UNIT-1

MICROWAVE TRANSMISSION
LINES-I
MICROWAVE TRANSMISSION LINE
 MICROWAVES

 Microwaves are EM waves with frequency range from 1GHz

to 1000 GHz
 Microwave frequency range includes the UHF, SHF, &

EHF.
 To solve Microwave network theory problems Maxwell's

equations or distributed circuit theory are applied.

2
MICROWAVE TRANSMISSION LINE
 TRANSMISSION LINES

 TL may be a power line or communication line

 power lines are used for transmission of electric

power with frequency 50 Hz or 60 Hz.

 Communication lines used for signal transmission.

3
MICROWAVE TRANSMISSION LINE
 Types of Transmission Lines @ Low & RF
Frequency are
 Co-axial Cable
 Parallel Wire Cable

 TV twin Lead cable

 Open wire line

 Twisted Pair cable

4
CO-AXIAL CABLE
 Co-axial cable consist of two conductors which are
separated by dielectric material like polythene.

6
CO-AXIAL CABLE

7
PARALLEL WIRE CABLE

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PARALLEL WIRE CABLE
 TV TWIN LEAD CABLE:
 Two conductors which are parallel to each other are
separated by a thin ribbon of plastic.

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PARALLEL WIRE CABLE
 TWISTED PAIR CABLE
 Used at Low frequency telephone application.
 Consist of number of pair of wires running parallel.

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PARALLEL WIRE CABLE
 Open Wire Line
 In this type amount of solid dielectric is not used, but
only few SPACERS are required to separate the
conductors.

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MICROWAVE TRANSMISSION LINE
 Open wire lines are not suitable for microwave
applications due to

1. High radiation loss

2. Skin effect- currents flows over the outer thin
surface of the conductors.

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MICROWAVE TRANSMISSION LINE
 Microwave transmission line are
Multiconductor lines such as co-axial lines, strip lines, micro strip
lines, slot lines, coplanar lines others.
 Transmission mode is TEM

 Single conductor lines such as rectangular or circular waveguides.

 Transmission mode is TE or TM

• Open boundary structured transmission lines

such as dielectric rods
 Transmission mode is Hybrid HE(TE&TM)

13
WAVEGUIDE

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OPTICAL FIBRES

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16
 APPLICATIONS OF MICROWAVE ENGINEERING

• Antenna gain is proportional to the electrical size of the antenna. At higher

frequencies, more antenna gain is therefore possible for a given physical
antenna size, which has important consequences for implementing miniaturized
microwave systems.

• More bandwidth can be realized at higher frequencies. Bandwidth is critically

important because available frequency bands in the electromagnetic spectrum
are being rapidly depleted.

• Microwave signals travel by line of sight are not bent by the ionosphere as
are lower frequency signals and thus satellite and terrestrial communication
links with very high capacities are possible.

• Effective reflection area (radar cross section) of a radar target is proportional

to the target’s electrical size. Thus generally microwave frequencies are
preferred for radar systems.
• Various molecular, atomic, and nuclear resonances occur at microwave
frequencies, creating a variety of unique applications in the areas of basic
science, remote sensing, medical diagnostics and treatment, and heating
methods.

Today, the majority of applications of microwaves are related to radar and

communication systems. Radar systems are used for detecting and locating
targets and for air traffic control systems, missile tracking radars, automobile
collision avoidance systems, weather prediction, motion detectors, and a wide
variety of remote sensing systems.

Microwave communication systems handle a large fraction of the world’s

international and other long haul telephone, data and television transmissions.

Most of the currently developing wireless telecommunications systems, such

as direct broadcast satellite (DBS) television, personal communication
systems (PCSs), wireless local area networks (WLANS), cellular video (CV)
systems, and global positioning satellite (GPS) systems rely heavily on
microwave technology.
WAVEGUIDES
 Rectangular Waveguides
 TEM, TE and TM waves
 Cutoff Frequency
 Wave Propagation
 Wave Velocity,
 Waveguides
Rectangular Circular
 In the previous chapters, a pair of waveguide waveguide
conductors was used to guide
electromagnetic wave propagation.
This propagation was via the
transverse electromagnetic (TEM)
mode, meaning both the electric and
magnetic field components were Optical Fiber
transverse, or perpendicular, to the
direction of propagation. Dielectric Waveguide
 In this chapter we investigate wave-
guiding structures that support
propagation in non-TEM modes,
namely in the transverse electric (TE)
and transverse magnetic (TM) modes.
 In general, the term waveguide refers
to constructs that only support non-
TEM mode propagation. Such
constructs share an important trait:
they are unable to support wave
propagation below a certain
frequency, termed the cutoff
frequency.
 Rectangular Waveguide
• Let us consider a rectangular waveguide Rectangular Waveguide
with interior dimensions are a x b,
• Waveguide can support TE and TM modes.
– In TE modes, the electric field is transverse
to the direction of propagation.
– In TM modes, the magnetic field that is
transverse and an electric field component is
in the propagation direction.
• The order of the mode refers to the field Location of modes
configuration in the guide, and is given by m
and n integer subscripts, TEmn and TMmn.
– The m subscript corresponds to the number
of half-wave variations of the field in the x
direction, and
– The n subscript is the number of half-wave
variations in the y direction.
• A particular mode is only supported above
its cutoff frequency. The cutoff frequency is
given by
2 2 2 2
1 m n c m n
fcmn  
        
2   a  b 2 r  r  a  b
1 1 1 1 c
u   
 o  r  o r  o o r  r r r where c  3 108 m/s
 Rectangular Waveguide
The cutoff frequency is given by
Rectangular Waveguide
For air r  1
and  r  1 2 2
2 2 c m n
c m n fcmn     
fcmn      2  a  b
2 r  r  a  b
where c  3 108 m/s
Location of modes
Table 7.1: Some Standard Rectangular Waveguide
Waveguide a b t fc10 freq range
Designation (in) (in) (in) (GHz) (GHz)
WR975 9.750 4.875 .125 .605 .75 – 1.12
WR650 6.500 3.250 .080 .908 1.12 – 1.70
WR430 4.300 2.150 .080 1.375 1.70 – 2.60
WR284 2.84 1.34 .080 2.08 2.60 – 3.95
WR187 1.872 .872 .064 3.16 3.95 – 5.85
WR137 1.372 .622 .064 4.29 5.85 – 8.20
WR90 .900 .450 .050 6.56 8.2 – 12.4
WR62 .622 .311 .040 9.49 12.4 - 18
To understand the concept of cutoff frequency, you can use the analogy of a
road system with lanes having different speed limits.
 Rectangular Waveguide
• Let us take a look at the field pattern for two Rectangular Waveguide
modes, TE10 and TE20
– In both cases, E only varies in the x direction;
since n = 0, it is constant in the y direction.
– For TE10, the electric field has a half sine
wave pattern, while for TE20 a full sine wave
pattern is observed.
 Rectangular Waveguide
Example
Let us calculate the cutoff frequency for the first four modes of WR284 waveguide.
From Table 7.1 the guide dimensions are a = 2.840 mils and b = 1.340 mils.
Converting to metric units we have a = 7.214 cm and b = 3.404 cm.

2 2
c m n
fcmn      where c  3 108 m/s
2  a  b

c 3x108 m TM11
TE10: fc10   s 100cm  2.08 GHz
2a 2  7.214cm  1m TE10 TE20 TE01 TE11

c 3x108 m 2.08 GHz 4.16 GHz 4.41 GHz 4.87 GHz

TE01: fc 01   s 100cm  4.41 GHz
2b 2  3.404cm  1m
c
TE20: fc 20   4.16 GHz
a
3x108 m 2 2

TE11: fc11  s  1   1  100cm

     4.87 GHz
2  7.214cm   3.404cm  1m
 Rectangular Waveguide
Example

For air c  3 108 m/s

 Rectangular Waveguide - Wave Propagation
We can achieve a qualitative understanding of
wave propagation in waveguide by considering
the wave to be a superposition of a pair of TEM
waves.

Let us consider a TEM wave propagating in the z

direction. Figure shows the wave fronts; bold
lines indicating constant phase at the maximum
value of the field (+Eo), and lighter lines
indicating constant phase at the minimum value
(-Eo).

The waves propagate at a velocity uu, where the

u subscript indicates media unbounded by guide
walls. In air, uu = c.
 Rectangular Waveguide - Wave Propagation

Now consider a pair of identical TEM waves,

labeled as u+ and u- in Figure (a). The u+ wave is
propagating at an angle + to the z axis, while the
u- wave propagates at an angle –.

These waves are combined in Figure (b). Notice

that horizontal lines can be drawn on the
superposed waves that correspond to zero field.
Along these lines the u+ wave is always 180 out of
phase with the u- wave.
 Rectangular Waveguide - Wave Propagation
Since we know E = 0 on a perfect conductor, we can replace
the horizontal lines of zero field with perfect conducting
walls. Now, u+ and u- are reflected off the walls as they
propagate along the guide. (a)

The distance separating adjacent zero-field lines in Figure

(b), or separating the conducting walls in Figure (a), is given
as the dimension a in Figure (b). a

The distance a is determined by the angle  and by the

distance between wavefront peaks, or the wavelength . For (b)
a given wave velocity uu, the frequency is f = uu/.

If we fix the wall separation at a, and change the frequency,

we must then also change the angle  if we are to maintain
a propagating wave. Figure (b) shows wave fronts for the
u+ wave.

The edge of a +Eo wave front (point A) will line up with the
edge of a –Eo front (point B), and the two fronts must be /2
apart for the m = 1 mode.
 Rectangular Waveguide - Wave Propagation

For any value of m, we can write by simple trigonometry

m 2 2a uu
sin    sin  
m f
a
The waveguide can support propagation as long as the
wavelength is smaller than a critical value, c, that occurs at  =
90, or
2a uu
c  
m fc

Where fc is the cutoff frequency for the propagating mode.

We can relate the angle  to the operating frequency and

the cutoff frequency by

 f
sin    c
c f
 Rectangular Waveguide - Wave Propagation
The time tAC it takes for the wavefront to move from A
to C (a distance lAC) is
Distance from A to C l AC m 2
t AC   
Wavefront Velocity uu uu

A constant phase point moves along the wall from A to D. Calling

this phase velocity up, and given the distance lAD is
m 2
l AD 
cos 

Then the time tAD to travel from A to D is

l m 2
t AD  AD 
up cos  u p

Since the times tAD and tAC must be equal, we have

uu
up 
cos 
 Rectangular Waveguide - Wave Propagation
The Wave velocity is given by Phase velocity
1 1 1 1 c up Wave velocity
uu    
 o  r  o r  o o r  r r  r Group velocity
where c  3 108 m/s
The Phase velocity is given by
uu
uu up 
up 
 
2
fc
cos  1 Analogy!
using f
Beach
Point of contact
cos   cos   1  sin   1   fc f 
2 2 2

u p Phase velocity
Wave velocity
The Group velocity is given by uu

uG  uu cos 
uG Group velocity

 
2
fc
uG  uu 1 
f
uu
Ocean
 Rectangular Waveguide - Wave Propagation
The phase constant is given by

 
2
fc
  u 1 
f

The guide wavelength is given by

u

 
2
fc
1
f

The ratio of the transverse electric field to the transverse magnetic field for a
propagating mode at a particular frequency is the waveguide impedance.

For a TE mode, the wave impedance is For a TM mode, the wave impedance is
u
TE
Z mn  , 2
f 
2
 f 
1  c 
TM
Z mn  u 1   c  .
 f   f 
 Rectangular Waveguide
Example
 Rectangular Waveguide
Example

Let’s determine the TE mode impedance looking into a 20 cm long section of shorted
WR90 waveguide operating at 10 GHz.

