuration

E

B

E

CTwo portNetwork

The emitter lead is common to both ports

E

CB

E

Two-Port representation of a BJT Transistor symbol in a common-emitter configuration

BiCi

Cout

Bin

ii

ii

B

C

in

outi i

i

i

iA

ini outi

The common-emitter current gain is

BEv

Ci

Ei

Bi

BIBD SI

E

B C

iC is out of phase with iB

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Page BJT 4.1-11

Injected Diffusing Collected holes holes holes

Operation of the pnp Transistor in the Active Mode

p n p

E C

B

EiBi

CiEiEi

Bi

Ci

CiInjected electrons (iB1)

EBV BCV

EBv BCv

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Page BJT 4.1-12

Equivalent pnp Circuit Models

Ci

Ei

Bi

SIB

BD

E

C

EBv TEB VvSeI

Bi

Ei

Ci

T

EB

V

V

SeI

EBv

B

E

DE

C

SI

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Page BJT 4.1-13

Circuit Symbols and Conventions - npn

B

C

E

B

C

E

BiEi

CiCBV

BEV

npn BJT

Voltage polarities and current flow in a transistor biased in the active mode.

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Page BJT 4.1-14

Circuit Symbols and Conventions - pnp

B

E

C

B

E

C

BiCi

EiEBV

BCV

pnp BJT

Voltage polarities and current flow in a transistor biased in the active mode.

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Page BJT 4.1-15

Example 4.1

The transistor in the circuit below has = 100 and exhibits a vBE of 0.7V at iC = 1 mA. Design the circuit so that a current of 2 mA flows through the collector and a voltage of +5V appears at the collector.

V15

V15

CR

ER

V15

V15

CR

ER

VVC 5

BEE VV

mAIC 2

BCE III

k

I

VR

mAI

I

VVV

VVV

mAiVV

kmA

V

mA

VVR

E

EE

CE

BEE

TBE

CBE

C

07.702.2

150717.

15

02.299.0

2 thus

99.0101100 ,100for

717.0 and

717.01

2ln7.0

,1at 7.0 since

52

10

2

515

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Page BJT 4.1-16

Graphical Representation of Transistor Characteristics

Similar to diodes, except we talk about the voltage across one junction VBE and the current through the other terminal iC. For most of the conditions we will encounter in working with BJTs the ideality factor, n will be considered to be 1.

0 0.5 0.7

Ci

VvBE

Ci

BEv

T1>T2>T3

T1 T3T2

I

iC-vBE characteristics

Effect of temperature on iC-vBE characteristic.At a constant current, vBE changes by –2mV/oC.

TBE VvSC eIi

0 0.5 0.7

S

E

Ii

VvBE0 0.5 0.7

S

B

Ii

VvBE

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Page BJT 4.1-17

iC versus vCB Characteristics

npn transistor in active mode

Ei

CiCBv

0 1 2 3

EC imAi

VvCB

mAiE 4

mA 3

mA 2

mA 1 1 2 3

4

+Vnp = reverse bias-Vnp = forward bias

saturation

0 1 2 3

mAiC

VvCE

4Bi

3Bi

2Bi

1Bi

saturation

See next pageCEC vvsi

Current controlledcurrent source

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Page BJT 4.1-18

iC=vCE Characteristics

The Early Voltage (typically 50 -100 Volts), also known as the Base-Width Modulation parameter.

A

CEVvSC V

veIi TBE 1

Ci

CEv

BEv

1

constant

BEvCE

CO v

ir

C

AO I

Vr

AV CEv0

Ci

Saturation

region

Activeregion

. . . BEv

. . . BEv

. . . BEv

. . . BEv

As the base-collector junction reverse bias is increased the depletion layer expands and consumes some of the base narrowing it and causing an increase in the collector current.

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Page BJT 4.1-19

Example 4.2

We wish to analyze this circuit to determine all node voltages and branch currents. We will assume that is specified to be 100.

V10

kRC 7.4

kRE 3.3

V4

kRC 7.4

kRE 3.3

V 10

V 4

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Page BJT 4.1-20

Example 4.2, cont’d

We don’t know whether the transistor is in the active mode or not. A simple approach would be to assume that the device is in the active mode, and then

check our results at the end

V10

k 7.4

k 3.3

V4

EV

CV

EI

CI

BI

mAI

I

VRIV

mAI

II

mAR

VI

VVV

EB

CCC

C

EC

E

EE

BEE

01.0101

1

1

3.57.499.01010

99.01 99.0

99.0101

100

1 ,

13.3

3.30

3.37.044

1

2

3

4

5

1

2

3

4

5

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Page BJT 4.1-21

Example 4.3

We wish to analyze the circuit shown below to determine the voltages at all nodes and the currents through all branches. Note that this circuit is identical to the previous circuit except that the voltage at the base is now +6 V.

