Module 4Ultrasonics and Microwaves(1)(New)

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Module 4. Ultrasonics and Microwaves

Sound is caused by tiny, fast movements called vibrations

(e.g., from vibrating vocal cords to our ears). A sound wave involves the transfer of energy through a m

(solid, liquid, or gas). The human ear is sensitive to sound waves of frequency ranging from 20Hz to 20 kHz. This

range of frequencies is known as audible range as

above this range are called ultrasonic waves, i.e. waves of frequencies beyond upper audible limit (f >20 kHz) are

called ultrasonic waves. Human ear cannot sense ultrasonic sounds but dogs, cats and other animals are endowed

with an ability to hear the high frequency sounds.

and in industry. Bats and Dolphins can generate ultrasonic waves and use the reflections of the waves to find their

way.

Properties of Ultrasonic Waves 1. The speed of propagation of ultrasonic w

2. Since their wavelength is very small, they

3. Good directionality: They can travel over long

able to travel along well-defined straight paths, even in the presence of obstacles

4. High power: They are highly energetic owing to the high frequencies involved.

Production of Ultrasonic Waves

The main techniques used to produce ultrasonic sound waves are:

a. Mechanical Method

b. Magnetostriction Oscillator.

c.. Piezoelectric Oscillator.

A. Mechanical method:This is one of the earliest method of producing Ultrasonic waves up to a frequency of

100 kHz with the help of a Galton’s whistle.

Module 4. Ultrasonics and Microwaves

Sound is caused by tiny, fast movements called vibrations, and it travels in waves from its source to a receiver

(e.g., from vibrating vocal cords to our ears). A sound wave involves the transfer of energy through a m

The human ear is sensitive to sound waves of frequency ranging from 20Hz to 20 kHz. This

s known as audible range as human ear can hear it. The sound waves having frequency

ltrasonic waves, i.e. waves of frequencies beyond upper audible limit (f >20 kHz) are


with an ability to hear the high frequency sounds. However, we can use ultrasound in medicine, in ship navigation,

Bats and Dolphins can generate ultrasonic waves and use the reflections of the waves to find their

Waves

The speed of propagation of ultrasonic waves increases with increase in frequency.

Since their wavelength is very small, they exhibit negligible diffraction.

They can travel over long distances without appreciable loss of energy.

defined straight paths, even in the presence of obstacles.

ighly energetic owing to the high frequencies involved.

Production of Ultrasonic Waves:

used to produce ultrasonic sound waves are:

Magnetostriction Oscillator.

This is one of the earliest method of producing Ultrasonic waves up to a frequency of

kHz with the help of a Galton’s whistle. This method is rarely used due to its limited frequency range.

, and it travels in waves from its source to a receiver

(e.g., from vibrating vocal cords to our ears). A sound wave involves the transfer of energy through a medium

The human ear is sensitive to sound waves of frequency ranging from 20Hz to 20 kHz. This

human ear can hear it. The sound waves having frequency

ltrasonic waves, i.e. waves of frequencies beyond upper audible limit (f >20 kHz) are


we can use ultrasound in medicine, in ship navigation,

Bats and Dolphins can generate ultrasonic waves and use the reflections of the waves to find their

appreciable loss of energy. Ultrasonic waves are

This is one of the earliest method of producing Ultrasonic waves up to a frequency of

limited frequency range.

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B. Magnetostriction Method: This method is based on the phenomenon of Magnetostriction, which was

discovered by Joule in 1874. When a rod of ferromagnetic material such as iron or nickel, is kept in a magnetic

field parallel to its length, the rods suffers a change in its length. This change in length is independent of the

direction of magnetic field and depends only on the magnitude of the field and nature of material. This

phenomenon is known as magneostriction. If the applied magnetic field is alternating, the rod extends and

contract in length alternately. Since the change in length is independent of the direction of applied field, the

frequency of vibration of rod is twice the frequency of field. Ordinary the amplitude of vibration of rod is small.

But, when the frequency of magnetic field is the same as the natural frequency of the rod, the resonance occurs

and the amplitude of vibration is considerably increased. Thus sound waves now emitted from the ends of rod.