From the Waveguide Table 7.1, a = 0.9 inch (or) 2.286 cm and b = 0.450 inch (or) 1.143
cm.
2
c m n
2
Mode Cutoff Frequency Mode Cutoff Frequency
fcmn     
2  a  b TE10 6.56 GHz TE10 6.56 GHz
TE01 13.12 GHz Rearrange TE01 13.12 GHz
TE11 14.67 GHz TE20 13.13 GHz

TE20 13.13 GHz TE11 14.67 GHz

TE02 26.25 GHz TE02 26.25 GHz

TM11
TE10 TE01 TE20 TE11 TE02

6.56 GHz 13.12 GHz 14.67 GHz 26.25 GHz

13.13 GHz

At 10 GHz, only the TE10 mode is supported!

 Rectangular Waveguide
Example

The impedance looking into a short circuit

is given by

Z IN  jZ10
TE
tan   l 
 rad 
Z IN  j  500  tan 158  0.2m 
 m 
Z IN  j  500  tan  31.6   j100

The TE10 mode impedance The TE10 mode propagation constant is

given by

120  2 2
Z TE
  500. f  2 f f 
10
2   u 1  c   1  c 
 6.56GHz 
1-   f  c  f 

 10GHz  
2 10 x109 Hz  2
 6.56GHz  rad
 1    158
3 x108 m  10GHz  m
s
 UNIT-II
MICROWAVE TRANSMISSION LINES-II

• POWER TRANSMISSION AND POWER LOSSES

• IMPOSSIBILITY OF TEM MODE.
• MICROSTRIP LINES
• CAVITY RESONATORS
 POWER TRANSMISSION

• To determine power flow in the waveguide, we first find the average

Poynting vector
 IMPOSSIBILITY OF TEM MODE

• since tem wave do not have axial component of either e or h, it cannot

propagate within a single conductor waveguide. consider a tem wave to
exist within a hollow guide.
 MICROSTRIP LINES

• Microstrip is a type of electrical transmission line which can be fabricated

using printed circuit board technology, and is used to convey microwave-
frequency signals. It consists of a conducting strip separated from a ground
plane by a dielectric layer known as the substrate.

•
 Contd.
• Microstrip transmission lines consist of a conductive strip of width "W"
and thickness "t" and a wider ground plane, separated by a dielectric layer
of thickness "H" as shown in the above figure .

• Microstrip is by far the most popular microwave transmission line,

especially for microwave integrated circuits and MMICs.
 CHARACTERISTIC IMPEDANCE(ZO) RELATIONS

• Characteristic impedance Z0 of microstrip is also a function of the ratio of

the height to the width W/H (and ratio of width to height H/W) of the
transmission line, and also has separate solutions depending on the value of
W/H. According to Bahl and Trivedi, the characteristic impedance Z0 of
microstrip is calculated by:

•
 EFFECTIVE DIELECTRIC CONSTANT

• Because part of the fields from the microstrip conductor exist in air, the
effective dielectric constant "Keff" is somewhat less than the substrate's
dielectric constant(also known as the relative permittivity). the "relative
dielectric constant" is an oxymoron only used my microwave morons
According to Bahl and Trivedi, the effective dielectric constant εeff of
microstrip is calculated by
 LOSSES

• conductor loss , radiation loss and dielectric heating loss

• CONDUCTOR LOSS
• To reduce conductor loss simply shorten the transmission line or use a
larger diameter wire. Conductor loss depends somewhat on frequency
because of a phenomenon called the skin effect.

• The skin effect is the tendency of an alternating electric current (AC) to

distribute itself within a conductor so that the current density near the
surface of the conductor is greater than that at its core. That is, the electric
current tends to flow of the conductor
 RADIATION LOSS

• If the separation between conductors in a metallic transmission line is

appreciable fraction of wavelength. The electrostatic and electromagnetic
fields that surround the conductor. Cause the line to act as if it were an
antenna and transfer energy to any nearby conductive material. The energy
radiated is called radiation loss and depends on dielectric material
conductor spacing and length of transmission line. It reduces by properly
shielding the cable.
• e.g. STP and coaxial has less radiation loss It is also directly proportional to
the frequency
 DIELECTRIC HEATING LOSS

• A difference of potential Between two conductors of a metallic

transmission line causes dielectric heating. Heat is form of energy and must
be taken from the energy propagating down the line. For air dielectric
transmission lines the heating is negligible. For solid core transmission
lines dielectric heating loss increases with frequency.
 CAVITY RESONATORS

• A cavity resonator is a hollow closed conductor such as a metal box or a

cavity within a metal block, containing electromagnetic waves (radio
waves) reflecting back and forth between the cavity's walls.

• Cavity Resonators are two types

Rectangular and cylindrical .

• DOMINANT MODE
the mode with the lowest cutoff frequency
the Dominant Mode is the TE101
THANK YOU
 UNIT-III
WAVEGUIDE COMPONENTS AND APPLICATIONS - I

• COUPLING MECHANISMS
• WAVEGUIDE DISCONTINUITIES
• WAVEGUIDE ATTENUATORS
• PHASE SHIFTERS WAVEGUIDE
• WAVEGUIDE MULTIPORT JUNCTIONS
• DIRECTIONAL COUPLERS
 COUPLING MECHANISMS

• LOOP COUPLING
 Contd.
• For the most efficient coupling to the waveguide, the loop is inserted at
one of several points where the
magnetic field will be of greatest strength
• When less efficient coupling is desired, you can
rotate or move the loop until it encircles a smaller
number of H lines. When the diameter of the loop
is increased, its power-handling capability also increases.
The bandwidth can be increased by increasing the size of the wire used
to make the loop
• When a loop is introduced into a waveguide in
which an H field is present, a current is induced in the loop.
When this condition exists, energy is removed from the waveguid
PROBE COUPLING
 WAVEGUIDE DISCONTINUITIES

• An iris is a thin metal plate across the waveguide with one or more holes in it.
It is used to couple together two lengths of waveguide and is a means of
introducing a discontinuity. Some of the possible geometries of irises are
shown in figure
• An iris which reduces the width of a rectangular waveguide has an equivalent
circuit of a shunt inductance, whereas one which restricts the height is
equivalent to a shunt capacitance.
• An iris which restricts both directions is equivalent to a parallel LC resonant
circuit A series LC circuit can be formed by spacing the conducting portion of
the iris away from the walls of the waveguide.
• Narrowband filters frequently use irises with small holes. These are always
inductive regardless of the shape of the hole or its position on the iris.
Circular holes are simple to machine, but elongated holes, or holes in the
shape of a cross, are advantageous in allowing the selection of a particular
mode of coupling.
WAVEGUIDE DISCONTINUITIES
 Contd.

• Tuning screws and posts

• Tuning screws are screws inserted into resonant cavities which can be
adjusted externally to the waveguide. They provide fine tuning of the
resonant frequency by inserting more, or less thread into the waveguide
• For screws inserted only a small distance, the equivalent circuit is a shunt
capacitor.
• Increasing in value as the screw is inserted. However, when the screw has
been inserted a distance λ/4 it resonates equivalent to a series LC circuit.
• it further it causes the impedance to change from capacitive to inductive,
that is, the arithmetic sign changes
 WAVEGUIDE BENDS

• Types of waveguide bend

• There are several ways in which waveguide bends can be accomplished.
They may be used according to the applications and the requirements.
• Waveguide E bend
• Waveguide H bend
• Waveguide sharp E bend

• Waveguide sharp H bend

• WAVEGUIDE E BEND

• This form of waveguide bend is called an E bend because it distorts or

changes the electric field to enable the waveguide to be bent in the required
direction.
Contd .
 WAVEGUIDE H BEND

• This form of waveguide bend is very similar to the E bend, except that it
distorts the H or magnetic field. It creates the bend around the thinner side
of the waveguide.
 WAVEGUIDE SHARP E BEND

• In some circumstances a much shorter or sharper bend may be required.

This can be accomplished in a slightly different manner. The techniques is
to use a 45° bend in the waveguide. Effectively the signal is reflected, and
using a 45° surface the reflections occur in such a way that the fields are
left undisturbed, although the phase is inverted and in some applications
this may need accounting for or correcting.

•
 WAVEGUIDE SHARP H BEND

• This for of waveguide bend is the same as the sharp E bend, except that the
waveguide bend affects the H field rather than the E field.

•
 WAVEGUIDE TWISTS

• There are also instances where the waveguide may require twisting. This
too, can be accomplished. A gradual twist in the waveguide is used to turn
the polarisation of the waveguide and hence the waveform.
• In order to prevent undue distortion on the waveform a 90° twist should be
undertaken over a distance greater than two wavelengths of the frequency
in use. If a complete inversion is required, e.g. for phasing requirements,
the overall inversion or 180° twist should be undertaken over a four
wavelength distance.
• Waveguide bends and waveguide twists are very useful items to have when
building a waveguide system. Using waveguide E bends and waveguide H
bends and their srap bend counterparts allows the waveguide to be turned
through the required angle to meet the mechanical constraints of the overall
waveguide system. Waveguide twists are also useful in many applications
to ensure the polarisation is correct
 WAVEGUIDE ATTENUATORS

• A device, such as an interposed energy-absorbing plate, that is used for

signal attenuation in a waveguide.
• There are two types
Fixed and variable attenuators
 ROTARY VANE TYPES

•
 WAVEGUIDE PHASE SHIFTERS

• There two types of phase shifters

Dielectric and Rotary Vane types

• Dielectric shifter is movable by means of a micrometer inside the

waveguide. These Phase Shifters provides a phase-shift of around 180°.
 WAVEGUIDE MULTIPORT JUNCTIONS

• Different types of junctions affect the energy in different ways. The “T–
Junction” is the most simple of the commonly used waveguide junctions.
T–junctions are divided into two basic types, the E–TYPE and the H–
TYPE.
• H-TYPE T-JUNCTION
An H-type T-junction is illustrated in the beside figure. It is called an H-
type T-junction because the long axis of the “B” arm is parallel to the plane
of the magnetic lines of force in the waveguide. The E-field is fed into arm
A and in-phase outputs are obtained from the B and C arms. The reverse is
also true.
 Contd.

•
 E-TYPE T-JUNCTION

• This junction is called an E- type T junction because the junction arm

extends from the main waveguide in the same direction as the E-field in the
waveguide. The outputs will be 180° out of phase with each other .
 MAGIC-T-HYBRID JUNCTION

• A simplified version of the magic-T-hybrid junction is shown in the

figure. The magic-T junction can be described as a dual
electromagnetic plane type of T-junction. It is a combination of the
H-type and E-type T.junction therefore. The most common
applications of this type of junction are for example as the mixer
section for microwave radar receivers or as a part of a measurement
system.
• If a signal is fed into the E-plane arm of the magic-T, it will divide
into two out-of-phase components (arm B and C). The signal
entering the E-arm will not enter the H-plane arm because of the
zero potential existing at the entrance of the H-plane arm. The
potential must be zero at this point to satisfy the boundary
conditions of the E-plane arm.
• Normally a magic-T needs an impedance matching (shown in the
figure as matching screws).
Contd.
Thank you
 UNIT IV
WAVEGUIDE COMPONENTS AND APPLICATIONS - II

• FERRITES
• FERRITE COMPONENTS
• SCATTERING MATRIX
• S MATRIX CALCULATION

1
 ELECTRONIC AND PHOTONIC MATERIALS
• Introduction
Magnetic materials
• Magnetic materials are the materials, which get magnetized in a
magnetic field. These materials are having the ability to create a
self magnetic field in the presence of external magnetic field.
• Important magnetic materials
• diamagnetic,
• paramagnetic,
• ferromagnetic,
• antiferromagnetic
• and ferrimagnetic materials.

