Unit – I Semiconductors, Diodes and Bipolar transistors - MR

Dr. I. Manimehan, Department of Physics Mannai Rajagopalasamy Govt. Arts College, Mannargudi - 614001. Page 1

Unit – I Semiconductors, Diodes and Bipolar

transistors

Semiconductor

In terms of resistivity, it is a substance which has the resistivity in

between conductor and insulator.

Eg: Ge, Si

Energy Band:

The range of energies possessed by the electrons in a solid. There are

two important energy bands

1) Valance band 2) Conduction band

Valance Band:The range of energies possessed by the valance

electrons.

Conduction Band:The range of energies possessed by the conduction

electrons.

Forbidden energy Gap:

The energy gap between the bottom of the conduction band and top of

the valance band.

Semiconductor definition in terms of energy band:

It is a substance which has filled valance band and empty conduction

band with small energy gap nearly 1eV

Properties of semiconductor:

1. The resistivity of a semiconductor is greater than conductor and

less than the insulator

2. They have negative temperature coefficient of resistance. (i.e.)

when temperature increases, resistance decreases. At high

temperature, the semiconductor behaves as a conductor. At low

temperature, it behaves as an insulator.

3. When a suitable impurity is added to a pure semiconductor its

current conducting property increases.

4. They have crystalline structure.

5. They are formed by covalent bonds.

Types of semiconductor:

Based on the purity, the semiconductors are classified into two types

1) Intrinsic semiconductor 2)Extrinsic semiconductor

Intrinsic semiconductor:

1. A semiconductor in an extremely pure form is known as intrinsic

semiconductor.

2. In an intrinsic semiconductor, even at room temperature, the

electron-hole pairs are created due to the breaking up of covalent

bonds by thermal energy.

3. Due to the breaking up of covalent bonds, electrons are released.

At the same time holes are created in

valance band.

4. Therefore, number of electron is

equal to the number of holes.

5. When an electric field is applied

across a pure semiconductor, the

current conduction takes place by

both free electrons and holes.

6. Therefore total current inside the semiconductor is sum of the

currents due to electrons and holes.At room temperature, it has

little current conduction.

Extrinsic semiconductor:


1. At room temperature, intrinsic semiconductor has little current

conduction. So it must be altered to increase the current conducting

properties.

2. This is achieved by adding suitable impurity to a pure

semiconductor called extrinsic (or) impure (or) doped

semiconductor.

3. The purpose of adding impurities is to increase either the number

of electrons or holes.

4. Depending upon the type of impurity added, the extrinsic

semiconductors are classified into two types.

1. n type semiconductor 2. P type semiconductor

n-type semiconductor:

When a small amount of pentavalent impurity is added to a pure

semiconductor, then it is called n-type semiconductor.

1. The addition of pentavalent impurity provides large number of

free electrons to pure semiconductor. Such impurities are called

donor impurities because they donate free electrons. Eg. As, P, N

2. Consider a germanium crystal its atom has four valence electrons.

3. When a pentavalent impurity like arsenic is added to germanium

atom, the four valence electrons are involved in the covalent bond

with four neighbouring germanium atoms.

4. The fifth valence electron of arsenic atom finds no place in the

covalent bond and is free.

5. For each arsenic atom added one free electron is created and a

small amount of impurity provides millions of free electrons. In n-

type semiconductor majority charge carriers are free electrons and

minority carriers are holes.

6. The energy level of fifth electron is called donor energy level.

P-type semiconductor:

When a small amount of trivalent impurity is added to a pure

semiconductor, then it is called p-type semiconductor.

1. The addition of trivalent impurity provides large number of holes to

pure semiconductor. Such impurities are called acceptor impurities

because holes created can accept free electrons. Eg. Ga, B, I, Al

2. Consider a germanium crystal its atom has four valence electrons.

3. When a trivalent impurity Like Boron ‘B’ is added to Ge. The

three valence electrons of boron are engaged in three covalent

bond with three Ge atoms.

4. In the fourth covalent bond germanium is ready to contribute one

electron but boron has no electron to contribute. i.e. the forth


covalent bond is incomplete being shortage of one electron. The

missing electron is called a hole.

