Basic Electronics [1 ed.] 9789350433072, 9788184885286

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Basic Electronics

D.C. Tayal

.BASIC ELECTRONICS

DR. D.C. TAVAl M.Phi/., Ph.D.

Director B.S. Anangpuria Educational Institutes Alampur, Faridabad

K~II GJIimalaya GJlublishing GJIouse • Mumbai • Delhi • Bangalore • Hyderabad • Chennai • Ernakulam • Nagpur • Pune • Ahmedabad • Lucknow

©

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Contents Chapter 1.

Introduction

Pages "1-23

Electronics, Electronic Applications, Electronic Components (resistors, capacitors, inductors), Actual Elements, Voltage Source-ideal and practical, Current Source-ideal and practical, Four Terminal Network (impedance, admittance, hybrid parameters), Self Test, Short Answer Questions. 2.

Semiconductor Physics

24-74

Bonding in Solids, Bohr Model of the Hydrogen Atom, Band Theory of Solids, Band Structures of Crystals, Electrons and Holes in an Intrinsic Semiconductors, Carrier Concentrations in Intrinsic Semiconductors, Fermi Levels in Intrinsic Semiconductors, Semiconductor Doping (Extrinsic Semiconductor), n-type of semiconductor, p-type of semiconductor, Charge den~sities in an Extrinsic Semiconductor, Fermi Levels in Extrinsic Sermiconductors, Drift and Diffusion Currents (Transport equation, Einstein relations), Contacts and Junctions, Qualitative Theory of p-n Junctio~, Properties of Depletion Region, The p-n Junction as a Diode, Junction Diode Characteristics (Experiment), The p-n Diode Equation, Temperature Dependence of p-n Characteristics, Zener and Avalanche Breakdown, Zener Diode and its Characteristics (Experiment), Exercises, Self Test, Short Answer Questions, Problems, Questions. 3.

Transistor Amplifiers Transistors, Junction Transistor, Biasing of a Transistor, Transistor Configurations, Current and Voltage Symbols and Sign Conventions, Transistor Equivalent Circuits, Transistor Current Components, Current Amplification Factors, Leakage Currents in a Transistor, Characteristic Curves of a Transistor, Limits of Operation, Amplifiers and their Classifications, Basic Amplifier, Load Lines and Operating Point, Bias Stabilization, Methods of Transistor Biasing, Cascading of Transistor Amplifiers, Coupling and by-pass Capacitor, Single Stage Transistor Amplifier, Two Stage Resistance-Capacitance Coupled Transistor Amplifier, Feedback, Advantages of Negative Feedback, Effect of Feedback on Amplifier Gain and Bandwidth, Exercises, Self Test, Short Answer Questions, Problems, Questions.

75-

4.

Oscillators

144-160

Oscillators, LC-Oscillators, RC-Oscillators, Crystal Oscillator, Exercises, Self Test, Short Answer Questions, Problems, Questions.

5.

Operational Amplifiers

161-192

The Differential Amplifier, Operational Amplifier, Equivalent Circuit of an OP-AMP, Differential and Common Mode Operation, Basic OPAMP, Characteristics of Practical OP-AMPS, Comparison of Ideal and Practical OP-AMP, OP-AMP Configurations, Applications of ,..A-741 Operational Amplifiers, Exercises, Self Test, Short Answer Questions, Problems, Questions. 6.

Power Supplies

193-241

Rectifiers, Half Wave Rectifier, Full Wave Rectifier, Full Wave Bridge Rectifier, Filter Circuits (series inductor, shunt capacitor, inductor input L-section, capacitor input 1t-section), Power Supply (unregulated), Voltage Regulation in Power Supplies, Voltage Regulation with Feedback Amplifier, Switching Regulators, Switched Mode Power Supplies, Invertors, Bridge Invertors, Uninterruptible Power Supply (UPS), Exercises, Self Test, Short Answer Questions, Problems, Questions.

7.