2
 Angular momentum of an atom
1. Orbital angular momentum of the electrons
This corresponds to permanent orbital angular magnetic dipole
moments.
2. Electron spin angular momentum
This corresponds to electron spin magnetic moments.
3. Nuclear spin angular momentum
This corresponds to nuclear magnetic moments.

Basic Definitions
Magnetic dipole
Any two opposite magnetic poles separated by a distance ‘d’
constitute a magnetic dipole

3
Magnetic dipole moment
When an electric current of ‘i’ amperes flows through a circular
wire of 1 turn having an area of cross section ‘a’ m2, then it is said to
have a magnetic moment of,

Fig. Magnetic moment

m = i  a Unit: ampere (metre)2

4
 Magnetic Flux
Total number of magnetic lines of force passing perpendicular through a
given area. Unit: weber.
Magnetic flux density or Magnetic Induction (B)
Number of magnetic lines of force passing through an unit area of
cross section. It is given by,

Magnetic field strength or Magnetic field

intensity (H)
Magnetic field intensity or magnetic field strength
at any point in a magnetic field is equal to  1 
 

times the force acting on a unit north pole placed at the

point.

5
Magnetization or Intensity of Magnetization (M)

Intensity of magnetization (M) is defined as the magnetic moment

per unit volume. It is expressed in ampere/metre.

Magnetic susceptibility

The ratio of magnetization produced in a sample to the magnetic field

intensity. i.e. magnetization per unit field intensity.

Magnetic permeability

It is defined as the ratio of magnetic flux density in the sample to the applied
magnetic field intensity.

6
Relative permeability
It is the ratio of permeability of the medium to the permeability of
free space.

i.e.  r = 0

Relation between r and 

When a magnetic material is kept in a magnetic field (H), then

two types of lines of induction passes through the material.

One is due to the magnetic field (H) and the other one is due
to self-magnetization of the material itself.
total flux density (B) in a solid can be given as,
B = 0 (H+M)
(1)
7
Classification of Magnetic Materials

Those not having any permanent magnetic moment – diamagnetic

materials, and Those having permanent magnetic moment, para, ferro,
antiferro and ferrimagnetic materials.

Ferrimagnetic Materials (Ferrites)

Ferrimagnetic materials are also called as Ferrites. Ferrites are the
modified structures of iron with no carbon and are composed of two or
more sets of different transition metals. These materials have anti parallel
magnetic moments of different magnitudes, giving rise to large magnetic
moment in the presence of external magnetic field.

Properties
The susceptibility () is very large and positive. It is represented by,
 = C / (T), when T > TN
When T<TN, they behave as ferrimagnetic materials.

8
Mechanically, they have pure iron character. They have low tensile strength and
are brittle and soft.
In these, all valence electrons are tied up by ironic bonding and they are bad
conductors with high resistivity of 1011  m.
Ferrites are manufactured by powder metallurgical process by mixing,
compacting and then sintering at high temperatures followed by age hardening
in magnetic fields.
They are soft magnetic materials and so they have low eddy current losses and
hysteresis losses.

Structure of Ferrites
The general chemical formula of a ferrite molecule is M2+Fe23+O42-, where
M2+ represents a divalent metal ion such as Zn2+, Fe2+, Mg2+, Mn2+, Cd2+ etc.,
Ferrites crystallize in the form of a cubic structure. Each corner of a ferrite
unit cell consists of a ferrite molecule

9
• Therefore, in a ferrite unit cell there are eight molecules. Therefore in a ferrite
unit cell, there are eight divalent metal ions, 16 ferric ions and 32 Oxygen ions.

• If only the oxygen ions in ferrite crystal are considered, it is found that
they constitute a close packed face centered cubic structure.

• In these arrangement it is found that for every four O2 ions there are 2
octahedral sites (surrounded by 6 O2 ions) and one tetrahedral site (surrounded
by4 O2 ions).

 The metal ions are distributed over these tetrahedral sites (A sites) and
octahedral sites (B sites). Thus in ferrites the number of octahedral sites is twice
the number of tetrahedral sites.

 Normally there are two types of structures in ferrites.

Regular spinel and

Inverse spinel
10
i) Regular spinel structure
In this type, each divalent metal ion occupies 1 tetrahedral site and each trivalent
metal ion occupies 1 octahedral site. Totally in an unit cell, there will be 8 tetrahedral
(8 A) sites and 16 octahedral (16B) sites.
Hence, the sites A and B combined to form a regular spinel ferrite structures
as shown in Fig.
The schematic representation of zinc ferrite molecule as shown in Fig.

Fig. Regular spinel structure

11
 Inverse spinel structure

In this type half of the B sites (8sites) are occupied by divalent

metal ions and the remaining half of the B sites (8 sites) and
all the A sites are occupied by the trivalent metal ions, as
shown in Fig.

The schematic representation of a ferrous ferrite molecule is shown in Fig.

12
 The anti parallel alignment of a ferrous ferrite molecule in inverse spinel
structure is explained by the calculation of its magnetic moment. In a ferrous
ferrite molecule, there are one ferrous ion and 2 ferric ions.

When the Fe atom is ionized to form the Fe2+ ions, there are 4 unpaired
3d electrons left after the loss of two 4s electrons.

When the Fe atom is ionized to form the Fe3+ ions, there are 5 unpaired 3d
electrons left after the loss of two 4s electrons and one 3d electron. It is shown in
the following electronic configuration

Table 3d electronic configuration of Fe2+ and Fe3+

No. of 3d electronic Ionic magnetic
Ion
electrons configuration moment
    
Fe 2+ 24  4µB

Fe 3+ 23      5µB

13
 Since each unpaired 3d electron has a magnetic moment of one B, the Fe 2+
ion has a moment of 4B, and Fe3+ ion has a moment of 5B.
 If parallel alignments of ferrous and ferric ions are considered, the total dipole
moment = 4 + (25)=14 B. This observed value doesn’t coincide with the
experimental value.
 Consider anti parallel alignment of ferrous and ferric ions in inverse spinel
structure.
 If one ferrous ion and one ferric ion are in one direction and another ferric ion is
in opposite direction then the dipole moment is, 51) + 4  (51) = 4B
 This observed value is in good agreement with the experimental value and hence
this confirms the anti parallel alignment of dipoles in ferrites.

Applications of Ferrites
 Ferrite is used in radio receivers to increase the sensitivity and
selectivity of the receiver.
 Ferrites are used as cores in audio and TV transformers.

14
 Ferrites are used in digital computers and data processing circuits.
Ferrites are used to produce low frequency ultra sonic waves by
magnetostriction principle.

Ferrites are widely used in non-reciprocal microwave devices. Examples for

non-reciprocal microwave devices are Gyrator, Isolator and Circulator.

Ferrites are also used in power limiting and harmonic gyration devices.

Ferrites can also be used in the design of ferromagnetic amplifiers of

microwave signals.

Ferrite core can be used as a bitable element.

The rectangular shape ferrite cores can be used as a magnetic shift register.

Hard ferrites are used to make permanent magnets.

The permanent magnets (hard ferrites) are used in instruments like

galvanometers, ammeter, voltmeter, flex meters, speedometers, wattmeter,
compasses and recorders.
15
 FERRITE COMPONENTS

• GYRATOR, ISOLATOR AND CIRCULATOR

• GYRATOR

16
UNIT-5
MICROWAVE TUBES-I
TOPICS
 Klystron Oscillator
 Reflex Klystron
 Traveling Wave Tube
 Biological effect of microwaves

2
KLYSTRON OSCILLATOR
A klystron is a vacuum tube that can be
used either as a generator or as an
amplifier of power, at microwave
frequencies.

3
TWO CAVITY KLYSTRON AMPLIFIER

4
APPLICATIONS
 As power output tubes
1. in UHF TV transmitters
2. in troposphere scatter transmitters
3. satellite communication ground station
4. radar transmitters
 As power oscillator (5 – 50 GHz), if
used as a klystron oscillator

5
REFLEX KLYSTRONS

 The reflex klystron has been the most used source

of microwave power in laboratory applications.

6
 CONSTRUCTION

 A reflex klystron consists of an electron gun, a cavity

with a pair of grids and a repeller plate as shown in the
above diagram.
 In this klystron, a single pair of grids does the functions
of both the buncher and the catcher grids.
 The main difference between two cavity reflex klystron
amplifier and reflex klystron is that the output cavity is
omitted in reflex klystron and the repeller or reflector
electrode, placed a very short distance from the single
cavity, replaces the collector electrode.

7
WORKING
 The cathode emits electrons which are accelerated
forward by an accelerating grid with a positive voltage
on it and focused into a narrow beam.
 The electrons pass through the cavity and undergo
velocity modulation, which produces electron bunching
and the beam is repelled back by a repeller plate kept at
a negative potential with respect to the cathode.
 On return, the electron beam once again enters the
same grids which act as a buncher, therby the same pair
of grids acts simultaneously as a buncher for the
forward moving electron and as a catcher for the
returning beam.

8
REFLEX KLYSTRON
OSCILLATOR

9
 WORKING
 The feedback necessary for electrical oscillations is
developed by reflecting the electron beam, the velocity
modulated electron beam does not actually reach the
repeller plate, but is repelled back by the negative
voltage.
 The point at which the electron beam is turned back can
be varied by adjusting the repeller voltage.
 Thus the repeller voltage is so adjusted that complete
bunching of the electrons takes place at the catcher
grids, the distance between the repeller and the cavity is
chosen such that the repeller electron bunches will reach
the cavity at proper time to be in synchronization.
 Due to this, they deliver energy to the cavity, the result
is the oscillation at the cavity producing RF frequency.

10
PERFORMANCE CHARACTERISTICS
1. Frequency: 4 – 200 GHz
2. Power: 1 mW – 2.5 W
3. Theoretical efficiency : 22.78 %
4. Practical efficiency : 10 % - 20 %
5. Tuning range : 5 GHz at 2 W – 30
GHz at 10 mW

11
APPLICATIONS
 The reflex klystrons are used in

1. Radar receivers
2. Local oscillator in microwave receivers
3. Signal source in microwave generator
of variable frequency
4. Portable microwave links
5. Pump oscillator in parametric
amplifier

12
TRAVELING WAVE TUBE

Traveling Wave Tube (TWT) is the most

versatile microwave RF power amplifiers.

The main virtue of the TWT is its

extremely
13
wide band width of operation.
BASIC STRUCTURE OF A
TRAVELING WAVE TUBE (TWT)

14
BASIC STRUCTURE
 The basic structure of a TWT consists of a cathode and
filament heater plus an anode that is biased positively
to accelerate the electron beam forward and to focus it
into a narrow beam.
 The electrons are attracted by a positive plate called the
collector, which has given a high dc voltage.
 The length of the tube is usually many wavelengths at
the operating frequency.
 Surrounding the tube are either permanent magnets or
electromagnets that keep the electrons tightly focused
into a narrow beam.

