unit-iii electron optics...applications: electron lens forms the most important component of an...

Department Of Applied Physics, ACET. BE-Second Semester – Advanced Physics

UNIT-III

ELECTRON OPTICS


UNIT III- ELECTRON OPTICS

Electron Refraction (Bethe’s Law) :

The motion of electron beam in non-uniform electric field can be understood by studying Bethe’s

law. The non uniform electric field is a field in which electric intensity varies from point to point

and field lines are not straight and evenly spaced. Electron motion in non-uniform electric field is

better understood with the help of equipotential surfaces. Equipotential surfaces are those surfaces

where electric potential remains constant and electric lines are perpendicular to the surface at any

point. Therefore the normal to the equipotential surface shows the line of action of electric force on

the electron.

Let us consider a uniform electric field produced in an infinitesimally thin region. This

uniform electric field being set up by two metal plates charged to appropriate potentials. The

electrons are allowed to pass through the electric field being set up by two closely spaced metal

grids as shown in fig.

Consider an equipotential surface AB. It is considered as the boundary across which the

potential V1 abruptly changes to V2. Let an electron travel through the region-I with a uniform

velocity v1 and enter the region-II and moves with a velocity v2.

As the electrons passes through equipotential surface AB it experiences a force which alters

its velocity. Because the electric field exists only in the vertical direction (Y-direction). Hence the

normal component of electron velocity vy undergoes a change whereas the tangential component vx

remains constant.

If V2>V1, vy increases and if V2<V1, vy decreases.

Fig : Electron Refraction

In the above fig., V2>V1 i.e. V2 is taken to be greater than V1 and hence vy increases. The electron

path is therefore bent nearer to the surface normal.

As the tangential component of the velocity remains constant in region-I and region-II we can write, '

xx vv

2211 sinsin vv

)1(sin

sin

1

2

2

1 v

v

The velocity of electron in terms of potential is given by


m

eVv

2

So,

meV

meV

1

2

2

1

2

2

sin

sin

1

2

2

1

sin

sin

V

V

)2(sin

sin 21

1

2

2

1

V

V

The Eqn. (2) is similar to Snell’s law of refraction in optics and is known as Bethe’s law for

electron refraction. When light enters from rarer to denser medium it gets slowed down and bends

towards the normal. However when electrons are moving from region of lower potential to region

of higher potential gets accelerated and bends toward the normal.

Comparison Between Snell’s Law and Bethe’s Law:

Snell’s Law Bethe’s Law

1. 1

2

2

1

sin

sin

v

v

r

i 1.

1

2

1

2

2

1

sin

sin

V

V

v

v

2. It deals with refraction of light.

2. It deals with refraction of electrons.

3. A light entering from a rarer

medium to denser medium bends

towards the normal.

3. An electron entering from a region of

low potential to high potential bends

toward the normal (i.e. bends toward

the direction of electric field).

4. A light entering from a rarer

medium to denser medium

decreases in velocity.

4. An electron entering from a region of

low potential to a region of high

potential increases in velocity.

Eqn. (2) can be extended to any arbitrary electrostatic field which is non uniform.

Fig. demonstrates the motion of an electron in

a nonuniform electric field represented by

equipotential surfaces separating equipotential

regions of potentials V1 ,V2 ,V3 ,V4 etc. At each

surface electron path bends towards or away from the

higher or lower potential region. It is seen that the

electron motion occurs along a curved path in a

nonuniform electric field.

Fig : Electron Refraction in a Non uniform Electric field

V1

V2 > V1

V3 > V2

V4 > V3


Electron Lens or Electrostatic Lens: An electron lens is an electrical component that focuses an electron beam to a point.

Principle: A stream of electrons bends at each equipotential surface when it travels through a non-

uniform electric field. Thus non-uniform electric field can be used to focus or defocus electron rays.

C.J. Davisson and C.J. Calbick demonstrated in 1931 such optical properties of electrostatic

fields.

Construction / Description:

An electrostatic lens consists of two coaxial short cylindrical metal tubes T1 and T2 of same

size and separated by small distance. They are held at different potentials V1 and V2 respectively

such that V2 > V1. Electric field does not exist inside the cylindrical metal tubes; however a non-

uniform electric field is produced in the gap between the tubes as a result of different potentials

applied to the tubes. Fig. shows a schematic of a simple electrostatic lens wherein electric field lines

and equipotential surfaces are demonstrated. The equipotential surfaces are perpendicular to the

electric field lines everywhere.

Fig : Schematic of Electron Lens Working:

Let us consider a thin bundle of electron rays parallel to the axis and entering the system

from the side of the cylindrical metal tube which is at a lower potential V1.

Electron moving along the axis of the two tubes (shown by position 1) on reaching the

equipotential surface, experience an electric force acting along the axis in forward direction so the

electrons would be accelerated in forward direction towards tube T2 along the axis and would not

deviate from their initial direction of travel.

The electrons traveling at a distance above the axis (shown by position 2) on reaching the

convex equipotential surface in the gap experience electrostatic force F acting at an angle to the

direction of their motion. This force F experienced by the electrons at the convex equipotential

surface can be resolved in to two rectangular components; Fll parallel to the axis and F┴

perpendicular to the axis of the tube.