V10

kRC 7.4

kRE 3.3

V6

V10

k 7.4

k 3.3

V4

EV

CV

EI

CI

BI 1

2

3

4

Assuming active-mode:

VIV

mAII

mAI

VVV

CC

CC

E

BEE

48.252.7107.410

6.1

6.13.3

3.5

3.57.066.5

Collector voltage > base voltagesaturation mode, not active mode

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Page BJT 4.1-22

Example 4.4

We wish to analyze the circuit below to determine the voltages at all nodes and the currents through all branches. This circuit is identical to that considered in the previous two examples except that now the base voltage is zero.

V10

kRC 7.4

kRE 3.3

V10

k 7.4

k 3.3

cutoff 0VVE

VVC 10

mAIE 0

mAIC 0

mAIB 0

1

2

3

45

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Page BJT 4.1-23

Example 4.6

We will analyze the following circuit to determine the voltages at all nodes and currents through all branches. Assume =100.

V10

kRC 2

kRB 100

V5

CI

BI

V10

kRC 2

k 100V5

mAIC 3.4

mAIB 043.0 mAIE 343.4

VVC 4.1

mAII

VRIV

mAII

mAR

VI

VVV

BE

CCC

BC

B

BEB

BEB

3.4043.01011

4.123.41010

3.4043.0100

043.0100

7.055

7.0

1

2

3

4

55

4

3

2

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Page BJT 4.1-24

Example 4.7

We want to analyze the circuit shown below to determine the voltages at all nodes and currents through all branches. Assume =100.

kRC 5

kRE 3

V 15

k

RB

1001

k

RB

502

V 15

k

RBB

3.33

kRC 5

kRE 3

VVBB 5

1

3.3350//100//

550100

501515

21

21

2

E

B

EEBEBBBBB

BBBB

BB

BBB

II

RIVRIV

kRRR

VRR

RV

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Page BJT 4.1-25


V 15

k 3.33

k 5

k 3

V 5

V 8.6

V 3.87mA 013.0

mA 29.1

mA 28.1 k 001

k 05

mA 103.0

mA 013.0

mA 09.0

VRIV

mAII

V

RIVV

mAI

RR

VVI

CCC

EC

EEBEB

B

BBE

BEBBE

6.8528.11515

28.129.199.0

operation, mode-active assuming

57.43 29.17.0

0128.0101

29.1

1

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Page BJT 4.1-26

The BJT as an Amplifier

Objectives

1. Biasing

2. DC equations

3. Transconductance

4. Input resistance looking into the base

5. Input resistance looking into the emitter

6. Voltage gain

7. Gummel plots

Lesson

1. Biasing

1) 1) For our amplifiers, the BJT must be biased in the FORWARD-ACTIVE

2) 2) However, it’s a difficult challenge to establish a CONSTANT DC CURRENT

3)3) Our goal: A Q point insensitive to TEMPERATURE , ß , VBE .

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Page BJT 4.1-27


2. DC Equations (learn ‘em now)(learn ‘em now)

1) 1)

2)2)

3)3)

4)4)

3. Transconductance (remember the small-signal approximation from before?)remember the small-signal approximation from before?)

- - Valid only for vBE< 10 mV

- Defined as the incremental change in output current for an incremental change in input voltage at a DC operating point…..

TBE VVSC eII /

/CE II

/CB II

CCCCC RIVV 1001

99.01

CC IiBE

Cm v

ig

© REP 04/19/23 ENGR224


Page BJT 4.1-28


Note that iC = IC at vBE = VBE, so…...

CI Q

BEV

ci

BEv

TbeTbeTBETbeBETBE VvC

VvVVS

VvVS

VVSC eIeeIeIeIi ////)(/

If vbe<< VT .......)!3!2

1(32

xx

xex

bembeT

CC

T

beCC

T

beCC vgv

V

Ii

V

vII

V

VIi )1(

T

C

Ii

VvS

BEm V

IeI

vg

CC

TBE

/

© REP 04/19/23 ENGR224


Page BJT 4.1-29


Input Resistance “ looking into looking into “ the Base ( highlight this highlight this in your text & on this page!)

Defined as the incremental change input voltage for an incremental change in base current at a DC operating point…

Other important relationships ( be prepared to use any of these!)be prepared to use any of these!)

C

T

IiB

BE

IiB

BE

I

V

i

v

i

vr

CCCC

mgr

B

T

I

Vr

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Page BJT 4.1-30


Input Resistance “looking intolooking into “ “ the Emitter (hightlight this hightlight this in your text & on this page)

Define as the incremental change in input voltage for an incremental change in emitter current at DC operating point…..

