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NEHRU COLLEGE OF ARTS AND SCIENCE
MICRO WAVE AND FIBER OPTICS COMMUNICATION SYSTEMS
UNIT – I
Section A
1. What is wave guide?
A hollow conducting metallic tube of uniform cross section is used for propagating EM
waves that are guided along the surfaces of the tube is called waveguide.
2. Mention the applications of waveguide
The wave guides are employed for transmission of energy at very high
frequencies where the attenuation caused by wave guide is smaller.
3. Why is rectangular or circular form used as wave guide?
Waveguides usually take the form of rectangular or circular cylinders because of its
simpler forms in use and less expensive to manufacture.
4. Define a wave?
If a physical phenomenon that occurs at one place at a given time is reproduced at other
places at later times, the time delay being proportional to the space separation from the
first location, then the group of phenomena constitutes a wave.
Section B
1. Write a short note about Rectangular Waveguides...
Rectangular waveguides are th one of the earliest type of the transmission lines. They are
used in many applications. A lot of components such as isolators, detectors, attenuators,
couplers and slotted lines are available for various standard waveguide bands between 1
GHz to above 220 GHz.
A rectangular waveguide supports TM and TE modes but not TEM waves because we
cannot define a unique voltage since there is only one conductor in a rectangular
waveguide. The shape of a rectangular waveguide is as shown below. A material with
permittivity e and permeability m fills the inside of the conductor.
A rectangular waveguide cannot propagate
below
some
certain
frequency.
This
frequency is called the cut-off frequency.
Here, we will discuss TM mode rectangular
waveguides and TE mode rectangular
waveguides separately. Let’s start with the
TM mode.
TM Modes
Consider the shape of the rectangular waveguide above with dimensions a and b (assume
a>b) and the parameters e and m. For TM waves Hz = 0 and Ez should be solved from
equation for TM mode;
Ñ2xy Ez0 + h2 Ez0 = 0
Since Ez(x,y,z) = Ez0(x,y)e-gz, we get the following equation,
If we use the method of separation of variables, that is Ez0(x,y)=X(x).Y(y) we get,
Since the right side contains x terms only and the left side contains y terms only, they are
both equal to a constant. Calling that constant as kx2, we get;
where ky2=h2-kx2
Now, we should solve for X and Y from the preceding equations. Also we have the
boundary conditions of;
Ez0(0,y)=0
Ez0(a,y)=0
Ez0(x,0)=0
Ez0(x,b)=0
From all these, we conclude that
X(x) is in the form of sin kxx, where kx=mp/a, m=1,2,3,…
Y(y) is in the form of sin kyy, where ky=np/b, n=1,2,3,…
So the solution for Ez0(x,y) is
(V/m)
From ky2=h2-kx2, we have;
For TM waves, we have
From these equations, we get
where
Here, m and n represent possible modes and it is designated as the TMmn mode. m
denotes the number of half cycle variations of the fields in the x-direction and n denotes
the number of half cycle variations of the fields in the y-direction.
When we observe the above equations we see that for TM modes in rectangular
waveguides, neither m nor n can be zero. This is because of the fact that the field
expressions are identically zero if either m or n is zero. Therefore, the lowest mode for
rectangular waveguide TM mode is TM11 .
Here, the cut-off wave number is
and therefore,
The cut-off frequency is at the point where g vanishes. Therefore,
Since l=u/f, we have the cut-off wavelength,
At a given operating frequency f, only those frequencies, which have fc<f will propagate.
The modes with f<fc will lead to an imaginary b which means that the field components
will decay exponentially and will not propagate. Such modes are called cut-off or
evanescent modes.
The mode with the lowest cut-off frequency is called the dominant mode. Since TM
modes for rectangular waveguides start from TM11 mode, the dominant frequency is
The wave impedance is defined as the ratio of the transverse electric and magnetic fields.