If the applied frequency is in the order of ultrasonic frequency, the rod produces ultrasonic waves.

As shown in above figure, two more coils L1 and L 2 are wound over a nickel or iron rod and connected to a

oscillator circuit. When the power is switched on, the circuit L2C sets up an alternating current of frequency

[n=1/(2π√(L2C))] in the collector circuit. This alternating current flows through the coil L2 and produces alternating

magnetic field of frequency n along the length of the rod AB, As a result, the rod starts vibrating due to

magnetostrictive effect. This vibration of rod produces ultrasonic waves from the ends of the rod. When current

in L2 changes, it causes a variation in magnetic flux through coil L1 and induces an e.m.f in the coil L1. This e.m.f.

acts as a positive feedback to the base of transistor to sustain oscillations. The frequency of oscillator can be

tuned by the capacitor C. When the frequency of oscillatory circuit becomes equal to the frequency of vibration

of rod, resonance occurs and the sound waves of maximum amplitude are generated as ultrasonic waves.

For fundamental mode of vibration, the natural frequency of rod of length given by

ρ

γ

ln

2

1=

Where,γ is the Young’s modulus and ρ is density of rod material.

Magnetostriction method is used to produce waves in the frequency range 20 kHz to 100 kHz.

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Piezoelectric Method: This is most modern method for the production of ultrasonic waves of very high and

constant frequencies. The method is based on Piezoelectric effect. When a crystal such as Quartz, Rochelle salt or

tourmaline is subjected to mechanical stress along an axis (mechanical axis), a potential difference appears on the

faces of the crystal along an axis (electrical axis) which is perpendicular to mechanical axis.

Figure 1.Piezoelectric effect Figure2. Circuit for production of US waves using Piezoelectric method

Conversely, by applying potential difference across opposite faces along electrical axis, mechanical stress is

produced on faces along mechanical axis. If the applied voltage is alternating, the crystal plate will alternatively

expand and contract and will thus, be forced to vibrate at the frequency of the applied field. When the frequency

of the applied field coincides with the natural frequencies of the crystal resonance occurs resulting in large

amplitude of vibration. This converse effect is utilized for the production of ultrasonic waves in Piezoelectric

generator.Langevin in 1917 developed this method of production of ultrasonic waves by using converse

Piezoelectric effect.

Figure (ii) represents a suitable schematic arrangement of a simple Piezoelectric generator. The high frequency

alternating voltage is generated by a Hartley oscillator, which consists of a tank circuit (inductor L1 and a variable

capacitor C1in parallel). One end of this circuit is connected to base and other to emitter of the circuit. The

capacity of the variable capacitor C1 is adjusted so that the frequency of the oscillating circuit is tuned to the

natural frequency of the crystal. A slice of a quartz crystal Q is placed between two metal foils. This combination

forms a parallel plate condenser with crystal as dielectric. This is coupled to oscillator through coil L3 of the

transformer. Thus, an alternating potential difference is applied on the opposite faces of the crystal and the

crystal is set into vibrations along its mechanical axis producing longitudinal ultrasonic waves in the surrounding

medium. When the capacity of the variable capacitor is adjusted for obtaining the resonance condition, the

longitudinal vibrations of the crystal are maximum.

The natural frequency of the quartz crystal of thickness t may be expressed as

ρ

Y

tv

2

1=

………(i)

where Y is the Young’s modulus for the particular axis chosen and the density of the material.

The velocity of compresssional waves in the quartz is given by

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.sec/55002654

100.8 10

mY

v ≈×

==ρ

Hence, from equation (i), we have

Hz

ttv

2750

2

5500==

If t is expressed in millimeters, then

( )kHz

ttv

2750

1000/

2750==

For a crystal plate of quartz of thickness 1mm, the natural frequency is

kHzv 2750= or 2.750 MHz

At resonance, the frequency of the tank circuit (L-C) becomes equal to the natural frequency of the crystal plate,

that is,

LCv

π2

1=

Detection of Ultrasonic waves. 1. Piezoelectric method.