5. Each boron atom is added one hole is created and a small amount

of impurity provides millions of holes.

6. In p-type semiconductor majority charge carriers are holes and

minority charge carriers are free electrons.

DIFFERENCE BETWEEN INTRINSIC AND EXTRINSIC

SEMICONDUCTORS

Intrinsic Semiconductor Extrinsic Semiconductor

1) It is a pure form of semiconductor. It is an impure form of

semiconductor

2) At room temperature current

conducting property is low.

At room temperature current

conducting property is high.

3) Number of electrons are equal to

the number of holes.

Number of electron is not equal to the

number of holes.

4) The Fermi level lies between

valence band and conduction band.

In n-type , Fermi level lies between

donar energy level and conduction

band.

In p-type, Fermi level lies between

acceptor energy level and valence

band.

DIFFERENCE BETWEEN n-TYPE AND p-TYPE

SEMICONDUCTORS

PN junction Diode

When a p-type semiconductor is suitably joined to n-type semiconductor,

the contact surface is called PN junction. A pn junction is known as a semi-conductor or

*crystal diode. The outstanding property of pn

junction diode is to conduct current in one

direction. PN junction diode is usually

represented by the schematic symbol shown in Fig. The arrow in the symbol

indicates the direction of easier conventional current flow.

(i) If arrowhead of diode symbol is positive w.r.t. bar of the symbol, the

diode is forward biased.

(ii) If the arrowhead of diode symbol is negative w.r.t. bar, the diode is

reverse biased.

n-TYPE p-TYPE

1) It is formed by addition of

pentavalent impurity to pure

semiconductor.

It is formed by addition of trivalent

impurity to pure semiconductor.

2) Electrons are the majority carriers

and holes are the minority carriers.

Holes are the majority carriers and

electrons are the minority carriers

3) Fermi level lies between donor

energy level and conduction band.

Fermi level lies between the acceptor

level and valence band

4) When the temperature increases

the electrons moves from donor

energy level to conduction band.

When the temperature increases the

electrons moves from valence band

to acceptor energy level.


Depletion region (or Depletion layer). At the instant of pn-junction

formation, the free electrons

near the junction in the n

region begin to diffuse across

the junction into the p region

where they combine with holes

near the junction. The result is

that n region loses free

electrons as they diffuse into

the junction. This creates a

layer of positive charges near

the junction. Similarly the electrons move across the junction, the p

region loses holes as the electrons and holes combine. The result is that

there is a layer of negative charges near the junction. These two layers of

positive and negative charges form the depletion region (or depletion layer). Biasing of pn Junct ion

In electronics, the term bias refers to the use of d.c. voltage to establish

certain operating conditions for an electronic device. In relation to a pn

junction, there are following two bias conditions :

1. Forward biasing 2. Reverse biasing

1. Forward biasing. When external d.c. voltage applied to the junction is in

such a direction that it cancels the potential barrier, thus permitting current

flow, it is called forward biasing.

To apply forward bias, connect positive terminal of the battery to p-type and

negative terminal to n-type as shown in Fig.1

2. Reverse biasing. When the external d.c. voltage applied to the junction is

in such a direction that potential barrier is increased, it is called reverse

biasing.

To apply reverse bias, connect negative terminal of the battery to p-type and

positive terminal to

n-type as shown in Fig.2

Fig.1 Fig.2

Volt-Ampere Characteristics of pn Junct ion Volt-ampere or V-I characteristic of a pn junction is the curve between

voltage across the junction and the circuit current. Usually, voltage is taken

along x-axis and current along y-axis.

(i) Forward bias. With forward bias to the pn junction i.e. p-type connected

to positiv e terminal and n-type

connected to negative terminal.

At some forward voltage (0.7 V

for Si and 0.3 V for Ge), the

potential barrier is altogether

eliminated and current starts

flowing in the circuit. From now

onwards, the current increases

with the increase in forward voltage. Thus, a rising curve OB is obtained

with forward bias as shown in Fig. From the forward characteristic, it is

seen that at first (region OA),the current increases very slowly and the curve

is non-linear. It is because the external applied voltage is used up in

overcoming the potential barrier. However, once the external voltage

exceeds the potential barrier voltage, the pn junction behaves like an


ordinary conductor. Therefore, the current rises very sharply with increase

in external voltage (region AB on the curve). The curve is almost linear.