Other important relationship ( be prepared to use either of them!) be prepared to use either of them!)

C

T

IiIiE

BEe I

V

i

vr

CCCC

11

1

E

Te I

Vr

mme ggr

1

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Page BJT 4.1-31


Relationship between r and re

- The same input resistance . . . just “ viewed from two different places ! viewed from two different places ! “

err )1(

1rre

B

T

I

Vr

E

Te I

Vr

BE II )1(

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Page BJT 4.1-32


Lets look at Voltage Gain again

A BJT senses vbe and causes a proportional current gm vbe

This is a VOLTAGE - CONTROLED CURRENT SOURCE

So . . . How do we obtain an output voltage so that we get a voltage gain?

Out of phase withthe input

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Page BJT 4.1-33

Voltage Gain

CCC

CCCCCC

CCCCC

CCCCC

RiV

RiRIV

RiIV

RiVv

beCm

CbemCCC

vRg

RvgRiv

Signal voltage: Voltage gain:

Cmbe

c Rgv

vgain Voltage

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Page BJT 4.1-34

Small-signal equivalent circuit models

Every current and voltage in the amplifier circuit is composed of two components: a dc component and a signal component.

The dc components are determined from the dc circuit below on the left. By eliminating the dc voltages, we are left with the signal components (on the right). The

resulting circuit is equivalent to the transistor as far as small-signal operation is concerned.

Amplifier circuit with dc sources Amplifier circuit with dc sources eliminated

CR

e

bee r

vi

bemc vgi

rvi beb

cev

bev +-

bev

CR

EI

CCV

BEV

CI

BI

CEv+-

bev

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Page BJT 4.1-35

The Hybrid- Model

E

BEv

ci

ei

bi

bemvgr

B C

BEv

ci

ei

bi

BI

E

B C

r

voltage-controlledcurrent source

current-controlledcurrent source

ebee

bebe

mbe

bembe

e

bebbemc

rvi

rv

r

v

rgr

vvg

r

vi

rvivgi

11

1

and

bbem

bm

bmbem

ivg

irg

rigvg

m

TCm

gr

VIg

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Page BJT 4.1-36

The T Model

These models explicitly show the emitter resistance re rather than the base resistance rp featured in the hybrid- model.

r

v

r

vi

r

v

r

v

rgr

vvg

r

vi

be

e

beb

e

be

e

be

eme

bebem

e

beb

1

111

1

E

BEv

ci

ei

bi bemvgB

C

er

BEv

ci

ei

bi eiB

C

er

E



ebem

eem

eembem

ivg

irg

rigvg

© REP 04/19/23 ENGR224


Page BJT 4.1-37

Application of the Small-Signal Equivalent Circuits

The availability of the small-signal BJT circuit models makes the analysis of transistor amplifier circuits a systematic process consisting of the following steps: Determine the dc operating point of the BJT and in particular the dc collector current IC. Calculate the values of the small-signal model parameters:

Eliminate the dc sources by replacing each dc voltage source with a short circuit and each dc current source with an open circuit.

Replace the BJT with one of its small-signal equivalent circuit models. Although any one of the models can be used, one might be more convenient than the others for the particular circuit being analyzed. This point will be made clearer later in this chapter.

Analyze the resulting circuit to determine the required quantities (e.g., voltage gain, input resistance).

mE

Te

mT

Cm gI

V

gr

V

Ig

1r and , ,

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Page BJT 4.1-38

Example 4.9

We wish to analyze the transistor amplifier shown below to determine its voltage gain. Assume = 100.

mAI

R

VVI

v

B

BB

BEBBB

i

023.0100

7.03

current base dc thefind to0 Assume

VVCC 10

kRC 3

kRBB 100

+-

VVBB 3

mAII

T

BC 3.2023.0100

be llcurrent wicollector dc he

VV

RIVV

T

C

CCCCC

1.333.210

be willcollector at the voltagedc he

1 2

3

V10

k 3

k 100V 3

A .3232 m

A .0230 m

A .32 m

V 7.01

2

3

V 1.3

iv

© REP 04/19/23 ENGR224


Page BJT 4.1-39


Having determined the operating point, we now proceed to determine the small-signal model parameters

ii

BBibe

vv

Rr

rvv

011.009.101

09.1

VVv

v

i

o / 04.3

:gain Voltage

kg

r

VmAmV

mA

V

Ig

mA

mV

I

Vr

m

T

Cm

E

Te

09.192

100

/ 92 25

3.2

8.10 99.03.2

25

BEvbemvg

rB C

E

+-iv

kRBB 100

kRC 3

iio

Cbemo

vvv

Rvgv

04.33 011.092

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Page BJT 4.1-40

A note about Output Signal Swing

The collector voltage (and vo) can have a maximum value of zero volts before the transistor goes from forward active mode to saturation mode since the base is grounded.