Quartz crystal is used for the detection of Ultrasonic waves. One pair of faces of quartz crystal is subjected to

ultrasonics. On the other face, which is perpendicular to the previous one, charges are produced. Obviously charges

are small. These charges are, therefore amplified and then detected by some suitable means.

2. Kundt’s method

A Kundt’s tube can be used to detect ultrasonic waves of relatively large wavelengths as done for the sound waves.

When ultrasonic weaves are passed through the tube, the lycopodium powder sprinkled in the tube collects in the

form of heaps at the nodal points and is blown off at the antinodes. The average distance between the two adjacent

heaps is equal to half the wavelength.

3. Sensitive flame method.

When a narrow sensitive flame is moved in a medium where ultrasonic waves are present, the flame remains

stationary at the antinodes and flickers at the nodes.

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4. Thermal detector method.

In this method a fine platinum wire is moved in the medium of ultrasonic waves. The temperature changes due to

alternate compressions and rarefractions. There is the change in the temperature at the nodes, while at the

antinodes the temperature remains constant. Hence, the resistance of the wire changes at the nodes and remains

constant at the antinodes. This change can be detected by using a sensitive Wheatstone bridge. The bridge will be

balanced at the antinodes.

Application of Ultrasonic Waves

.Industrial Applications of Ultrasonic Waves

Ultrasounds are used extensively in industry. Here are a few examples.

Drilling holes or making cuts of desired shape

You can use a hammer and a steel punch to make holes in metal plates, plastic

sheets or other solid materials. Such holes can also be made using ultrasonic

vibrations produced in a metallic rod, called a horn. The horn acts like a hammer,

hammering the plate about a hundred thousand times per second. The shape of the

hole is the same as that of the tip of the horn. The shape of the tip can be designed

as per the requirement of the application. Ultrasonic cutting and drilling are very

effective for fragile materials like glass, for which ordinary methods might not

succeed.

Ultrasonic cleaning

We normally clean dirty clothes, plates or other large objects by dipping in a detergent solution, and then

rubbing and washing. But for small parts such as those used in watches, electronic components, odd-

shaped parts such as a spiral tube, and parts located in hard-to-reach places, this method is inconvenient

and sometimes impossible. Such objects are placed in a cleaning solution and ultrasonic waves are sent

into the solution. This causes high-frequency vibrations in the solution. This knocks off all dirt and

grease particles from the objects.

Ultrasonic detection of defects in metals

Metallic components are used in buildings, bridges, machines, scientific equipment, and so on. If there

are cracks or holes inside the metal used, the strength of the

structure or component is reduced and it can fail. Such defects

are not visible from the outside. Ultrasonic waves can be used to

detect such defects.

Ultrasonic waves are sent through the metallic object under

study. If there is no crack or cavity in its path, it goes through the

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object. A detector placed on the other side detects the transmitted wave. A defect present in the path of

the wave reflects the wave. Thus, the intensity of the emerging waves falls in the region that is in line

with the defect.When this happens, we know that the object has a defect inside.

Why cannot ordinary sound be used for this application? This is because ordinary sound will bend

considerably round the corners of cracks or cavities, and will emerge on the other side at almost full

intensity.

Medical Applications of Ultrasound

Imaging of organs

Ultrasonic waves have given doctors powerful and safe tools for

imaging human organs. Echocardiography is a technique in which

ultrasonic waves, reflected from various parts of the heart, form an

image of the heart. Ultrasonography is routinely used to show doctors

images of a patient's organs such as the liver, gall bladder, uterus, etc.

It helps doctors detect abnormalities such as stones in the gall

bladder, tumours, etc. It is also used to monitor the growth of a foetus

inside the mother's womb.

These applications are based on the high directionality of ultrasound

waves and their capability to reflect from the boundaries between

different kinds of material. Ultrasonic waves of low intensity are sent to the desired area of the body. The

waves travel along straight lines till they hit an internal structure. A part of the wave is reflected from

here, and the rest is transmitted to the next structure. It is again reflected at the next boundary, and so on.