Knee voltage. It is the forward voltage at which the current through the

junction starts to increase rapidly.

(ii) Reverse bias.

With reverse bias to the pn junction i.e.p-type connected to negative

terminal and n-type connected to positive terminal, potential barrier at the

junction is increased.

Therefore, the junction

resistance becomes very

high and practically no

current flows through the

circuit. However, in

practice, a very small

current (of the order of μA)

flows in the circuit with

reverse bias as shown in

the reverse characteristic.

This is called reverse

saturation current (Is) and

is due to the minority

carriers. If reverse voltage

is increased continuously,

the kinetic energy of

electrons (minority

carriers) may become high

enough to knock out

electrons from the

semiconductor atoms. At

this stage breakdown of

the junction occurs,

characterised by a sudden

rise of reverse current and a sudden fall of the resistance of barrier region.

This may destroy the junction permanently.

Breakdown voltage. It is the minimum reverse voltage at which pn junction

breaks down with sudden rise in reverse current.

Rectification:

The process of converting alternating current (AC) into direct current

(DC) is called rectification. In this section, we will discuss two types

of rectifiers namely, half wave rectifier and full wave rectifier.

Half wave rectifier circuit

The half wave rectifier circuit is

shown in Figure. The circuit

consists of a transformer, a p-n

junction diode and a resistor. In a

half wave rectifier circuit, either

a positive half or the negative

half of the AC input is passed

through the diode, the other half

is blocked. Only one half of the

input wave reaches the output.

Therefore, it is called half wave

rectifier. Here, a p-n junction

diode acts as a rectifier diode.

1. When the positive half cycle

of the ac input signal passes through the circuit, terminal A becomes

positive with respect to terminal B. The diode is forward biased and

hence it conducts. The current flow through the load resistor RL and

the AC voltage is developed across the RL constitutes the output

voltage V0.


2. When the negative half cycle of the ac input signal passes through

the circuit, terminal A is negative with respect to terminal B. Now

the diode is reverse biased and does not conduct and hence no

current passes through RL. The reverse saturation current in a diode

is negligible. Since there is no voltage drop across RL, the negative

half cycle of ac supply is suppressed at the output. The output

waveform is shown in Fig(b).

Efficiency h(ɳ) is the ratio of the output dc power to the ac input

power supplied to the circuit. Its value for half wave rectifier is 40.6

%

Full wave rectifier

The positive and negative

half cycles of the AC input

signal pass through the full

wave rectifier circuit and

hence it is called the full

wave rectifier. The circuit

is shown in Fig(a). It

consists of two p-n

junction diodes, a center

tapped transformer, and a

load resistor RL ( ).

The centre is usually taken

as the ground or zero

voltage reference point.

Due to the centre tap

transformer, the output

voltage rectified by each

diode is only one half of

the total secondary voltage.

1. When the positive half cycle of the ac input signal passes through the

circuit, terminal M is positive, G is at zero potential and N is at negative

potential. This forward biases diode D1 and reverse biases diode

D2. Hence, being forward biased, diode D1 conducts and current flows

along the path MD1AGC. As a result, positive half cycle of the voltage

appears across RL in the direction G to C

2.When the negative half cycle of the ac input signal passes through the

circuit, terminal N is positive, G is at zero potential and M is at negative

potential. This forward biases diode D2 and reverse biases diode D1. Hence,

being forward biased, diode D2 conducts and current flows along the path

ND2 BGC. As a result, negative half cycle of the voltage appears across RL

in the same direction from G to C. Hence in a full wave rectifier both

positive and negative half cycles of the input signal pass through the load in

the same direction as shown in Fig.(b).

The efficiency (η) of full wave rectifier is twice that of a half wave rectifier

and is found to be 81.2 %. It is because both the positive and negative half

cycles of the ac input source are rectified.

Full-Wave Bridge Rectifier

The need for a centre tapped power transformer is eliminated in the bridge

rectifier. It contains four diodes D1, D2, D3 and D4 connected to form

bridge as shown in Fig. The a.c. supply to be rectified is applied to the


diagonally opposite ends of the bridge through the transformer. Between

other two ends of the bridge, the load resistance RL is connected.