15
FEATURES
 The unique feature of the TWT is a helix or coil that
surrounds the length of the tube and the electron
beam passes through the centre or axis of the helix.
 The microwave signal to be amplified is applied to the
end of the helix near the cathode and the output is
taken from the end of the helix near the collector.
 The purpose of the helix is to provide path for RF
signal.
 The propagation of the RF signal along the helix is
made approximately equal to the velocity of the
electron beam from the cathode to the collector

16
FUNCTIONING
 The passage of the microwave signal down the
helix produces electric and magnetic fields that
will interact with the electron beam.
 The electromagnetic field produced by the helix
causes the electrons to be speeded up and
slowed down, this produces velocity modulation
of the beam which produces density
modulation.
 Density modulation causes bunches of electrons
to group together one wavelength apart and.
these bunch of electrons travel down the length
of the tube toward the collector.

17
 FUNCTIONING
 The electron bunches induce voltages into the helix
which reinforce the voltage already present there.
Due to that the strength of the electromagnetic field
on the helix increases as the wave travels down the
tube towards the collector.
 At the end of the helix, the signal is considerably
amplified. Coaxial cable or waveguide structures
are used to extract the energy from the helix.

18
ADVANTAGES

1. TWT has extremely wide bandwidth. Hence,

it can be made to amplify signals from UHF
to hundreds of gigahertz.
2. Most of the TWT’s have a frequency range of
approximately 2:1 in the desired segment of
the microwave region to be amplified.
3. The TWT’s can be used in both continuous
and pulsed modes of operation with power
levels up to several thousands watts.
19
PERFORMANCE CHARACTERISTICS
1. Frequency of operation : 0.5 GHz – 95 GHz
2. Power outputs:
5 mW (10 – 40 GHz – low power TWT)
250 kW (CW) at 3 GHz (high power TWT)
10 MW (pulsed) at 3 GHz
3. Efficiency : 5 – 20 % ( 30 % with depressed
collector)

20
 APPLICATIONS OF TWT
1. Low noise RF amplifier in broad band microwave
receivers.
2. Repeater amplifier in wide band communication
links and long distance telephony.
3. Due to long tube life (50,000 hours against ¼th for
other types), TWT is power output tube in
communication satellite.
4. Continuous wave high power TWT’s are used in
troposcatter links (due to larger power and larger
bandwidths).
5. Used in Air borne and ship borne pulsed high power
radars.

21
 BIOLOGICAL EFFECTS OF MICROWAVES
 Electromagnetic radiation in the 1 mm to 1 m
wavelength range (300 MHz to 300 Ghz) is
referred to as microwave radiation.
 A part of which is known as radiofrequency
(RF) radiation, which covers 0.5 MHz to 300
GHz range and is considered in the context of
adverse biological effects.

22
IONIZING AND NON – IONIZING RADIATIONS
OF ELECTROMAGNETIC ENERGY

23
 IONIZING RADIATION
 Ionization is a process by which electrons are
stripped from atoms and molecules and this
can produce molecular changes that can lead
to damage in biological tissue, including effects
on DNA, the genetic material.
 This process requires interaction with high
levels of electromagnetic energy to ionize
biological material, this include X-radiation
and gamma radiation.
 The energy levels associated with RF and
microwave radiations are not great enough to
cause the ionization of atoms and molecules,
therefore, it is a type of non-ionizing radiation.
24
 EFFECT OF MICROWAVES IN HUMAN BODY

 The blood vessels are dilating and the blood flow

increases substantially as the thermoregulatory
mechanism is activated in order to keep the body
temperature constant.

 With rising body temperature the metabolic rate

rises, which may lead to Stress-Adaptation-Fatigue
Syndrome.

25
 EFFECTS PRODUCED BY THE
ELECTROMAGNETIC WAVES AT DIFFERENT
FREQUENCY LEVEL
 Above 10 GHz (3 cm wavelength or less) heating
occurs mainly in the outer skin surface.
 From 3 GHz to 10 GHz (10 cm to 3 cm) the
penetration is deeper and heating higher
 .From 150 MHz to about 1 GHz (200 cm to 25 cm
wavelength), penetration is even deeper and
because of high absorption, deep body heating
can occur.
 Any part of the body that cannot dissipate heat
efficiently or is heat sensitive may be damaged
by microwave radiation of sufficient power.

26
 MEASUREMENT OF MICROWAVE EXPOSURE
 The microwave energy exposure is measured in terms of
SAR (Specific Absorption Rate) or PD (Power Density).
 SAR is the energy which is absorbed in a unit of mass or
volume of the body per unit time.
 The standards that limit microwave exposure were set at
0.4 W/kg SAR for occupational and 0.08W/Kg for public
exposure.
 The averaging time for determination of SAR was 6
minutes. Power density is the energy absorbed per unit
area in unit time. The high power microwaves definitely
cause some adverse effects in the human system

27
 EFFECTS OF MICROWAVE ENERGY
Power
level Long-term effect Remarks
(mW /cm2) on human body
0.01 Nothing
0.1 Nothing
1 Nothing
5 Nothing Accepted standard for microwave
oven leakage
10 Nothing Accepted standard for maximum
continuous exposure to radiated
emissions (cell phones, etc.)
30 You can feel heat
100 Cataracts can be Summer sunlight is at this level
produced 28

1000 Pain is induced

Do you know YOUR Brain can be FRIED???

What do Microwave Ovens, Cell Phones and

Cordless Phones have in common?
They all emit... Dangerous Microwave
Radiation!
The GOOD NEWS is... with Microwave radiation
you can...
Boil water
Cook meat
Fry eggs
29
The BAD NEWS is...
with Microwave radiation you can...

Fry Your Brain

Your head and brain heat up significantly when you talk

on your cell phone or cordless phone.

30
Want proof?
After 15 minutes of using a cell phone, the orange, red and pink show
significant, dangerous HEAT. Most heat is generated in your ear canal,
which is directly connected to YOUR BRAIN

31
 After 15 minutes of using a cell phone WITH the BIOPRO
Harmonization Chip applied to it, the green and blue colors
show cool tissue.

Your head's temperature remains normal, providing you with the

protection you deserve. 32
33
UNIT- 6
HELIX TRAVELING-WAVE TUBES(TWT’S)
TRAVELING WAVE TUBE(TWT)

 The traveling wave tube is a form of thermionic valve or tube that

is used for high power microwave amplifier designs.
 The travelling wave tube can be used for wideband RF amplifier
designs where even now it performs well against devices using
newer technologies.
 TWTs are used in applications including broadcasting, radar and
in satellite transponders.
 The TWT is still widely used despite the fact that semiconductor
technology is advancing all the time.
 Two types of TWT’s are available
 Low power TWT
 High power TWT
Low-power TWT for receivers
 occurs as a highly sensitive, low-noise and wideband amplifier
in radar equipment's

High-power TWT for transmitters

 These are in use as a pre-amplifier for high-power transmitters.
Differences Between TWT and Klystrons:
- The microwave circuit is non-resonant in TWT , while resonant
circuits are used in klystrons.
- The interaction of electron beam and RF field in the TWT is
continuous over the entire length of the circuit , but the interaction
in the klystron occurs only at the gaps of a few resonant cavities.
- The wave in the TWT is a propagating wave , The wave in the
klystron is not.
- In the couple cavity TWT there is coupling effect between the
cavities, whereas each cavity in the klystron operates
independently.
 HELIX TWT CONSTRUCTION

 The Helix Travelling wave tube(TWT) , can be split into a

number of separate major elements:
 Vacuum tube

 Electron gun

 Magnet and

focusing structure
 RF input

 Helix

 RF output

 Collector
 The detailed diagram of Helix TWT can be viewed as,
 The simplified circuit is,

Working Operation:
- A Helix twt consists of an electron Gun and a Slow wave structure.

- First element-Electron gun comprising primarily of a heated cathode

and grids. This produces and then accelerates a beam of electrons
that travels along the length of the tube.
- The electron beam is focused by a constant magnetic field along the
electron beam and the slow wave structure. This is termed as O-type
traveling tube.
- The slow wave structure is either the helical type or folded-Back line. A
helix is an essential part of the traveling wave tube. It acts as a delay line,
in which the RF signal travels at near the same speed along the tube as
the electron beam.
- The applied signal propagates around the turns of the helix and produces
an electric field at the center of the helix , directed along the helix axis.
- The axial electric field progresses with a velocity that is very close to the
light multiplied by the ratio of helix pitch to helix circumference.
- When the electrons enter the helix tube , an interaction takes place
between the moving axial electric field and the moving electrons.
- On the average , the electrons transfer energy to the wave on the helix.
This interaction cause the signal wave on the helix to become larger.
- Amplification process : The electrons entering the helix at zero
field are not affected by the signal wave , those electrons entering
the helix at the accelerating field are accelerated and those
entering the helix at the retarding field are decelerated.
- As the electrons travel further along the helix , they begin forming
bunch centered about those electrons that enter the helix during
the zero field and collected at the collector end . The bunching
shifts the phase by π/2,
- Since the dc velocity of electrons is slightly greater than the axial
wave velocity, more electrons are in the retarding field than in the
accelerating field. And a great amount of energy is transferred
from the beam to the electromagnetic field . The amplification of
the signal wave is accomplished.
- The bunch becomes more compact and a larger amplification of
the signal voltage occurs at the end of the helix.
- The magnet produces an axial magnetic field to prevent spreading
of the electron beam as it travels down the tube.
- An attenuator placed near the center of the helix reduces all the
waves traveling along the helix to nearly zero so that the reflected
waves from the mismatched loads can be prevented from reaching
the input and causing oscillation.
- The bunched electrons emerging from the attenuator induce a new
electric field with the same frequency. This field in turn induces a
new amplified microwave signal on the helix.
- Amplified helix signal can be viewed as,
Characteristics of TWT:
 The Traveling Wave Tube (TWT) is a high-gain, low-noise , wide-
bandwidth microwave amplifier.
 It is capable of gains greater than 40dB with bandwidths exceeding an
octave. (A bandwidth of one octave is one in which the upper cutoff
frequency is twice the lower cutoff frequency.)
 Traveling-wave tubes have been designed for frequencies a slow as
300Megahertz and as high as 50 Gigahertz.
 The TWT is primarily a voltage amplifier. The wide-bandwidth and low-
noise characteristics make the TWT ideal for use as an RF amplifier in
microwave equipment.
 TWT amplifiers and they are typically capable of developing powers of
up to 2.5 kW. For narrowband RF amplifier applications it is possible to
use coupled cavity TWTs and these can deliver power levels of up to 15
Kw.
 Efficiency of 20 to 40 % is possible .
Physical Construction Of TWT
 Electron beam bunching and a detail photo of helix
 The electron-beam bunching already starts at the beginning of the
helix and reaches its highest expression on the end of the helix. If
the electrons of the beam were accelerated to travel faster than the
waves traveling on the wire, bunching would occur through the
effect of velocity modulation. Velocity modulation would be
caused by the interaction between the traveling-wave fields and the
electron beam.
 Bunching would cause the electrons to give up energy to the
traveling wave if the fields were of the correct polarity to slow
down the bunches. The energy from the bunches would increase
the amplitude of the traveling wave in a progressive action that
would take place all along the length of the twt.
 The helix may be replaced by some other slow wave structure
such as a ring-bar, ring loop, or coupled cavity structure. The
structure is chosen to give the characteristic appropriate to the
desired gain/bandwidth and power characteristics.
Slow-Wave Structures
 As the operating frequency is increased , both the inductance
and capacitance in the resonating circuit must be decreased in
order to maintain the resonance at the operating frequency.
 Because the gain-bandwidth product is limited by the resonating
circuit, the ordinary resonator cannot generate the large output.
 Non resonating or slow-wave structures are designed for
producing larger gain over a wide bandwidth.
 Slow-wave structures are special circuits that are used in
microwave tubes to reduce the wave velocity in a certain
direction so that the electron beam and the signal wave can
interact.
 The phase velocity of a wave in ordinary waveguides is greater
than the velocity of light in vacuum.
 In the operation of traveling wave and magnetron type devices ,
the electron beam must keep in step with the microwave signal.
 Since the electron beam can be accelerated only to the velocities
that are about the fraction of the velocity of light , a slow-wave
structure must be incorporated in the microwave devices so that
the phase velocity of the microwave signal can keep pace with that
of electron beam for effective interactions.
 The phase velocity of some of the spatial harmonics in the axial
direction obtained by the Fourier analysis of the waveguide field
may be smaller than the velocity of light.
 In the helical slow-wave structure a translation back or forth
through a distance of one pitch length results in identically the
same structure again . Thus the period is its pitch.
-Different slow wave structures are,
Axial Electric Field in TWT
-
-
Wave modes:
-

-
-Substituting (Eq.10) in (Eq.9) yields to ,

(Eq.11) is a fourth order in γ and thus has four roots . Its exact
solutions can be found using numerical methods and a digital
computer.
- How ever the approximate solutions may be found by equating the
dc electron beam velocity to the axial phase velocity of the
travelling wave and the four propagation constants γ are given by,
-
CROSSED-FIELD TUBES (M-TYPE TUBES)
Introduction

 In linear beam tubes like Klystron or Travelling wave tube (TWT)

, the dc Magnetic field parallel to the dc Electric field is used to
focus the electron beam .
 Crossed-field tubes derive their name from the fact that the dc
magnetic field is perpendicular to the dc electric field . In this
tubes, the dc magnetic field plays a direct role in the RF
interaction process.
 These tubes are also called M-Type tubes.