Waves are sent from different angles, and all the reflected waves are gathered by a receiver. These waves

are then converted into electrical signals that are used to generate images of an organ. These images are

then displayed on a monitor, and if required printed on film.

Ultrasonography is safer than the older X-ray imaging technique. Repeated X-rays can harm tissues,

especially those of a foetus.

Sonar

Sonar stands for sonographic navigation ranging. This is a method for

detecting and finding the distance of objects under water by means of

reflected ultrasonic waves. The device used in this method is also called

sonar.

From the observation centre on board a ship, ultrasonic waves of high

frequencies, say 1,000 kHz, are sent in all directions under the water. These

waves travel in straight lines till they hit an object such as a submarine, a

sunken ship, a school of fish, etc. The waves are then reflected, and are

received back at the observation centre. The direction from which a reflected wave comes to the

observation centre tells the direction in which the object is located. From the time between sending the

ultrasonic wave and receiving its echo, and the speed of sound in sea water, the distance of the object

from the observation centre is calculated. Reflections from various angles can be ultilized to determine

the shape and size of the object.

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Let d = distance between the sonar and an underwater object,

t = time between sending an ultrasonic wave and receiving its echo from the object, and v = speed of

sound in water. The total distance covered by the wave from the sonar to the object and back is 2d. Using

s = ut,

This method of finding distances is also called echo ranging. Marine geologists use this method to

determine the depth of the sea and to locate underwater hills and valleys.

Echolocation

In 1944, Donald R. Griffin coined the term echolocation. Echolocation is the use of echoes of sound produced by

certain animals to detect obstacles and food. Animals that live where lighting is unpredictable use echolocation.

Some of these animals are bats, porpoises, some kinds of whales, several species of birds, and some shrews. The

first step in echolocation is emitting a sound. High-frequency sounds provide better resolution of targets than

lower-frequency sounds. Not every animal uses ultrasonic sounds in echolocation, but they are more effective.

Still, sounds used in echolocation can be produced in the voice box, the mouth, or some other part of the head.

Then, a highly refined auditory system detects the returning echoes (the sounds that bounced of the object). In

order for echolocation to work, the outgoing pulses of sound need to register in the organism's brain, so it can be

compared to its echo. Using echolocation, some animals can effectively catch prey and "see" in the dark.

Non-Destructive testing (NDT): In this type of testing, the specimen under the investigation is not

destroyed and can be used after the test.. The tests are normally performed on finished samples. Ultrasonic NDT

uses high frequency ultrasound waves (20 kHz to 20 MHz). Ultrasonic NDT can be used for flaw detection/

evaluation, dimensional measurements, material characterization, and more.

Pulse-Echo System:

In this method, a sending transducer generates high frequency ultrasonic waves by piezoelectric effect. They

propagate through the material and are reflected back from surfaces or flaws. When there is a discontinuity (such

as a crack) in the wave path, part of the energy will be reflected back from the flaw surface.

The reflected wave signal is transformed into an electrical signal by the transducer and is displayed on a screen.

Signal travel time can be directly related to the distance that the signal travelled. From the signal, information

about the reflector location, size, orientation and other features can sometimes be gained. An oily glycerine–

based structure is used as a couplant that performs two major functions: (1) it removes air between the

transducer and the test specimen. (2) It provides a medium for the transfer of the vibrations.

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Advantages: The specimen may be of any shape and access to only one side of the test piece is required.

Only one coupling point exists, thus minimizing error. The distance of the defects from the probe can be

measured.

Applications of NDT:

1. For routine inspection of aircraft, rail and road vehicles

2. Routine inspection of locomotive axles and wheel pins for fatigue cracks

3. To find weld defects

4. To find radial defects in cylindrical tubes and shafts.

5. To check the bonding defects between the two metals

6. Inspection of moving strip or plate (for laminations) as regards its thickness etc.

Mathematical basics of vector calculus:

Del operator (∇ ):

It is a differential vector operator defined as

z

ky

jx

i∂

∂+

∂

∂+

∂

∂≡∇ ˆˆˆ

It is operated in three ways-

Gradient of a scalar )( V∇

z

Vk

y

Vj

x

ViV

∂

∂+

∂

∂+

∂

∂≡∇ ˆˆˆ

It gives the maximum rate of change of a scalar function.