When no input (ac) voltage is applied the output (collector) was found to be at a DC level of -5.4V.

If we desire a symmetric output signal (about the -5.4V DC level) the signal would have to go to -5.4 - 5.4 or -10.8 Volts (this is a large output signal swing).

This causes a problem, since our lower voltage supply is only -10V. In order to avoid possibly producing a distorted output signal the input signal range

must be limited so that the output is not clipped as shown below. Limiting the input signal to smaller values to limit clipping is not the same as using a small signal to invoke the linear approximation as indicated in the next bullet item.

Another important point to be made about the output signal is that it is shown to be linear in the figure below but in fact the iC-vbe characteristic is not linear for a large output signal swing.

0

-10

-5.4

VvC

t

clipping

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Page BJT 4.1-41

Modifying the Hybrid- Model to Include the Early Effect

The Early effect causes the collector current to depend on vBE as well as vCE. The dependence on vCE is modeled by assigning a finite output resistance to the

controlled current-source. By including ro in the equivalent circuit shown below, the gain will be somewhat

reduced.

vvgm

r

B C

E

orbir

B C

E

or

oCbemo rRvgv //

C

A

vCE

Co I

V

v

ir

be

1

0



bi

© REP 04/19/23 ENGR224


Page BJT 4.1-42

Summary of the BJT Small-Signal Model Parameters

Keep these at your fingertips (I.e. formula sheet for an exam or homework or in lab) See Table 4.3

Model parameters in terms of DC bias currents

Model parameters in terms of the transconductance, gm

Model parameters in terms of re

Relationships between the common-emitter current gain and the common-base gain

C

Ao

C

T

B

T

C

T

E

Te

T

Cm

I

Vr

I

V

I

Vr

I

V

I

Vr

V

Ig

mm

e gr

gr

11

1 e

mee

m rrgrr

rg

1

11

1

1

© REP 04/19/23 ENGR224


Page BJT 4.1-43

Graphical Analysis

ivBi

Ci

CEv

BEv

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Page BJT 4.1-44

Graphical Analysis (cont.)

CECC

CCC

CCCCCE

vRR

Vi

RiVv

1

© REP 04/19/23 ENGR224


Page BJT 4.1-45


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Page BJT 4.1-46


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Page BJT 4.1-47

Single Power Supply

Biasing the BJT involves establishing a constant dc current in the emitter which is calculable, predictable, and insensitive to temperature variations and to (for transistors of the same type).

The bias point should allow for maximum output signal swing. To design for a stable IE, the design constraints (shown below) must be satisfied.

Circuit topology for biasing a BJT amplifier

CCVCCV

1R CR

ER2R

21

2

RR

RVV CCBB

21

21

RR

RRRBB

CCV

CR

ER

BBV

BBR CI

EI 1

BE

BEBBE RR

VVI

1 and

BEBEBB

RRVV

Design constraints:

© REP 04/19/23 ENGR224


Page BJT 4.1-48

Single Power Supply, cont’d

CCCCCCCECBCCBB VRIVVVVV3

1

3

1)(or

3

1

From the previous page, our design constraints are as follows:

When biasing the BJT, we must make sure of the following: VBB must not be too large, or it will lower the sum of voltages across RC and VCB

RC should be large enough to obtain high voltage gain and large signal swing

VCB (or VCE) should be large enough to provide a large signal swing

Rules of thumb:

We’d like for RB to be small, which is achieved by low values of R1 and R2. This could result in higher current drain from the power supply, hence lower input resistance (if the input signal is coupled to the base). This means that we want to make the base voltage independent of and solely determined by the voltage divider. In order to achieve this, another rule of thumb is practiced: select R1 and R2 such that their current is in the range of

1 and

BEBEBB

RRVV

EE II 1.0 to

© REP 04/19/23 ENGR224


Page BJT 4.1-49

Example 4.12

We wish to design the bias network of the amplifier shown below to establish a current IE = 1mA using a power supply VCC = +12 V.