 In a crossed-field tube, the electrons emitted by the cathode are

accelerated by the electric field and gain velocity , but the greater
their velocity , the more their path is bent by the magnetic field.
Cross-Field Effect:
 In a crossed-field tube, the electrons emitted by the cathode are
accelerated by the electric field and gain velocity , but the greater their
velocity , the more their path is bent by the magnetic field.
 If an RF field is applied to the circuit , those electrons entering the circuit
during retarding field are decelerated and give up some of their kinetic
energy to the RF field. Consequently , their velocity is decreased and
these slower electrons will then travel the dc electric field far enough to
regain essentially the same velocity as before.
 Because of crossed-field interactions, only those electrons that have given
up sufficient energy to the RF field can travel all the way to the anode.
This phenomenon would make the M-type devices relatively efficient.
 Those electrons entering the circuit during the accelerating field are
accelerated by means of receiving enough energy from the RF field and
are returned back towards the cathode. This back bombardment of the
cathode produces heat in the cathode and decreases the operational
efficiency.
 The classification of crossed-field tubes is,
Magnetron Oscillators

 Hull invented magnetron, but it was only on interesting laboratory

device.
 During the world war II an urgent need for high power microwave
generators for RADAR transmitters led to the rapid development of
Magnetron
 Magnetrons provide microwave oscillations of very high frequency
 All magnetrons consists of some form of anode & cathode operated
in dc Magnetic field between cathode & anode.
 Because of cross field between cathode & anode , the electrons
emitted from cathode are influenced by the cross field to move in a
curved path.
 If the dc magnetic field is strong enough the electrons will not arrive
at in the anode but return to the cathode, consequently anode current
is cutoff.
.
 Magnetrons can be classified in to three types as follows,
1. Negative resistance Magnetrons or Split-Anode Magnetron :
 Make use of static negative resistance between two anode
segments. Low efficiency and are useful only at low
frequencies (< 500 MHz).
2.Cyclotron-frequency Magnetrons :
 Operates under the influence of synchronism between an
alternating component of electric field and periodic oscillation
of electrons in a direction parallel to this field.
 Useful only for frequencies greater than 100 MHz
3. Cavity or Traveling-wave Magnetrons :
 Depends upon the interaction of electrons with a traveling
electromagnetic field of linear velocity.
 These are customarily referred as Magnetrons
 Provide oscillations of very high peak power and hence are
useful in radar applications
Cylindrical Magnetrons

 Cylindrical magnetron Oscillator is also called as conventional

Magnetron.
 In a cylindrical magnetron , several reentrant cavities are connected
to the gaps and hence some times called as Cavity Magnetron.
 Schematic diagram illustrating the major elements of the
magnetron oscillator is shown below ,
 The detailed diagram of cavity magnetrons is,
Construction:
 Each cavity in the anode acts as an inductor having only one turn and the
slot connecting the cavity and the interaction space acts as a capacitor.
 These two form a parallel resonant circuit and its resonant frequency
depends on the value of L of the cavity and the C of the slot.
 The frequency of the microwaves generated by the magnetron oscillator
depends on the frequency of the RF oscillations existing in the resonant
cavities. Cross sectional view of anode assembly can be viewed as,
Working principle:
 Magnetron is a cross field device as the electric field between the
anode and the cathode is radial whereas the magnetic field
produced by a permanent magnet is axial.
 A high dc potential can be applied between the cathode and anode
which produces the radial electric field.
 Depending on the relative strengths of the electric and magnetic
fields, the electrons emitted from the cathode and moving towards
the anode will traverse through the interaction space.
 In the absence of magnetic field (B = 0), the electron travel straight
from the cathode to the anode due to the radial electric field force
acting on it as given by the path ‘a’ in the following figure.
 If the magnetic field strength is increased slightly, the lateral force
bending the path of the electron as given by the path ‘b’ in the
following figure.
 The radius of the path is given by, if the strength of the magnetic
field is made sufficiently high , then the electrons can be
prevented from reaching the anode as indicated path ‘c’ in figure
shown below.
 The magnetic field required to return electrons back to the cathode
just grazing the surface of the anode is called the critical magnetic
field (Bc) or the cut-off magnetic field.
 If the magnetic field is larger than the critical field (B > Bc), the
electron experiences a greater rotational force and may return back
to the cathode quite faster.
 The various motion of electrons in the presence of different
magnitudes of magnetic field can be viewed in the following
figures,
 The RF oscillations of transient nature produced when the HT is
switched on, are sufficient to produce the oscillations in the cavities,
these oscillations are maintained in the cavities reentrant feedback
which results in the production of microwaves.
 Reentrant feedback takes place as a result of interaction of the electrons
with the electric field of the RF oscillations existing in the cavities.
 The cavity oscillations produce electric fields which fringe out into the
interaction space from the slots in the anode structure, as shown in
figure , which illustrates possible trajectory of electrons from cathode to
anode in an eight cavity magnetron operating in  mode .
 Energy is transferred from the radial dc field to the RF field by the
interaction of the electrons with the fringing RF field.
 Due to the oscillations in the cavities, the either sides of the slots (which
acts as a capacitor) becomes alternatively positive and negative and
hence the directions of the electric field across the slot also reverse its
sign alternatively.
 The following figure illustrates possible trajectory of electrons
from cathode to anode in an eight cavity magnetron operating in 
mode,
 At any instant the anode close to the spiraling electron goes positive, the
electrons gets retarded and this is because; the electron has to move in
the RF field, existing close to the slot, from positive side to the negative
side of the slot.
 In this process, the electron loses energy and transfer an equal amount
of energy to the RF field which retard the spiraling electron.
 On return to the previous orbit the electron may reach the adjacent
section or a section farther away and transfer energy to the RF field if
that part of the anode goes positive at that instant.
 This electron travels in a longest path from cathode to the anode as
indicated by ‘a’ in above Figure , transferring the energy to the RF field
are called as favored electrons and are responsible for bunching effect
and give up most of its energy before it finally terminates on the anode
surface.
 An electron ‘b’ is accelerated by the RF field and instead of imparting
energy to the oscillations, takes energy from oscillations resulting in
increased velocity, such electrons are called unfavored electrons which
do not participate in the bunching process and cause back heating.
 Every time an electron approaches the anode “in phase” with the
RF signal, it completes a cycle. This corresponds to a phase shift
2.
 For a dominant mode, the adjacent poles have a phase difference
of  radians, this called the  - mode.
 At any particular instant, one set of alternate poles goes positive
and the remaining set of alternate poles goes negative due to the
RF oscillations in the cavities.
 As the electron approaches the anode, one set of alternate poles
accelerates the electrons and turns back the electrons quickly to
the cathode and the other set alternate poles retard the electrons,
thereby transferring the energy from electrons to the RF signal.
 This process results in the bunching of electrons, the mechanism
by which electron bunches are formed and by which electrons are
kept in synchronism with the RF field is called phase focusing
effect.
 The number of bunches depends on the number of cavities in the
magnetron and the mode of oscillations. In an eight cavity
magnetron oscillating with  - mode, the electrons are bunched in
four groups as shown in following figure.

 Two identical resonant cavities will resonate at two frequencies

when they are coupled together; this is due to the effect of mutual
coupling.
 Commonly separating the pi mode from adjacent modes is by a
method called strapping. The straps consist of either circular or
rectangular cross section connected to alternate segments of the
anode block.
Hull cutoff Magnetic Equation:
 The equation for the cutoff magnetic field can be obtained by
considering the equations for the motion of electrons in the
cylindrical magnetron which can be written as,
Hartree Condition:
 The Hull cutoff condition determines the anode voltage or
magnetic field necessary to obtain nonzero anode current as a
function of the magnetic field or anode voltage in the absence of
an electromagnetic field. The Hartree condition can be derived as
follows and as shown in the following figure 10-1-9.
 UNIT-7
Gunn Diode
Definition:

Such type of semiconductor device which have only N type doped

(semiconductor) material, is called “Gunn Diode.”

It’s a unique component.

Gunn Diode is also known as:

Transferred Electron Device (TED).

Microwave Semiconductor Device.
Symbols for Circuit Diagram:
History:
Gunn diode was invented by a Physicist, John
Battiscombe Gunn, in 1963, in IBM.
Transferred Electron Effect was first published by:
Ridley and Watkins in 1961.
Further work by Hilsum in 1962,
Finally J.B. Gunn, observed it, using GaAs
semiconductor, in 1963.
Construction:

Gunn diodes are fabricated from a single piece of n-type

semiconductor,

Source Material:

Tri-methylgallium and arsenic (10% in H2).

Most Common Materials :

Gallium Arsenide (GaAs)

and Indium Phosphide (InP).
Three main areas:

Top/Upper Area,
Middle Area,
Bottom Area.

Middle area (Active layer) has a doping level between

1014 cm-3 to 1016 cm-3 .
Substrate has doping
density
n = 1.3x10 ^18 cm-³.

Thickness varies according to the

frequency required.
Metal contacts consist of three layers, namely a
80 nm layer of AuGe sandwiched between two
layers of 10 nm of Ni.

Additional AuGe is evaporated on the

existing contacts to a depth of 0.7μm.
Use Of Gold.
Its relative stability,
and high conductivity.

Requirements:

The material must be defect free , and it must also

have a very uniform level of doping.
Types of Materials Used For Gunn Diodes
To Get Different Frequencies:

Gallium arsenide for frequencies up

to 200 GHz,

Gallium nitride can reach up to 3 THz.

GUNN DIODE

Negative
Resistance
In Gunn Diode
 GaAs (Galliam Arsenide ) has a property of negative
resistance.