Divergence of a vector →

∇ A.

z

A

y

A

x

AAdivA zyx

∂

∂+

∂

∂+

∂

∂==∇

→→

.

Divergence of a vector is scalar quantity. Divergence means the spreading or diverging of a quantity from a point.

Laplacian:

)(.2VgraddivVV =∇∇=∇

2

2

2

2

2

22

zyx ∂

∂+

∂

∂+

∂

∂≡∇

Curl of a vector )(→

×∇ A

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Curl of a vector is a vector

zyx AAA

zyx

kji

AAcurl∂

∂

∂

∂

∂

∂=×∇=

→→

ˆˆˆ

=

∂

∂−

∂

∂+

∂

∂−

∂

∂+

∂

∂−

∂

∂xyzxyz A

yA

xkA

xA

zjA

zA

yi ˆˆˆ

It is measure of the tendency of a vector quantity to rotate or twist or curl.

Some identities:

( ) ( )mmm VVVVVV ∇+∇=∇

0. =

×∇∇

→

A

( ) 0=∇×∇ V

→→→

∇+∇=

∇ AVVAAV ...

→→→

×∇+×∇=

×∇ AVAVAV

→→→

∇−

∇∇=×∇×∇ AAA 2.

Maxwell’s Equations: Maxwell's equations describe how electric and magnetic fields are generated

and altered by each other and by charges and currents.

1. Gauss's law describes the relationship between an electric field and the electric charges that cause it.

0

.ε

ρ=∇

→

E (1)

2. Gauss's law for magnetism states that there are no "magnetic charges" (also called magnetic monopoles),

analogous to electric charges. Instead, the magnetic field due to materials is generated by a dipole.

0. =∇→

B (2)

3. Faraday's law describes how a time varying magnetic field creates ("induces") an electric field.

t

BE

∂

∂−=×∇

→→

(3)

4. Ampère's law with Maxwell's correction states that magnetic fields can be generated in two ways: by electrical

current (this was the original "Ampère's law") and by changing electric fields (this was "Maxwell's correction").

t

EJB

∂

∂+=×∇

→→→

000 εµµ (4)

here =→

CJ conduction current density (A/m2)

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→

E =electric field intensity (V/m) →

B =magnetic flux density (Wb/m2)

ρ = volume charge density (C/m3)

Electromagnetic waves: EM waves couple electric and magnetic oscillations that move with speed of light and

exhibit typical wave behaviour. EM wave travel with velocity of light and it is transverse in nature. EM wave

carries both energy and momentum which can be delivered to a surface.

Wave equation in free space:

In free space, →

J =0 and ρ =0.

σ =0, conduction current density CJ→

=0 and volume charge density Vρ =0

So the Maxwell’s equations become

0. =∇→

E (1)

0. =∇→

B (2)

t

BE

∂

∂−=×∇

→→

(3)

t

EB

∂

∂=×∇

→→

00εµ (4)

Taking curl of eqn. 3,

2

2

0000 )(t

E

t

E

tB

tt

BE

∂

∂−=

∂

∂

∂

∂−=×∇

∂

∂−=

∂

∂×−∇=×∇×∇

→→→→

εµεµr

But, →→→→

−∇=∇−

∇∇=×∇×∇ EEEE

22. , since 0. =∇→

E

Hence →

∇− E2=

2

2

00t

E

∂

∂−

→

εµ

or →

∇ E2=

2

2

00t

E

∂

∂→

εµ

Similarly, taking curl of eqn. 4, we get

2

2

00

2

t

HH

∂

∂=∇

→→

µε

Comparing this with wave equation 2

2

2

2 1

t

H

vf

∂

∂=∇

→→

, we get

sec/1031 8

00

2 mvv ×=⇒=µε

Thus electromagnetic waves travel with velocity of light.

