Physics Project Reports

Rectifier

Introduction

Although in our daily life we use A.C. current devices.  But rectifier is a ‘Electronic device which converts A.C. power into D.C. power’.

The study of the junction diode characteristics reveals that the junction diode offers a low resistance path, when forward biased, and a high resistance path, when reverse biased.  This feature of the junction diode enables it to be used as a rectifier.

The alternating signals provides opposite kind of biased voltage at the junction after each half-cycle.  If the junction is forward biased in the first half-cycle, its gets reverse biased in the second half.  It results in the flow of forward current in one direction only and thus the signal gets rectified.

In other words, we can say, when an alternating e.m.f. signal is applied across a junction diode, it will conduct only during those alternate half cycles, which biased it in forward direction.

Type of rectifier

Mainly we have two types of rectifier :

1.         Half wave rectifier.

2.         Full wave rectifier.

Junction diode as half wave rectifier

When a single diode is used as a rectifier, the rectification of only one-half of the A.C. wave form takes place. Such a rectification is called half-wave rectification.  The circuit diagram for a half-wave rectifier is shown in Fig.

Principle :

It is based upon the principle that junction diode offers low resistance path when forward biased, and high resistance when reverse biased.

Arrangement :-

The A.C. supply is applied across the primary coil(P) of a step down transformer.  The secondary coil(S) of the transformer is connected to the junction diode and a load resistance RL.  The out put D.C. voltage is obtained across the load resistance(RL)

Theory :

Suppose that during the first half of the input cycle, the junction diode gets forward biased the conventional current will flow in the direction of the arrow-heads.  The upper end of RL will be at positive potential w.r.t. the lower end.  During the negative half cycle of the input a.c. voltage, the diode is reverse biased.  No current flows in the circuit, and therefore, no voltage is developed across (RL).  Since only the positive half cycle of the input appears across the load, the a.c. input is converted into pulsating direct current (d.c.).

Disadvantage of Half-Wave-Rectifier :

1.         Half wave rectification involves a lot of wastage of energy and hence it is not preferred.

2.         A small current flows during reverse bias due to minority charge carriers.  As the output across  (RL) is negligible.

3.         The resulting d.c. voltage is not steady enough for some purpose.  The following device is used when a very steady d.c. voltage is required.

Junction diode as a full wave rectifier

“A rectifier which rectifies both waves of the a.c. input is called a full wave rectifier”.

Principle :-      It is based upon the principle that a junction diode offers low resistance during forward biased and high resistance, when reverse biased.

Difference from half-wave-rectifier :-            The main difference is that in full wave rectifier we use two diodes.  For this when we apply a.c. current to the rectifier then the first half wave get forward biased due to first diode.  And when the second half wave comes.  Then at that time the second diode comes in action and gets forward biased.  Thus output obtained during both the half cycles of the a.c. input

Arrangement :- The a.c. supply is applied across the primary coil(P) of a step down transformer.  The two diodes of the secondary coil(S) of the transformer are connected to the P-sections of the junction diodes (D1) and (D2).  A load resistance (RL) is connected across the n-sections of the two diodes and at centre of the secondary coil.  The d.c. output will be obtained across the load resistance (RL).

Theory :-

Suppose that during first half of the input cycle, upper end of (S) coil is at positive potential.  And lower end is at negative potential.  The junction diode (D1) gets forward biased, while the diode. (D2) get reverse biased.  When the second half of the input cycle comes, the situation will be exactly reverse.  Now the junction diode (D2) will conduct.  Since the current during both the half cycles flows from right to left through the load resistance (RL) the output during both the half cycles will be of same nature.

Thus, in a full wave rectifier, the output is continuous but pulsating in nature.  However it can be made smooth by using a filter circuit.

Reverse biasing on a junction diode

A P-n junction is said to be reverse biased if the positive terminal of the external battery B is connected to n-side and the negative terminal to p-side of the p-n junction.  In reverse biasing, the reverse bias voltage supports the potential barrier VB. (Now the majority carriers are pulled away from the junction and the depletion region become thick.  There is no conduction across the junction due to majority carriers.  However, a few minority carriers (holes in n-section and electrons in p-section) of p-n Junction diode cross the junction after being accelerated by high reverse bias voltage.  Since the large increase in reverse voltage shows small increase in reverse current, hence, the resistance of p-n junction is high to the flow of current when reverse biased.

