electronics ch4

NTUEE Electronics – L. H. Lu 4‐1

CHAPTER 4 BIPOLAR JUNCTION TRANSISTORS (BJTs)

Chapter Outline4.1 Device Structure and Physical Operation4.2 Current‐Voltage Characteristics4.3 BJT Circuits at DC4.4 Applying the BJT in Amplifier Design4.5 Small‐Signal Operation and Models4.6 Basic BJT Amplifier Configurations4.7 Biasing in BJT Amplifier Circuits4.8 Discrete‐Circuit BJT Amplifiers

4.1 Device Structure and Physical Operation

Physical structure of bipolar junction transistor (BJT)Both electrons and holes participate in the conduction process for bipolar devicesBJT consists of two pn junctions constructed in a special way and connected in series, back to backThe transistor is a three‐terminal device with emitter, base and collector terminalsFrom the physical structure, BJTs can be divided into two groups: npn and pnp transistors

Modes of operationThe two junctions of BJT can be either forward or reverse‐biasedThe BJT can operate in different modes depending on the junction biasThe BJT operates in active mode for amplifier circuitsSwitching applications utilize both the cutoff and saturation modes


Mode EBJ CBJ

Cutoff Reverse Reverse

Active Forward Reverse

Saturation Forward Forward

Operation of the npn transistor in the active mode

Electrons in emitter regions are injected into base due to the forward bias at EBJ

Most of the injected electrons reach the edge of CBJ before being recombined if the base is narrowElectrons at the edge of CBJ will be swept into collector due to the reverse bias at CBJEmitter injection efficiency ( ) = iEn/(iEn+iEp)Base transport factor (T) = iCn/iEnCommon‐base current gain () = iCn/iE = T < 1Terminal currents of BJT in active mode:

iE(emitter current) = iEn(electron injection from E to B) + iEp(hole injection from B to E)iC(collector current) = iCn(electron drift) + iCBO(CBJ reverse saturation current with emitter open) iB(base current) = iB1(hole injection from B to E) + iB2(recombination in base region)


Terminal currents:Collector current:Base current: Hole injection into emitter due to forward bias:

Eelectron‐hole recombination in base:

Total base current:

Emitter current:


TBETBE VvS

Vv

B

inBEBnBEBnBECnC eIe

WNnqDAWnqDAdxxdnqDAii //2

/)0(/)(

TBE Vv

pEE

ipEEEpEEB e

LNnqDA

dxxdpqDAi /2

1 /)(

TBE VvSCCBCE eIiiiii /1

TBE Vv

nB

iEnBEnnB e

NqWnAWnqAQi /

2

2 2/)0(

21/

CVv

nnBpEE

B

nB

pESBBB

ieDW

LW

NN

DD

Iiii TBE /2

21 )21(

Large‐signal model and current gain for BJT in active region

Common‐emitter current gain:

Common‐base current gain:

The structure of actual transistorsIn modern process technologies, the BJT utilizes a vertical structureTypically, is smaller and close to unity while is large


)1/()21( 1

2

nnBpEE

B

nB

pE

B

C

DW

LW

NN

DD

ii

)1/(

Common‐base current gain

iB

iCiE

1

(+1)

1

Common‐emitter current gain

iB

iE

iC(1)

Operation of the npn transistor in the saturation modeSaturation mode: both EBJ and CBJ are forward biasedCarrier injection from both emitter and collector into baseBase minority carrier concentraiton change accordingly leading to reduced slope as vBC increasesCollector current drops from the value in active mode for negative vCBFor a given vBE, iC drops sharply to zero at vCB around 0.5 V and vCE around 0.2 VBJT in saturation: VCEsat = 0.2 VCurrent gain reduces (from to forced):


np0

np0exp(vBE/VT) np0exp(vBC/VT)

vBC increases

saturationB

Cforced i

i

Ebers‐Moll modelIn EM model, the EBJ and CBJ are represented by two back to back diodes iDE and iDC

Current transported from one junction to the other is presented by F (forward) and R (reverse)EM model can be used to describe the BJT in any of its possible modes of operationEM model is used for more detailed dc analysisThe diode currents:The terminal currents:

Application of the EM modelThe forward active mode:

The saturation mode:


iDE iDC

FiDERiDC

iCiE

iB

CEB iii SSCRSEF III

FS

Vv

F

SE IeIi TBE

11/

11/

RS

VvSC IeIi TBE

RFS

Vv

F

SB IeIi TBE

11/

)1( / TBE VvSEDE eIi )1( / TBC Vv

SCDC eIi

DEFDCC iii DCRDEE iii

TBCTBE VvS

VvSEE eIeIi //

TBCTBE VvSC

VvSC eIeIi //

TBCTBE VvRSC

VvFSEB eIeIi // )1()1(

The cutoff mode ICBO (CBJ reverse current with emitter open‐circuited)ICBO = (1RF)ISCBoth EBJ and CBJ are reverse‐biasedIn real case, reverse current depends on vCB ICEO (CBJ reverse current with base open‐circuited)ICEO = ICBO/(1F)F is always smaller than unity such that ICEO > ICBOCBJ current flows from (C to B) so CBJ is reverse‐biasedEBJ current flows from (E to B) so EBJ is slightly forward‐biased


+

E C

B

(2) RISC

ISC (1)

iCiE = 0

iB(3) RISC

RFISC (4)

iC = ICBO = (1RF)ISC (5)iB = (R1)ISC+(1F)iDE = 0 iDE = ISC(1R)/(1F) (5)

E C

B

(2) RISC

ISC (1)

iC

iB = 0

iE

+

(3) iDE

FiDE (4)

iC = ISC+FiDE = ISC(1RF)/(1F) ICEO = ICBO/(1F) (6)

The pnp transistorTransistor structure: emitter and collector are p‐type base is n‐type

Operation of pnp is similar to that of npn

Operation of pnp in the active modeCollector current:Base current:Emitter current:

Large‐signal model and current gain for BJT in active region

Exercise 4.1 (Textbook)Exercise 4.3 (Textbook)


TEB VvSC eIi /

/CB ii

BCE iii

Common‐base current gain

iB

iCiE

1

(+1)

1

Common‐emitter current gain

iB

iE

iC(1)

4.2 Current‐Voltage Characteristics

Circuit symbols, voltage polarities and current flowTerminal currents are defined in the direction as current flow in active modeNegative values of current or voltage mean in opposite polarity (direction)

Summary of the BJT current‐voltage relationships in the active modeThe terminal currents for a BJT in active mode solely depend on the junction voltage of EBJThe ratios of the terminal currents for a BJT in active mode are constantThe current directions for npn and pnp transistors are opposite


TBE VvSC eIi /

TBE VvSCB eIii /

TBE VvSCE eIii /

TEB VvSC eIi /

TEB VvSCB eIii /

TEB VvSCE eIii /

BCE iii

1

1

pnp transistornpn transistor

Current‐voltage characteristics of BJT

The Early effectAs CBJ reverse bias increases, the effective base width Weff reduces due to the increasing depletionFor a constant junction voltage vBE: The slope of nB(x) increases iC increases Charge storage Qn reduces iB decreases Current gain a and b increases

Early voltage (VA) is used for the linear approximation of Early EffectLinear dependence of iC on vCE:

Exhibit finite output resistance:


The iC‐vCB characteristics The iC‐vCE characteristics

nB (0)

nB0

0 WX WY WZ

VY

VZ

VX

)/1(/ACE

VvSC VveIi TBE

C

Aconstantv

CE

Co I

Vvir

BE

1

Common‐base output characteristics

iC versus vCB plot with various iE as parameter is known as common‐base output characteristicsThe slope indicates that iC depends to a small extent on vCB Early effect iC increases rapidly at high vCB breakdownBCJ is slightly forward‐biased for 0.4V < vCB < 0

No significant change is observed in iCThe BJT still exhibits I‐V characteristics as in the active mode

BCJ turns on strongly and the iC starts to decrease for vBC < 0.4V I‐V characteristics in the saturation mode and vCEsat is considered a constant ( 0.2 V)

Current gain (): large‐signal iC/iE and small‐signal (incremental) iC/iE


breakdownEarly effect

Common‐emitter output characteristics (I) iC versus vCE plot with various vBE as parameter Common‐emitter current gain is defined as = iC / iBThe BCJ turns on with a positive vBC at low vCE

BJT operates in saturation modeThe iC curve has a finite slope due to Early effectThe characteristics lines meet at vCE = VA

VA is called the Early Voltage (~ 50 to 100 V)