1. During the positive half-cycle of secondary voltage, the end P of the

secondary winding becomes positive and end Q negative. This makes diodes

D1 and D3 forward biased while diodes D2 and D4 are reverse biased.

Therefore, only diodes D1 and D3 conduct. These two diodes will be in

series through the load RL. It may be seen that current flows from A to B

through the load RL .

2. During the negative half-cycle of secondary voltage, end P becomes

negative and end Q positive. This makes diodes D2 and D4 forward biased

whereas diodes D1 and D3 are reverse biased. Therefore, only diodes D2

and D4 conduct. These two diodes will be in series through the load RL. It

may be seen that again current flows from A to B through the load i.e. in the

same direction as for the positive half-cycle. Therefore, d.c. output is

obtained across load RL.

Breakdown mechanism

The reverse current or the reverse saturation current due to the

minority charge carriers is small. If the reverse bias applied to a p-n

junction is increased beyond a point, the junction breaks down and the

reverse current rises sharply. The voltage at which this happens is

called the breakdown voltage and it depends on the width of the

depletion region, which in turn depends on the doping level. There are

two mechanisms that are responsible for breakdown under increasing

reverse voltage.

Zener breakdown

Heavily doped p-n junctions have narrow depletion layers. When a reverse

voltage across this junction is increased to the breakdown limit, it rupture

the covalent bonds in the lattice and thereby generating electron-hole pairs.

This effect is called Zener effect.

Avalanche breakdown

Avalanche breakdown occurs in lightly doped junctions which have wide

depletion layers. Here, in this case, the electric field is not strong enough to

produce breakdown. Alternatively, the thermally generated minority charge

carriers accelerated by the electric field gains sufficient kinetic energy,

collide with the semiconductor atoms while

passing through the depletion region. This leads to the breaking of covalent

bonds and in turn generates electron-hole pairs.

ZENER DIODE

A zener diode is a special type of diode

that is designed to operate in the reverse

breakdown region. An ordinary diode

operated in this region will usually be

destroyed due to excessive current. This

is not the case for the zener diode.

A properly doped crystal diode which has a sharp breakdown voltage

is known as a zenerdiode. Fig.1 shows the symbol of a zener diode.

A zener diode is heavily

doped to reduce the reverse

breakdown voltage. This

causes a very thin depletion

layer. As a result, a zener

diode has a sharp reverse

breakdown voltage VZ. This is

clear from the reverse

characteristic of zener diode


shown in Fig. 2. Note that the reverse characteristic drops in an

almost vertical manner at reverse voltage VZ. As the curve reveals,

two things happen when VZ is reached :

The following points may be noted about the zener diode:

(i) A zener diode is like an ordinary diode except that it is properly

doped so as to have a sharp breakdown voltage.

(ii) A zener diode is always reverse connected i.e. it is always

reverse biased.

(iii) A zener diode has sharp breakdown voltagee, called zener

voltage VZ.

(iv) When forward biased, its characteristics are just those of

ordinary diode.

(v) The zener diode is not immediately burnt just because it has

entered the *breakdown region. As long as the external circuit

connected to the diode limits the diode current to less than

burn out value, the diode will not burn out.

Zener diode as a voltage regulator

A Zener diode working in the breakdown region can serve as a

voltage regulator. It maintains a constant output voltage even when

input voltage Vi or load current IL varies. The circuit used for the

same is shown in Fig. In this circuit, the input voltage Vi is

regulated at a constant output voltage (V0). Here the, Zener voltage

Vz at the output represented as V0 using a Zener diode. The output

voltage is maintained constant as long as the input voltage does not

fall below Vz . When the potential developed across the diode is

greater than VZ , the diode moves into the Zener breakdown region.

It conducts and draws relatively large current through the series

resistance Rs. The total current I passing through Rs equals the

sum of diode current IZ and load current IL

I= IZ+ IL

It is to be noted that the total current is always less than the

maximum Zener diode current. Under all conditions Vo = Vz.

Thus, output voltage is regulated.