VVV

VV

BEE

B

3.34

4

kV

IR

E

EE 3.3

kRkR

VVRR

R

kI

RR

CC

E

80 and 40 Thus

4

1201.0

12

12

21

2

21

CCVCCV

1R CR

ER2R

neglecting base current:

for nonzero base current:

mARR

VVI

BE

BEBBE 93.0

267.03.3

3.3

1

for voltage divider current = 0.1IE

mAI

kRkR

E 10266.03.3

3.3

4 and 8 21

for voltage divider current = IE

© REP 04/19/23 ENGR224


Page BJT 4.1-50


Depending on what the emitter current is, we can have two designs: Design 1: the voltage divider current = 0.1IE, and

Design 2: the voltage divider current = IE

mARR

VVI

kRkR

BE

BEBBE 93.0

267.03.3

3.3

1

40 and 80 21

mAI

kRkR

E 10266.03.3

3.3

4 and 8 21

Design 1 Design 2

kR

I

VR

C

C

CC

34.493.099.0

812

12

kR

I

VR

C

C

CC

04.4199.0

812

12

© REP 04/19/23 ENGR224


Page BJT 4.1-51

Biasing Using Two Power Supplies

A somewhat simpler bias arrangement is possible if two power supplies are available. If the transistor is to be used with the base grounded, then RB can be eliminated altogether. If the input signal is to be coupled to the base, then RB is needed.

CCV

CR

1

EB

II

ER

EI

EEV

BR

1

BE

BEEEE RR

VVI

1 and

BEBEBB

RRVV

Design constraints:

© REP 04/19/23 ENGR224


Page BJT 4.1-52

An Alternative Biasing Arrangement

1

1select

1

1

BEBBCB

CB

BC

BECCE

BEBE

CECC

BEBBCECC

RIRIV

RR

RR

VVI

VRI

RIV

VRIRIVCCV

CR

EI

BR CIBBBEC RIVV

BI

BEV

© REP 04/19/23 ENGR224


Page BJT 4.1-53

Biasing Using a Current Source

The BJT can be biased using a current source The advantage is that the emitter current is independent of the values and RB

Current-source biasing leads to significant design simplification

BE

BEEECCREF

VQQR

VVVII

same thehave and since 21

CCV

CR

IBR

CI

CCV

RI

CI

REFI

BEV

V

EEV

1Q 2Q

R

VVVI BEEECCREF

© REP 04/19/23 ENGR224


Page BJT 4.1-54

Common-Emitter Amplifier

Circuit AC Hybrid -based model

© REP 04/19/23 ENGR224


Page BJT 4.1-55

Common-Emitter Amplifier (cont.)

rRi

Input Resistance:

rR

rR

v

vA

rRgv

v

rRvgv

rR

r

v

v

s

oc

s

ov

ocmo

ocmo

ss

Voltage Gain:

Current Gain:

Co

oi

Co

om

b

oi

Rr

rA

rv

Rrrvg

i

iA

oCo rRR

Output Resistance:

© REP 04/19/23 ENGR224


Page BJT 4.1-56

Exercise 4.31

kmAV

IVr

kVmAgr

VmAmVmA

VIg

mAII

C

Ao

m

T

Cm

C

1001100

5.2/40100

/4025.1

1

What is Av if a 5k load resistor is added to the circuit:

krRi 5.2

VV

kk

kk

rR

rR

v

vA

s

oc

s

ov

/5.63

5.25

1005100

AA

kk

k

Rr

rA

Co

oi

/2.95

5100

100100

For a CE amplifier, let I=1 mA, RC=5k, =100, VA=100V, and Rs=5k. Find Ri, Av, Ai, and Ro:

kkkrRR oCo 76.41005

VVkk

k

RR

RAA

oL

Lnoloadvloadv /5.32

76.45

55.63

© REP 04/19/23 ENGR224


Page BJT 4.1-57

Common-Emitter Amplifier with an Emitter Resistor

© REP 04/19/23 ENGR224


Page BJT 4.1-58

Common-Emitter Amplifier with an Emitter Resistor (cont.)

eeeb Rriv

Input Resistance:

1

1

eeb

iii

eeb

bi Rr

i

vR 1

eme

e

e

ee

i

i

Rgr

R

r

Rr

R

R

11

1

1

)R(without

included) R(with

e

e

Voltage Gain:

ceo Riv

ee

c

b

o

Rr

R

v

v

1 since

ee

c

b

o

Rr

R

v

v

si

i

s

b

RR

R

v

v

ees

c

s

ov RrR

R

v

vA

1

© REP 04/19/23 ENGR224


Page BJT 4.1-59

Common-Emitter Amplifier with an Emitter Resistor (cont.)