Therefore, we get from the expressions for Ex and Hy (see the equations above);
The guide wavelength is defined as the distance between two equal phase planes along
the waveguide and it is equal to
which is thus greater than l, the wavelength of a plane wave in the filling medium.
The phase velocity is
which is greater than the speed of light (plane wave) in the filling material.
Attenuation for propagating modes results when there are losses in the dielectric and in
the imperfectly conducting guide walls. The attenuation constant due to the losses in the
dielectric can be found as follows:
TE Modes
Consider again the rectangular waveguide below with dimensions a and b (assume a>b)
and the parameters e and m.
For TE waves Ez = 0 and Hz should be
solved from equation for TE mode;
Ñ2xy Hz + h2 Hz = 0
Since Hz(x,y,z) = Hz0(x,y)e-gz, we get the
following equation,
If we use the method of separation of variables, that is Hz0(x,y)=X(x).Y(y) we get,
Since the right side contains x terms only and the left side contains y terms only, they are
both equal to a constant. Calling that constant as kx2, we get;
where ky2=h2-kx2
Here, we must solve for X and Y from the preceding equations. Also we have the
following boundary conditions:
at x=0
at x=a
at y=0
at y=b
From all these, we get
(A/m)
From ky2=h2-kx2, we have;
For TE waves, we have
From these equations, we obtain
where
As explained before, m and n represent possible modes and it is shown as the TEmn mode.
m denotes the number of half cycle variations of the fields in the x-direction and n
denotes the number of half cycle variations of the fields in the y-direction.
Here, the cut-off wave number is
and therefore,
The cut-off frequency is at the point where g vanishes. Therefore,
Since l=u/f, we have the cut-off wavelength,
At a given operating frequency f, only those frequencies, which have f>fc will propagate.
The modes with f<fc will not propagate.
The mode with the lowest cut-off frequency is called the dominant mode. Since TE10
mode is the minimum possible mode that gives nonzero field expressions for rectangular
waveguides, it is the dominant mode of a rectangular waveguide with a>b and so the
dominant frequency is
The wave impedance is defined as the ratio of the transverse electric and magnetic fields.
Therefore, we get from the expressions for Ex and Hy (see the equations above);
The guide wavelength is defined as the distance between two equal phase planes along
the waveguide and it is equal to
which is thus greater than l, the wavelength of a plane wave in the filling medium.
The phase velocity is
which is greater than the speed of the plane wave in the filling material.
The attenuation constant due to the losses in the dielectric is obtained as follows:
After some manipulation, we get
Example:
Consier a length of air-filled copper X-band waveguide, with dimensions a=2.286cm,
b=1.016cm. Find the cut-off frequencies of the first four propagating modes.
Solution:
From the formula for the cut-off frequency
2. Write a short note about Gauss's law
This article is about Gauss's law concerning the electric field. For an analogous law concerning
the magnetic field, see Gauss's law for magnetism. For an analogous law concerning the
gravitational field, see Gauss's law for gravity. For Gauss's theorem, a general theorem relevant to
all of these laws, see Divergence theorem.
In physics, Gauss's law, also known as Gauss's flux theorem, is a law relating the
distribution of electric charge to the resulting electric field. Gauss's law states that:
The electric flux through any closed surface is proportional to the enclosed electric charge.
The law was formulated by Carl Friedrich Gauss in 1835, but was not published until
1867.[1] It is one of the four Maxwell's equations, which form the basis of classical
electrodynamics. Gauss's law can be used to derive Coulomb's law,[2] and vice versa.
Gauss's law may be expressed in its integral form:
where the left-hand side of the equation is a surface integral denoting the electric flux
through a closed surface S, and the right-hand side of the equation is the total charge
enclosed by S divided by the electric constant.
Gauss's law also has a differential form:
where ∇ · E is the divergence of the electric field, and ρ is the charge density.
The integral and differential forms forms are related by the divergence theorem, also
called Gauss's theorem. Each of these forms can also be expressed two ways: In terms of
a relation between the electric field E and the total electric charge, or in terms of the
electric displacement field D and the free electric charge.