Transistor

A transistor consists of two pn junctions formed by sandwiching

either p-type or n-type semiconductor between a pair of opposite

types. Accordingly ; there are two types of transistors, namely;

(i) n-p-n transistor (ii) p-n-p transistor


An n-p-n transistor is composed of two n-type semiconductors

separated by a thin section of p type as shown in Fig. 1 (i). However,

a p-n-p transistor is formed by two p-sections separated by a thin

section of n-type as shown in Fig. 1 (ii).

In each type of transistor, the following points may be noted:

(i) These are two pn junctions. Therefore, a transistor may be

regarded as a combination of two diodes connected back to back.

(ii) There are three terminals, one taken from each type of

semiconductor.

(iii) The middle section is a very thin layer. This is the most important

factor in the function of a transistor.

A transistor (pnp or npn) has three sections of doped semiconductors.

The section on one side is the emitter and the section on the opposite

side is the collector. The middle section is called the base and forms

two junctions between the emitter and collector.

Emitter: The section on one side that supplies charge carriers

(electrons or holes) is called the emitter. The emitter is always

forward biased w.r.t. base so that it can supply a large number of

majority carriers

Collector: The section on the other side that collects the charges is

called the collector. The collector is always reverse biased. Its

function is to remove charges from its junction with the base.

Base: The middle section which forms two pn-junctions between the

emitter and collector is called the base. The base-emitter junction is

forward biased, allowing low resistance for the emitter circuit. The

base-collector junction is reverse biased and provides high resistance

in the collector circuit.

Transistor Action:

The emitter-base junction of a transistor is forward biased

whereas collector-base junction is reverse biased.

Practically no current would flow in the collector circuit

because of the reverse bias.

However, if the emitter-base junction is also present, then

forward bias on it causes the emitter current to flow.

It is seen that this emitter current almost entirely flows in the

collector circuit.

Therefore, the current in the collector circuit depends upon the

emitter current. If the emitter current is zero, then collector

current is nearly zero.

We shall now discuss this transistor action for npn and pnp

transistors.

Working of npn transistor:

Fig. shows the npn transistor with forward bias to emitter base

junction and reverse bias to collector-base junction.

The forward bias causes the electrons in the n-type emitter to

flow towards the base.

This constitutes the emitter current IE. As these electrons flow

through the p-type base, they tend to combine with holes.


As the base is lightly doped and very thin, therefore, only a

few electrons (less than 5%) combine with holes to constitute

base current IB.

The remainder (more than 95%) cross over into the collector

region to constitute collector current IC.

In this way, almost the entire emitter current flows in the

collector circuit. It is clear that emitter current is the sum of

collector and base currents i.e.

IE = IB + IC

Working of pnp transistor:

Fig. shows the basic connection of a pnp transistor.

The forward bias causes the holes in the p-type emitter to flow

towards the base. This constitutes the emitter current IE.

As these holes cross into n-type base, they tend to combine

with the electrons.

As the base is lightly doped and very thin, therefore, only a

few holes (less than 5%) combine with the electrons.

The remainder (more than 95%) cross into the collector region

to constitute collector current IC.

In this way, almost the entire emitter current flows in the

collector circuit.

It may be noted that current conduction within pnptransistor is

by holes.

However, in the external connecting wires, the current is still

by electrons.


Transistor Connections:

1. There are three leads in a transistor viz., emitter, base and

collector terminals.

2. However, when a transistor is to be connected in a circuit, we

require four terminals; two for the input and two for the

output.

3. This difficulty is overcome by making one terminal of the

transistor common to both input and output terminals.

4. The input is fed between this common terminal and one of the

other two terminals.

5. The output is obtained between the common terminal and the

remaining terminal. Accordingly; a transistor can be

connected in a circuit in the following three ways

(i)

(ii) (i) Common base connection

(ii) Common emitter connection

(iii) Common collector connection

Characteristics of Common Base Connection:

The complete electrical behaviour of a transistor can be described by

stating the interrelation of thevarious currents and voltages. These

relationships can be conveniently displayed graphically and the

curves thus obtained are known as the characteristics of transistor.

The most important characteristicsof common base connection are

input characteristics and output characteristics.