The action of the Fll component is to accelerate the electrons along the axial direction. These

electrons would be acted upon by F┴ component and get deflected towards the axis and are also

simultaneously accelerated toward tube T2 due to the force component Fll. Similarly electrons


moving below the axis (shown by position 3) are deflected upward towards the axis and are

accelerated in forward direction. Thus all the off axis electron paths around the axis tend to

converge toward the axis.

However on crossing the midplane MM’ of the gap, the converging electron rays encounter

equipotential surface of concave shape. In this region the normal component F┴ is directed away

from the axis and hence the electrons tend to diverge. However the parallel component Fll acts to

accelerate the electrons further in the direction parallel to the axis. Similarly electrons traveling at a

distance below the axis of the tube would be deflected towards the axis in the first half of the gap

and deflected away from the axis in the second half of the gap and the net result is that the field

between T1 and the midplane MM’ converges the electron beam like a convex lens while the field

between the midplane MM’ and T2 diverges the electron beam like a concave lens.

The electrons spends a greater time in the first half of the gap as it travels slower and the

impulse ‘Fll t’ is greater for the convergence interval. In the second half the electrons move faster

and spends less time and the impulse ‘Fll t’ is smaller for the divergence interval. Consequently ,

the electrons rays are less diverged by the second half than converged by the first half of the gap.

Therefore the converging action of the first half of the gap will be stronger than diverging action of

the second half of the gap and the electron ray emerge from T2 will be sufficiently convergent as

shown in fig.

Comparison of electrostatic lens with glass lens

Light rays are bent only at the two boundaries of a lens but electron beam is refracted

continuously through successive equipotential surfaces.

Secondly focal length of glass lens is fixed while focal length of electron lens may be varied

by adjusting the potentials V1 and V2 of the tubes.

Applications: Electron lens forms the most important component of an electron gun used for

producing narrow intense electron beam. Electron lens action is utilized in particle accelerators to

focus charged particles into a narrow beam.

Magnetic Lens :

The principle of magnetic focusing using localized concentrated magnetic field is shown in

Fig. An electron having a component of velocity at right angles to the direction of magnetic flux

lines, experiences a force that causes it to rotate about the axis. This rotational effect , combined

with

P׀

Current Carrying

Coils Magnetic Flux Lines

Image Plane

Object Plane

P

Correct Field Strength

Field Too Weak

Field Too Strong

Fig.: Schematic Magnetic Focusing Lens


the axial velocity, bends the path of the electron through an arc. If the strength of the magnetic field

is properly adjusted, all the electrons leaving a particular point P on the object plane at different

angles with the axis of the system will be deflected so as to return to a common point P׀ on an

image plane or screen. The crossover is thus focused to a point on the fluorescent screen with the

aid of magnetic field. The strength of the magnetic field which can be varied by varying the DC

current through the coil, required to give this focusing action is quit critical. If the magnetic field is

too weak the electron path do not bend sufficiently so as to meet in a common point on the screen

and if the field is too strong they are bent too much as shown in the Fig.

Electron Gun:

An electron gun is a device which produces (focuses and accelerates) a narrow

electron beam of high intensity. It was designed by V. K. Zworykin in 1933.

Principle: The electron gun makes use of the fact that non-uniform electric field causes bending of

electron paths and an appropriate configuration of non-uniform electric field leads to focusing of

electrons.

Construction: The schematic diagram of an electron gun is shown in fig.

Fig : Electron Gun

The electron gun consists of a cathode K, a filament F, a control grid G and three anodes A1-

Preaccelerating Anode, A2-Focussing Anode and A3-Accelerating Anode. The cathode is a short

hollow Nickel cylinder and encloses the filament heater F. The front face of the cathode is coated

with thoriated tungsten or Barium and Strontium oxides. The coating helps thermionic emission of

electrons to occur at moderate temperatures of about 700°C to 900°C. The cathode is surrounded by

the control grid G which also is a hollow metal cylinder with a small central aperture in its front

face to allow electrons to pass through. Three short metal cylinders with central apertures are placed

co-axial beyond the control grid. The entire assembly is kept in an evacuated glass tube. A power

supply provides the necessary voltage to the electrodes.

Working:

When the power is turned on, the filament heater heats up the cathode. At a temperature

characteristic of the cathode material, electrons are emitted from its front surface and they pass

through the control grid. The grid is held at a negative potential with respect to cathode and controls

the number of electrons passing through it. If the grid is held at lesser negative potential, a large


number of electrons pass through it. On the other hand, If the grid is held at higher negative

potential, smaller number of electrons pass through it. Thus grid with a negative potential (0 to

50V) on it acts as a gate and regulates the passage of electrons through it.

The anodes of the electron gun provide an electron lens system for focusing the electron

beam on the screen. The preaccelerating anode A1 and accelerating anode A3 are connected to high

positive potential and are held at same voltage and focusing anode A2 is connected to lower positive

potential. The grid and anode A1 constitutes the first electron lens of the system. The convex

equipotential surfaces bend the electron paths towards the central axis. Consequently all the

electrons passing through the aperture in the control grid converges toward a point P just inside the

first anode. The point P is located on the axis of the gun and known as the cross over point. The

area of the point P would be very small compared to the relatively large cathode surface emitting

the electrons. Therefore electrons emerging from point P can be easily focused to a fine point better

than the electrons emerging than the cathode. Thus the role of first lens is to converge the beam to

the cross over point which then acts as a point source of the electrons for the second lens.