Gauss's law has a close mathematical similarity with a number of laws in other areas of
physics. See, for example, Gauss's law for magnetism and Gauss's law for gravity. In fact,
any "inverse-square law" can be formulated in a way similar to Gauss's law: For example,
Gauss's law itself is essentially equivalent to the inverse-square Coulomb's law, and
Gauss's law for gravity is essentially equivalent to the inverse-square Newton's law of
gravity.
Gauss's law can be used to demonstrate that there is no electric field inside a Faraday
cage with no electric charges. Gauss's law is something of an electrical analogue of
Ampère's law, which deals with magnetism.
In terms of total charge
Integral form
For a volume V with surface S, Gauss's law states that
where ΦE,S is the electric flux through S, Q is total charge inside V, and ε0 is the electric
constant.
The electric flux is given by a surface integral over S:
where E is the electric field, dA is a vector representing an infinitesimal element of
area,and · represents the scalar product.
Applying the integral form
If the electric field is known everywhere, Gauss's law makes it quite easy, in principle, to
find the distribution of electric charge: The charge in any given region can be deduced by
integrating the electric field to find the flux.
However, much more often, it is the reverse problem that needs to be solved: The electric
charge distribution is known, and the electric field needs to be computed. This is much
more difficult, since if you know the total flux through a given surface, that gives almost
no information about the electric field, which (for all you know) could go in and out of
the surface in arbitrarily complicated patterns.
An exception is if there is some symmetry in the situation, which mandates that the
electric field passes through the surface in a uniform way. Then, if the total flux is
known, the field itself can be deduced at every point. Common examples of symmetries
which lend themselves to Gauss's law include cylindrical symmetry, planar symmetry,
and spherical symmetry. See the article Gaussian surface for examples where these
symmetries are exploited to compute electric fields.
Differential form
In differential form, Gauss's law states:
where: ∇ · denotes divergence, E is the electric field, and ρ is the total electric charge
density (including both free and bound charge), and ε0 is the electric constant.
This is mathematically equivalent to the integral form, because of the divergence
theorem.
Equivalence of integral and differential forms
Beginning with the integral form of Gauss's law, Q can be rewritten in terms of charge
density so that
where dτ is an infinitesimal element of volume.
It follows from the divergence theorem that
Thus
and so
Thus the integral and differential forms are equivalent.
In terms of free charge
Free versus bound charge
The electric charge that arises in the simplest textbook situations would be classified as
"free charge"—for example, the charge which is transferred in static electricity, or the
charge on a capacitor plate. In contrast, "bound charge" arises only in the context of
dielectric (polarizable) materials. (All materials are polarizable to some extent.) When
such materials are placed in an external electric field, the electrons remain bound to their
respective atoms, but shift a microscopic distance in response to the field, so that they're
more on one side of the atom than the other. All these microscopic displacements add up
to give a macroscopic net charge distribution, and this constitutes the "bound charge".
Although microscopically, all charge is fundamentally the same, there are often practical
reasons for wanting to treat bound charge differently from free charge. The result is that
the more "fundamental" Gauss's law, in terms of E, is sometimes put into the equivalent
form below, which is in terms of D and the free charge only.
Integral form
This formulation of Gauss's law states that, for any volume V in space, with surface S, the
following equation holds:
where ΦD,S is the flux of the electric displacement field D through S, and Qfree is the free
charge contained in V. The flux ΦD,S is defined analogously to the flux ΦE,S of the electric
field E through S. Specifically, it is given by the surface integral
Differential form
The differential form of Gauss's law, involving free charge only, states:
where ∇ · D is the divergence of the electric displacement field, and ρfree is the free
electric charge density.
The differential form and integral form are mathematically equivalent. The proof
primarily involves the divergence theorem.