Digital Electronics

242-304

Digital and Analog Circuits, Number Systems, Numbers Base Conversion, Binary Arithmetic, Negative Binary Numbers, Logic Gates (AND, OR, NOT, NAND, NOR), Boolean Algebra, Theorems of Boolean Algebra-Logic Rules, De Morgan's Theorem, Duals, Implementation of Logic Functions, Combinational and Sequential Systems, Arithmetic Digital Circuits (Adders, Subtractors, Multipliers, Dividers, Comparators), Flip-Flops (SR, JK, Edge Triggered), Exercises, Self Test, Short Answer Questions, Problems, Questions. 8.

Electronic Instruments

305-329

Multimeters, VTVM, Solid State Multimeter, Digital Multimeter, Digital Voltmeters, CRO, Uses of CRO, Function Generator, Exercises, Self Test, Short Answer Questions, Problems, Questions. 9.

Digital Displays

330-346

Digital Display Devices, Segmental Displays, LED-Display, LCDDisplay, Liquid Crystal Materials, Liquid Crystal Cells, Self Test, Short Answer Questions, Questions.

to.

Experiments

347-350

11.

Index

351-354

Basic Electronics ECE-IOIF SECTION A Semiconductor Physics: Basic concepts, Intrinsic and extrinsic semiconductors, diffusion and drift currents, p - n junction under open-circuit, reverse bias and forwardbias conditions, p - n junction in the breakdown region, Ideal diode, Terminal characteristics of junction diode. Amplifiers : Introduction of different types of amplifiers and their characteristics, Principle of simplification, Frequency response of RC coupled amplifiers, Amplifier bandwidth and Concept of Cascaded Amplifiers, Feedback amplifiers, Effect of positive and negative feedback on amplifier gain and bandwidth.

SECTION B Oscillators : Criteria for oscillations, Qualitative analysis of LC, RC and Crystal Oscillators, Study of Wein Bridge Oscillators. Operational Amplifiers : Op-amps, its characteristics and its applications. Power Supplies: Introduction and Working of Switched Mode Power Supply (SMPS), Voltage Regulator, Introduction to inverters and UPS.

SECTION C Digital Electronics: Binary, Octal and Hexadecimal number systems and conversions, Boolean Algebra, Truth tables of logic gates (AND, OR, N01), NAND, NOR as universal gates, Difference between combinational circuits and sequential circuits, Introduction to flip-flops (S - Rand J - K). I 100 MQ). This resistance is in parallel with the capacitor. The leakage resistance is about 0.5M Q for electrolytic capacitors. The absorption loss dissipated in dielectric is represented (b) by a small series resistance (~ 0.5 Q), as such a loss is associated with the same current that charges the L capacitor. Capacitors with a coiled construction have (e)LOoOOOO~ some internal inductance. The larger the capacitor, the greater is its series inductance. Mica and ceramic capacitors have very little inductance and are thus used Fig. 1.9 : (a) Resistor, (b) Capacitor, for radio frequencies, Fig. 1.9(b). An inductance coil has and (e) Inductor. distributed capacitance between turns, as each turn is a conductor separated from the next turn by an insulator and thus acts as a capacitor. The equivalent circuit of an rf-coil consists of an internal effective ac resistance in series with the coil and the total distributed capacitance for all the turns in parallel, Fig. 1.9(c). To minimize this capacitance, the turns are spaced far apart.

1.5. Voltage Source-Ideal and Practical An ideal voltage source is an active device which provides a fixed terminal voltage even though the current supplied by it to the load connected between its terminals may vary. Thus for an ideal voltage source also called constant voltage source, the terminal voltage always equals its open circuit voltage. This corresponds to the zero internal impedance [Fig. 1.10(b)].

1.1 1I

A

Ideal source

.=.

(a)

t

VL B (b)

B (e)

(d)

Fig. 1.10 : (a) Voltag'e source symbols. (b) Ideal voltage source. (e) Practical (or Actual) voltage source and (d) VI-charactel'lstics of a practical voltage source,

An ideal voltage source is practically impossible. There is no voltage source which can maintain its terminal voltage constant when the terminals are short circuited. A practical voltage source consists of an ideal voltage source in series with an impedance (called the internal impedance of the source) as shown in Fig. 1.1O(c).