The anodes, A2 and A3 constitute the second lens system which focuses and accelerates the

electron beam to a fine point on the fluorescent screen. The diaphragm D in anode A1 cuts off wide

angle electrons emerging from P. The anode A3 imparts further acceleration to the electrons as they

emerge out of the electron gun. The focus of the beam is adjusted by varying the positive

potential on A2.

Applications:

Electron gun is used in a CRO to display wave shapes, in a TV to display pictures, in an

electron microscope to obtain a magnified image and in EBM and EWM for machine and welding

jobs.

CRT (Cathode Ray Tube) : A Cathode Ray Tube (CRT) is a specially constructed vacuum tube in which an

electron beam controlled by electric or magnetic fields generates a visual display of input

electrical signals on a fluorescent screen. It consists of three important parts,

i) Electron Gun

ii) Deflection System

iii) Fluorescent Screen

Construction/Description:


The CRT resembles a horizontally placed conical flask sealed at its open end. The electron

gun consisting of several electrodes is mounted at one end of the tube as a single unit and electrical

connections are given to them through base pins. The deflection system consists of two pairs of

parallel metal plates mounted in the neck of the tube. They are oriented in such a way that they are

in mutually perpendicular directions to the axis of the CRT. The screen consists of a thin coating of

phosphors deposited on the inner face of the wide end of the glass envelope. The inner surface of

the flare of the envelope is coated with conductive graphite called acquadag. A power supply

provides the required potentials to the various elements of CRT.

Working:

In the CRT, the electron gun generates an electron beam, focuses it and accelerates it

towards a fluorescent screen located at the further end of the tube. The electron beam may be

moved to any spot on the screen with the help of deflection system.

I) Electron Gun:

The indirectly heated cathode K emits a stream of electrons from its coated front face. The

electrons pass through the control grid G held at a negative potential. The effective size of the

aperture in the grid varies depending upon the potential difference between grid and cathode. The

intensity of the glow produced at the screen is determined by the number of electrons striking the

screen. Therefore by varying the negative dc voltage on the grid, the intensity of the luminous spot

on the screen is controlled. The grid bias is usually varied between 0 to -50V. The anodes A1 and

A3 are internally connected and held at a higher positive potential of a few kilovolts and A2 is

maintained at a relatively low positive potential. The anode A1 accelerates the incoming electrons.

The Grid G and anode A1 forms the first lens system which prefocusses the electron beam. The

anode A2 and A3 constitutes the second lens system which focuses the electron beam to a fine point

on the fluorescent screen. The focus of the beam is adjusted by varying the positive potential on A2.

The anode A3 imparts further acceleration to the electrons as they emerge out of the electron gun.

II) Deflection System:

There are two types of deflection system namely electrostatic type and electromagnetic type.

In the electrostatic deflection system, two pairs of metal plates are employed for deflecting the

electron beam. The two plates in each pair are aligned strictly parallel to each other as shown in fig

and the two pairs of plates are mounted at right angles to each other and also at right angles to the

path of electrons.

One pair of plates is arranged horizontally. When a potential difference is applied to the

plates then the uniform electric field is produced in vertical direction. The fields acts perpendicular

to the beam and deflects the beam vertically, so these are called as vertical deflecting plates or Y-

plates.

The second set of plates is oriented vertically and produces the uniform horizontal field,

when a potential difference is applied between them. The field acts normal to the beam and deflects

the beam horizontally so this set of plates is called horizontal deflection plates or X-plates.


When voltages are not applied to X-plates and Y-plates, the electron beam travels along the

CRT axis and strikes the geometrical centre of the viewing screen. When a dc voltage is applied to

Y-plates, the electron beam gets deflected vertically and when a dc voltage is applied to the X-

plates, the electron beam is deflected horizontally as shown in figures. The amount of deflection

depends on the magnitude of the applied voltage. When dc voltages are applied to both the X and Y

plates, the electron beam will be acted upon simultaneously by two forces due to vertical and

horizontal electric fields and gets deflected along the direction of their resultant as shown in fig.

Thus by varying the dc voltages the vertical and horizontal plates, the luminous spot may be moved

to any position in the plane of the screen.

III) Fluorescent Screen:

The interior surface of circular front face of the CRT is coated with a thin translucent layer of

phosphors. The phosphor coating glows at the point where it is struck by high energy electron

beam. At that spot the coating continues to glow for a short period of time even after the electron

beam moves away. So electron beam position can be located with the help of a fluorescent screen.