 The negative resistance in Gunn diode is due to

(a) electron transfer to a less mobile energy level
(b) high reverse bias
(c) electron domain formation at the junction
 (a) How electron move into low mobility ?
According to Einstein Equation

E=mc2
 (b) High reverse bias

 (c) Electron domain formation at the

junction
EFFECT OF NEGATIVE RESISTANCE
ON CURRENT
GUNN DIODE

Gunn Effect
GRAPH BETWEEN RESISTANCE
AND VOLTAGE
 As a result we arrange that average voltage on the Gunn
diode is as illustrated in figure. The diode is said to be
biased into the negative resistance region.
 CHANGE IN ENERGY

R= RL + R(V)

WHEN R >0

THE ENERGY OF ANY OSCILLATION TENDS TO BE

REDUCED BY RESISTIVE DISSIPATION.
WHEN R <0
 The oscillation energy tends to be increased.

 According to law of conservation of energy

 The amount of energy at r > 0 = The amount of

energy at r < 0
GRAPH BETWEEN RESISTANCE AND
CURRENT
WORKING OF GUNN DIODE
 In this case, each diode induced fluctuation travels up
the cavity and reflected from the far end, returning to
the diode after a time

 L = length of cavity

 c= speed of light
 The oscillator may therefore oscillate at any frequency
such that.

 n= the “number of half-waves”

FOR A BETTER RESULT
n=1
The system won't oscillate at a lower frequency because
the cavity is too short to permit it. It can't oscillate at a
higher frequency because the diode is ‘too slow’, hence
we ensure a single-valued oscillation frequency.
 Real Gunn devices have a response time which varies
with the applied voltage, hence we can electronically
tune the oscillation frequency by slightly adjusting the
bias voltage
GUNN DIODE

Difference between
Gunn diode and P-N
junction
 DIFFERENCE BETWEEN GUNN DIODE AND
P-N JUNCTION
Gunn diode P-N junction diode

Construction
 It only consists of N type  It consists of P & N type
semiconductor material semiconductor material
 It has N+ n N+ material  It has P type,N type and

No depletion region is formed depletion region between

these materials
DIFFERENCE BETWEEN GUNN DIODE AND
P-N JUNCTION
Gunn Doiode P-N junction Diode
DIFFERENCE BETWEEN GUNN DIODE AND
P-N JUNCTION
Symbols of Gunn Diode P-N junction
DIFFERENCE BETWEEN GUNN DIODE AND
P-N JUNCTION
Gunn Doiode P-N junction Diode
DIFFERENCE BETWEEN GUNN DIODE AND
P-N JUNCTION
Gunn Doiode P-N junction Diode
DIFFERENCE BETWEEN GUNN DIODE AND
P-N JUNCTION
I-V characteristics I-V characteristics
Of Gunn diode Of P-N junction Diode
GUNN DIODE

Applications
 A Gunn diode can be used to amplify signals because of
the apparent "negative resistance". Gunn diodes are
commonly used as a source of high frequency and high
power signals
Sensors and measuring Instruments
 Anti-lock brakes
 Sensors for monitoring the flow of traffic
 Pedestrian safety systems
 Distance traveled" recorders
 Traffic signal controllers
 Automatic traffic gates
GUNN DIODE
TRANSFERRED ELECTRON DEVICES (TED)
 TED’s are semiconductor devices with no junctions and
gates.

 They are fabricated from compound semiconductors like

GaAs, InP, CdTe etc.

 TED’s operate with hot electrons whose energy is much

greater than the thermal energy.
GUNN DIODE

 Invented by J.B Gunn

Gunn Effect:

 Above some critical voltage (Corresponding to Electric field of

2k-4k V/cm) the current passing through n-type GaAs becomes
a periodic fluctuating function of time.
 Frequency of oscillation is determined mainly by the
specimen, not by the external circuit.
 Period of oscillation is inversely proportional to the specimen
length and is equal to the transit time of electrons between
the electrodes
 The current waveform was produced by applying a
voltage pulse of 16V and 10ns duration to an n-type
GaAs of 2.5 x 10-3 cm length. The oscillation frequency
was 4.5Ghz
RWH THEORY
 Explanation for Gunn Effect:
Ridley – Watkins – Hilsum (RWH) Theory

 Two concepts related with RWH Theory.

 Differential negative resistance
 Two valley model
DIFFERENTIAL NEGATIVE RESISTANCE
 Fundamental concept of RWH Theory.
 Developed in bulk solid state III-V compound
when a voltage is applied
 Differential negative resistance make the sample
electrically unstable.
TWO VALLEY
MODEL
THEORY
 Data for two valleys in GaAs
ELECTRON TRANSFER MECHANISM
 Conductivity of n-type GaAs:

 e = Electron charge
 μ = Electron mobility

 = Electron density in the lower valley

 = Electron density in the upper valley
 is the electron density
 According to RWH theory, in order to exhibit negative
resistance the energy band structure of semiconductor
should satisfy

 The energy difference between two valleys must be several

times larger than the thermal energy (KT ~ 0.0259eV)
 The energy difference between the valleys must be smaller
than the bandgap energy (Eg)
 Electron in lower valley must have a higher mobility and
smaller effective mass than that of in upper valley

 Possessed by GaAs, InP, CdTe etc

FORMATION OF HIGH FIELD DOMAIN
 In GaAs, at
electric fields
exceeding the
critical value of
Ec ≈ 3.2 kV/cm
the differential
mobility is –ve.

 When the field

exceeds Ec and
further increases,
the electron drift
velocity
decreases.
 MODES OF OPERATION
 Gunn Oscillation Mode:
 (f x L) = 107 cm/s and (n x L) > 1012 /cm2
 Cyclic formation of High field domain
 Stable Amplification Mode
 (f x L) = 107 cm/s and 1011/cm2 < (n x L) >1012/cm2
 LSA Oscillation Mode
 (f x L) >107 cm/s and 2 x 104 < (n/f) > 2 X105/cm2
 Bias-circuit
 (f x L) is small. L is very small. When E=Eth current
falls as Gunn oscillation begins, leads to oscillation in
bias circuit (1KHz to 100MHz)
GUNN OSCILLATION MODE
 Condition for successful domain drift:
Transit time (L/vs) > Electric relaxation time

 Frequency of oscillation = vdom/Leff.

 Gunn diode with a resistive circuit -> Voltage change

across diode is constant-> Period of oscillation is the
time required for the domain to drift from the cathode
to anode. Not suitable for microwave applications
because of low efficiency.
 Gunn diode with a resonant circuit has high efficiency.
 There are three domain modes for Gunn oscillation
modes.
1. Transit time domain mode, (Gunn mode)
2. Delayed domain mode

 Here domain is collected while

 New domain cannot form until E rises above threshold
again.
 ,
 Also called inhibited mode.
 Efficiency: 20%
3. Quenched domain mode:

 If bias field drops below Es, domain collapses before it

reaches anode.
 When the bias field swings above Eth, a new domain starts
and process repeats.
 Frequency of oscillation is determined by resonant circuit.
 Efficiency : 13%
 Limited Space charge Accumulation Mode (LSA)

Most Important mode for Gunn oscillator.

Domain is not allowed to form.
Efficiency : 20%
GUNN CHARACTERISTICS
 Power: 1W (Between 4HHz and 16GHz)
 Gain Bandwidth product : >10dB

 Average gain : 1 – 12 dB

 Noise figure : 15 dB
APPLICATIONS OF GUNN DIODE
 In radar transmitters
 Air traffic control (ATC) and Industrial
Telemetry
 Broadband linear amplifier

 Fast combinational and sequential logic circuit

 Low and medium power oscillators in microwave

receivers
 As pump sources
INP DIODE
PEAK TO VALLEY CURRENT RATIO
AVALANCHE
TRANSIT TIME
DEVICES
 INTRODUCTION
Rely on the effect of voltage breakdown across a reverse biased p-n
junction.

The avalanche diode oscillator uses carrier impact ionization and drift
in the high field region of a semiconductor junction to produce a
negative resistance at microwave frequencies.
 INTRODUCTION
Two distinct modes of avalanche oscillator is observed i)
IMPATT(impact ionization avalanche transit time operation)
Dc-to-RF c.e is 5 to 10%
ii) TRAPPAT (Trapped plasma avalanche triggered transit operation).
20 to 60%
Another type of active microwave device is BARITT (barrier injected
transit time diode)
 IMPATT DIODE
Form of high power diode used in high frequency electronics and
microwave devices
Typically made from silicon carbides due to their high breakdown
fields.
3 to 100 GHz
High power capability
From low power radar systems to alarms
Generate high level of phase noise – avalanche process.
IMPATT DIODE AS OSCILLATOR
The IMPATT diode family includes many different junctions and
metal semiconductor devices.

The first IMPATT oscillation was obtained from a simple silicon p-n
junction diode biased into a reverse avalanche break down and
mounted in a microwave cavity.
Electron–hole pairs are generated in the high field region.

The generated electron immediately moves into the N region, while the
generated holes drift across the P region.
The time required for the hole to reach the contact constitutes the
transit time delay.
The original proposal for a microwave device of the IMPATT type was
made by Read.
The Read diode consists of two regions (i) The Avalanche region (a
region with relatively high doping and high field) in which avalanche
multiplication occurs and (ii) the drift region (a region with essentially
intrinsic doping and constant field) in which the generated holes drift
towards the contact.
Read diode is the basic type in the IMPATT diode family
 IMPACT IONIZATION
If a free electron with sufficient energy strikes a silicon atom, it can
break the covalent bond of silicon and liberate an electron from the
covalent bond.

If the electron liberated gains energy by being in an electric field and

liberates other electrons from other covalent bonds then this process
can cascade very quickly into a chain reaction producing a large
number of electrons and a large current flow.

This phenomenon is called impact avalanche.

 PHYSICAL DESCRIPTION

+ very high doping

i or v intrinsic material
Two regions
1) Thin p region (High field/Avalanche region) – avalanche
multiplication occurs
2) Intrinsic region (Drift region) – generated holes must drift towards
the p+ contact
PHYSICAL DESCRIPTION
The space between n+ -p junction and the i –p+ junction is called the
space charge region

The diode is reverse biased and mounted in a microwave cavity. The

impedance of the cavity is mainly inductive which is matched with the
capacitive impedance of the diode to form a resonant circuit.

Such device can produce a negative ac resistance that in turns delivers

power from the dc bias to the oscillation
 AVALANCHE MULTIPLICATION
When the reverse bias voltage is above the breakdown voltage, the
space charge region always extends from n+ -p junction to the i –p+
junction through the p and the i regions.
The fixed charges are shown in the figure.
A positive charge moves from left to right and gives a rising field. The
maximum field which is at the n+ -p junction is about several
hundred kilovolt/cm

Carriers (holes) in the high field region near the n+ -p junction

acquire energy to knock down the valence electrons in the conduction
band and hence electron hole pairs are generated. This is avalanche
multiplication
The electrons move into the n+ region and the holes drift through the
space charge region to the p+ region with a constant velocity vd.

The field throughout the space charge is about 5 kV/cm.

The transit time of a hole across the drift i-region L is given by

And the avalanche multiplication factor is

The breakdown voltage for a silicon p+ -n junction can be expressed as
BREAKDOWN VOLTAGE VS IMPURITY DOPING
 CARRIER CURRENT IO(T) AND EXTERNAL
CURRENT IE(T)
The diode can be mounted in a microwave resonant circuit
An ac voltage can be maintained at a given frequency in the circuit, and
the total field across the diode is the sum of ac and dc fields which
causes breakdown at the n+ -p junction during the positive half cycle of
the ac voltage cycle if the field is above the breakdown voltage.
The carrier current (hole current in this case) Io(t) generated at the n+
-p junction by the avalanche multiplication grows exponentially with
time while the field is above critical voltage.
During the negative half cycle, when the field is below breakdown
voltage, the carrier current decays exponentially.