Characteristics of CE amplifier with resistance Re:

emee

e

b RgRr

r

v

v

1

1

Output Resistance:

co RR

b

oi i

iA

Input resistance is increased by the factor of (1+gmRe)

An input signal of (1+gmRe) times larger can be applied to the input without inducing nonlinear distortion

The voltage gain is reduced The voltage gain is less dependent on the

value of The high frequency response is significantly

improved

Current Gain:

© REP 04/19/23 ENGR224


Page BJT 4.1-60

Exercise 4.32

251

25

mA

mV

I

Vr

E

Te

VVk

k

k

k

RrR

RA

ees

cv

/2025

500

1732511005

)5(100

1

173

251100

120

e

e

eei

R

R

RrkR

For a CE amplifier with Re, let I=1 mA, RC=5k, =100, and Rs=5k. Find Re such that the amplifier has an input resistence of 4 times that of the source. Find Av, Ai, and Ro:

AAAi /100

kRR co 5

© REP 04/19/23 ENGR224


Page BJT 4.1-61

Exercise 4.32

For the same CE amplifier, find the maximum vs without Re and with Re if v is to be limited to 5mV:

9901.101

100

1

310604.3925

9901. Xr

ge

m

252510604.39

1003Xg

rm

mVv

v

rR

rvmVv

s

s

ss

9.1425255000

2525

5

(max)

(max)

(max)(max)

mV

XmV

RgRvRv emee

40

173*10064.3915

1without with 3

(max)(max)

mVk

kkmV

R

RRvv

i

iss

50 20

20540

(max)(max)

© REP 04/19/23 ENGR224


Page BJT 4.1-62

Common-Base Amplifier

© REP 04/19/23 ENGR224


Page BJT 4.1-63

Common-Base Amplifier (cont.)

ei rR

Input Resistance:

Voltage Gain:

ceo Riv

es

c

s

ov rR

R

v

vA

es

se rR

vi

Current Gain:

e

e

b

oi i

i

i

iA

Output Resistance:

co RR

© REP 04/19/23 ENGR224


Page BJT 4.1-64

Exercise 4.33

251

25

mA

mV

I

VrR

E

Tei

VV

k

k

rR

RA

es

cv

/985.0

255

)5(9901.0

For a CB amplifier with Re, let I=1 mA, RC=5k, =100, and Rs=5k. Find RiAv, Ai, and Ro:

9901.101

100

1

AAAi /99.0

kRR co 5

Note that RiAv, Ai are much lower than the CE amplifier using the same components although the voltage gain of the CB amplifier can be almost equivalent if Rs is low.

© REP 04/19/23 ENGR224


Page BJT 4.1-67


Li

oLe

Loei

RR

rRr

RrrR

1

if

1

Input Resistance: Voltage Gain:

oLes

oL

s

ov rRrR

rR

v

vA

1

1

Current Gain:

Lo

o

b

oi Rr

r

i

iA

1

Loes

Loe

s

b

RrrR

Rrr

v

v

1

1

Loe

Lo

b

o

Rrr

Rr

v

v

oLes

oL

s

ov

rRrR

rR

v

vA

1

© REP 04/19/23 ENGR224


Page BJT 4.1-68


seeex Ririv 1

Output Resistance:

se

xe Rr

vi

1

eo

xx i

r

vi

se

x

o

xx Rr

v

r

vi

1

seox

x

o Rrrv

i

R

1

111x

xo i

vR since

1

seoo

RrrR

seo

o

Rrr

R

1 and of

equivalent parallel theis Thus

© REP 04/19/23 ENGR224


Page BJT 4.1-69


Output Resistance (cont.):

large is when or

1

seo

RrR

Voltage Gain revisited:

oes

oRv

rrR

rA

L

1

oL

LRvv RR

RAA

L

Open-circuit voltage gain:

© REP 04/19/23 ENGR224


Page BJT 4.1-70

Exercise 4.34

55

25

mA

mV

I

Vr

E

Te

For an emitter follower with a load resistence, RL=1k, let I=5 mA, =100, VA=100V, and

Rs=10k. Find :

9901.101

100

1

iRvos

o

b

o

s

bi AAR

v

v

v

v

v

vR

L and ,,,,,,

KmA

V

I

V

I

Vr

E

A

C

A 2.2059901.

1000

k

kk

RrrR Loei

74.96

12.2051100

1

VVkk

k

RR

R

v

v

is

i

s

b /906.07.9610

7.96

VV

kk

kk

Rrr

Rr

v

v

Loe

Lo

b

o /995.01205

120

VVv

v

v

v

v

v

s

b

b

o

v

o /901.0906.0995.0

© REP 04/19/23 ENGR224


Page BJT 4.1-71

Exercise 4.34 (cont.)

