Chapter3 Bipolar Junction Transistor (BJT)

SJTU Zhou Lingling 1

Chapter 3

Bipolar Junction Transistor (BJT)


Outline

• Introduction• Operation in the Active Mode• Analysis of Transistor Circuits at DC• The transistor as an Amplifier• Graphical Analysis• Biasing the BJT for Discrete-Circuit Design• Configuration for Basic Single Stage BJT Amplifier• High frequency Model


Introduction

• Physical Structure

• Circuit Symbols for BJTs

• Modes of Operation

• Basic Characteristic


Physical Structure

A simplified structure of the npn transistor.


Physical Structure

A dual of the npn is called pnp type. This is the simplified structure of the pnp transistor.


Circuit Symbols for BJTs

The emitter is distinguished by the arrowhead.


Modes of Operation

Modes EBJ CBJ Application

Cutoff Reverse ReverseSwitching application

in digital circuitsSaturation Forward Forward

Active Forward Reverse Amplifier

Reverse active

Reverse ForwardPerformance degradation


Basic Characteristics

• Far more useful than two terminal devices (such as diodes)

• The voltage between two terminals can control the current flowing in the third terminal. We can say that the collector current can be controlled by the voltage across EB junction.

• Much popular application is to be an amplifier


Operation in the Active Mode

• Current flow

• Current equation

• Graphical representation of transistor’s characteristics


Current Flow

Current flow in an npn transistor biased to operate in the active mode.


Collector Current

• Collector current is the drift current.• Carriers are successful excess minority

carriers.• The magnitude of collector current is almost

independent of voltage across CB junction.• This current can be calculated by the

gradient of the profile of electron concentration in base region.


Base Current

• Base current consists of two components.Diffusion current Recombination current

• Recombination current is dominant.

• The value of base current is very small.


Emitter Current

• Emitter current consists of two components.

• Both of them are diffusion currents.

• Heavily doped in emitter region.

• Diffusion current produced by the majority in emitter region is dominant.


Profiles of Minority-Carrier Concentrations


Current Equation

• Collector current

• Base current

• Emitter currentT

BEV

vsC

E eIi

i

T

BEV

v

snC eIIi

T

BEV

vsC

B eIi

i


Explanation for Saturation Current

• Saturation current is also called current scale.• Expression for saturation current:

• Has strong function with temperature due to intrinsic carrier concentration.

• Its value is usually in the range of 10-12A to 10-18A.

WN

nqDAW

nqDAI

A

inEpnEs

20


Explanation for Common-Emitter Current Gain

• Expression for common –emitter current gain:

• Its value is highly influenced by two factors.

• Its value is in the range 50 to 200 for general transistor.

bnPD

A

n

p

DW

LW

NN

D

D

2

21

1＝


Explanation for Common-Base Current Gain

• Expression for common –base current gain:

• Its value is less than but very close to unity.

• Small changes in α correspond to very large changes in β.

＋＝

1


Recapitulation

• Collector current has the exponential relationship with forward-biased voltage as long as the CB junction remains reverse-biased.

• To behave as an ideal constant current source.

• Emitter current is approximately equal to collector current.

BEv


Graphical Representation of Transistor’s Characteristics

• Characteristic curve relates to a certain configuration.

• Input curve is much similar to that of the diode, only output curves are shown here.

• Three regions are shown in output curves.

• Early Effect is shown in output curve of CE configuration.


Output Curves for CB Configuration


Output Curves for CB Configuration

• Active region

EBJ is forward-biased, CBJ is reverse-biased;

Equal distance between neighbouring output curves;

Almost horizontal, but slightly positive slope.

• Saturation region

EBJ and CBJ are not only forward-biased but also turned on;

Collector current is diffusion current not drift current.

Turn on voltage for CBJ is smaller than that of EBJ.

• Breakdown region

EBJ forward-biased, CBJ reverse-biased;

Great voltage value give rise to CBJ breakdown;

Collector current increases dramatically.


Output Curves for CE Configuration

(a) Conceptual circuit for measuring the iC –vCE characteristics of the BJT.

(b) The iC –vCE characteristics of a practical BJT.