Io(t) is in the form a pulse of very short duration and it reaches its
maximum in the middle of the ac voltage cycle or one quarter of the
cycle later than the voltage.
Under the influence of electric field the generated holes are injected
into the space region towards the negative terminal.
As the injected holes traverse the drift space,
1) they induce a current Ie(t) in the external circuit.
2) Cause a reduction of the field
Since the velocity of the holes in the space charge is constant
The external current Ie(t) because of the moving holes is delayed by 90
relative to the pulsed Io(t).

Since the carrier current Io(t) is delayed by one quarter cycle or 90

relative to the ac voltage, Ie(t) is then delayed by 180 relative to the
voltage.
Hence negative conductance occurs and the diode can be used for
microwave oscillation and amplification.
 INTRODUCTION
 Trapped Plasma Avalanche Triggered Transit mode
 High efficiency microwave generator capable of operating from several hundred
MHz to several GHz
 n+ -p -p+ or (p+ -n –n+)
 The doping of the depletion region is such that the diodes are well “punched
through” at breakdown; i.e the dc electric field in the depletion region just prior to
breakdown is well above saturated drift velocity level.
 PRINCIPLES OF OPERATION

A high field avalanche zone propagates through the diode and

fills the depletion layer with a dense plasma of electrons and holes that
become trapped in the low field region behind the zone.
VOLTAGE AND CURRENT WAVEFORMS
At point A the electric field is uniform throughout the sample and its
magnitude is large but less than the value required for avalanche
breakdown.
The current density is

At the instant of time at point A, the diode current is turned on.

The charge carriers present are those due to thermal generation,
hence the diode initially charges up like a linear capacitor,
driving the magnitude of electric field above the breakdown voltage.
When a sufficient number of carriers are generated, the particle
current exceeds the external current and the electric field is depressed
throughout the depletion region, causing the voltage to decrease.
(B to C)
(B to C) During this time interval the electric field is sufficiently large
for the avalanche to continue, and a dense plasma of electrons and
holes are created.
Some of the electrons and holes drift out of the ends of the depletion
layer, the field is further depressed and “traps” the remaining plasma.
The voltage decreases to point D.
A long time is required to remove the plasma because the total plasma
charge is large compared to the charge per unit time in the external
current.
At point E the plasma is removed, but a residual charge of electrons
remains in one end of the depletion layer and a residual charge of holes
in the other end.

As the residual charge is removed, the voltage increases (E to F).

At F, all the charge that was generated internally has been removed.
From point F to G, the diode charges up again like a fixed capacitor.
At G, the diode current goes to zero for half a period and the voltage
remains constant at VA until the current comes back on and the cycle
repeats
The electric field expression
Thus the time t at which the electric field reaches Em at a given
distance x into the depletion region is

Differentiating w r t time t
- nominal transit time of the diode in the high field.
Therefore the TRAPATT mode is still a transit-time mode
That is the time delay of carriers in transit (time between injection and
collection) is utilized to obtain a current phase shift favorable for
oscillation.
BARITT DIODES
INTRODUCTION
Barrier injected transit time diodes
Long drift regions

The carriers traversing the drift regions are

generated by minority carrier injection from
forward biased junctions instead of being
extracted from the plasma of an avalanche
region
P-n-p, p-n-v-p, p-n-metal and metal-n-metal
For a p-n-v-p BARITT diode the forward biased p-n junction emits holes
into the v region. These holes drift with saturation velocity through the
v region and are collected at the p contact.

The diode exhibits a negative resistance for transit angles between π

and 2 π.
CHARACTERISTICS
Much less noisy than IMPATT diodes.
Noise figures are as low as 15 dB with Si BARITT amplifiers.
Narrow Bandwidth and power outputs limited to a few mill
watts.
PRINCIPLE OF OPERATION

A crystal n-type Si wafer with 11 Ω-cm

resistivity and 4 x 1014 per cubic cm doping
is made of a 10-um thin slice.
The wafer is sandwiched between two PtSi
Scotty barrier contacts of about 0.1 um
thickness.
The energy band diagram at thermal equilibrium is shown.

For the PtSi-Si-PtSi structure = 0.85 eV.

The hole barrier height for the forward biased contact is about
0.15 eV
Fig c shows the energy band diagram when a voltage is applied.
The mechanisms responsible for oscillations are derived from:
1. The rapid increase of the carrier injection process caused by
decreasing potential barrier of the forward biased metal
semiconductor contact.
2. An apparent 3π/2 transit angle of the injected carrier that traverses
the semiconductor depletion region.
The rapid increase
in terminal current
with applied
voltage (above 30
V) is caused by
thermionic hole
injection into the
semiconductor as
the depletion layer
of the reverse-
biased contact
reaches through
the entire device
thickness.
The critical voltage is given by
 UNIT- 8
MICROWAVE MEASUREMENTS
 8.1 Understand types of measurements.
 8.2.1 Draw the block diagram of instrument in microwave
testing.
 8.2.2 Explain the function of each block and the overall
measurement process:
a. Frequency measurement using wave meter.
b. VSWR measurement using slotted line.
c. Power measurement using low powered Bolometer or
Crystal Rectifier.
TYPES OF MEASUREMENT
TYPES OF EQUIPMENTS
MEASUREMENT
 Wavemeter s (absorption, transmission or reaction).
 Slotted lines.
FREQUENCY-DOMAIN
 Spectrum analyzer, frequency sweepers and
frequency counters.
 Sampling oscilloscope.
DISPLAY OF TIME-
DOMAIN  Oscilloscope.

 Slotted lines ( direct method or double minimum

VSWR
method)
 Power meters.
 Detectors with oscilloscopes.
POWER
 Spectrum analyzers.

WAVELENGTH  Coaxial and waveguide slotted lines

NOISE  Noise meters.
 Network analyzer – multifunctional test equipment.
 BLOCK DIAGRAM OF INSTRUMENT IN
MICROWAVE TESTING.

MICROWAVE
SOURCE

POWER VSWR
METER INDICATOR

ISOLATOR

ATTENUATOR WAVEMETER DIRECTIONAL SLOTTED LINE TUNER TERMINATOR

COUPLER
FUNCTION OF EACH BLOCK
MICROWAVE SOURCE – generates microwave source in X-
band (8 – 12 GHz);
e.g klystron, magnetron or TWT
ISOLATOR /CIRCULATOR - Allow wave to travel through in
one direction while being attenuated in the other
direction or it is use to eliminate the unwanted
generator frequency pulling (changing the frequency of
the generator) due to system mismatch or discontinuity.
(to prevent reflected energy from reaching the source)
◦ ATTENUATOR - Control the amount of power level in a
fixed amount, variable amount or in a series of fixed
steps from the from the microwave source to the
wavemeter.
◦ WAVEMETER - Used to select / measure resonant cavity
frequencies by having a plunger move in and out of the
cavity thus causes the the cavity to resonate at different
frequencies.
◦ DIRECTIONAL COUPLER - Samples part of the power
travelling through the main waveguide and allows part
of its energy to feed to a secondary output port. Ideally it
is used to separate the incident and reflected wave in a
transmission line.
◦ SLOTTED LINE - Used to determine the field strength
through the use of a detector probe that slides along the
top of the waveguide.
 VSWR INDICATOR - Denotes the value of VSWR measured by
the slotted line.

 TUNER - Allows only the desired frequency to appear at the

output. Any harmonic frequencies that appear at the output
are reduced to an acceptable level.

 TERMINATOR - May range from a simple resistive termination

to some sort of deep-space antenna array, active repeater or
similar devices. 3 special cases of transmission line i.e short
circuit, open circuit, match impedance.
 FREQUENCY MEASUREMENT

 The frequency meter used has a cavity which is coupled to

the waveguide by a small coupling hole which is used to
absorb only a tiny fraction of energy passing along the
waveguide.

 Adjusting the micrometer of the Frequency Meter will vary

the plunger into the cavity. This will alters the cavity size
and hence the resonance frequency.

 The readings on the micrometer scales are calibrated

against frequency. As the plunger enters the caviy, its sized is
reduced and the frequency increases.
 The wavemeter is adjusted for maximum or minimum power
meter readings depending on whether the cavity is a
transmission or absorption type device. With the
transmission-type device, the power meter will be adjusted
for a maximum. It only allows frequency close to resonance
to be transmitted through them. Other frequencies are
reflected down the waveguide. The wavemeter acts as a
short circuit for all other frequencies.

 For the absorption-type wavemeter, the power meter will be

adjusted for a minimum. Its absorp power from the line
around resonant frequency and act as a short to other
frequencies.

 The absorbing material used is to absorb any unwanted

signal that will cause disturbance to the system.
VSWR ( VOLTAGE STANDING WAVE RATIO )
MEASUREMENT
 Used to determine the degree of mismatch between
the source and load when the value VSWR ≠ 1.
 Can be measured by using a slotted line. Direct Method
Measurement is used for VSWR values upto about 10.
Its value can be read directly using a standing wave
detector .
 The measurement consists simply of adjusting
attenuator to give an adequate reading, making sure
that the frequency is correct and then using the dc
voltmeter to measure the detector output at a
maximum on the slotted section and then at the
nearest minimum.
The ratio of the voltage maximum to the minimum gives the VSWR
i.e

VSWR = Vmax / Vmin

ISWR = Imax / Imin

= k (V max)2 / k (V min)2
= ( V max / V min)2
= VSWR2

VSWR = √ ( Imax / Imin ) =

√ ISWR
 Methods used depends on the value of VSWR whether it is
high or low. If the load is not exactly matched to the line,
standing wave pattern is produced.

 Reflections can be measured in terms of voltage, current or

power. Measurement using voltage is preffered because it is
simplicity.

 When reflection occured, the incident and the reflected

waves will reinforce each other in some places, and in others
they will tend to cancel each other out.
 DOUBLE MINIMUM METHOD
MEASUREMENT ( VSWR > 10)
 ‘Double Minimum’ method is usually employed for VSWR
values greater than about 10.
E2MAX
d

2E2MIN SWR PATTERN

E2MIN λ/2

d/2 distance along the line

 The detector output (proportional to field strength squared)
is plotted against position. The probe is moved aling the line
to find the minimum value of signal.

 It is then moved either side to determine 2 positions at which

twice as much detector signal is obtained. The distance d
between these two positions then gives the VSWR according
to the formula :

S = √ 1 + 1/Sin2(πd/λ)
POWER MEASUREMENT
 Power is defined as the quantity of energy dissipated or
stored per unit time.
 Methods of measurement of power depend on the
frequency of operation, levels of power and whether the
power is continuous or pulsed.
 The range of microwave power is divided into three
categories :-
i. Low power ( < 10mW @ 0dBm)
ii. Medium power ( from 10 mW - 10 W @ 0 – 40 dBm)
iii. High power ( > 10 W @ 40 dBm)
 The microwave power meter consists of a power sensor,
which converts the microwave power to heat energy.
 The sensors used for power measurements are the Schottky
barrier diode, bolometer and the thermocouple.
SCHOTTKY BARRIER DIODE
 A zero-biased Schottky Barrier Diode is used as a
square-law detector whose output is proportional to
the input power.
 The diode detectors can be used to measure power
levels as low as 70dBm.
BOLOMETERS
 A Bolometer is a power sensor whose resistance
changes with temperature as it absorbs microwave
power.
 Are power detectors that operate on thermal principles.
Since the temperature of the resistance is dependent
on the signal power absorbed, the resistance must also
be in proportion to the signal power.
 The two most common types of bolometer are, the
barretter and the thermistor. Both are sensitive power
detectors and is used to indicate microwatts of power.
They are used with bridge circuits to convert resistance
to power using a meter or other indicating devices.
BOLOMETER
BARETTERS

 Are usually thin pieces of wire such as platinum. They

are mounted as terminating devices in a section of
transmission line. The section of transmission line with
the mounting structure is called a detector mount.
 The increase of temperature of the baretter due to the
power absorbed from the signal in the line causes the
temperature of the device to increase.
 The temperature coefficient of the device causes the
resistance to change in value in proportion to the
change in temperature of the device (positive
temperature coefficient i.e the resistance increases with
increasing temperature; R α t).
BARETTER
THERMISTOR

 Are beads of semiconductor material that are mounted

across the line. They have a negative temperature
coefficient i.e the resistance decreases with increasing
temperature; R α 1/ t.