Common‐emitter output characteristics (II)Plot of iC versus vCE with various iB as parameterBJT in active region acts as a current source with

high (but finite) output resistanceThe cutoff mode in common‐emitter configuration

is defined as iB = 0Current gain: large‐signal bdc iC/iB and bac iC/iB


breakdownEarly effect

Saturation of common‐emitter configurationIn saturation region, it behaves as a closed switch with a small resistance RCEsat

The saturation IV curve can be approximated by a straight line intersecting the vCE axis at VCEoff

The saturation voltage VCEsat VCEoff+ICsatRCEsat

VCEsat is normally treated as a constant of 0.2 V for simplicity regardless the value of iCIncremental b in saturation is lower than that in active region: forced ICsat/IB < Overdrive factor /forced


Transistor breakdownTransistor breakdown mechanism: Avalanche breakdown: avalanche multiplication mechanism takes place at CBJ or EBJ Base punch‐through effect: the base width reduces to zero at high CBJ reverse bias

In CB configuration, BVCBO is defined at iE = 0The breakdown voltage is smaller than BVCBO for iE > 0In CE configuration, BVCEO is defined at iB =0The breakdown voltage is smaller than BVCEO for iB > 0Typically, BVCEO is about half of BVCBO

Breakdown of the BCJ is not destructive as long as the power dissipation is kept within safe limitsBreakdown of the EBJ is destructive because it will cause permanent degradation of


Exercise 4.13 (Textbook)Exercise 4.14 (Textbook)Example 4.3 (Textbook)Exercise 4.21 (Textbook)


4.3 BJT Circuits at DC

BJT operation modesThe BJT operation mode depends on the voltages at EBJ and BCJThe I‐V characteristics are strongly nonlinearSimplified models and classifications are needed to speed up the hand‐calculation analysis

Simplified models and classifications for the operation of the npn BJTCut‐off mode: iE = iC = iB = 0 vBE < 0.5 V and vBC < 0.4 V

Active mode: vBE = 0.7 V and iB : iC : iE = 1: : (1+) vCE > 0.3 V

Saturation mode: vBE = 0.7 V and vCE = 0.2 V iC/iB = forced <


Mode EBJ CBJ

Active Forward Reverse

Cutoff Reverse Reverse

Saturation Forward Forward

Inverse Reverse Forward

vBE

vBC

Active ModevBE 0, vBC 0

Saturation ModevBE 0, vBC 0

Inverse ModevBE 0, vBC 0

Cutoff ModevBE 0, vBC 0

npn transistor

vEB

vCB

Active ModevEB 0, vCB 0

Saturation ModevEB 0, vCB 0

Inverse ModevEB 0, vCB 0

Cutoff ModevEB 0, vCB 0

pnp transistor

Equivalent circuit models


DC analysis of BJT circuitsStep 1: assume the operation modeStep 2: use the conditions or model for circuit analysisStep 3: verify the solutionStep 4: repeat the above steps with another assumption if necessary

Example 4.4

Example 4.5


Example 4.9 (Textbook)

Example 4.11 (Textbook)


Exercise 4.22 (Textbook)Exercise 4.23 (Textbook)Exercise 4.24 (Textbook)Exercise 4.25 (Textbook)Exercise 4.28 (Textbook)Example 4.12 (Textbook)


4.4 Applying the BJT in Amplifier Design

BJT voltage amplifierA BJT circuit with a collector resistor RC can be used as a simple voltage amplifierBase terminal is used the amplifier input and the collector is considered the amplifier outputThe voltage transfer characteristic (VTC) is obtained by solving the circuit from low to high vBE Cutoff mode:0 V vBE < 0.5 V and iC = 0vO = vCE = VCC

Active mode:vBE > 0.5 V and iC = ISexp(vBE/VT)vO = VCC iCRC = VCC RCISexp(vBE/VT) Saturation:vBE further increasesvCE = vCEsat = 0.2 VvO = 0.2 V


Biasing the circuit to obtain linear amplificationThe slope in the VTC indicates voltage gainBJT in active mode can be used as voltage amplificationPoint Q is known as bias point or dc operating point

IC = ISexp(VBE/VT)The signal to be amplified is superimposed on VBE

vBE(t) = VBE+vbe(t)The time‐varying part in vCE(t) is the amplified signalThe circuit can be used as a linear amplifier if: A proper bias point is chosen for gain The input signal is small in amplitude

The small‐signal voltage gainThe amplifier gain is the slope at Q:

Voltage gain depends on IC and RC

Maximum voltage gain of the amplifier


CT

CVv

BE

CEv R

VI

dvdvA

BEBE

|| maxvT

CC

T

CECCC

T

Cv A

VV

VVVR

VIA

Determining the VTC by graphical analysisProvides more insight into the circuit operationLoad line: the straight line represents in effect the load

iC = (VCCVCE)/RC

The operating point is the intersection point

Locating the bias point QThe bias point (intersection) is determined by properly choosing the load lineThe output voltage is bounded by VCC (upper bound) and VCEsat (lower bound)The load line determines the voltage gainThe bias point determines the headroom or maximum upper/lower voltage swing of the amplifier


4.5 Small‐Signal Operation and Models

The collector current and the transconductanceThe total quantities (ac + dc) of the collector current:

Small‐signal approximation: vbe << VT

The transconductance indicates the incremental change of iC versus change of vBEThe transconductance gm is determined by its dc collector current ICGeneral, BJTs have relatively high transconductance compared with FETs at the same current level

The base current and the input resistance at the baseThe total quantities (ac + dc) of the base current:

Small‐signal approximation:

Resistance r is the small‐signal input resistance between base and emitter (looking into the base)


TbeTbeTBETBE VvC

VvVVS

VvSC

beBEBE

eIeeIeIi

vVv//// )(

beT

CC

T

beCcCC v

VII

VvIiIi

1

T

CIi

BE

Cm V

Ivig

CC

TbeTbeTBETBE VvB

VvVVSVvSCB eIeeIeIIi ////

beT

BB

T

beBbBB v

VII

VvIiIi

1

B

T

mb

be

IV

givr

The emitter current and the input resistance at the emitterThe total quantities (ac + dc) of the emitter current:

Small‐signal approximation:

Relation between r and re:

Output resistance accounting for Early effectUse the collector current equation with linear vCE dependence:

The output resistance ro is included to represent Early Effect of the BJTThe resulting ro is typically a large resistance and can be neglected to simplify the analysis


cCC

eEEiIIiIi

mmE

T

e

bee ggI

Vivr 1

beT

Ebe

T

Cbe

mce v

VIv

VIvgii

err )1(

m

me

gr

gr

A

CEVvSC V

veIi TBE 1/

C

Aconstantv

CE

Co I

Vvir

BE

1

BJT small‐signal modelsTwo models are exchangeable and does not affect the analysis resultThe hybrid‐model Typically used as the emitter is grounded

The T model Typically used as the emitter is not grounded


Neglect ro

Neglect ro

4.6 Basic BJT Amplifier Configuration

Three basic configurations

Characterizing amplifiersThe BJT circuits can be characterized by a voltage amplifier model (unilateral model)The electrical properties of the amplifier is represented by Rin, Ro and Avo

The analysis is based on the small‐signal or linear equivalent circuit (dc components not included)

Voltage gain:

Overall voltage gain:


Common‐Emitter (CE) Common‐Base (CB) Common‐Collector (CC)

vooL

L

i

ov A

RRR

vvA

vosoL

L

sigin

inv

sigin

in

sig

ov A

RRR

RRRA

RRR

vvG

The common‐emitter (CE) amplifierCharacteristic parameters of the CE amplifier Input resistance: Output resistance: Open‐circuit voltage gain: Voltage gain:


CE amplifier can provide high voltage gain

Input and output are out of phase due to negative gainLower IC increases Rin at the cost of voltage gainOutput resistance is moderate to highSmall RC reduces Ro at the cost of voltage gain


rRin

CoCo RrRR ||

CmoCmvo RgrRgA )||(

)||()||||( LCmoLCmv RRgrRRgA

)||()||||( LCsig

moLCmsig

v RRRr

rgrRRgRr

rG

The common‐emitter (CE) with an emitter resistanceCharacteristic parameters (by neglecting ro) Input resistance:

Output resistance:

Open‐circuit voltage gain:

Voltage gain:


Emitter degeneration resistance Re is adoptedInput resistance is increased by adding (1+)Re