Basic Electronics

16

Let Vs be its open circuit voltage and Zs be its internal impedance. Let this source be connected to a load impedance ZL' For a given value ofload, the current in the circuit IS gIven as

IL

= VsI(Zs

... (21)

+ ZL)'

Therefore, the terminal voltage of the source is F

'AB=

\'

L=

I

LX

Z

VsZ L

... (22)

L=Z.c;+ZL

Thus we see that if the ratio ZSIZL « 1, the terminal voltage remains almost same as the voltage Vs' If the load impedance changes provided the ratio ZSIZL is quite small, the source acts as nearly an ideal source (called good constant voltage source) and V l13 = Viand = Vs = ILZ L· If the output terminals are short circuited, ZL = 0 and Isc = co. No practical source can produce infinite current and thus can be an ideal voltage source. If the value of ZSIZL ~ 1, the VAB does not remain constant but has a large variation. Substitution of the numerical values shows that it is not the absolute value of the internal impedance that decides whether a source is a good constant voltage source or not. The value of ZSIZL is important. The lesser the ratio, the better is the source as a constant voltage source.

1.6. Current Source-Ideal And Practical Ideal current source is a source that can supply constant current even if its terminals are open circuited. Its internal impedance is infinity [Fig. 1.1l(b)]. It cannot exist in practice, thus an ideal current source is merely an idea. A practical current source is represented by the symbol shown in Fig. 1.1l(c). The mternal impedance of the source Z s is put in parallel with the ideal current source Is. A

A

t

iL

zi.

ZL

Vs

1

vL

V--+

B (([ )

(b)

B (c)

(d)

Fig. 1.11 : (17) Current source symbols, (b) Ideal current source. (c) Practical current source (d) Vanation ofload current.

If a load ZL is connected across the terminals A and B, the source current Is is divided in two parts, one through the source impedance Z s and other through load impedance ZL' Thus

Is

= is

+ iL'

Since the impedances Z sand Z L are in parallel, therefore

17

In traduction

isZs

= iLZ L·

These two equations give the value of the load current as

.

'L

I sZ s I s = 1 + (ZL/ZS)' + ZL

= Zs

... (23)

The load current is equal to the source current for ZL = O. For the smaller values of the ratio of ZL/ZS (i.e., Z « 1), the load current is nearly constant and the source behaves as a good current source. The increase of load impedance increases the terminal voltage VEA = ILZ L and thus decreases the load current, as shown m FIg. 1. l1(d). Practically a current source is not different from a voltage source. The source can either work as a voltage source or as a current source. depending upon its working conditions. For ZL > Zs' it is better to represent the source as a voltage source. On the other hand for ZL < Zs' it is advantageous to treat the source as a current source. Conversion of Voltage Source into Current Source and Vice Verse: The voltage and current sources are indistinguishable from each other, if the values of load currents are same in both the cases. The voltage source representation consists of an ideal voltage source Vs in series with a source impedance Zs' and the current source representation consists of an ideal current Is in parallel with source impedance Zs' The short circuit current of the voltage source is the same as the maximum current delivered by the current source. In both the cases the open circuit voltage is the same. A

A

, ,

,

z~

source B Fig. 1.12 : (0) A source connected wIth a load.

B (b)

··· B

Voltage source and (c) CUl'l'ent source.

The load current due to the voltage source = IL = VS/(ZL + Zs)' Its value when the current source is used is obtained by the current division rule. The load current due to the current source Is is IL' = IsZs'/(ZL + Zs). ... (24)

U 8ing these relatIOns a voltage source is converted into current source and vice versa. Here we see that a voltage source in series with an impedance can be replaced by an eqUIvalent circuit consists of a current source in parallel with that same impedance and vice versa.

1.7. Four Terminal Network A fOlll' terminal networh, also called two terminal pair network, is treated as a black box with two input terminals and two output terminals, as shown in Fig. 1.13. The black box may contain linear network (either active or passive) such as transformer, fIlter. transistor and amplifier. A four terminal network is also called two port network, if for all t and all possible external connections at these terminals, the current entering the network by terminal 1 is equal to that leaving the network by terminal l' and the

18

Basic Electronics

current entering the network by terminal 2 is equal to that leaving the network by terminal 2'. Thus a four terminal network is more generaI"than a two port network. The port at the left is usually referred to as the input port, whereas the port at the right is usually referred to as the output port.