 The impedance of baretters and thermistors must

match that of the transmission so that all power is
absorbed by the device.
Thermistor mount
 Variations in resistance due to thermal-sensing devices must
be converted to a reading on an indicating device such as a
meter. This can be done accurately using a balanced bridge
arrangement as shown below:-

DC VOLTAGE
R1

DETECTORS
 With no power to the detector that contains the sensor
element, the sensor-line R1 is adjusted to zero reading
through the meter M1 and the bridge circuit is balanced.

 When signal is applied to the sensor element, causing its

temperature to change, the sensor resistance changes,
causing the bridge to become unbalanced.

 Resistor R1 is adjusted to balance meter M1. The change in

the reading of meter M2 in the sensor element leg is a direct
measure of the microwave power.
 THERMOCOUPLES

 Are used as power monitors in the low-to-medium power

regions and are very sensitve.
 Is a thin wire made of two disimilar metals. Hence there will
be two junctions (hot & cold).
 When the temperature at two junctions are different, a
voltage is developed across the thermocouple (i.e across both
junctions). This developed voltage is proportional to the
difference between the two junction temperatures.
 When the temperature at both junctions are the same, the
difference in voltage = 0.
Thermocouple
 MICROWAVE CRYSTALS

 Are non-linear detectors that provide current in proportion

to the power. It is limited to making low-power
measurements.
 The current is proportional to the power due to the square-
law characteristic of the crystal. This square-law characteristic
only occurs for small signal levels.
 At larger signal levels the relationship is linear, as with any
diode. Therefore the proportional relationship between power
and current output is only true at power levels below 10mW.
Microwave Crystal
CALORIMETERS
 The calorimeters are the most accurate of all instruments
for measuring high power. Calorimeters depend on the
complete conversion of the input electromagnetic energy
into heat.
 Power measurement with true calorimeter methods is
based solely on temperature, mass, and time. Substitution
methods use a known, low-frequency power to produce
the same physical effect as an unknown of power being
measured.
 Calorimeters are classified as STATIC (non flow) types and
CIRCULATING (flow) types.
CALORIMETER
 SMITH CHART

DEFINITION :-

 plot of complex reflection overlaid with an

impedance and/or admittance grid referenced to a 1-
ohm characteristic impedance.
CARTA SMITH
Contains almost all possibleSMITH
CARTA impedances, real
or imaginary, within one circle.

Represent all imaginary impedances from - infinity to

+ infinity.
COMPONENTS OF A SMITH CHART

• Horizontal center line – resistance / conductance.

• Zero resistance / conductance – located on the left

end of the line.

• Infinite resistance / conductance - located on the

right end of the line.

• Horizontal centerline – resistive / conductive

horizontal scale of the chart. It is independent of
the characteristic impedance of the transmission
line by normalizing the input values.
COMPONENTS OF A SMITH CHART
Normalized impedance, zL = R ± j X
Z0

Normalized resistance, rL = R / Z0

Normalized conductance, gL = G / Z0

• The center of the line and also of the chart is 1.0

point, where R = Z0 or G = Y0 . (Z0 = 1 / Y0 )

• At point 1.0, the line termination = characteristic

impedance of the line and no reflection will occur.
COMPONENTS OF A SMITH CHART

• Circles tangent to the right side of chart – circles

of constant resistance / conductance.

• Are drawn on the SC tangent to the right-hand

side of the chart and its intersection with the
centerline.

• The curved lines from the outer circle that

terminate on the centerline at the right side are
lines of constant impedance / susceptance.
COMPONENTS OF A SMITH CHART

• Lines of Constant Reactance and Susceptance.

• Shown on SC with curves that start from a given

reactance value on the outer circle and end at the
right hand side of the centerline.

• Upper half of the outer circle scale of SC represents:

Inductive reactive component / Capacitive reactive

component
xL = + j XL OR b= +jB
Z0 Y0
COMPONENTS OF A SMITH CHART

• Lower half of the outer circle scale of SC

represents the :

Capacitive reactive component / Inductive

susceptance component

xC = - j XC OR b = - jB
Z0 Y0
IMPEDANCE, Z AND ADMITTANCE, Y

• Z is the steady state AC term.

• Combined effect of both resistance (R), and

reactance (X),

where
Z=R+jX
(X = jwL for an inductor, and

X = 1 / jwC for a capacitor,

where w is the radian frequency or 2 π f.)

Generally, Z is a complex quantity having a real part

(resistance) and an imaginary part (reactance).
• In terms of impedance and its constituent
quantities of resistance and reactance refers
to series- connected circuits where impedances
add together

• Circuits have elements connected in parallel

or "shunt" are a natural fit for the
"acceptance" quantity of admittance (Y) and
its constituent quantities of conductance (G)
and susceptance (B),
Where

Y= G + jB

( B = jwC for a capacitor, and

B = 1/jwL for an inductor.)

• Admittances add together for shunt-connected
circuits.

Remember that

Y = 1/Z = 1/(R+jX),

so that G = 1/R

only if X = 0,

and B = -1/X

only if R = 0
• When working with a series-connected
circuit or inserting elements in series
with an existing circuit or transmission
line, the resistance and reactance
components are easily manipulated on
the "impedance" Smith chart.
• When working with a parallel- connected
circuit or inserting elements in parallel with an
existing circuit or transmission line, the
conductance and susceptance components are
easily manipulated on the "admittance" smith
chart.
ORIENTATION OF THE SMITH CHART

• Places the resistance axis horizontally with

the short circuit (SC) location at the far left.

• The voltage of the reflected wave at a short

circuit must cancel the voltage of the incident
wave so that zero potential exists across the
short circuit.

• In other words, the voltage reflection

coefficient must be -1 or a magnitude of 1 at
an angle of 180°.
FOR AN OPEN CIRCUIT (OC),

• The reflected voltage is equal to and in phase

with the incident voltage (reflection
coefficient of +1) so that the open circuit
location is on the right.

• In general, the reflection coefficient has a

magnitude other than unity and is complex.
 Inductive
Center C/Smith ; r = 1.0 reactance + jx

Wavelength Angle of
towards reflection
generator coefficient
0 λ - 0.5λ

Normalised
Resistance
Normalised
r = 0 (short
Resistance
circuit)
r = ∞ (Open
Circuit)

Wavelength
Angle of
towards load
transmission
0 λ - 0.5λ
coefficient

Capasitive
Reactance -jx
 SOLUTIONS TO MICROWAVE
PROBLEMS USING SMITH CHART
1. Plotting a complex impedance on a Smith chart
2. Finding VSWR for a given load
3. Finding the admittance for a given impedance
4. Finding the input impedance of a transmission line
terminated in a short or open.
5. Finding the input impedance at any distance from a load ZL.
6. Locating the first maximum and minimum from any load
7. Matching a transmission line to a load with a single series
stub.
8. Matching a transmission line with a single parallel stub
9. Matching a transmission line to a load with two parallel
stubs.
 PLOTTING A COMPLEX IMPEDANCE
ON
A SMITH CHART

 To locate a complex impedance, Z = R+-jX or admittance Y = G

+jB on a Smith chart, normalize the real and imaginary part of
the complex impedance.
 Locating the value of the normalized real term on the
horizontal line scale locates the resistance circle.
 Locating the normalized value of the imaginary term on the
outer circle locates the curve of constant reactance.
 The intersection of the circle and the curve locates the
complex impedance on the Smith chart.
 FINDING THE VSWR FOR A GIVEN
LOAD
1. Normalize the load and plot its location on the Smith
chart.
2. Draw a circle with a radius equal to the distance
between the 1.0 point and the location of the
normalized load and the center of the Smith chart as
the center.
3. The intersection of the right-hand side of the circle
with the horizontal resistance line locates the value of
the VSWR.
FINDING THE INPUT IMPEDANCE AT
ANY DISTANCE FROM THE LOAD
1. The load impedance is first normalized and is located
on the Smith chart.
2. The VSWR circle is drawn for the load.
3. A line is drawn from the 1.0 point through the load to
the outer wavelength scale.
4. To locate the input impedance on a Smith chart of the
transmission line at any given distance from the load,
advance in clockwise direction from the located point,
a distance in wavelength equal to the distance to the
new location on the transmission line.
SMITH CHART USAGE :

• Plot real, imaginary & complex load

• Find VSWR for a given transmission line

transmission.

• Find input impedance at any point in

front of a transmission line terminated in an
open, short or complex load.

• Locate the distance to the minimum and

maximum points of standing waves in front
of any line termination.
SMITH CHART USAGE :

• Locate the distance to the minimum and

maximum points of standing waves in front
of any line termination.

• Match a line termination to the

transmission line using single- and double-
stub tuners.
REFLECTION COEFFICIENT

REFLECTION
VSWR,
COEFFICIENT, LOAD, ZL REMARK
σ
ρ
Due to phase reversal i.e
short circuit, change of phase thus the
ρ = -1 σ=0
ZL = 0; incident and reflected wave
will be cancelled.
Total refelection occurs
open circuit ,
ρ=1 σ = ∞ because the 2 waves are in
ZL = ∞
phase.
Matching
No reflection occurs only have
ρ=0 load, ZL = σ = 1
incident wave.
Z0
STUB MATCHING
•When a line is ‘matched’ the reflection coefficient ρ = 0 and
so the standing wave ratio, S = 1. Most system are therefore
designed to work with S as near to 1 as possible.

•A value of S > 1, represent mismatched and end to loss of

power at the receiving end. In other cases it may caused a
voltage breakdown as in high power radar system or distortion
in tv.

•It it therefore necessary to match a line. Matching in the case

of two wire lines, may be done by using one or more stub and
is called ‘stub matching’ or by the use of quarter wave
transformer.
•The use of stub in matching a complex load to the line
is to achieve a complete power transfer (VSWR =
1.0).The stub used has to be placed in parallel with the
line and load, thus has to deal with admittance, not
impedance
 EXAMPLE
Given : ZL = 50 + j 50 Ω , Z0 = 50 Ω.
Calculate
(i) Normalize impedance
(ii) Draw the SWR circle
(iii)VSWR
(iv)Reflection coefficient
(v) Angle of reflection
(vi)Rmin and Rmax
(vii) Stub length
(viii) Stub distance.
EXERCISES :

1. Construct the SWR circle for the given complex load :

(a) ZL = 28 - j 60 Ω , Z0 = 50 (b) ZL = 70 - j 55 Ω , Z0 = 50

2. Matched line-load condition between :-

(a) ZL = 31.25 + j 10 Ω & Z0 = 50
(b) ZL = 41.25 - j 22.5 Ω & Z0 = 75

3. Given : R = 45 Ω, C = 26.5pF, f = 0.12 GHz, Z0 = 30 Ω.

Find :- (i) stub distance (ii) stub length
(iii) reflection coefficient & angle of reflection
(iv) actual Rmin and Rmax