Material required

1.         Transformer :

It is device which is used to increase or decrease the alternating current and alternating voltage. For the rectifier, it may be step down or step up.

2.         Junction Diode :

It is made up of p-type and n-type semiconductor which conducts when the p terminal of diode to connect to positive terminal of battery and n region is connected to negative terminal of battery i.e. during forward biased and does not conduct during reverse biased.

Logic Gates

A gate is defined as a digital circuit which follows some logical relationship between the input and output voltages.  It is a digital circuit which either allows a signal to pass through as stop, it is called a gate.

The Logic Gates are building blocks at digital electronics.  They are used in digital electronics to change on voltage level (input voltage) into another (output voltage) according to some logical statement relating them.

A logic gate may have one or more inputs, but it has only one output.  The relationship between the possible values of input and output voltage is expressed in the form of a table called truth table or table of combinations.

Truth table of a Logic Gates is a table that shows all the input and output possibilities for the logic gate.

George Boole in 1980 invented a different kind of algebra based on binary nature at the logic, this algebra of logic called BOOLEAN ALGEBRA.  A logical statement can have only two values, such as HIGH/LOW, ON/OFF, CLOSED/OPEN, YES/NO, TRUE/FALSE, CONDUCTING/NON-CONDUCTING etc.  The two values of logic statements one denoted by the binary number 1 and 0.  The binary number 1 is used to denote the HIGH value.  The logical statements that logic gates follow are called Boolean expressions.

Types of Gates

There are three types of basic logic gates which follows Boolean expression.

i)          OR gate

ii)         AND gate

iii)      NOT gate

the “or gate”

The OR gate is a two inputs and one output logic gate.  It combing the input A and B with the output Y following the Boolean expression.

Y = A + B

The Boolean algebra, the addition symbol (+) is called OR (i.e. OR operation OR operator).

The various possible combinations of the input and output of the OR gate can be easily understand with the help of the electrical circuit.  In this electric circuit, a parallel combination of two switches A and B is connected to a battery and a lump L.

The following interference can be easily drawn from the working of electrical circuit is :

a)         If switch A & B are open lamp do not glow (A=0, B=0)

b)         If Switch A open B closed then (A=0, B=1) Lamp glow.

c)         If switch A closed B open then (A=1, B=0) Lamp glow.

d)         If switch A & B are closed then (A=1, B=1) Lamp glow.

As we see truth table we found same as it is observation.

the “and gate”

The AND gate is also a two inputs and one output logic gate.  It combines the input A and B with the output Y following the Boolean expression.

Y = A . B

The Boolean algebra, the multiplication symbol (. dot or x Gross) is taken to mean AND.

Y = A . B have Y is equal to A AND B.

The various possible combination of the input and outputs of the AND gate can be easily found with the help of the electrical circuit.  Here a series combination of the switch A and B is connected to a battery and a lump L.

The following conclusions can be easily drawn from the working of electrical circuit :

a)         If both switches A&B are open (A=0, B=0) then lamp will not glow.  (y=0)

b)         If Switch A closed & B open (A=1, B=0) then Lamp will not glow. (y=0)

c)         If switch A open & B closed (A=0, B=1) then Lamp will not glow. (y=0)

d)         If switch A & B both closed (A=1, B=1) then Lamp will glow. (y=1)

As we see truth table we found same as it is observed experimentally.

the “not gate”

The NOT gate is a one inputs and one output logic gate.  It combines the input A with the output following the Boolean expression.

Y = A

i.e. Y not equal A.  The way, the NOT gate gives the output it is also called inverter.  It is represented by the symbol.

The Boolean algebra, the negative sign (-) is called NOT.  The equation Y= A  called Boolean expression.