: .:

{

,-__ N_e_t'_"I'o_l_'k_--,

Fig. 1.13 : Four terminal network.

In applying two port network theory, the actual two port is transformed into an equivalent two port model with specially defined parameters. The most commonly used such parameters are impedance parameters, admittance parameters and hybrid parameters. The first two are used when elements of the two port consist of resistors, inductors and capacitors. Hybrid parameters are generally used in transistors, amplifiers, etc. The equivalent two port parameters may be calculated from current and voltage measurements made at the input and output terminals. Let the terminal quantities are vI' ip v2 and i z. Any pair of these variables may be arbitrarily chosen as independent, giving two equations. The solution of these equations give two other dependent variables. We may choose two independent variables out of the four in different ways. Let us discuss three important cases in details as under : (a) Impedance Parameters: Making the choice of il and i2 as independent variables implies the general relations VI

=f

(iI,

i 2) and v2 = f (ii' i2)·

These may be written as

= (dv/di l ) di l

+ (dV/di 2) di2 dV 2 = (dvidiI) dil + (dv zldi 2) di 2 · dV I

For sufficiently small a - c signals these equations may be written in the phaseor form as

VI V2

or

= ZIl = Z21

11 + Zl2 12 II + Z22 12 ,

Z12] [I 1]

z22

12

... (25)

Here z-parameters have been defined as the slopes of the v - i relations and are known as open circuit impedance parameters of the network and are useful in general network analysis but not for transistor studies.

= 0 or 12 = 0 in equation (25), we have Z11 = dv1/di 1 = Open circuit input impendance (1 2 = 0) Zl2 = dV/di 2 = Open circuit reverse transfer impedance (11 = 0) z21 = dvidil = Open circuit forward transfer impedance (1 2 = 0) Using II

19

Introduction Z22

= dV/di 2 = Open circuit output impedance (11 = 0).

Equation (25) may be written as

V

= ZI,

Z

= [:::

where the matrix

:::J

... (26)

is called the open circuit impendance matrix of the two port network. Z-parameterf:l may be 'determined experimentally from phasor current and phasor voltage measurements made during open circuit tests. (b) Admittance Parameters: If the choice of variables is made, then the general relations become

vI

and

u2

as the independent

dil = (di/dU 1) dU I + (di/dU,};) dV 2 di2

= (di/dU 1)

dV I + (di/dU 2) dv 2 •

For sufficiently small a - c signals where the partial derivatives are constant, we have the phasor relations 11 = Yu VI +

Y12

V2

... (27)

or

Here y-parameters are known as short circllit admittance parameters. Using VI = 0 or V 2 = 0 in equation (27), we have

Y1:2

= di/dU l = Short-circuit input admittance :;::' di/dV 2 = Short-circuit reverse transfer admittance

Y21

= diidVI = Short-circuit forward transfer admittance (V2 = 0)

Y22

= di/dU 2 = Short-circuit output admittance

Yu

Equation (27) may be written as I y = [Yll Y21

= YV where

(V2 (VI

= 0) = 0)

(VI = 0)

the matrix

Y12] Y22

... (28)

is called the short circuit admittance matrix of the two port network. y-parameters may be determined experimentally from phasor current and phasor voltage measurements made during short circuit tests.

It is easy to prove from equations (26), and (28) that Z = y-l or y = Z-l zn

=

Y22

,1.y , z12

=-

Y12

,1.y , z21

... (29)

Basic Electronics

20

Zll

= -~Z

w here

~y

= det I Y I I

and

~z

= det I Z I .