Aquadag Coating:

Electrons impinging on the screen tend to charge it negatively and repel the electrons arriving

afterwards it will reduce the number of electrons reaching the screen leading to a decrease in the

brightness of the glow. Therefore the electrons are to be conducted away. Similarly the cathode

assumes gradually a positive charge as electrons are emitted from it in large numbers. It again leads

to a reduction in the intensity of the glow on the screen. Therefore the cathode is to be replenished

with electrons. This is accomplished by the Aquadag coating. The inner surface of the flare of the

glass envelope of CRT is coated with conductive graphite coating called Aquadag. It is used to

complete the circuit from screen to cathode. The electrons striking the fluorescent screen not only

causes emission of light, but also produce secondary emission of electrons. The secondary electrons

are attracted by the Aquadag coating which is electrically connected to anode A3. The electrons are

restricted to cathode through the ground.

Application: The electrostatic CRT is used in CRO as a display device and study of wave forms.

________________________________________________________________________________

(CRO) Cathode Ray Oscilloscope:

Cathode Ray Oscilloscope is a very important electronic measuring instrument which

is used to display and measure electrical signals, time intervals and phase shift between two

electrical signals.

Non electrical quantities such as pressure, strain and temperature can be measured by first

converting them into an equivalent voltage using an appropriate transducer. Any CRO basically

consists of the following seven major sections

i) Cathode Ray Tube (CRT)

ii) Time base circuits

iii) Trigger circuits

iv) Vertical Circuits

v) Horizontal Circuits

vi) High Voltage Power Supply

vii) Low Voltage Power Supply


The arrangement of these sections in a CRO is shown in fig in the form of Block diagram.

Fig : Block diagram of CRO

I) CATHODE RAY TUBE (CRT):

A cathode ray tube with electrostatic deflection forms the central part of a CRO. The CRT

generates the electron beam, focuses it and accelerates it towards the fluorescent screen. The rest of

the sections are electronic circuits which cause the desired movement of luminous spot on the

screen. In its action the electron beam is similar to pen. It writes on the fluorescent screen in the

form of bright trace. Writing on paper involves two motions i.e. horizontal motion of the pen

sweeping across the page and other is vertical motion of the pen indicating the message. It is

obvious that the electron beam should be made to move both horizontally and vertically. A

transparent graph called graticule marked in centimeter lines (divisions) both vertically and

horizontally, is attached to the face of the CRT for making measurements.

When a signal is to be displayed, it is applied to the Y-plates of CRO by connecting it to the

Y input of CRO. For example, let the signal be a simple harmonic wave. Because of the application

of the signal to the Y plates, the luminous spot moves up and down on the screen at the same

frequency as that of applied voltage. The successive positions of the spot can be seen as shown in

fig.(a).,when the frequency of the signal is less than about 20 Hz. At higher frequencies the path of

the beam is seen as a vertical line (fig b). This is due to the persistence of vision and the

fluorescence of the coating. The luminous line is called trace. The length of the vertical trace

corresponds to the peak to peak value of applied voltage.


II) TIME BASE CIRCUIT : The faithful display of the signal variation by the electron beam requires the beam to move

horizontally at a uniform rate across the screen, covering equal distances in equal intervals of

time. This condition is satisfied by ramp voltage or sawtooth voltage. The ramp voltage is

generated by Time Base Circuit

The time base circuit consists of time base generator . The time base generator is a

variable frequency oscillator which produces an output voltage of sawtooth shape.

To obtain a visual display of the waveform of applied voltage, it is necessary to apply this

A.C. voltage to one set of the deflection plates say Y-plates and the other time base voltage or ramp

voltage, generated by time base generator, to X-plates. This time base voltage is periodic in nature

and its frequency can be varied. This voltage increases linearly with time and after reaching a

maximum value (Vx)max, it suddenly drops to minimum value (Vx)min. When this voltage is applied

to the horizontal deflection plates, the luminous spot sweeps the face of the screen at a uniform

velocity from left edge to right edge depending on the polarity of the voltage. Because of this reason

ramp voltage is also called as sweep voltage. The deflection of spot becomes maximum when


voltage reaches the value (Vx)max after which the spot suddenly returns to its original position. If the

frequency of the time base voltage is sufficiently high the trace of the spot appears as a straight line.

Due to resemblance of sweep voltage to teeth of saw, it is also called saw-tooth voltage.

Sweep Time or Trace Time (ts): The time taken by the sweep voltage to rise from its

maximum negative voltage to its maximum positive voltage is called sweep time or a trace time tS.

Retrace Time or Flyback Time (tr): The time taken by the sweep voltage to dip from its

maximum positive voltage to its maximum negative voltage is called retrace time or fly back time

tR.

Sweep Period (Tsweep): The sum of sweep time and retrace time constitutes the sweep

period Tsweep. Tsweep = ts + tr ≈ ts

Blanking :

The retrace path , if seen on the screen , gives a bad visual effect. By making the retrace

time equal to zero , the retrace path can be eliminated. The trace during the flyback time or retrace

time can be made invisible by applying a high negative voltage pulse to control grid in the electron

gun which turns off the electron beam momentarily. The process of making retrace path

invisible is known as Blanking of the trace.

Display of the signal shape:

As the signal is applied to the Y-plates and time base voltage (sweep voltage) to the X-

plates, the electron beam is simultaneously subjected to two forces acting in perpendicular

direction. The deflection of the beam at any instant is determined by resultant of these two forces.

