circuit and analog electronics ch6

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.



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



Standard bipolar junction transistor symbols

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



BJT in Active Mode

Two external voltage sources set the bias conditions for active mode

– EBJ is forward biased and CBJ is reverse biased



BJT in Active Mode

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

IE ＝ IEN ＋ IEP IEN



BJT in Active Mode

• 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



BJT in Active Mode

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

IC = ICN + ICBO



BJT in Active Mode

IE ＝ IEN ＋ IEP

IEN IC = ICN + ICBO

IE = IB + IC

Let ICN ＝ IE

E

C

I

I ---common-base current gain

IC (1 － ) = IB + ICBO

IB ＝ IBN ＋IEP



BJT in Active Mode

IE ＝ IEN ＋ IEP

IEN IC=ICN+ICBO IE=IB+IC

E

C

I

I IC (1 － )= IB+ICBO

IB ＝ IBN ＋IEP

1

Let

EC

BCEOBC

BBCE

II

IIII

IIII

)1(

CBOBC III )1(

B

C

I

I ---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



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

II

II

IIII

)1(




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.


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


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

Δ



i i B

o L C

v R i

v R i

Discussion of an amplification effect

CEBEi L

B C

vvR R

i i

B Ci iWith i ov v

50 ~ 300ov

i

vA

v

E.g. for common-base configuration transistor:



DC Load Line and Quiescent Operation Point

DC load line

.Q

Q-point

ICQ

VCEQ

VCC

)(40 AR

V

R

VVI

b

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

mAI

mVr

Ebe


1E C B B CI I I I I

0.7VBEV

C BI I

BJT fundamentals:




Key WordsKey Words:

Common-Emitter Amplifier

Graphical Analysis

Small-Signal Models Analysis

Common-Collector Amplifier

Common-Base Amplifier



C-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)



C-E Amplifiers

iV

Vi

+

iV



C-E Amplifiers

vBE=vi+VBE

bBB iIi

Apply a small signal input voltage and see ib



C-E Amplifiers

• vi = 0 IB 、 IC 、 VCE

ceCECE

CCC

bBBi

vVv

iIi

iIiv 0

)()( ioiMoM ffVV •

• vo out of phase with vi

iC=ic+IC

vCE=vce+VCE

See how ib translates into vce.



C-E Amplifiers Considering (all the capacitors are replaced by open circuits)

CV

Considering (all the capacitors are replaced by short circuits)

iV



C-E AmplifiersConsidering (all the capacitors are replaced by open circuits)

CV

Considering (all the capacitors are replaced by short circuits)

iV



Graphical 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?



Graphical Analysis

VCC

')//( LcLCcce RiRRiv



Graphical Analysis

Q-point is centered on the ac load line:

VCC

VCC



Graphical Analysis

Clipped at cutoff(cutoff distortion)

Q-point closer to cutoff:

VCC



Graphical Analysis

Clipped at cutoff(saturation distortion)

Q-point closer to saturation:



Graphical 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 short circuits 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 2

vs

CCbb

bB V

RR

RV

21

2

eBe

BEBEC RV

R

VVII /

C

B

II

)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




eEBEbBCC RIVRIV eBBEbB RIVRI )1(

eb

CC

eb

BECCB RR

V

RR

VVI

1)1(

BC II

eCCEeECECC RIVRIVV

eCCCCE RIVV

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

oV iV BEV

1VA




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 RRIRRIV

1)//)(1(

)//(

)//)(1(

)//)(1(

Lebe

Le

Lebe

Le

i

O

V RRr

RR

RRr

RR

V

VA

Let’s find Av ，

Ai ：




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

b

bLeb

b

bLebebi R

RRRI

R

RRRrII

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

L

Lebo R

RRII

)//)(1(

bLe

b

L

Lei RRR

R

R

RRA

)//)(1(

)//)(1(

L

Le

R

RR )//)(1(

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

iAL

Le

R

RR )//)(1( >>1

Let’s find Av ，

Ai ： )//()1()//( LebLeeLo RRIRRIRI oI

iI




)//)(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

RRrRi

vR

Re eI I I Re eI I I

1Re e Re bI I I I I

bsbee RRr

v

R

v

//)1(

1

)//(// bsbe

e

RRrR

IeI

ReI




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

1

)//(// bsbe

eoRRr

RR




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

1

)//(// bsbe

eoRRr

RR

C-C amp characteristics:• Voltage 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