Input characteristics:

1. It is the curve between

emitter current IE and

emitter-base voltage VEB at

constant collector-base

voltage VCB. The emitter

current is generally taken

along y-axis and emitter-base

voltage along x-axis.

2. Fig. shows the input characteristics of a typical transistorin CB

arrangement.

3. The emitter current IE increases rapidly with small increase in

emitter-base voltage VEB.

4. It means that input resistance is very small.

5. The emitter current is almost independent of collector-base

voltage VCB.

6. This leads to the conclusion that emitter current is almost

independent of collector voltage.


7. Input resistance. It is the ratio of changein emitter-base voltage

(ΔVEB) to the resultingchange in emitter current (ΔIE) at constant

collector-base voltage (VCB) i.e.

Input resistance, 𝒓𝒊 =∆𝑽𝑬𝑩

∆𝑰𝑬at constant VCB

Output characteristics:

1. It is the curve between

collector current IC and

collector-base voltageVCBat

constant emitter current IE.

2. Generally, collector current is

taken along y-axis and

collector base voltage along x-

axis.

3. Fig. shows the output

characteristics of a typical transistor in CBarrangement.

4. The collector current IC varieswith VCB only at very low voltages (

< 1V).The transistor is never operated in this region.

5. When the value of VCB is raisedabove 1 − 2 V, the collector

current becomesconstant as indicated by straighthorizontal curves.

6. It means that now IC isindependent of VCB and depends upon

IEonly.

7. This is consistent with the theory thatthe emitter current flows

almost entirely tothe collector terminal. The transistor isalways

operated in this region.

8. A very large change in collector-base voltage produces only a tiny

change in collector current.This means that output resistance is

very high.

9. Output resistance. It is the ratio of change in collector-base

voltage (ΔVCB) to the resultingchange in collector current (ΔIC) at

constant emitter current i.e.

Output resistance, 𝒓𝒐 =∆𝑽𝑪𝑩

∆𝑰𝑪at constant IE

Characteristics of Common Emitter Connection:

Input characteristics:

1. It is the curve between base current IB and base-emitter voltage VBE

at constant collector-emitter voltage VCE.

2. The input characteristics of a CE connection can be determined by

the circuit shown in Fig.

3. Keeping VCE constant (say at 10 V), note the base current IB for

various values of VBE.

4. Then plot thereadings obtained on the graph, taking IB along yaxis


and VBE along x-axis.

5. The characteristic

resembles that of a

forwardbiased diode

curve. This is expected

since thebase-emitter

section of transistor is a

diode and it isforward

biased.

6. As compared to CB

arrangement, IBincreases

less rapidly with VBE.

Therefore, inputresistance

of a CE circuit is higher

than that of CBcircuit.

7. Input resistance. It is the ratio of change inbase-emitter voltage

(ΔVBE) to the change in basecurrent (ΔIB) at constant VCE i.e.

Input resistance, 𝒓𝒊 =∆𝑽𝑩𝑬

∆𝑰𝑩 at constant VCE

Output characteristics:

1. It is the curve between collector current IC and collector-emitter

voltage VCE at constant base current IB.

2. The output characteristics of a CE circuit isshown in Fig.

3. Keeping the base current IB fixed at some value say, 5 μA, note the

collector current IC forvarious values of VCE.

4. Then plot the readings on a graph, taking IC along y-axis and VCE

along x-axis.

5. The collector current IC varies with VCE,for VCE between 0 and 1V

only.

6. After this, collectorcurrent becomes almost constant and

independent of VCE.

7. This value of VCEupto

which collectorcurrent IC

changes with VCE is called

the knee voltage (Vknee).

The transistors are always

operated inthe region

above knee voltage.

8. Above knee voltage, IC

is almost constant.

However, a small increase

in IC with increasing VCE

is caused by the collector

depletion layer getting wider and capturing a few more majority

carriersbefore electron-hole combinations occur in the base area.

9. For any value of VCE above knee voltage, the collector current IC is

approximately equal toβ × IB.

10. Output resistance. It is the ratio of change in collector-emitter

voltage (ΔVCE) to the change incollector current (ΔIC) at constant IB

i.e.Output resistance, 𝒓𝒐 =∆𝑽𝑪𝑬

∆𝑰𝑪 at constant IB

Emitter Current amplification factor (𝛂).