Equivalence of total and free charge statements
In linear materials
In homogeneous, isotropic, nondispersive, linear materials, there is a nice, simple
relationship between E and D:
where ε is the permittivity of the material. Under these circumstances, there is yet another
pair of equivalent formulations of Gauss's law:
3. write a short note about FARADAY’S LAW
Electromagnetic induction
Electromagnetic induction is the production of voltage across a conductor situated in a
changing magnetic field or a conductor moving through a stationary magnetic field.
Michael Faraday is generally credited with having discovered the induction phenomenon
in 1831
Technical details
Faraday found that the electromotive force (EMF) produced around a closed path is
proportional to the rate of change of the magnetic flux through any surface bounded by
that path.
In practice, this means that an electrical current will be induced in any closed circuit
when the magnetic flux through a surface bounded by the conductor changes. This
applies whether the field itself changes in strength or the conductor is moved through it.
Electromagnetic induction underlies the operation of generators, all electric motors,
transformers, induction motors, synchronous motors, solenoids, and most other electrical
machines.
Faraday's law of electromagnetic induction states that:
,
Thus:
is the electromotive force (emf) in volts
ΦB is the magnetic flux in webers
For the common but special case of a coil of wire, composed of N loops with the same
area, Faraday's law of electromagnetic induction states that
where
is the electromotive force (emf) in volts
N is the number of turns of wire
Section C
1. Write a short note about Electromagnetic wave equation
The electromagnetic wave equation is a second-order partial differential equation that
describes the propagation of electromagnetic waves through a medium or in a vacuum.
The homogeneous form of the equation, written in terms of either the electric field E or
the magnetic field B, takes the form:
where c is the speed of light in the medium. In a vacuum, c = c0 = 299,792,458 meters per
second, which is the speed of light in free space.[1]
The electromagnetic wave equation derives from Maxwell's equations.
It should also be noted that in most older literature, B is called the "magnetic flux
density" or "magnetic induction".
Speed of propagation
In vacuum
If the wave propagation is in vacuum, then
metres per second
is the speed of light in vacuum, a defined value that sets the standard of length, the metre.
The magnetic constant μ0 and the vacuum permittivity
are important physical
constants that play a key role in electromagnetic theory. Their values (also a matter of
definition) in SI units taken from NIST are tabulated below:
Symbol Name
speed of light in vacuum
electric constant
magnetic constant
characteristic impedance
of vacuum
Numerical Value
SI
Unit
of
Measure
metres
per
second
farads
Type
defined
per derived;
metre
henries
metre
ohms
per
defined
derived;
μ0c0
In a material medium
The speed of light in a linear, isotropic, and non-dispersive material medium is
where
is the refractive index of the medium,
is the magnetic permeability of the medium, and
is the electric permittivity of the medium.
The origin of the electromagnetic wave equation
Conservation of charge
Conservation of charge requires that the time rate of change of the total charge enclosed
within a volume V must equal the net current flowing into the surface S enclosing the
volume:
where j is the current density (in Amperes per square meter) flowing through the surface
and ρ is the charge density (in coulombs per cubic meter) at each point in the volume.
From the divergence theorem, this relationship can be converted from integral form to
differential form:
Ampère's circuital law prior to Maxwell's correction
In its original form, Ampère's circuital law relates the magnetic field B to the current
density j:
where S is an open surface terminated in the curve C. This integral form can be converted
to differential form, using Stokes' theorem:
Inconsistency between Ampère's circuital law and the law of conservation of charge
Taking the divergence of both sides of Ampère's circuital law gives:
The divergence of the curl of any vector field, including the magnetic field B, is always
equal to zero:
Combining these two equations implies that
Because
is nonzero constant, it follows that
However, the law of conservation of charge tells that
Hence, as in the case of Kirchhoff's circuit laws, Ampère's circuital law would appear
only to hold in situations involving constant charge density. This would rule out the
situation that occurs in the plates of a charging or a discharging capacitor.