Gain is reduced by the factor (1+gmRe)The overall gain is less dependent on It is considered a negative feedback of the amplifier


eeein RrRrR )1())(1(

Co RR

em

Cm

ee

Cmvo Rg

RgrR

RgA

1/1

em

LCm

CL

L

em

Cmv Rg

RRgRR

RRg

RgA

1

)||(1

em

LCm

sigCL

L

em

Cm

sigv Rg

RRgRr

rRR

RRg

RgRr

rG

1

)||(1

The common‐base (CB) amplifierCharacteristic parameters of the CE amplifier (by neglecting ro) Input resistance: Output resistance: Open‐circuit voltage gain: Voltage gain:


CE amplifier can provide high voltage gain

Input and output are in‐phase due to positive gainInput resistance is very lowA single CB stage is not suitable for voltage amplificationOutput resistance is moderate to highSmall RC reduces Ro at the cost of voltage gainThe amplifier is no longer unilateral if ro is included


ein rR

Co RR

Cmvo RgA

)||( LCmv RRgA

)||( LCmsige

ev RRg

RrrG

The common‐collector (CC) amplifierCharacteristic parameters of the CC amplifier (by neglecting ro) Input resistance: Output resistance: Open‐circuit voltage gain:


CC amplifier is also called emitter follower. Input resistance is very highOutput resistance is very lowThe voltage gain is less than but can be close to 1CC amplifier can be used as voltage bufferIt is noted that, in the analysis, the amplifier is not unilateral


))(1( Lein RrR

/sigeo RrR

1)/( eLLvo rRRA

1))(1(

)1(

sigeL

L

eL

L

sigin

inv RrR

RrR

RRR

RG

4.7 Biasing in BJT Amplifier Circuits

DC bias for BJT amplifierThe amplifiers are operating at a proper dc bias pointLinear signal amplification is provided based on small‐signal circuit operationThe DC bias circuit is to ensure the BJT in active mode with a proper collector current IC

The classical discrete‐circuit bias arrangementA single power supply and resistors are neededThevenin equivalent circuit: VBB = VCCR2/(R1+R2) RB = R1||R2

BJT operating point:

RC is chosen to ensure the BJT in active (VCE > VCEsat)

A two‐power‐supply version of the classical bias arrangementTwo power supplies are neededSimilar dc analysisBJT operating point:


)/11(/

EB

BEBBC RR

VVI

)/11(/

EB

BEEEC RR

VVI

Biasing using a collector‐to‐base feedback resistorA single power supply is neededRB ensures the BJT in active (VCE > VBE 0.7 V)

BJT operating point:

The value of the feedback resistor RB affects the small‐signal gain

Biasing using a constant‐current sourceThe BJT can be biased with a constant current source IThe resistor RC is chosen to operate the BJT in active modeThe current source is typically implemented by a BJT current mirrorCurrent mirror circuit: Both BJT transistors Q1 and Q2 are in active mode Assume current gain is very high:

When applying to the amplifier circuit, the voltageV has to be high enough to ensure Q2 in active

Exercise 4.49 (Textbook)Exercise 4.50 (Textbook)


)/11(/

CB

BECCC RR

VVI

RVVVII BEEECC

REF

4.8 Discrete‐Circuit BJT Amplifiers

Circuit analysis:DC analysis: Remove all ac sources (short for voltage source and open for current source) All capacitors are considered open‐circuit DC analysis of BJT circuits for all nodal voltages and branch currents Find the dc current IC and make sure the BJT is in active mode

AC analysis: Remove all dc sources (short for voltage source and open for current source) All large capacitors are considered short‐circuit Replace the BJT with its small‐signal model for ac analysis The circuit parameters in the small‐signal model are obtained based on the value of IC


Complete amplifier circuit DC equivalent circuit AC equivalent circuit

The common‐emitter (CE) amplifier

The common‐emitter amplifier with an emitter resistance


The common‐base (CB) amplifier

The common‐collector (CC) amplifier


The amplifier frequency responseThe gain falls off at low frequency band due to the effects of the coupling and by‐pass capacitorsThe gain falls off at high frequency band due to the internal capacitive effects in the BJTsMidband: All coupling and by‐pass capacitors (large capacitance) are considered short‐circuit All internal capacitive effects (small capacitance) are considered open‐circuit Midband gain is nearly constant and is evaluated by small‐signal analysis The bandwidth is defined as BW = fH – fL A figure‐of‐merit for the amplifier is its gain‐bandwidth product defined as GB = |AM|BW


Exercise 4.52 (Textbook)Exercise 4.53 (Textbook)Exercise 4.54 (Textbook)Exercise 4.55 (Textbook)


electronics ch4

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