The ratio of change in collector current to the change in emitter

current at constant collectorbasevoltage VCB is known as current

amplification factor i.e𝛂 =∆𝐈𝐂

∆𝐈𝑬

Base current amplification factor ( 𝛃).


The ratio of change in collector current (ΔIC) to the change in base

current (ΔIB) is known as base current amplification factor

i.e. 𝛃 =∆𝐈𝐂

∆𝐈𝐁

Relation between β and α.

A simple relation exists between β and α. This can be derived as

follows

β =∆IC

∆IB ---------- (1)

α =∆IC

∆I𝐸----------(2)

we know that

𝐼𝐸 = 𝐼𝐵 + 𝐼𝐶

∆𝐼𝐸 = ∆𝐼𝐵 + ∆𝐼𝐶

∆𝐼𝐵 = ∆𝐼𝐸 − ∆𝐼𝐶 ------------ (3)

Substituting the value of ΔIB in eqn. (1), we get

β =∆IC

∆𝐼𝐸 − ∆𝐼𝐶

Dividing the numerator and denominator of R.H.S. of eqn. (3) by ΔIE,

we get,

β =∆IC ∆𝐼𝐸

∆𝐼𝐸 − ∆𝐼𝐶 ∆𝐼𝐸

𝛃 =𝛂

𝟏 − 𝜷

It is clear that as α approaches unity, β approaches infinity

Transistor Load Line Analysis

d.c. load line.

1. Consider a common emitter npntransistor circuit shown in Fig.

(i) where no signal is applied.

2. Therefore, d.c. conditions prevail in the circuit. The output

characteristics of this circuit are shown in Fig. (ii).

3. The value of collector-emitter voltage VCEat any time is given

by VCE= VCC– IC RC

4. As VCCand RCare fixed values, therefore, it is a first degree

equation and can be represented bya straight line on the output

characteristics.

5. This is known as d.c. load line and determines the locusof

VCE− ICpoints for any given value of RC.

6. To add load line, we need two end points of the straightline.

These two points can be located as under :

(i) When the collector current IC= 0, then collector-emitter voltage is

maximum and is equal toVCC i.e.

Max. VCE= VCC– IC RC

= VCC(∵IC= 0)

This gives the first point B (OB = VCC) on the collector-emitter

voltage axis as shown inFig. (ii).


(ii) When collector-emitter voltage VCE = 0, the collector current is

maximum and is equal toVCC /RC i.e.

VCE= VCC− IC RC

or 0 = VCC− IC RC

∴ Max.IC= VCC/RC

This gives the second point A (OA = VCC /RC) on

the collector current axis as shown in Fig. (ii).

By joining these two points, d.c. *load line AB is

constructed.

Transistor Biasing:

The proper flow of zero signal collector current and the maintenance

of proper collector-emittervoltage during the passage of signal is

known as transistor biasing.

Stabilization:

The process of making operating point independent of temperature

changes or variations intransistor parameters is known as

stabilization.

Methods of Transistor Biasing

In the transistor amplifier circuits drawn so far biasing was done with

the aid of a battery VBB whichwas separate from the battery VCC

used in the output circuit. However, in the interest of simplicity

and economy, it is desirable that transistor circuit should have a single

source of supply—the one inthe output circuit (i.e. VCC). The

following are the most commonly used methods of obtaining

transistorbiasing from one source of supply (i.e. VCC ) :

(i) Base resistor method or fixed bias

(ii) Emitter bias method

(iii) Biasing with collector-feedback

resistor

(iv) Voltage-divider bias

Base Resistor Method or fixed bias:

1. In this method, a high resistance RB (several hundred kΩ)

isconnected between the base and +ve end of supply for npntransistor

(See Fig.) and between base and negative endof supply for pnp

transistor.

2. Here, the required zero signal

base current is provided by VCC and it flows through RB.

3. Itis because now base is positive w.r.t. emitter i.e. base-

emitterjunction is forward biased.

4. The required value of zerosignal base current IB (and hence IC =

βIB) can be made to

flow by selecting the proper value of base resistor RB.

