Analog Circuit Electronics

Ch6 Basic BJT Amplifiers Circuits

6.1 Bipolar junction transistors (BJTs)

6.2 Single-Stage BJT Amplifiers

6.3 Frequency Response

6.4 Power Amplifiers

ReferencesReferences: Floyd-Ch-3, 5, 6; Gao-Ch7;

Circuits and Analog ElectronicsCircuits and Analog Electronics



Key WordsKey Words:

Construction of BJT

BJT in Active Mode

BJT DC Model and DC Analysis

C-E Circuits I-V Characteristics

DC Load Line and Quiescent Operation Point

BJT AC Small-Signal Model



This lecture will spend some time on understanding how the bipolar junction transistor (BJT) works based on what we have known about PN junctions. One way to look at a BJT transistor is two back-to-back diodes, but it has very different characteristics.

Once we understand how the BJT device operates, we will take a look at the different circuits (amplifiers) which we can build.


6.1 Bipolar junction transistors (BJTs)Construction of Bipolar junction transistors

Base region(very narrow)

Emitter region

Collector region

Collector

Base

Emitter

Emitter-base junction

Collector-base junction



NPN BJT shown• 3 terminals: emitter, base, and collector• 2 junctions: emitter-base junction (EBJ) and collector-base junction (CBJ) – These junctions have capacitance (high-frequency model)• BJTs are not symmetric devices – doping and physical dimensions are different for emitter and collector

Construction of Bipolar junction transistors


6.1 Bipolar junction transistors (BJTs)Standard bipolar junction transistor symbols

Depending on the biasing across each of the junctions, different modes of operation are obtained – cutoff, active and saturation


6.1 Bipolar junction transistors (BJTs)BJT in Active Mode

Two external voltage sources set the bias conditions for active mode

– EBJ is forward biased and CBJ is reverse biased



Forward bias of EBJ injects electrons from emitter into base (small number of holes injected from base into emitter)

IE ＝ IEN ＋ IEP IEN



• Most electrons shoot through the base into the collector across the reverse bias junction• Some electrons recombine with majority carrier in (P-type) base region

IB ＝ IBN ＋ IEP



Electrons that diffuse across the base to the CBJ junction are swept across the CBJ depletion region to the collector.

IC = ICN + ICBO



IE ＝ IEN ＋ IEP

IEN IC = ICN + ICBO

IE = IB + IC

Let ICN ＝ IE

E

C

II

---common-base current gainIC (1 － ) = IB + ICBO

IB ＝ IBN ＋IEP



IE ＝ IEN ＋ IEP

IEN IC=ICN+ICBO IE=IB+IC

E

C

II

IC (1 － )= IB+ICBO

IB ＝ IBN ＋IEP

1

Let

EC

BCEOBC

BBCE

IIIIIIIIII

)1(

CBOBC III )1(

B

C

II

---common-emitter current gain Beta:

＋＋

－－

vBE vCE

iB

iB iC

iE



BJT Equivalent Circuits

BJT DC model

＋＋

－－

VBE＝Von VCE

IB

IB IC

IE

•Use a simple constant-VBE model – Assume VBE = 0.7V


6.1 Bipolar junction transistors (BJTs)BJT DC Analysis

• Make sure the BJT current equations and region of operation match VBE > 0, VBC < 0, VE < VB <VC

• Utilize the relationships (β and α) between collector, base, and emitter currents to solve for all currents

EC

BC

BBCE

IIII

IIII

)1(


6.1 Bipolar junction transistors (BJTs)C-E Circuits I-V Characteristics

Base-emitter Characteristic(Input characteristic)

CCEvBEB vfi

)(



Collector characteristic (output characteristic)

CiVC BCEfi )(

AμiB 40=



Collector characteristic (output characteristic) CiVC BCEfi )(

Saturation

Vsat



Collector characteristic

Saturation occurs when the supply voltage, VCC, is across the total resistance of the collector circuit, RC.

IC(sat) = VCC/RC

Once the base current is high enough to produce saturation, further increases in base current have no effect on the collector current and the relationship IC = IB is no longer valid. When VCE reaches its saturation value, VCE(sat), the base-collector junction becomes forward-biased.




Cutoff

When IB = 0, the transistor is in cutoff and there is essentially no collector current except for a very tiny amount of collector leakage current, ICEO, which can usually be neglected. IC 0.