VV

kk

k

rrR

rA

oes

oRv

L

/995.0

205101

1020

1

For an emitter follower with a load resistence, RL=1k, let I=5 mA, =100, VA=100V, and

Rs=10k. Find :

AA

kk

k

Rr

rA

L

oi

/2.96

120

201011

0

iRvos

o

b

o

s

bi AAR

v

v

v

v

v

vR

L and ,,,,,,

5.103

1100

105 20

1

kk

RrrR seoo

© REP 04/19/23 ENGR224


Page BJT 4.1-72

The BJT as a switch-cutoff and saturation

The BJT has 4 modes of operation: Cutoff Forward Active Saturation Inverse Active

So far, we have studied the forward active mode in great detail. Now we will look at the BJT in cutoff mode and at the BJT in saturation mode. These two extreme modes of operation are very useful if the transistor is used as a switch, such as in digital logic circuits.

Mode EBJ CBJ

Cutoff Reverse ReverseForward Active Forward ReverseSaturation Forward ForwardInverse Active Reverse Forward

© REP 04/19/23 ENGR224


Page BJT 4.1-73

Cutoff Region

Consider the circuit shown below. If voltage source vI is goes lesss than about 0.5V, the Emitter-Base Junction will conduct negligible current (reverse-biased). The CBJ is also reverse-biased since VCC is positive.

The device will be in the cutoff mode. It follows that:

0Bi CCC Vv 0Ci 0Ei

BR

CCV

CR

Iv+-

Cv

Bi

Ci

© REP 04/19/23 ENGR224


Page BJT 4.1-74

Active Region

To turn the transistor on, vI must be increased to above 0.7V. This gives base current:

The collector current is given by which applies only if the device is in active mode. At this point, we don’t know for sure, therefore we assume active mode and calculate the collector current from

BR

CCV

CR

Iv+-

Cv

Bi

Ci

B

I

B

BEIB R

v

R

Vvi

7.0

BC ii

CCCCC iRVv

7.0CBv0Cv

Next, we check whether or not. In our case, just check whether or not . If so, then our original assumption is true. If not, the device is in saturation.

© REP 04/19/23 ENGR224


Page BJT 4.1-75

Saturation Region

Saturation occurs when we attempt to force a current in the collector higher than the collector circuit can support while maintaining active-mode operation.

C

CC

C

BCCC

CB

R

V

R

VVI

v

7.0ˆ

calculate we,0 settingBy

C

CECCCsat R

VVI

C

B

II ˆ

Csat

EOSB

II )(

B

Csatforced I

I

Maximum collector current

Bi BIIncreasing above , the collector current will increase and the collector voltage will fall below that of the base. This will continue until the CBJ becomes forward-biased.

BR

CCV

CR

Iv+-

Cv

BI

CsatI

CEsatV

BEV

EOS=edge of saturation

Constant currentIB is usually higher than IB(EOS) by a factor of 2 to 10 -- overdrive factor.

This value can be set “at will.”

MAXIMUM BASE current in forward active

© REP 04/19/23 ENGR224


Page BJT 4.1-76

Model for the Saturated BJT

A simple model for the npn and pnp transistors in saturation mode is shown on the left.

For quick approximate calculations one may consider VBE and VCEsat to be zero and use the three-terminal short circuit shown on the right to model a saturated transistor.

E

B

C

E

CB

E

CB

npn

pnp

approximate model

V 2.0ECsatV

V 2.0CEsatV

V 7.0EBV

V 7.0BEV

© REP 04/19/23 ENGR224


Page BJT 4.1-77

Example 4.13

We wish to analyze the circuit to determine the voltages at all nodes and currents in all branches. Assume the transistor is specified to be at least 50.

V10

kRC 7.4

kRE 3.3

V6

V10

k 7.4

k 3.3

V6

EV

CV

EI

CI

BI 1

2

3

4

Assuming saturation:

5.164.0

96.0

mA 64.096.06.1

mA 0.967.4

5.510

5.52.03.5

6.13.3

3.5

3.57.066

forced

B

C

CEB

C

CEsatEC

E

BEE

I

I

III

I

VVVV

mAI

VVV

1

2

3

4

5

5

saturated is transistor ,min forced

© REP 04/19/23 ENGR224


Page BJT 4.1-78

Example 4.14

The transistor shown below is specified to have in the range 50 to 150. Find the value of RB that results in saturation with an overdrive factor of at least 10.

kRR

mAI

mAI

I

mAI

VVV

BB

B

CsatEOSB

Csat

CEsatC

2.294.1

3.4 96.1

7.05

96.1196.010

10, offactor overdrivean For

196.050

8.9

,lowest r with the transisto thesaturate To

8.91

2.010

2.0

min)(

V10

V 5BR

k 1

CEsatV

CV

CsatI

BI

© REP 04/19/23 ENGR224


Page BJT 4.1-79

Example 4.15

We want to analyze the circuit below to determine the voltages at all nodes and the currents through all branches. The minimum value of is specified to be 30.