(c) Hybrid Parameters: The third choice of i l and v2 as independent variables leads to a set of network parameters of considerable value in transistor circuit analysis. It gives VI

=

f (iI' v2), i2

=

f (iI' v 2)·

dV l = (av/ai l ) di l + (av/av 2) dU 2 and di2 = (ai/ail) di l + (ai/au 2) du 2· For sufficiently small a - c signals where the partial derivatives become constants, we have the phasor relations VI = h 11 11

+ h 12 V 2

or

... (30)

Here h-parameters are known as hybrid parameters, as they are mixed parameters compared to purely impedance and admittance parameters. These are defined under either open or short-circuit conditions. We have V 2 = 0 for a short circuit and 11 = 0 for an open circuit. Thus we have two sets of h-parameters, as defined below hll = av/ail = Short-circuit input impedance h12

= av/av 2 = Open-circuit

reverse voltage gain

h2l = ai/ail = Short-circuit forward current gain h22 = aizlau 2 = Open-circuit output admittance

(V2 (11 (V2 (11

= 0) = 0) = 0) = 0)

Here we see that one parameter is an impedance, one an admittance and two are dimensionless ratios. The condition for the two port to be reciprocal is that h2l = - h 12 . In equation (30) we may define the matrix ... (31)

The matrix H is called a hybrid matrix. The hybrid matrix describes a two port network when the voltage of one port and the current of the other port are taken as the independent variables. The h-parameters may be determined experimentally from phasor current and phasor voltage measurements made during output port short-circuited and input port open-circuited. These three sets of parameters have been found useful in electronic circuit analysis. They can be measured under the specified conditions or evaluated from the

21

Introduction

characteristics. If one set of parameters are gIVen, other two can be calculated using equations (25), (27) and (28). One can find Zll

Z21

= hll - h12h21lh22; Z12 = h121h22' = - h2/h22; z22 = lIh 22 ·

... (32)

Conversion chart of two port matrices is shown in Table 1.3. Table 1.3 : Conversion Chart of Matrices y

Z Zl1

z12

Z21

z22

z z 2~

y

H

/J.z

-z1~

/J.z

H

Y 22

-Y12

/J. y

/J. }'

/J. H h ~2

h22

h12

-Y21

bl

-h21

1

/J. y

/J. y

h22

h22

Yll

Y12

Y22

-z~l

zll

/J.z

/J.z

Y21

~

Z 12

1

-Y12

z22

"" 22

Yll

Yll

-z ~11

1

Y 21

Z11

z22

Yll

~ Yu

1

-h12

hll

~

h21

'r;;;

hll

/J. H

h11

h12

h21

h22

For each set of equations represented in matrix form we may write down an equivalent circuit. The equivalent circuit that satisfies equation (25) is shown in Fig. 1.13(a) and has been called the zequivalent or z-parameter equivalent circuit (model). Each of the z-parameters have the dimensions of impedance and the quantities z12 12 and Z21 11 are dependent voltage sources. The zparameters are not particularly only for transistor studies. The equivalent circuit that satisfies (b) Eq. (27) is shown in Fig. 1.13(b) and is known as the y-equivalent. Each of the yparameters have the dimensions of admittance. Y12 V 2 and Y21 V 1 are the two dependent current generators. The y-parameters are primarily applicable at high frequencies and are often employed to (c) describe a transistor at a particular Fig. 1.14 : Equivalent circuit, frequency.

(a) z-parameter model, (b) y-parameter model and (c) h-parameter model

· 22

Basic Electronics

The equivalent circuit that satisfies Eq. (30) is shown in Fig. 1.13(c) and is known as ·the hybrid (or h) parameter equivalent. Since the defining equations must obey Kirchhoffs laws. Hence hll must be an impedance, h22 an admittance while h12 and h21 are dimensionless. For low-frequency analysis of junction transistor hll and h22 will be resistive.

SELF TEST 1. Which has more resistance, carbon or copper? 2. Which is the best conductor, silver, carbon or iron? 3. Is it true or false that the neutral condition means equal positive and negative charges. 4. In a liquid, what type of moving charges are responsible for conducting current? 5. Is' it true or false that the resistance tests with an ohmmeter can be made with power off in the circuit.