In cutoff both the base-emitter and the base-collector junctions are reverse-biased.




linearity



i i B

o L C

v R iv R i

Discussion of an amplification effect

CEBEi L

B C

vvR Ri i

B Ci iWith i ov v

50 ~ 300ov

i

vAv

E.g. for common-base configuration transistor:

Ch6 Basic BJT Amplifiers Circuits 6.1 Bipolar junction transistors (BJTs)

DC Load Line and Quiescent Operation Point

DC load line

.Q

Q-point

ICQ

VCEQ

VCC

)(40 AR

VR

VVIb

CC

b

BECCB

Base-emitter loop:

kiRiVv CCCCCCE 410 Collector-emitter loop:

＋＋

－－

vBE vCE

iB

iB iC

iE



BJT AC Small-Signal Model

＋＋

－－

vce ib

ib ic

ie

vbe rbe

• We can create an equivalent circuit to model the transistor for small signals – Note that this only applies for small signals (vbe < VT)• We can represent the small-signal model for the transistor as a voltage controlledcurrent source ( ) or a current-controlled current source (ic = ib).• For small enough signals, approximate exponential curve with a linear line.

)()(26)1(300

mAImVr

Ebe


1E C B B CI I I I I

0.7VBEV

C BI I

BJT fundamentals:

C-C C-E C-B

Input

Output

Functions

Summary for three types of diodes:

at inZ Z

BI BIBI

EI CI CIat inZ Z at inZ Z

at inV Vat inV V



6.2 Single-Stage BJT Amplifiers

Key WordsKey Words:

Common-Emitter Amplifier

Graphical Analysis

Small-Signal Models Analysis

Common-Collector Amplifier

Common-Base Amplifier


6.2 Single-Stage BJT AmplifiersC-E Amplifiers

To operate as an amplifier, the BJT must be biased to operate in active mode and then superimpose a small voltage signal vbe to the base.

oC

CER

cii

BBEC

i vviivv CBC 12

DC + small signal

OC vi Bi iv CB ii

coupling capacitor (only passes ac signals)



iV

Vi

+

iV



vBE=vi+VBE

bBB iIi

Apply a small signal input voltage and see ib



• vi = 0 IB 、 IC 、 VCE

ceCECE

CCC

bBBi

vVviIi

iIiv 0

)()( ioiMoM ffVV •

• vo out of phase with vi

iC=ic+IC

vCE=vce+VCE

See how ib translates into vce.


6.2 Single-Stage BJT AmplifiersC-E Amplifiers Considering (all the capaertors are replaced

by open circuits)CV

Considering (all the capaertors are replaced by short circuits)

iV



Considering (all the capaertors are replaced by open circuits)

CV

Considering (all the capaertors are replaced by short circuits)

iV


6.2 Single-Stage BJT AmplifiersGraphical Analysis

VCC

• Can be useful to understand the operation of BJT circuits.• First, establish DC conditions by finding IB (or VBE)• Second, figure out the DC operating point for IC

Can get a feel for whether the BJT will stay in active region of operation – What happens if RC is larger or smaller?



VCC

'' LCQCEQCC RIVV

')//( LcLCcce RiRRiv



Q-point is centered on the ac load line:

VCC

VCC



Clipped at cutoff(cutoff distortion)

Q-point closer to cutoff:

VCC



Clipped at cutoff(saturation distortion)

Q-point closer to saturation:


6.2 Single-Stage BJT AmplifiersSmall-Signal Models Analysis

Steps for using small-signal models1. Determine the DC operating point of the BJT － in particular, the collector current2. Calculate small-signal model parameters: rbe

3. Eliminate DC sources – replace voltage sources with shorts and current sources with open circuits4. Replace BJT with equivalent small-signal models5. Analysis



IC ≈ βIB,

IE = IC + IB = (1+β)IB

eEBEbBCBC RIVRIR)II(V

))(1( eb

BECB RRR

VVI

)( eECCCCE RRIRIVV

Example 1



Example 1



Example 2

vs

CCbb

bB V

RRRV

21

2

eBe

BEBEC RV

RVVII /

C

BII

)RR(IVV eCCCCCE



There are three basic configurations for single-stage BJT amplifiers:

– Common-Emitter

– Common-Base

– Common-Collector

VBB VCC

RcN

NP

c

e

b

(b)

VBB

VCC

Re

N

NP

c

e

b

(c)

E B CV V V E B CV V V E B CV V V


6.2 Single-Stage BJT AmplifiersCommon-Collector Amplifier

eEBEbBCC RIVRIV eBBEbB RIVRI )1(

eb

CC

eb

BECCB RR

VRR

VVI

1)1(

BC II

eCCEeECECC RIVRIVV

eCCCCE RIVV

Note : is slightly less than due to the voltage drop introduced by

oV iV BEV1VA



The last basic configuration is to tie the collector to a fixed voltage, drive an input signal into the base and observe the output at the emitter.