O

V RRr

RR

V

VA

iAL

Le

R

RR )//)(1( >>1




2b2b1b

CCB R

RR

VV

eEBEB RIVV

e

B

e

BEBEC R

V

R

VVII

C

B

II )( eCCCCeECCCCCE RRIVRIRIVV

Ground the base and drive the input signal into the emitter




Ri Ro

be

Lc

beb

Lccv r

RR

ri

RRiA

)//()//(

i

oi I

IA

1

)1(

)(

//)1(

)(

C

ELC

C

ebe

be

LC

C

I

IRRR

Rr

rRR

R

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

RR

RRRR

)1(

)(

For RL<<RC, 1)1(

iA

)1(//

)1(

be

ebe r

Rr

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

C-C C-E C-B

Input

Output

Functions

Summary for three types of diodes:

BI BIBI

EI CI CI


Zout < Zin

Vout > Vin

Zout > Zin

Vout > VinVout ≈ Vin

Zout > Zin



Key WordsKey Words:

Basic Concepts

High-Frequency BJT Model

Frequency Response of the CE Amplifier



Basic 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



Basic Concepts

Frequency0Hz 2KHz 4KHz 6KHz 8KHz 10KHz 12KHz 14KHz 16KHz 18KHz 20KHz

V(2) V(1)0V

200mV

400mV

600mV

800mV

Frequency

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

0V

0.5V

1.0V



Basic Concepts

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 、 Parasitic capacitive elements of the network (at high f)

3 、 Dissappearance of changing current (for transformer 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



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

2

1

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

f

fj

f

fj

f

fj

AA

frequency-mid0,, —vmv

HLHL AA

f

f

f

ffffFor

frequency-low1

,0),( —

L

Lvmv

HHL

ff

j

ff

jAA

f

fffffFor

frequencyHigh

ff

jAA

f

fffffFor

H

vmvL

LH

—1

1,0)(



vs

)1)(1(HL

Lvmv

f

fj

f

fj

f

fj

AA

H

HH

L

LL ff

2

1

22

1

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

oM IVIV

P2

1

22The output power delivered to the load RL:

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

%100S

OM

P

P


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

mCEQmT

CQ

TCCET

PPVIVI

dttVVtIIT

dtivT

P

2

1

)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)



Assuming tVv omo sinoCCCE vVv

tdR

vvVtdivP

L

OOCCCCET

001 2

1

2

1

L

omomomO R

VVIP

2

2

1

22

L

CCOM R

VP

2

2

1

Complementary Symmetry Power Amplifier (Class-B)

2 2

1 0 0

sin1sin

2CC on on

TL L

V V V tP td t d t

R R

22

0 0

1sin sin

2CC on on

L L

V V Vtd t td t

R R

2

0 0

1 1sin 1 cos 2

2 2CC on on

L L

V V Vtd t td t

R R

2 2 2

0

1 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 Vt

R R R R R


L

CCTTT R

VPPP

2

21 2

4

CCOm VV

4

42

1

L

CCT R

VP

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

TP



L

omomomO R

VVIP

2

2

1

22

L

CCOM R

VP

2

2

1

L

CCTTT R

VPPP

2

21 2

4

CCOm VV

4

42

1

L

CCT R

VP

L

CCOTE R

VPPP

22

422

1

2

2

L

CC

L

CC

E

O

R

VR

V

P

P=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.

circuit and analog electronics ch6

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bjt transistor

words construction of

bjt device

cbj junction

different circuits amplifiers

singlestage bjt amplifiers

collectorbase junction

emitterbase junction