mA 0.55 1.0

10

55.0

10

5

mA 1.010

mA 3.41

7.05

1

5

BBC

C

BB

B

BBE

E

VVV

I

VV

I

VVV

I

VV

VVV

III

B

BBB

CBE

13.32.1

75.3

55.01.01.03.4

using

5.02.07.0

7.0

BBECsatEC

BBEBE

VVVVV

VVVV

V 5

k 1

V 5

k 10

k 10CV

EV

CI

ECsatV

BI

EI

© REP 04/19/23 ENGR224


Page BJT 4.1-80


Substituting in the equations on the previous page, we obtain the following:

mAI

mAI

mAI

VV

VV

B

C

E

C

E

31.0

86.0

17.1

63.3

83.3

saturatedclearly isor transistthe

8.231.0

86.0

min

forced

forced

© REP 04/19/23 ENGR224


Page BJT 4.1-81

Introduction - Equation forms for use in SPICE

Consider the equation for the emitter current in an ideal pnp bipolar junction transistor

We can simplify the equations by collecting the terms into only a few constants, giving the coefficients different names, for example, half of the equation given above becomes;

The other half of the equation is similarly reduced

This allows the emitter current to be written in a much more compact form:

© REP 04/19/23 ENGR224


Page BJT 4.1-82

Equation forms for use in SPICE (continued)

Now consider the equation for the collector current in an ideal pnp bipolar junction transistor

The right half of the equation reduces to:

The left half of the equation is similarly reduced

This allows the collector current to be written in a much more compact form:

If we know two of the terminal currents we can find the current in the third terminal

© REP 04/19/23 ENGR224


Page BJT 4.1-83

The Ebers-Moll equations for an ideal PNP BJT

The key results are

The equivalent circuit (just another way to state the equations)

IB

IF

IE

IR

IC

RIR

FIF

C

E

B

C

E

B

IB

IC

IE

P

P

N

© REP 04/19/23 ENGR224


Page BJT 4.1-84

Use in SPICE

The current sources illustrate the interaction of the two junctions due to the narrow base region

IS is one of the three required SPICE parameters for a BJT in SPICE2 The reduced equations can be manipulated to show that:

Only three numbers, F , R and IS are needed for the Ebers-Moll equations to be completely specified. All other parameters can be calculated from these three The equations can be applied to all regions of operation

Can be extended to the nonideal case by defining coefficients in front of the exponential terms

For NPN transistors the diodes, currents and voltage polarities are reversedFor NPN transistors the diodes, currents and voltage polarities are reversed

© REP 04/19/23 ENGR224


Page BJT 4.1-85

An Alternative form of the Ebers-Moll Model, the Transport Model

In this model the diodes DBE and DBC have saturation currents IS/F and IS/F respectively

The base current, ib can be written as

iB

IS/F

iE

DBC

iC

iT

C

E

B

IS/R

DBE

iT is the current component of iC which arises from the minority carrier diffusion (transport) across the base, hence the name of this model

The transport model is exactly equivalent to the Ebers-Moll model but it highlights different aspects of BJT behavior. It uses one less circuit element and one less parameter in SPICE

11 T

BC

T

BE

V

v

R

SV

v

F

SB e

Ie

Ii

11 T

BC

T

BE

V

v

SV

v

ST eIeIi

© REP 04/19/23 ENGR224


Page BJT 4.1-86

Common-Base Characteristics

First-Order iC-vCB Characteristics

Second-Order iC-vCB Characteristics

© REP 04/19/23 ENGR224


Page BJT 4.1-87

Common-Emitter Characteristics

Second-Order iC-vCE Characteristics (refer to lesson 17)

© REP 04/19/23 ENGR224


Page BJT 4.1-88

DC and ac

“BETA DC” (spice)More accurate than F, because its determined at QCommon-emitter current gain at DC

“BETAAC” (spice) Input ac signal results in iB iC.

Thus changes, because Since vCE is constant, ac=short-circuit current gain.

Typically, ac=dc. Use ac in small-signal model.

© REP 04/19/23 ENGR224


Page BJT 4.1-89

“Complete” BJT Models

Low-frequency model rx=base resistance of bulk Si

r=

C

BV

i1

© REP 04/19/23 ENGR224


Page BJT 4.1-90

“Complete” BJT Models

High-frequency model

MJC

JC

CBJCJCμ V

V1CCC

MJE

JE

BEJEmJEDπ V

V1CTFgCCC

πμπdB3 CCr2ππ

1f

πμ

mT CC2π

gf

© REP 8/25/2015 ENGR224 Bipolar Junction Transistors Page BJT 4.1-1 Physical Structure and Modes of...

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Transcript of © REP 8/25/2015 ENGR224 Bipolar Junction Transistors Page BJT 4.1-1 Physical Structure and Modes of...