)//()]//)(1([ LeebebLebebi RRIrIRRrIV

)//)(1()//( LebLeeo RReIRRIV

1)//)(1(

)//()//)(1(

)//)(1(

Lebe

Le

Lebe

Le

i

OV RRr

RRRRr

RR

V

VA

Let’s find Av ， Ai ：



bbiLebeb RIIRRrI )())//)(1((

b

bLeb

b

bLebebi R

RRRIR

RRRrII

)//)(1()//)(1(

L

Lebo R

RRII )//)(1(

bLe

b

L

Lei RRR

RR

RRA

)//)(1(

)//)(1(

L

Le

RRR )//)(1(

)//)(1( Le RR << Rb

iAL

Le

RRR )//)(1(

>>1

Let’s find Av ， Ai ： )//()1()//( LebLeeLo RRIRRIRI



)//)(1()//( LebebLeebebi RRriRRiriv

b

ii i

vR )//)(1( Lebe RRr

)//(////)]//)(1([// LebbLebebii RRRRRRrRRR

Let’s find Ri ：



Let’s find Ro ：

bb IIII Re

)1()//(11

1

bsbee

o

RRrRivR

Re eI I I Re eI I I

1Re e Re bI I I I I

bsbee RRrv

Rv

//)1(

1

)//(// bsbee

RRrR

IeI

ReI



bLebei RRRrR //)]//)(1([

1)//(

// bsbeeo

RRrRR



bLebei RRRrR //)]//)(1([

1

)//(// bsbe

eoRRr

RR

C-C amp characteristics:• Gain is less than unity, but close (to unity) since β is large and rbe is small.• Also called an emitter follower since the emitter follows the input signal.• Input resistance is higher, output resistance is lower. - Used for connecting a source with a large Rs to a load with low resistance.

1)//)(1(

)//(

Lebe

Le

i

OV RRr

RR

V

VA

iAL

Le

RRR )//)(1(

>>1


6.2 Single-Stage BJT AmplifiersCommon-Base Amplifier

2b2b1b

CCB R

RRVV

eEBEB RIVV e

B

e

BEBEC R

VR

VVII

C

BI

I )( eCCCCeECCCCCE RRIVRIRIVV

Ground the base and drive the input signal into the emitter



Ri Ro

be

Lc

beb

Lccv r

RRri

RRiA

)//()//(

i

oi I

IA

1

)1()(

//)1(

)(

C

ELC

C

ebe

be

LC

C

IIRR

R

Rrr

RRR

For RL<<RC, CEi IIA

since1)1(

e

be Rr

//)1(

Ri=

Ro≈RC



be

Lcv r

RRA )//(

i

oi I

IA

LC

CLC

C

RRRRR

R

)1(

)(

For RL<<RC, 1)1(

iA

)1(//

)1(

be

ebe rRr

Ri=

Ro≈R

C CB amp characteristics:• current gain has little dependence on β• is non-inverting• most commonly used as a unity-gain current amplifier or current buffer and not as a voltage amplifier: accepts an input signal current with low input resistance and delivers a nearly equal current with high output impedance• most significant advantage is its excellent frequency response



Key WordsKey Words:

Basic Concepts

High-Frequency BJT Model

Frequency Response of the CE Amplifier


6.3 Frequency ResponseBasic Concepts

Time

0.5ms 1.0ms 1.5ms 2.0ms 2.5ms 3.0ms 3.5ms 4.0msV(1) V(2)

-1.0V

-0.5V

0V

0.5V

1.0V



)(tVO

Time0.5ms 1.0ms 1.5ms 2.0ms 2.5ms 3.0ms 3.5ms 4.0ms

V(1) V(2)-1.0V

-0.5V

0V

0.5V

1.0V



Frequency0Hz 2KHz 4KHz 6KHz 8KHz 10KHz 12KHz 14KHz 16KHz 18KHz 20KHzV(2) V(1)

0V

200mV

400mV

600mV

800mV

Frequency

10Hz 100Hz 1.0KHz 10KHz 100KHz 1.0MHzV(2)

0V

0.5V

1.0V



Lower cut off frequency Upper cut off frequency

)()()()( vvv AAorffAA

The drops of voltage gain (output/input) is mainly due to:

1 、 Increasing reactance of (at low f)

2 、 Porasitic capacetine elements of the net work (at high f)

3 、 Dissappearance of changing current(for trasformer coupled amp)

ecs CCC ,,



C

C

In BJTs, the PN junctions (EBJ and CBJ) also have capacitances associated with them

rbe

C

C

C'rbe C'

High-Frequency BJT Model


vs

6.3 Frequency ResponseFrequency Response of the CE Amplifier

C'rbe C'

There are three capacitors in the circuit.

At the mid frequency band, these are considered to be short circuits and internal capacitors and are considered to be open circuits.

C',C'


vs


At low frequencies, C1, C2 are an open circuit and the gain is zero. Thus C1 has a high pass effect on thegain, i.e. it affects the lower cutoff frequency of the amplifier.