The possible input and output combination of a NOT gate can be easily discussed with the help of electrical circuit.  Here, the switch is connected in parallel to the lump of the battery.  The following conclusion can be easily drawn from the working of the electrical circuit.

a)         If switch A is open (i.e. A=0), the lump will glow (i.e. Y=1)

b)         If Switch A is closed (i.e. A=1), the lump will not glow (Y=0).

It follows that in the given electrical circuit, the lump glows (or output is obtained), when the switch A is not closed.  Far this reason, the electrical circuit is called not gate.  The two possible input-output combinations can be written in the form of the table.  It is called truth table of NOT gate.

Semiconductors

Project Report on semiconductors - INTRODUCTION

Semiconductors :- Most of the solids can be placed in one of the two classes: Metals and insulators.  Metals are those through which electric charge can easily flow, while insulators are those through which electric charge is difficult to flow.  This distinction between the metals and the insulators can be explained on the basis of the number of free electrons in them.  Metals have a large number of free electrons which act as charge carriers, while insulators have practically no free electrons.

There are however, certain solids whose electrical conductivity is intermediate between metals and insulators. They are called ‘Semiconductors’.  Carbon, silicon and germanium are examples of semi-conductors.  In semiconductors the outer most electrons are neither so rigidly bound with the atom as in an insulator, nor so loosely bound as in metal.  At absolute zero a semiconductor becomes an ideal insulator.

semiconductors - Theory and Definition

Semiconductors are the materials whose electrical conductivity lies in between metals and insulator.  The energy band structure of the semiconductors is similar to the insulators but in their case, the size of the forbidden energy gap is much smaller than that of the insulator.  In this class of crystals, the forbidden gap is of the order of about 1ev, and the two energy bands are distinctly separate with no overlapping.  At absolute o0, no electron has any energy even to jump the forbidden gap and reach the conduction band.  Therefore the substance is an insulator.  But when we heat the crystal and thus provide some energy to the atoms and their electrons, it becomes an easy matter for some electrons to jump the small (»  1 ev) energy gap and go to conduction band.  Thus at higher temperatures, the crystal becomes a conductors.  This is the specific property of the crystal which is known as a semiconductor.

Effect of temperature on conductivity of Semiconductor

At 0K, all semiconductors are insulators.  The valence band at absolute zero is completely filled and there are no free electrons in conduction band.  At room temperature the electrons jump to the conduction band due to the thermal energy.  When the temperature increases, a large number of electrons cross over the forbidden gap and jump from valence to conduction band. Hence conductivity of semiconductor increases with temperature.

INTRINSIC SEMICONDUCTORS

Pure semiconductors are called intrinsic semi-conductors.  In a pure semiconductor, each atom behaves as if there are 8 electrons in its valence shell and therefore the entire material behaves as an insulator at low temperatures.

A semiconductor atom needs energy of the order of 1.1ev to shake off the valence electron.  This energy becomes available to it even at room temperature.  Due to thermal agitation of crystal structure, electrons from a few covalent bonds come out.  The bond from which electron is freed, a vacancy is created there.  The vacancy in the covalent bond is called a hole.

This hole can be filled by some other electron in a covalent bond.  As an electron from covalent bond moves to fill the hole, the hole is created in the covalent bond from which the electron has moved.  Since the direction of movement of the hole is opposite to that of the negative electron, a hole behaves as a positive charge carrier.  Thus, at room temperature, a pure semiconductor will have electrons and holes wandering in random directions.  These electrons and holes are called intrinsic carriers.

As the crystal is neutral, the number of free electrons will be equal to the number of holes.  In an intrinsic semiconductor, if ne denotes the electron number density in conduction band, nh the hole number density in valence band and ni the number density or concentration of charge carriers, then

ne = nh = ni

extrinsic semiconductors

As the conductivity of intrinsic semi-conductors is poor, so intrinsic semi-conductors are of little practical importance.  The conductivity of pure semi-conductor can, however be enormously increased by addition of some pentavalent or a trivalent impurity in a very small amount (about 1 to 106 parts of the semi-conductor).  The process of adding an impurity to a pure semiconductor so as to improve its conductivity is called doping.  Such semi-conductors are called extrinsic semi-conductors.  Extrinsic semiconductors are of two types :