Referring to above fig it is seen that at any instant 1, the input signal (signal voltage) is zero

and sweep voltage is (Vx)min, the resultant of the forces due to them acts along the left direction and


the beam is deflected to the left extreme. At the instant 2, the signal amplitude is positive and sweep

voltage is at a lesser negative value. The beam is deflected left upward in the second quadrant of the

screen. At the instant 3, both the input and sweep voltages are zero. The resultant force is zero and

the beam stays at the centre of the screen. At the instant 4, the signal amplitude is negative and the

sweep voltage is positive. The beam is deflected to right down in the fourth quadrant of the screen.

At the instant 5, the signal voltage is zero and sweep voltage is (vx)max, the electron beam is

deflected toward the right extreme along the horizontal direction. Then the beam returns to position

1 and the process repeats. By joining the resultant positions of the spot, it is seen that waveform of

the input voltage is faithfully displayed.

III) TRIGGER CIRCUIT :

To display a stationary wave pattern on the CRO screen, the horizontal deflection should

start at the same point of the input signal in each sweep cycle. When it occurs it is said that the

horizontal sweep voltage is synchronized with input signal. If the sweep and signal voltages are not

synchronized a stand still pattern is not displayed on the screen; the wave pattern moves

continuously to the right or left of the screen.

Thus synchronization is the method of locking the frequency of the time base

generator to the frequency of input signal so that a stationary display of wave pattern is seen

on the CRO screen.

The signal will be properly synchronized only when its frequency equals the sweep

frequency or sub multiple of sweep frequency. That is

fsignal = n fsweep

sweepsignal Tn

T

11

signalsweep nTT


As an example, if the sweep frequency is 50Hz and signal frequency is 50Hz, one wave is

displayed on the screen. On the other hand if the sweep frequency is 50Hz and the signal frequency

is 100Hz, the time period of sweep voltage is 20ms and time period of signal is 10ms. In the sweep

time which actually is horizontal trace length, the signal goes through two complete cycles. As a

result the two cycles of the signal voltage are displayed on the screen.

One of the methods of achieving synchronization is the use of trigger circuit.

The trigger circuit initiates the time base so that the horizontal deflection sweeps in

synchronization with vertical signal. For this a delay line circuit is used which delays the signal

before it reaches to y-deflecting plates. A part of the output obtained from the vertical amplifier is

fed to the trigger generator. Trigger generator is sensitive to the level of the voltage applied at its

input. The circuit monitors the input signal and detects the point when it reaches selected level

while moving towards the selected polarity. When predetermined level is reached the circuit

produces a trigger pulse. This trigger pulse is fed to the time base generator and it acts as command

signal to the time base generator and start one sweep cycle of the time base. The sweep voltage is

not developed in the trigger mode if the input signal is not given. A portion of the trigger pulse is

fed to a second circuit, which produces an unblanking bias voltage to bring the grid of CRT to a

potential, which allows electron beam to appear. Thus a stationary display of the wave is seen only

above a predetermined level of the input voltage. It happens in each cycle. Because the signal

voltage is initiating the sweep cycle, both voltages will be synchronized. By proper adjustment of

controls, the trigger pulse may be made to originate when the input signal is going positive or

negative or at any particular voltage level. However in AUTO trigger mode the trigger circuit will

automatically provide a trigger pulse to the sweep generator even when the input signal is not

applied to it and the horizontal trace is seen even without signal at Y-input.

IV) VERTICAL CIRCUITS:

The vertical circuits mainly consist of an attenuator and a voltage amplifier. The signal is applied at

the Y-input. It goes to the input of the attenuator. The signal amplitude is increased or decreased by

changing the amount of attenuation and then fed to the input of the voltage amplifier so that

adequate deflection is obtained on the screen.

V) HORIZONTAL CIRCUITS:

The sweep generator output cannot directly drive the horizontal plates. Therefore it must be initially

amplified. The horizontal circuits mainly consist of a voltage amplifier. When the sweep selector

switch is in ‘INT’ position, the sweep voltage is applied to the horizontal amplifier. The output of

the amplifier is fed to the X-plates and a linear trace is produced on the CRO screen. When the

sweep selector switch is held in ’EXT’ position the horizontal amplifier input is disconnected from

the internal sweep generator and is instead connected to the horizontal input jack. In this position,

the electron beam remains stationary and produces a luminous spot on the CRO screen.

VI) LOW VOLTAGE POWER SUPPLY: The low voltage power supply powers the electronic circuits such as amplifiers, time base

generator, trigger circuit. It gives an output of the order of few tens to a few hundreds of volts.

VII) HIGH VOLTAGE POWER SUPPLY: The high voltage power supply provides voltages to anodes in the electron gun assembly. It

supplies voltages of the order of 1600V to 2200V.


DELAY LINE:

All electronic circuitry in the CRO causes a certain amount of time delay in the transmission

of signal voltages to the deflection plates. Comparing the vertical and horizontal circuits in the CRO

block diagram, we obtain that a portion of the output signal applied to the vertical CRT plates

triggers the horizontal signal. Signal processing in the horizontal circuit consists of generating

trigger pulse that starts the time base generator (sweep generator) then output of this is given to the

horizontal amplifier and then to the horizontal plates. This whole process takes time. The signal of

the vertical CRT plates must therefore be delayed by the same amount of time so as to reach the

signal at the same instant as that of horizontal one. This is the function of the delay line.