The Early Effect

• Curves in active region are more sloped than those in CB configuration.

• Early voltage.

• Effective base width and base width modulation.


The Early Effect(cont’d)

• Assuming current scale remains constant, collector current is modified by this term:

• Narrow base width, small value of Early voltage, strong effect of base width modulation, strong linear dependence of on . Ci CEv

)1(A

CEVv

sC V

veIi T

BE


Analysis of Transistor Circuit at DC

• Equivalent Circuit Models

• Analysis Steps

• Examples


Equivalent Circuit Models

Large-signal equivalent-circuit models of the npn BJT operating in the forward active mode. In practical DC analysis, constant voltage drop model is popular used.


DC Analysis Steps

a. Using simple constant-voltage drop model, assuming , irrespective of the exact value of currents.

b. Assuming the device operates at the active region, we can apply the relationship between IB, IC, and IE, to determine the voltage VCE or VCB.

c. Check the value of VCE or VCB, if

i. VC>VB (or VCE>0.2V), the assumption is correct.

ii. VC<VB (or VCE<0.2V), the assumption is incorrect. It means the BJT is operating in saturation region. Thus we shall assume VCE=VCE(sat) to obtain IC. Here the common emitter current gain is defined as forced=IC/IB, we will find forced< .

VvBE 7.0


Examples

• Example 5.4 shows the order of the analysis steps indicated by the circled numbers.

• Example 5.5 shows the analysis of BJT operating saturation mode.

• Example 5.6 shows the transistor operating in cutoff mode.


Examples(cont’d)

• Example 5.7 shows the analysis for pnp type circuit. It indicates the the current is affected by ill-specified parameter β. As a rule, one should strive to design the circuit such that its performance is as insensitive to the value of β as possible.

• Example 5.8 is the bad design due to the currents critically depending on the value of β.

• Example 5.9 is similar to the example 5.5 except the transistor is pnp type.


Examples(cont’d)

• Example 5.10 shows the application of Thévenin’s theorem in calculating emitter current and so on. This circuit is the good design for the emitter is almost independent of β and temperature.

• Example 5.11 shows the DC analysis for two stage amplifier.

• Example 5.12 shows the analysis of the power amplifier composed of the complimentary transistors.


The Transistor as an Amplifier

• Conceptual Circuits• Small-signal equivalent circuit models• Application of the small-signal equivalent circuit

models• Augmenting the hybrid π model.


Conceptual Circuit

(a) Conceptual circuit to illustrate the operation of the transistor as an amplifier.

(b) The circuit of (a) with the signal source vbe eliminated for dc (bias) analysis.


Conceptual Circuit(cont’d)

With the dc sources (VBE and VCC) eliminated (short circuited), thus only the signal components are present.

Note that this is a representation of the signal operation of the BJT and not an actual amplifier circuit.


Small-Signal Circuit Models

• Transconductance

• Input resistance at base

• Input resistance at emitter

• Hybrid π and T model


Transconductance

• Expression

• Physical meaning

gm is the slope of the

iC–vBE curve at the bias point Q.

• At room temperature,

T

CQm V

Ig

msgm 40


Input Resistance at Base and Emitter

• Input resistance at base

• Input resistance at emitter

• Relationship between these two resistances

mBQ

T

b

be

gI

V

i

vr

mEQ

T

e

bee gI

V

i

vr

err )1(


The Hybrid- Model

• The equivalent circuit in (a) represents the BJT as a voltage-controlled current source (a transconductance amplifier),

• The equivalent circuit in (b) represents the BJT as a current-controlled current source (a current amplifier).


The T Model

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


Augmenting the Hybrid- Model

Expression for the output resistance.

Output resistance represents the Early Effect(or base width modulation)

'

1

. C

A

constvCE

Co

I

V

v

ir

BE


Models for pnp Type

• Models derived from npn type transistor apply equally well to pnp transistor with no changes of polarities. Because the small signal can not change the bias conditions, small signal models are independent of polarities.

• No matter what the configuration is, model is unique. Which one to be selected is only determined by the simplest analysis.


Graphical Analysis

a. Graphical construction for the determination of the dc base current in the circuit.

b. Load line intersects with the input characteristic curve.