)////( 2111 bebbs rRRRC

2 is the time constant for C2. 12 ---is neglected

11 2

1

Lf


vs


)////( 2111 bebbs rRRRC

12 ---is neglected

Capacitor Ce is an open circuit. The pole time constant is given by the resistance multiplied by Ce.

eebesb

e CRrRR

//

1)//(

222

211.1 LeLLL ffff

eLef

21

C'rbe C'



vs

At high frequencies, C1, C2 Ce are all short circuit. The frequency that dominates is thelowest pole frequency.

The time constant is neglected for)1( '

CjRL C'

CrRR besbC )////(

C

Hf

2

1

In summary:the lower cut off frequency is determined by network capacitence.

e.g. The higher cut off frequency is determined by the parasitic ferquency of the BJT. e.g. C

eCCC ,21

C'rbe C'



vs )1)(1(HL

Lvmv

ffj

ffj

ffj

AA

frequency-mid0,, —vmv

HLHL AA

ff

fffffFor

frequency-low1

,0),( —

L

Lvmv

HHL

ffj

ffj

AAffffffFor

frequencyHigh

ffj

AAffffffFor

H

vmvL

LH

—1

1,0)(



vs

)1)(1(HL

Lvmv

ffj

ffj

ffj

AA

H

HH

L

LL ff

21

221

2

C'rbe C'




decadedecade

0




Key WordsKey Words:

Power Calculation

Class-A, B, AB Amplifiers

Complementary Symmetry(Push-Pull) Amplifier

Biasing the Push-Pull Amplifier (OCL)

Single-Supply Push-Pull Amplifier (OTL)



Power Amplifiers

Voltage Amplifiers

Sensor Load

An Analog Electronics System Block

Energy conversion

Signal Amplifiers

Energy conversion



CCCC

T

CCCCC

T

S IVdttiT

VdttiVT

P )(1)(1

00

The average power delivered by the supply:

omomomom

o IVIV

P21

22The output power delivered to the load RL:

The efficiency in converting supply power to useful output power is defined as

%100S

OM

PP


6.4 Power AmplifiersPower Calculation

The DC power by the supply

CCQS

CQCCQCCCQCEQC

RIP

IRIVIVP2

)(

The DC power delivered to BJT by the supply


6.4 Power AmplifiersPower Calculation

The average power dissipated as heat in the BJT:

CLCmmCEQCQ

mCEQm

T

CQ

T

CCET

PPVIVI

tVVtIIT

dtivT

P

21

)cos)(cos(1

1

0

0


6.4 Power AmplifiersClass-A Amplifiers

Class-B Amplifiers


6.4 Power AmplifiersClass-AB Amplifiers


6.4 Power AmplifiersComplementary Symmetry Power Amplifier (Class-B)


6.4 Power AmplifiersComplementary Symmetry Power Amplifier (Class-B)

2 2

1 0 0

sin1 sin2

CC on onT

L L

V V V tP td t d tR R

22

0 0

1 sin sin2

CC on on

L L

V V Vtd t td tR R

2

0 0

1 1sin 1 cos 22 2

CC on on

L L

V V Vtd t td tR R

2 2 2

01 1 1cos 2

2 2 2 2 4CC on on CC on on CC on on

L L L L L

V V V V V V V V VtR R R R R



Assuming tVv omo sin oCCCE vVv

41

21

21

2

001

OmOmCC

L

L

OOCCCCET

VVVR

tdRvvVtdivP

for 0OmV01 TP

L

CCTTT R

VPPP2

21 24

L

omomomO R

VVIP

2

21

22

L

CCOM R

VP

2

21

CCOm VV

442

1

L

CCT R

VP

Complementary Symmetry Power Amplifier (Class-B)

Note: represents the amount of power dissipated by the BJT as heat

TP



L

omomomO R

VVIP

2

21

22

L

CCOM R

VP

2

21

L

CCTTT R

VPPP

2

21 24

CCOm VV

442

1

L

CCT R

VP

L

CCOTE R

VPPP

22

4221

2

2

L

CC

L

CC

E

O

RV

RV

PP =78.5%


Note that for class A: η 25 ~ 50﹦ ﹪ ﹪ class B: η 78.5﹦ ﹪ class AB: η=25 ~ 78.5﹪ ﹪



Crossover distortion



6.4 Power AmplifiersBiasing the Push-Pull Amplifier (Class-AB) (OCL)

To overcome crossover distortion, the biasing is adjusted to just overcome the VBE of the transistors; this results in a modified form of operation called class AB. In class AB operation, the push-pull stages are biased into slight conduction, even when no input signal is present.

Power Calculation is the same as class-B

}VCC

}VCC


6.4 Power AmplifiersSingle-Supply Push-Pull Amplifier (OTL)

The circuit operation is the same as that described previously, except the bias is set to force the output emitter voltage to be VCC/2 instead of zero volts used with two supplies. Because the output is not biased at zero volts, capacitive coupling for the input and output is necessary to block the bias voltage from the source and the load resistor.

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