APPLICATIONS of CRO :

The CRO is a versatile electronic instrument and it is used in measuring a verity of electrical

parameters.

a) Study of the Wave Forms: CRO is widely used in maintenance and trouble shooting where the

wave shapes of voltages in different electronic circuits are to be examined. The signal under study

is applied at the Y-input terminal and the sweep voltage is internally applied to X-plates. The size of

the figure displayed on the screen may be adjusted suitably by adjusting the gain control.

b) Measurement of D.C. Voltages: The D.C. voltage under study is applied at Y-input. The trace

gets deflected upward or downward depending upon the polarity of the applied voltage. The

deflection of the spot produce on the screen can be measured and by multiplying it with the

deflection sensitivity (volts/div), the magnitude of unknown voltage can be obtained.

c) Measurement of A.C. Voltages: For this measurement the trace is to be adjusted at the center of

the screen and the A.C. voltage under study is applied at Y-input. The peak to peak distance is

measured and on multiplying it with deflection sensitivity (volts/div), peak to peak value of applied

A.C. voltage can be calculated. The rms value and average value of the voltage are calculated using

the formulae, 2

PPP

VV

, 2

Prms

VV

, Paver VV 636.0

d) Measurement of Current: For this measurement current has to be passed through suitable

known resistor and the potential developed across it can be measured as has been explained above.

The current may then be calculated. However if the cathode ray oscilloscope having magnetic

deflection system, the currents may be measured by passing it through one of the deflection coil.

e) Measurement of Frequency: 1) Calibration Method: A sinusoidal signal whose frequency is to be determined is applied to

Y-input. The time base control is adjusted to obtain 2 or 3 cycles of the signal on the screen. The

horizontal spread of one cycle is noted. By multiplying it with the time base sensitivity (time/div),

the time period of the signal is obtained. The reciprocal of the time period gives the frequency of

the signal.

2) Lissajous Method: Alternatively, the frequency of a test signal can be determined using

Lissajous patterns. When two sine waves oscillating in mutually perpendicular planes are

combined, different types of closed loop patterns are obtained. They are called Lissajous

patterns in honour of the French physicist Lissajous. The signal of unknown frequency is applied to vertical input (Y) and a voltage of known frequency

obtained from standard variable frequency generator is given to horizontal input (X). The


T tt

t

V

Y

Fig. : Sinusoidal voltages VA and Vc

∆t

frequency of this frequency generator can be varied until a suitable stationary Lissajous figure is

obtained. Knowing the frequency from frequency generator and counting the number of tangency

points along horizontal and vertical axes, the unknown frequency can be determined. If fY and fX

are the unknown and known frequencies of the sinusoidal voltage fed to the vertical and horizontal

plates of CRO respectively and nx and ny are number of tangency points along X

and Y-axis respectively then the unknown frequency is calculated from ,

)1(Y

Xxy

n

nff

Where fx is the known frequency . Examples of measurements are :

a ) 1: 1 b) 3:1

f) Measurement of phase difference:

(i) Dual Sweep Method: It requires a dual trace CRO. The phase relationship between two

sinusoidal signals of same frequency may be directly measured by displaying both

waveforms on the CRO screen and determining the delay time between the two waveforms.

The sensitivity and trigger controls of each channel are adjusted for two stationary

sinusoidal signals. The sweep speed is initially adjusted

such that the time period T of the sine wave is measured.

Then the sweep speed is increased and the delay time

Td between the two sine waves is accurately

determined.

The difference is calculated using the relation

360

T

t

(ii) Lissajous Pattern Method: A second method for determining phase difference of two sine

waves of same frequency is to feed one sine wave to vertical input and other sine wave to

horizontal input. The sweep selector switch is kept in EXT

position.

A Lissajous pattern namely ellipse is obtained on the screen.

By measuring the lengths A= 2Y1 and B=2Y2 of the elliptical

pattern the phase shift is calculated.

2

11

1

2

2sin

sin

Y

Y

B

A


Bain Bridge Mass Spectrograph: Def

n:

The instrument developed for the purpose of measuring or separating atomic masses of isotopes of

an element is called mass spectrograph.

Principle:

The Bainbridge mass spectrograph is based on the principle that

1) uniform magnetic field acting perpendicular to the path of ions deflects them along

circular paths.

2) Ions having the same velocity but different masses are deflected along circular paths of

different radii, the radius of each circular path being linearly related to the mass of the

ion describing the circular path.

Construction:

Fig shows the schematic of Bainbridge mass spectrograph. It is essentially a vacuum

chamber placed in uniform magnetic field. A discharge tube produces positive ions of the element

under investigation. In this mass spectrograph a beam of positive ions from a discharge tube is

collimated by two slits S1 and S2. The deflecting plates are placed next to the slits. The electric field

produced by the charged deflection plates and the transverse magnetic field constitutes the velocity

selector. The electric field is in the plane of paper while magnetic field is at right angle to it but in

the plane of paper. Beyond the velocity filter, another slit S3 is arranged to further collimate the

mono-velocity beam. A photographic plate is mounted in the analyzing chamber in line with the slit

S3.