Graphical Analysis(cont’d)

Graphical construction for determining the dc collector current IC and the collector-to-emitter voltage VCE in the circuit.


Small Signal Analysis

Graphical determination of the signal components vbe, ib, ic, and vce when a signal component vi is superimposed on the dc voltage VBB


Effect of Bias-Point Location on Allowable Signal Swing

a. Load-line A results in bias point QA with a corresponding VCE which is too close to VCC and thus limits the positive swing of vCE.

b. At the other extreme, load-line B results in an operating point too close to the saturation region, thus limiting the negative swing of vCE.


Biasing in BJT Amplifier Circuit

• Biasing with voltageClassical discrete circuit bias arrangement

Single power supply Two-power-supply

With feedback resistor

• Biasing with current source


Classical Discrete Circuit Bias Arrangement

by fixing VBE by fixing IB.


Classical Discrete Circuit Bias Arrangement

• Both result in wide variations in IC and hence in VCE and therefore are considered to be “bad.”

• Neither scheme is recommended.


Classical Biasing for BJTs Using a Single Power Supply

Circuit with the voltage divider supplying the base replaced with its Thévenin equivalent.

Stabilizing the DC emitter current is obtained by considering the negative feedback action provided by RE


Classical Biasing for BJTs Using a Single Power Supply

• Two constraints

• Rules of thumb

1B

E

BEBB

RR

VV

),1.0(2!

31

31

31

EERR

CCCB

CCCC

CCBB

IIII

VV

VRI

VV

BB


Two-Power-Supply Version

• Resistor RB can be eliminated in common base configuration.

• Resistor RB is needed only if the signal is to be capacitively coupled to the base.

• Two constraints should apply.


Biasing with Feedback Resistor

Resistor RB provides negative feedback.

IE is insensitive to β provided that

The value of RB determines the allowable signal swing at the collector.

） 1(BC RR


Biasing Using Current Source

(a) Q1 and Q2 are required to be identical and have high β.

(b) Short circuit between Q1’s base and collector terminals.

(c) Current source isn’t ideal due to finite output resistor of Q2


Application of the Small-Signal Models

a. Determine the DC operating point of BJT and in particular the DC collector current IC(ICQ).

b. Calculate the values of the small-signal model parameters, such as gm=IC/VT, r=/gm=VT/IB, re=/gm=VT/IE.

c. Draw ac circuit path.

d. Replace the BJT with one of its small-signal models. The model selected may be more convenient than the others in circuits analysis.

e. Determine the required quantities.


Basic Single-Stage BJT Amplifier

• Characteristic parameters• Basic structure• Configuration

Common-Emitter amplifier Emitter directly connects to ground Emitter connects to ground by resistor RE

Common-base amplifierCommon-collector amplifier(emitter follower)


Characteristic Parameters of Amplifier

This is the two-port network of amplifier.

Voltage signal source.

Output signal is obtained from the load resistor.


Definitions

• Input resistance with no load

• Input resistance

• Open-circuit voltage gain

• Voltage gain

LRi

ii i

vR

i

iin i

vR

LRi

ovo v

vA

i

ov v

vA


Definitions(cont’d)

• Short-circuit current gain

• Current gain

• Short-circuit transconductance

0

LRi

ois i

iA

i

oi i

iA

0

LRi

om v

iG



• Open-circuit overall voltage gain

• Overall voltage gain

LRsig

vo v

vG 0

sigv v

vG 0



Output resistance of amplifier proper

0

ivx

xo i

vR

Output resistance

0

sigvx

xout i

vR



Voltage amplifier

Transconductance amplifier

Voltage amplifier


Relationships

• Voltage divided coefficient

sigin

in

sig

i

RR

R

v

v

oL

Lvov RR

RAA

omvo RGA

oL

Lvo

sigin

inv RR

RA

RR

RG

vosigi

ivo A

RR

RG

outL

Lvov RR

RGG


Basic Structure

Basic structure of the circuit used to realize single-stage, discrete-circuit BJT amplifier configurations.