Maxwell's correction to Ampère's circuital law
Maxwell conceived of displacement current in connection with linear polarization of a
dielectric medium. The concept has since been extended to apply to the vacuum. The
justification of this virtual extension of displacement current is as follows:
Gauss's law in integral form states:
where S is a closed surface enclosing the volume V. This integral form can be converted
to differential form using the divergence theorem:
Taking the time derivative of both sides and reversing the order of differentiation on the
left-hand side gives:
This last result, along with Ampère's circuital law and the conservation of charge
equation, suggests that there are actually two origins of the magnetic field: the current
density j, as Ampère had already established, and the so-called displacement current:
So the corrected form of Ampère's circuital law becomes:
Maxwell's hypothesis that light is an electromagnetic wave
A postcard from Maxwell to Peter Tait.
In his 1864 paper entitled A Dynamical Theory of the Electromagnetic Field, Maxwell
utilized the correction to Ampère's circuital law that he had made in part III of his 1861
paper On Physical Lines of Force. In PART VI of his 1864 paper which is entitled
'ELECTROMAGNETIC THEORY OF LIGHT'[2], Maxwell combined displacement
current with some of the other equations of electromagnetism and he obtained a wave
equation with a speed equal to the speed of light. He commented:
The agreement of the results seems to show that light and magnetism are affections of the
same substance, and that light is an electromagnetic disturbance propagated through the
field according to electromagnetic laws.[3]
Maxwell's derivation of the electromagnetic wave equation has been replaced in modern
physics by a much less cumbersome method involving combining the corrected version
of Ampère's circuital law with Faraday's law of induction.
To obtain the electromagnetic wave equation in a vacuum using the modern method, we
begin with the modern 'Heaviside' form of Maxwell's equations. In a vacuum and charge
free space, these equations are:
Taking the curl of the curl equations gives:
By using the vector identity
where
is any vector function of space, it turns into the wave equations:
where
meters per second
is the speed of light in free space.
UNIT – II
Section A
1. What is Esaki or tunnel diodes
These have a region of operation showing negative resistance caused by quantum tunneling, thus
allowing amplification of signals and very simple bistable circuits. These diodes are also the type
most resistant to nuclear radiation.
2. What is Gunn diodes
These are similar to tunnel diodes in that they are made of materials such as GaAs or InP that
exhibit a region of negative differential resistance. With appropriate biasing, dipole domains form
and travel across the diode, allowing high frequency microwave oscillators to be built.
3. What is Laser diodes
When an LED-like structure is contained in a resonant cavity formed by polishing the parallel end
faces, a laser can be formed. Laser diodes are commonly used in optical storage devices and for
high speed optical communication.
4. What is PIN diodes
A PIN diode has a central un-doped, or intrinsic, layer, forming a p-type/intrinsic/n-type
structure. They are used as radio frequency switches and attenuators. They are also used as large
volume ionizing radiation detectors and as photodetectors. PIN diodes are also used in power
electronics, as their central layer can withstand high voltages. Furthermore, the PIN structure can
be found in many power semiconductor devices, such as IGBTs, power MOSFETs, and
thyristors.
Section B
1. Write a short note about Two-cavity klystron amplifier
In the two-chamber klystron, the electron beam is injected into a resonant cavity. The electron
beam, accelerated by a positive potential, is constrained to travel through a cylindrical drift tube
in a straight path by an axial magnetic field. While passing through the first cavity, the electron
beam is velocity modulated by the weak RF signal. In the moving frame of the electron beam, the
velocity modulation is equivalent to a plasma oscillation. Plasma oscillations are rapid
oscillations of the electron density in conducting media such as plasmas or metals.(The frequency
only depends weakly on the wavelength). So in a quarter of one period of the plasma frequency,
the velocity modulation is converted to density modulation, i.e. bunches of electrons. As the
bunched electrons enter the second chamber they induce standing waves at the same frequency as
the input signal. The signal induced in the second chamber is much stronger than that in the first.