i)          n-type semiconductor

ii)         p-type semiconductor

n-type semiconductor

When an impurity atom belonging to group V of the periodic table like Arsenic is added to the pure semi-conductor, then four of the five impurity electrons form covalent bonds by sharing one electron with each of the four nearest silicon atoms, and fifth electron from each impurity atom is almost free to conduct electricity.  As the pentavalent impurity increases the number of free electrons, it is called donor impurity.  The electrons so set free in the silicon crystal are called extrinsic carriers and the n-type Si-crystal is called n-type extrinsic semiconductor.  Therefore n-type Si-crystal will have a large number of free electrons (majority carriers) and have a small number of holes (minority carriers).

In terms of valence and conduction band one can think that all such electrons create a donor energy level just below the conduction band as shown in figure.  As the energy gap between donor energy level and the conduction band is very small, the electrons can easily raise themselves to conduction band even at room temperature.  Hence, the conductivity of n-type extrinsic semiconductor is markedly increased.

In a doped or extrinsic semiconductor, the number density of the conduction band (ne) and the number density of holes in the valence band (nh) differ from that in a pure semiconductor.  If ni is the number density of electrons is conduction band, then it is proved that

ne nh = ni2

p-type semiconductor

If a trivalent impurity like indium is added in pure semi-conductor, the impurity atom can provide only three valence electrons for covalent bond formation.  Thus a gap is left in one of the covalent bonds.  The gap acts as a hole that tends to accept electrons.  As the trivalent impurity atoms accept electrons from the silicon crystal, it is called acceptor impurity.  The holes so created are extrinsic carriers and the p-type Si-crystal so obtained is called p-type extrinsic semiconductor.  Again, as the pure Si-crystal also possesses a few electrons and holes, therefore, the p-type si-crystal will  have a large number of  holes (majority carriers) and a small number of electrons (minority carriers).

It terms of valence and conduction band one can think that all such holes create an accepter energy level just above the top of the valance band as shown in figure.  The electrons from valence band can raise themselves to the accepter energy level by absorbing thermal energy at room temperature and in turn create holes in the valence band.

Number density of valence band holes (nh) in p-type semiconductor is approximately equal to that of the acceptor atoms (Na) and is very large as compared to the number density of conduction band electrons (ne).  Thus,

nh» Na > > ne

electrical resistivity of semiconductors

Consider a block of semiconductor of length l1 area of cross-section A and having number density of electrons and holes as ne and nh respectively.  Suppose that on applying a potential difference, say V, a current I flows through it as shown in figure.  The electron current (Ic) and the hole current (Ih) constitute the current I flowing through the semi conductor i.e.

I = Ie + Ih                                                                     (i)

It ne is the number density of conduction band electrons in the semiconductor and ve, the drift velocity of electrons then

Ie = eneAve

Similarly, the hole current, Ih = enhAvh

From (i)                       I = eneAve + enhAvh

I = eA(neve + nhvh)                               (ii)

If r is the resistivity of the material of the semiconductor, then the resistance offered by the semiconductor to the flow of current is given by :

R = r l/A                                                                     (iii)

Since V = RI, from equation (ii) and (iii) we have

V = RI = r l/A  eA (neve  + nh vh)

V = r le(neve + nhvh)                                                            (iv)

If E is the electric field set up across the semiconductor, then:

E = V/l                                                                                    (v)

from equation (iv) and (v), we have

E = re (neve + nhvh)

1/r = e (ne ve/E + nh vh/E)

On applying electric field, the drift velocity acquired by the electrons (or holes) per unit strength of electric field is called mobility of electrons (or holes).  Therefore,

mobility of electrons and holes is given by :

me = ve/E and mh = vh/E

1/r = e(ne me + nh mh)                                                  (vi)

Also, s = 1/r is called conductivity of the material of semiconductor

s          = e (ne me + nh mh)                                           (vii)

The relation (vi) and (vii) show that the conductivity and resistivity of a semiconductor depend upon the electron and hole number densities and their mobilities.  As ne and nh increases with rise in temperature, therefore, conductivity of semiconductor increases with rise in temperature and resistivity decreases with rise in temperature.