Circuit analysis:

It is required to find the value of RB sothat required collector current

flows in the zero signal conditions.

Let IC be the required zero signal collector current.

∴𝐼 𝐵 = 𝐼𝐶

𝛽

Considering the closed circuit ABENA and applyingKirchhoff 's

voltage law, we get,

VCC = IB RB + VBE

or IB RB = VCC − VBE

∴𝑅𝐵 =VCC − VBE

I𝐵 …………..... (i)

As VCC and IB are known and VBE can be seen from the transistor

manual, therefore, value of RB

can be readily found from exp. (i).

Since VBE is generally quite small as compared to VCC, the former can

be neglected with littleerror. It then follows from exp. (i) that

𝑅𝐵 =V𝐶𝐶

I𝐵


It may be noted that VCC is a fixed known quantity and IB is chosen at

some suitable value. Hence,RBcan always be found directly, and for

this reason, this method is sometimes called fixed-bias method.

Advantages :

(i) This biasing circuit is very simple as only one resistance RB is

required.

(ii) Biasing conditions can easily be set and the calculations are

simple.

(iii) There is no loading of the source by the biasing circuit since no

resistor is employed acrossbase-emitter junction.

Disadvantages :

(i) This method provides poor stabilisation. It is because there is no

means to stop a self-increasein collector current due to temperature

rise and individual variations. For example, if βincreases due to

transistor replacement, then IC also increases by the same factor as IB

is constant.

(ii) The stability factor is very high. Therefore, there are strong

chances of thermal runaway.Due to these disadvantages, this method

of biasing is rarely employed.

Voltage Divider Bias Method:

1. This is the most widely used method of providing biasing and

stabilisation to a transistor.

2. In thismethod, two resistances R1 and R2 are connected across

the supply voltage VCC (See Fig.) andprovide biasing.

3. The emitter resistance RE provides stabilisation.

4. The name ‘‘voltage divider’’ comesfrom the voltage divider

formed by R1 and R2.

5. The voltage drop across R2 forward biases the base-emitter

junction. This causes the base current and hence collector

current flow in the zero signalconditions.

Circuit analysis:

Suppose that the current flowing through resistance R1 is I1. As base

currentIB is very small, therefore, it can be assumed with reasonable

accuracy that current flowing through R2

is also I1.

(i) Collector current IC :

𝐼1 =𝑉𝐶𝐶

𝑅1 + 𝑅2

∴ Voltage across resistance R2 is

𝑉2 = 𝑉𝐶𝐶

𝑅1 + 𝑅2 𝑅2

Applying Kirchhoff 's voltage law to the base circuit of Fig.,

𝑉2 = 𝑉𝐵𝐸 + 𝑉𝐸

𝑉2 = 𝑉𝐵𝐸 + 𝐼𝐸𝑅𝐸

𝐼𝐸 = 𝑉2 − 𝑉𝐵𝐸

𝑅𝐸

Since IE≈ IC


𝐼𝐶 = 𝑉2−𝑉𝐵𝐸

𝑅𝐸...(i)

It is clear from exp. (i) above that IC does not at all depend upon β.

Though IC depends upon VBEbut in practice V2>> VBE so that IC is

practically independent of VBE. Thus IC in this circuit is almost

independent of transistor parameters and hence good stabilisation is

ensured. It is due to this reasonthat potential divider bias has become

universal method for providing transistor biasing.

(ii) Collector-emitter voltage VCE:

Applying Kirchhoff 's voltage law to the collector side,

VCC = IC RC + VCE + IE RE

= IC RC + VCE + IC RE (ä IE j IC)

= IC (RC + RE) + VCE

∴ VCE = VCC − IC (RC + RE)

Stabilisation: In this circuit, excellent stabilisation is provided by RE. Consideration

of eq. (i)reveals this fact.

V2 = VBE + IC RE

Suppose the collector current IC increases due to rise in temperature.

This will cause the voltagedrop across emitter resistance RE to

increase. As voltage drop across R2 (i.e. V2) isindependent of

IC, therefore, VBE decreases. This in turn causes IB to decrease. The

reduced value of IB tends torestore IC to the original value.

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Unit – I Semiconductors, Diodes and Bipolar transistors - MR