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Modes of propagation:

A mode of a beam of electromagnetic radiation is a particular electromagnetic field pattern of radiation

observed in a plane perpendicular (i.e., transverse) to the propagation direction of the beam. Different

modes occur in radio waves and microwaves confined to a waveguide, and also in light waves in an

optical fiber and in a laser's optical resonator. Various modes occur because of boundary conditions

imposed on the wave by the waveguide.

Modes are classified into different types:

1. TE modes: (Transverse Electric) no electric field in the direction of propagation

.i.e. Ez = 0 and Hz ≠0

2. TM modes: (Transverse Magnetic) no magnetic field in the direction of propagation.

i.e. .i.e. Hz = 0 and Ez ≠0.

3. TEM modes: (Transverse ElectroMagnetic) neither electric nor magnetic field in the direction

of propagation.i.e. .i.e. Ez = 0 and Hz =0

4. Hybrid modes: nonzero electric and magnetic fields in the direction of propagation.

.i.e. Ez ≠ 0 and Hz ≠ 0.

Microwaves: Microwaves are radio waves with frequencies betweenb1 GHz and 1000 GHz. Apparatus

and techniques may be described qualitatively as "microwave" when the wavelengths of signals are

roughly the same as the dimensions of the equipment. The prefix "micro-" in "microwave" is not meant

to suggest a wavelength in the micrometer range. It indicates that microwaves are "small" compared to

waves used in typical radio broadcasting, in that they have shorter wavelengths.

Microwaves are the principal means by which data, TV, and telephone communications are transmitted

between ground stations and to and from satellites. Microwaves are also employed in microwave ovens,

food processing and in radar technology. Unlike other radio frequencies these are not reflected and

practically not absorbed by the ionosphere. This makes them suitable for space and satellite

communications.

Gunn diode: A Gunn diode is also known as a transferred electron device (TED). It is somewhat unusual

that it consists only of n-doped semiconductor material, whereas most diodes consist of both P and N-

doped regions. In practice, a Gunn diode has a region of negative differential resistance, which makes it

useful to act as an oscillator. Gallium Arsenide Gunn Diodes are made for frequencies up to 200GHz

whereas Gallium Nitride can reach upto 3THz.

Gunn Diode Construction: Gunn diodes are fabricated from a single piece of n-type semiconductor.

The most common materials are gallium Arsenide, GaAs and Indium Phosphide, InP. The device is

simply an n-type bar with n+ contacts. Within the device there are three main areas, which can be

roughly termed the top, middle and bottom areas. Both top and bottom areas of the device are heavily

doped to give n+ material. This provides the required high conductivity areas that are needed for the

connections to the device.

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Principle: The Gunn diode, also known as Transferred Electron Device (TED), is an active two

terminal solid-state device. It is unique in the sense that its voltage controlled negative differential

resistance is only depending on bulk material properties rather than a junction or an interface. The

fundamental mechanism, the transferred

T.B. Watkins in 1961 [RW61]. In 1962,Hilsum predicted the possibility of transfer

and oscillators [Hil62]. In spite of Ridley

named after an IBM researcher J. B. Gunn observed microwave oscillations in a GaAs sample.

transferred-electron effect arises from the particular form of the band structure of some III/V compound

semiconductors like GaAs, InP and GaN.

valleys(a central valley (1) and a satellite valley (2))

shown above). In the lower valley, electrons exhibit a small effective mass and very high mobility, µ

the higher valley, electrons exhibit a large effective mass and very low mobility, µ

room temperature most electrons reside near the bottom of the lower valley. As a voltage is applied, these

electrons are accelerated and current starts increasing.

energy comparable to energy gap between

valley. At this point the conductivity is given by

The Gunn diode, also known as Transferred Electron Device (TED), is an active two

state device. It is unique in the sense that its voltage controlled negative differential


fundamental mechanism, the transferred-electron effect, was theoretically described by B. K. Ridley and

T.B. Watkins in 1961 [RW61]. In 1962,Hilsum predicted the possibility of transfer

and oscillators [Hil62]. In spite of Ridley-Watkins-Hilsum work, the transferred electroneffect was

d after an IBM researcher J. B. Gunn observed microwave oscillations in a GaAs sample.