Fig : Bainbridge Mass Spectrograph

Working:

The element under study is taken in the form of a gas and introduced into a discharge tube. When

potential difference of about 20 kv is applied across the electrodes, the gas is ionized and positive

ions are accelerated and conducted into the mass spectrograph through the slits S1 and S2. The ions

in the beam have wide range of differing velocities are allowed to pass through velocity filter. The


positive ions tend to be deflected towards the negative plate by the electric field while towards the

positive plate due to magnetic field. If E is the electric field strength and B is the magnetic field

strength the force experienced by the positive ions due to electric field will be qE and due to

magnetic field is Bqv. Where v is the velocity and q is the charge of the positive ions. If these two

forces are equal then Bqv = qE or B

Ev

Thus positive ions having this velocity will not be deviated while passing through the Velocity

Selector. All other ions will be deflected towards either of the plates and will be removed from the

stream.

Now the ions having the same velocity emerge out from the velocity selector through a slit

S3 and enter in to the analyzing chamber. Here again a magnetic field of strength B is applied

perpendicular to the path of the ion beam and the plane of paper. The transverse magnetic field

acting on the analyzing chamber constitutes the momentum selector and separates the ions of

different masses. Due to this magnetic field the ions emerge along a circular path and fall on the

photographic plate. They produce vertical lines on the photographic plate.

The visual record of ions in the form of vertical lines on the photographic plate is called the mass

spectrum.

Thus all these ions having same value of m

q traverse a semicircular path of radius R given

by )1(

2

qB

ME

qB

MvR

Since B and v are constant,

kMR

MR

Where k = E / qB2 = constant

Thus positive ions having same value of m

qare focused on the same line while the ions

having different values of m

qare focused on different positions of photographic plate. Hence we

get a linear mass scale on the photographic plate and unknown mass can be determined. The mass

spectrum contains lines whose number gives us the number of isotopes in the given element. The

distance of any line from S3 is equal to twice the radius of the corresponding circular path. Thus if x

is the distance

of line from S3 then

2

2

xR

Rx

xM

x

E

qBM

qB

MEx

)2(2

2

2

2

As the relation between M and x is a linear relation, The Mass scale is linear.


The relative masses of two isotopes involve only measurement of x and so can be obtained with

high precision. If M1 and M2 are the masses of two isotopes and if x1 and x2 are the distances from

S3, the line separation is given by,

Linear separation )3()(2

2

1212

qB

MMExxx

Advantages of this spectrograph:

i) Since linear mass scale is obtained , accuracy of measurement is increased.

ii) The sensitivity depends on the strength of the deflecting magnetic field B and the field area

of the chamber.

Particle Accelerator:

Investigation on nuclear reactions requires, charged particles accelerated to very high

energies. The devices that impart high energies to the particles are known as particle accelerator.

There are two different types of particle accelerators which are based on different concepts

1) Linear Accelerators: In linear accelerator, the charged particles are allowed to accelerate through a large

potential difference V maintained between two electrodes in an evacuated tube. Each

particle acquires energy of qV electron volts. However it is practically difficult to produce

and maintain potentials greater than about a few hundred of kilovolts, thus limiting the

maximum energy attainable by a particle to a fraction of MeV.

2) Cyclic Accelerators: In the cyclic accelerator the charged particles are accelerated through steps of

smaller potential difference for a number of times rather than accelerating them in a single

step through a large potential difference. E.g.: Cyclotron

CYCLOTRON

The cyclotron is the first cyclic accelerator developed by E. O. Lawrence and M.S.

Livingston in 1932. In linear accelerators the path of particles are approximately straight lines while

in cyclic accelerators they are circles or spirals.

Principle:

A charged particle moving in a transverse uniform magnetic field describes a circular path. The

frequency of revolution of the particle is determined by

m

qBf

2

The frequency is independent of the particle velocity. Therefore a fast moving particles travels in a

larger circles and slow moving particles travels in smaller circles, requires the same time for

completion of one revolution in a given uniform magnetic field. Hence charged particles having

different initial velocities can be uniformly accelerated to produce high energy particle beam using

a combination of electric and magnetic fields.


Construction: The schematic of cyclotron is shown in fig. A cyclotron consists of two hollow metal dees

formed by cutting a short , cylindrical box along its diameter. The dees are separated by a few

centimeters from each other They are insulated from each other and placed in a vacuum chamber

arranged between the pole pieces of a powerful electromagnet which provides magnetic field

perpendicular to the plane of the dees. A high frequency oscillator is connected to the dees which

produces a r.f. electric field in the gap between dees. A source of charged particles is located at the

centre of the gap between the dees.