=

6. State whether a resistor with R 100 kD. and power rating-l W would be a carbon or wire wound resistor. 7. How many terminal lugs are used on a rheostat? 8. What is the colour for 6? What is the tolerance for a silver stripe? 9. Two 10 kO 5 - W resistors are connected in (0) series and (b) parallel, calculate the total resistance and power rating in each cases. 10. What is the ohmmeter reading for a (0) short circuit, (b) open circuit? 11. In a capacitor, is the charge stored in the dielectric or in the metal plates? 12. Which has more capacitance, mica capacitor or ceramic capacitor if both have the same physical dimensions? 13. Which capacitor type has polarity? 14. Is it true or false that the coil has distributed capacitance between the turns. 15. Mutual inductance- is 8 mH with k = 0.2. If k is doubled, how much will LM (or M) be? 16. Which produces greater eddy current losses, an iron core or an air core? 17. What is electronics? 18. Explain in brief: What is (0) a capacitor, (b) an inductor, (c) a dielectric? 19. Name a few active components used in electronic circuits. 20. Which independent variables lead to hybrid parameters?

ANSWERS (1) . Carbon,

(2) Silver,

(3) True,

(4) Ions,

(6)

(7) Two,

(8)

(5)

True,

(9)

20 kW, lOW,' 5kW, lOW.

(10) OW,ooW,

(11).' Dielectric,

Ceramic,

(14) True,

(15)

mH,

(20)

i 1 and v2

(12)

(16) Iron core,

Carbon,

(13) Electrolytic,

(19) voltage and current sources.

Blue, ... J%,

23

Introduction

SHORT ANsweR QUeSTIONS 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38.

What is Electronics? How do you classify electronic components? What are the passive components? Name five electronic applications of common use. Define resistance. What is its unit? Write colour code for the resistor. What are the relative merits of the different types of resistors? What do you mean by noise? What is its unit? What do you mean by tolerance? Define resistivity? What is conductance? Why do you call a variable resistor, a potentiometer? Define capacitance. Sketch the symbols for resistors and capacitors. What is daraf'? On which factors the capacitance of a capacitor depend? What do you mean by voltage rating of a capacitor? Name the most commonly used fixed capacitors. What will happen if the Connections of the electrolytic capacitor in a circuit are interchanged? Write the colour code of a capacitor. What do you mean by the leakage resistance of a capacitor? Define the power factor of a capacitor. How can you test a capacitor? Define ~tray capacitance. Define an inductance. Write its unit. What is eddy current? Give the relative merits of ferrite core inductor over the iron core inductor. What is a transformer? On which principle it works? What is mutual inductance? Draw the equivalent circuit of an actual resistor. Define voltage source-ideal and practical. Define current source-ideal and practical. How can you convert a voltage source into current source. What is a four· terminal network? D~ne impedance and admittance parame~ers. Define hybrid parameters. Draw hybrid parameter-equivalent. Write relations for the conversion of impedance parameters to hybrid parameters.

SEMICONDUCTOR PHYSICS

2.1. Bonding in Solids We know that the solids are either crystals or non-crystals. The atoms in the crystals are arranged in a perfectly symmetrical periodic array. The non-crystalline or partially crystalline solids, such as concrete, glass and plastics, lack a perfectly repeated order over long distances, but the neighbourhood of any atom exhibits considerable local order. The attractive electrostatic interaction between the negatively charged electrons and positively charged protons of the nuclei is entirely responsible for the binding of atoms and molecules. The magnetic forces have only a weak effect, gravitational forces are negligible and the nuclear forces do not play any role in the formation of solids. The total energy of the solid, kinetic + potential, is smaller than the total energy of the atoms or molecules when free. The difference is known as Cohesive energy. It is a measure of the strength of a chemical bonding. The wide variation in cohesive energy is noticed. The inert gas crystals are weakly bound with a very small cohesive energies, the alkali metal crystals have intermediately values and the transition element metals are strongly bound. In terms of the type of bonding between atoms, the crystals are broadly divided into following five categories : Ionic Covalent Metallic Molecular Hydrogen

Alkali oxides, halides, etc. Silicon, Diamond, etc. Metals and alloys. Gases like He, Ne, A, Kr, Xe, H 2 , 02' Ice, compounds with water of crystalization.

However a rigid line of demarcation can not be drawn, as several crystals can not be put in a pa,rticular category precisely. For example, CuO and ZnS can be considered as the mixture of ionic and covalent bonding.