electron effect arises from the particular form of the band structure of some III/V compound

semiconductors like GaAs, InP and GaN. In these compounds,the conduction band consists of two

(a central valley (1) and a satellite valley (2)) separated by some energy(0.32 eV in GaAs as

In the lower valley, electrons exhibit a small effective mass and very high mobility, µ

alley, electrons exhibit a large effective mass and very low mobility, µ


electrons are accelerated and current starts increasing. When the applied voltage supplies sufficient

energy comparable to energy gap between the two valleys, the electrons start to move to

valley. At this point the conductivity is given by

The Gunn diode, also known as Transferred Electron Device (TED), is an active two-

state device. It is unique in the sense that its voltage controlled negative differential


, was theoretically described by B. K. Ridley and

T.B. Watkins in 1961 [RW61]. In 1962,Hilsum predicted the possibility of transfer-electron amplifiers

Hilsum work, the transferred electroneffect was

d after an IBM researcher J. B. Gunn observed microwave oscillations in a GaAs sample. The

electron effect arises from the particular form of the band structure of some III/V compound

he conduction band consists of two

separated by some energy(0.32 eV in GaAs as

In the lower valley, electrons exhibit a small effective mass and very high mobility, µ1. In

alley, electrons exhibit a large effective mass and very low mobility, µ2. In equilibrium at


When the applied voltage supplies sufficient

the two valleys, the electrons start to move to the second

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2211 µµσ nn +=

where 2211 ,, µµ nandn are number of electrons per unit volume and mobilities in the two valleys.

Now since the electrons in valley 1 have high mobility than those in valley 2, so the transfer of electrons

from valley 1 to 2 results in a decrease in conductivity i.e. with increase in voltage, current decreases.

Thus a negative resistance region exists. This decrease in current continues till all the electrons are

transferred from valley 1 to 2. After that the current again increases with increase in voltage. This results

in a VI characteristic as shown in figure below. This effect is called transferred electron effect and gives

rise to a negative resistance region which can be utilized for designing microwave oscillators.

Figure: VI characteristic of a Gunn diode showing negative resistance region.

Klystron: A klystron is a specialized vacuum tube (evacuated electron tube). Klystrons are used as

amplifiers at microwave and radio frequencies. Russell and Sigurd Varian of Stanford University

invented klystron.( Klyster is the German word for CLUSTER or BUNCH)

Principle: It works on the principle of velocity modulation of an electron beam by the interaction

with an alternating electric field. The operation of a velocity-modulated tube depends on a change in the

velocity of the electrons passing through its electrostatic field. A change in electron velocity causes the

tube to produce BUNCHES of electrons. These bunches are separated by spaces in which there are

relatively few

electrons. Velocity modulation is then defined as that variation in the velocity of a beam of electrons

caused by the alternate speeding up and slowing down of the electrons in the beam. This variation is

usually caused by a voltage signal applied between the grids through which the beam must pass.

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Construction and Working: Klystrons amplify RF signals by converting the kinetic energy in a

DC electron beam into radio frequency power. A beam of electrons produced by a thermionic cathode (a

heated pellet of low work function material), and accelerated by high-voltage electrodes (typically the

tens of kilovolts). This beam is then passed through an input cavity. RF energy is fed into the input cavity

at or near its natural frequency to produce a voltage which acts on the electron beam. The electric field

causes the electrons to bunch: electrons that pass through during an opposing electric field are accelerated

and later electrons are slowed, causing the previously continuous electron beam to form bunches at the

input frequency. To reinforce the bunching, a klystron may contain additional "buncher" cavities. The

function of the catcher cavity is to absorb energy from the electron beam. The catcher cavity is placed

along the beam at a pointwhere bunches are fully formed. The location is determined by the transit time

of the bunches at the natural resonant frequency of the cavities (the resonant frequency of the catcher

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cavity is the same as the buncher cavity). In the output cavity, the developed RF energy is coupled out.

The spent electron beam, with reduced energy, is captured in a collector.

Module 4Ultrasonics and Microwaves(1)(New)

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Transcript of Module 4Ultrasonics and Microwaves(1)(New)