Common-Emitter Amplifier


Common-Emitter Amplifier

Equivalent circuit obtained by replacing the transistor with its hybrid- model.


Characteristics of CE Amplifier

• Input resistance• Voltage gain


• Output resistance


rRin

)////( LComv RRrgA

sig

oLCv Rr

rRRG

)////(

Cout RR

isA


Summary of CE amplifier

• Large voltage gain

• Inverting amplifier

• Large current gain

• Input resistance is relatively low.

• Output resistance is relatively high.

• Frequency response is rather poor.


The Common-Emitter Amplifier with a Resistance in the Emitter


The Common-Emitter Amplifier with a Resistance in the Emitter


Characteristics of the CE Amplifier with a Resistance in the Emitter





))(1//( eeBin RrRR

ee

LCv Rr

RRA

//

))(1(

)//(

eesig

LCv RrR

RRG

Cout RR

isA


Summary of CE Amplifier with RE

• The input resistance Rin is increased by the factor (1+gmRe)

• The voltage gain from base to collector is reduced by the factor (1+gmRe).

• For the same nonlinear distortion, the input signal vi can be increased by the factor (1+gmRe).

• The overall voltage gain is less dependent on the value of β.


Summary of CE Amplifier with RE

• The reduction in gain is the price for obtaining the other performance improvements.

• Resistor RE introduces the negative feedback into the amplifier.

• The high frequency response is significant improved.


Common-Base Amplifier


Common-Base Amplifier


Characteristics of CB Amplifier





ein rR

)//( LCmv RRgA

esig

LCv rR

RRG

)//(

C outR R

isA


Summary of the CB Amplifier

• Very low input resistance

• High output resistance

• Short-circuit current gain is nearly unity

• High voltage gain

• Noninverting amplifier

• Current buffer

• Excellent high-frequency performance


The Common-Collector Amplifier or Emitter-Follower






Characteristics of CC Amplifier





)//)(1( Loeib RrrR

)//)(1(

)//)(1(

Loe

Lov Rrr

RrA

)//)(1(

)//)(1(

//

//

Loe

Lo

sigibB

ibBv Rrr

Rr

RRR

RRG

1

// sigBeout

RRrR

)1( isA


Summary for CC Amplifier or Emitter-Follower

• High input resistance

• Low output resistance

• Voltage gain is smaller than but very close to unity

• Large current gain

• The last or output stage of cascade amplifier

• Frequency response is excellent well


Summary and Comparisons

• The CE configuration is the best suited for realizing the amplifier gain.

• Including RE provides performance improvements at the expense of gain reduction.

• The CB configuration only has the typical application in amplifier. Much superior high-frequency response.

• The emitter follower can be used as a voltage buffer and exists in output stage of a multistage amplifier.


Internal Capacitances of the BJT and High Frequency Model

• Internal capacitanceThe base-charging or diffusion capacitanceJunction capacitances

The base-emitter junction capacitance The collector-base junction capacitance

• High frequency small signal model

• Cutoff frequency and unity-gain frequency


The Base-Charging or Diffusion Capacitance

• Diffusion capacitance almost entirely exists in forward-biased pn junction

• Expression of the small-signal diffusion capacitance

• Proportional to the biased current

T

CFmFde V

IgC


Junction Capacitances

• The Base-Emitter Junction Capacitance

• The collector-base junction capacitance

00 2

)1(je

m

oe

BE

jeje C

VV

CC

m

oc

CB

VV

CC

)1(

0


The High-Frequency Hybrid- Model

jede CCC • Two capacitances Cπ and Cμ , where

• One resistance rx . Accurate value is obtained form high frequency measurement.


The Cutoff and Unity-Gain Frequency

0

)(

CEvB

Cfe I

Ish• Circuit for deriving an expression for

• According to the definition, output port is short circuit


The Cutoff and Unity-Gain Frequency(cont’d)

• Expression of the short-circuit current transfer function

• Characteristic is similar to the one of first-order low-pass filter

rCCs

sh fe )(1)( 0


The Cutoff and Unity-Gain Frequency (cont’d)

rCC )(

1

CC

gmT

0

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Chapter3 Bipolar Junction Transistor (BJT)