2.2. Bohr Model of the Hydrogen Atom Niels Bohr in 1913 put forward a theory on the constitution of atoms and molecules, which combined the quantum theory of Planck and nuclear theory of Rutherford. This is called Bohr model. It has a very prominent place in the development of modern physical thought. In Bohr's words "... an atom consists of a positively chargeo nucleus surrounded by a system of electrons kept together by attractive Coulomb forces from the nucleus. The.atomic nucleus consisting of the major portion of atomic mass may be (24)

Semiconductor Physics

25

compared to the sun, about which planet like electrons circulate with electric forces in the atom taking the place of the gravitational forces in the solar system. Bohr's model was based on two postulates (a proposition offered without proof) namely-(i) the atomic electron remains moving in an orbit without radiating energy and hence at constant energy (stationary orbit), such that the angular momentum of the electron about the nucleus is an integral multiple of n (= h/2rt) , L.e. nllw

= nn,

... (1)

where n is the integer, called the principal quantum number. Bohr's second postulate dealt with the frequency of radiation emitted by an atom. It stated that a pulse or quantum of radiation was emitted or absorbed when an electron jumped from one allowed state to another, ~.e. ... (2) - E f = hv = he/A' where E t and E f are the energies of the initial and final states respectively. The v or A are the frequency or wavelength of the radiation quantum, known as a photon.

f1E

= E.

t

On the basis of these postulates, the expression for the energy associated with an electron in the nth orbit is given by

E 1/

:;: -

2 2 2 . m eZ 2 e 4/8E on h Joules,

... (3)

where me is the electron mass, Z the atomic number. of the atom, e the electronic charge, to is the permittivity of the free space and h the Planck constant. When the energy delivered to an E(eV) Continuum electron is sufficient to drive it out of the o atom, the remaining one is called iOIJ, and -0.56 5 the process the ionization. The minimum I '-0.87 4 energy required for this purpose is called a::1. a ionization energy. Thus the energies are 3 -1.53 Ci5 '::l ~s .". 00 ::l. C'1::1. negative for all finite values of 'n' because 0 0~l ..... ..... 2 -3.41 S of our choice of the zero point of the energy 8::l. ~ scale which corresponds to n = 00. The IN "",....,0 ...... variation of energy with the orbit number n 0 -13.60 0 1 is shown in Fig. 2.1, which is called an energy level diagram. Fig. 2.1 : Energy level diagram for hydrogen atom ::l.

J1 1.0 ..... t-

Bohr's original theory was extended to include elliptical orbits by Sommerfeld. He showed that the semi major axis of any orbit was determined solely by n. Goudsmit proposed that the electron spins like a top and therefore possesses spin angular momentum. Angular momentum i is a vector quantity and is the combination of orbitals angular momentum 1 and spin angular momentum s.

2.3. Band Theory of Solids The X-ray diffraction like studies reveal that most metals and semi-conductors are crystalline in structure. A crystal consists of a space array of atoms and molecules built up by regular repetition in three dimensions of some fundamental structural unit. The

Basic Electronics

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f

Energy

Ionization level

£

energy state of each electron is shown by an energy-level diagram, which is a sort of one dimensional scale of energy. The energy scale is usually measured in eV and is so oriented that electrons tend to move downward on the scale so as to be in the lowest possible energy state.

When atoms come closer to form solids, they are in such close proximity that the forces surrounding an atom have an important effect upon its neighbours. The .~nergy levels of each IS atem thus disturb slightly. The energy-level diagram ,of two identical germanium type atoms ~--R--#I in close proximity is shown in Fig. 2.2. The actual number of states in each atom does not Fig. 2.2 : Energy level diagram of two change, but shift slightly in energy. The identical atoms m close proximity. outermost electrons share the two highest levels, known as valence levels or valence electron levels. The levels above the valence levels are normally empty and called excitation levels. The electron can jump to excitation levels if gained sufficient energy by absorbing a photon or phonon. The zero energy level is called ionization level. The joining of atoms to form molecule does not alter the total number of quantum states with a particular quantum number. Thus a cl'ystal consisting of a large number of atoms may be thought of as an infinitely large molecule and' the total number of quantum states of one kind that it contains is equal to the total number of atoms in the crystal. For example in a crystal consisting of n-identical atoms each having two possible Is states, there are 2n such states. In a sample of any practical size there are 'so many atoms and the splitting is much too fine to detect experimentally. Thus the distributi