Working: The ion source injects a stream of charged particles say protons at the centre of the

cyclotron. The protons are accelerated by the r.f. electric field into the dee which is at negative

potential at that instant. The electric field is concentrated mainly across the gap and is of negligible

strength within the dees. However the transverse uniform magnetic field B acts on the moving

protons and deflects them along a circular path. The protons travel in the hollow region of the dee

and come back into the gap after completion of half revolution. The time taken for half revolution is

)1(2

Bq

mTt

Where T is the time period for the complete circular path in the magnetic field. The protons

will be further accelerated if the dees reverse their polarity at the instant when the proton emerges

into the gap. In such a case, the protons travel further in a semicircular path in the other dee and

reach the gap in the time T/2. If again at the same instant, the dees reverse their polarity, the

protons receive another dose acceleration. The process is repeated over and again many times. As

the velocity increases with each dose of acceleration, the protons describes a spiral path in the dees

as shown in fig. During each revolution, each proton receives energy of 2 qV electron volts and

after about a hundred or more revolutions, the protons acquire energies of the order of several

million electron volts. At the end of the journey, the proton bean is pulled out of the circular path

by a negatively

Charged deflector plate and emerges out of the chamber through a narrow aperture.

Fig.: Schematic of Cyclotron


Condition of resonance or Condition for Progressive Acceleration:

The condition for progressive acceleration of protons in a cyclotron is that the time period

To of r.f. electric field must equal the time period T of revolutions of protons in magnetic field

Time period To of r.f. electric field = Time period T of revolutions of protons in magnetic

field

)2(2

0 Bq

mTT

Or )3(

2

10

m

Bq

T

‘ 0 ’ is called resonance frequency or cyclotron frequency and above eqn is called the cyclotron

resonance condition.

Final Energy:

If the protons undergo N revolutions and receive an energy qV during each half revolution, the

final energy acquired by them is

)1(2 NqVE

If R is the radius of the final orbit is given by

qB

mvR max

Then final kinetic energy of the ion emerging from the cyclotron is given as

)2(22

1

2

1 2222

2

max

m

RBq

m

BqRmmvE

)3(2

m

qE

Thus it is seen from the Eqn.(2) that the maximum energy acquired by the charged particle

in a particular cyclotron is independent of alternating voltage. Because if voltage is small the ion

will describe large number of turns before reaching the periphery of the Dee, but when voltage is

high the number of turns are small. The total energy remains same in both cases provided B and R

are unchanged. Thus the importance of the cyclotron is that with relatively small voltages high

energies can be imparted to the charged particles.

Eqn (2) in MeV,

MeVm

RBqE

222

19 2

1

10602.1

1

MeV

m

RBqE

222121012.3

Role / Function of Electric field:-

• To impart high kinetic energy to the charged particle.

• To focus the charged particles into a sharp beam.

Role / Function of Magnetic field:-

• To deflect the charged particles along circular path.


Limitation of the cyclotron:

1) He kinetic energy acquired by the charged particles in a cyclotron is given by

m

RBqE

2

222

According to this relation, it appears that the maximum energy of the particle beam is

limited by the magnetic field B. Increasing the size of the magnet can increase B. However

there exists an ultimate limit for the size of magnet and electric current to drive the

electromagnet.

2) Electrons cannot be accelerated to high energy in cyclotron. Electron is a light particle. As

velocity of the electron approaches the velocity of light , its mass increases according to

relation:

where m0 is the rest mass of electron and c the

velocity of light.

Correspondingly, the time taken by the electron to cover the semicircular path within a dee

increases and the particle fails to reach the gap at the moment when the electric field reversal

occurs. As a result it gets decelerated. Hence, only heavy particles like protons can be accelerated

by a cyclotron.

The cyclotron principle is incapable for accelerating the electrons to high energies because of the

large relativistic increase of mass at low energies. The electrons even at low energies less than 1

MeV become a relativistic particle. Therefore it falls out of synchronization with the electric field

and electron cannot get accelerated further.

Or

The energies to which particles can be accelerated in a cyclotron are limited by the relativistic

increase of mass with velocity. As the velocity of the particle approaches the velocity of light, its

mass increases according to the relation

2

2

0

1c

v

mm

Where m0 is the rest mass and c the velocity of light.

T0 is the time period of the particle when v<<c.

qB

mT 0

0

2 (Non Relativistic)

T is the time period of the particle when v ≈ c.

qB

mT

2 (Relativistic)

0

2

0

2

000 /2

/2

E

E

cm

mc

m

m

qBm

qBm

T

T

0

0

0 E

Ek

T

T

00

1E

k

T

T

0

0 1E

kTT

2

2

0

1c

v

mm


0

0 12

E

k

qB

mT

As k increases with increasing particle velocity, T>T0 the above inequality shows that the

period of revolution significantly increases with increasing velocity. The result is that the

particle fails to reach the gap at the right moment when the electric field reversal occurs.

For example electrons have rest mass energy

MeVcmE 51.0103101.9 8312

0

It implies that even at low energies less than 1 MeV, the period of revolution T of the electron, is

almost doubled in comparison with that of non-relativistic electrons. As the period of reversal of

accelerating electric field is maintained constant, the electron will not reach the gap at the required

instant. Therefore they drop out of synchronization and cease to be accelerated further.

Hence cyclotron is capable of accelerating only non-relativistic particles with a kinetic

energy much less than their rest energy. Thus cyclotron is suitable only for accelerating relatively

heavy ions.

unit-iii electron optics...applications: electron lens forms the most important component of an...

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