2. Write a short note about Two-cavity klystron oscillator
The two-cavity amplifier klystron is readily turned into an oscillator klystron by providing a
feedback loop between the input and output cavities. Two-cavity oscillator klystrons have the
advantage of being among the lowest-noise microwave sources available, and for that reason have
often been used in the illuminator systems of missile targeting radars. The two-cavity oscillator
klystron normally generates more power than the reflex klystron—typically watts of output rather
than milliwatts. Since there is no reflector, only one high-voltage supply is necessary to cause the
tube to oscillate, the voltage must be adjusted to a particular value. This is because the electron
beam must produce the bunched electrons in the second cavity in order to generate output power.
Voltage must be adjusted to vary the velocity of the electron beam (and thus the frequency) to a
suitable level due to the fixed physical separation between the two cavities. Often several
"modes" of oscillation can be observed in a given klystron
3. Write a short note about Reflex klystron
In the reflex klystron (also known as a 'Sutton' klystron after its inventor), the electron beam
passes through a single resonant cavity. The electrons are fired into one end of the tube by an
electron gun. After passing through the resonant cavity they are reflected by a negatively charged
reflector electrode for another pass through the cavity, where they are then collected. The electron
beam is velocity modulated when it first passes through the cavity. The formation of electron
bunches takes place in the drift space between the reflector and the cavity. The voltage on the
reflector must be adjusted so that the bunching is at a maximum as the electron beam re-enters the
resonant cavity, thus ensuring a maximum of energy is transferred from the electron beam to the
RF oscillations in the cavity.The voltage should always be switched on before providing the input
to the reflex klystron as the whole function of the reflex klystron would be destroyed if the supply
is provided after the input. The reflector voltage may be varied slightly from the optimum value,
which results in some loss of output power, but also in a variation in frequency. This effect is
used to good advantage for automatic frequency control in receivers, and in frequency modulation
for transmitters. The level of modulation applied for transmission is small enough that the power
output essentially remains constant. At regions far from the optimum voltage, no oscillations are
obtained at all. This tube is called a reflex klystron because it repels the input supply or performs
the opposite function of a [Klystron].
There are often several regions of reflector voltage where the reflex klystron will oscillate; these
are referred to as modes. The electronic tuning range of the reflex klystron is usually referred to
as the variation in frequency between half power points—the points in the oscillating mode where
the power output is half the maximum output in the mode. It should be noted that the frequency
of oscillation is dependent on the reflector voltage, and varying this provides a crude method of
frequency modulating the oscillation frequency, albeit with accompanying amplitude modulation
as well.
Modern semiconductor technology has effectively replaced the reflex klystron in most
applications.
4. Write a short note about Multicavity klystron
The very large klystrons as used in the storage ring of the Australian Synchrotron to maintain the
energy of the electron beam
In all modern klystrons, the number of cavities exceeds two. A larger number of cavities may be
used to increase the gain of the klystron, or to increase the bandwidth.
5. Write a short note about Schottky diodes
Schottky diodes are constructed from a metal to semiconductor contact. They have a lower
forward voltage drop than p-n junction diodes. Their forward voltage drop at forward currents of
about 1 mA is in the range 0.15 V to 0.45 V, which makes them useful in voltage clamping
applications and prevention of transistor saturation. They can also be used as low loss rectifiers
although their reverse leakage current is generally higher than that of other diodes. Schottky
diodes are majority carrier devices and so do not suffer from minority carrier storage problems
that slow down many other diodes — so they have a faster “reverse recovery” than p-n junction
diodes. They also tend to have much lower junction capacitance than p-n diodes which provides
for high switching speeds and their use in high-speed circuitry and RF devices such as switchedmode power supply, mixers and detectors.
Shockley diode equation
The Shockley ideal diode equation or the diode law (named after transistor co-inventor William
Bradford Shockley, not to be confused with tetrode inventor Walter H. Schottky) is the I–V
characteristic of an ideal diode in either forward or reverse bias (or no bias). The equation is:
where
I is the diode current,
IS is the reverse bias saturation current,
VD is the voltage across the diode,
VT is the thermal voltage,
and n is the emission coefficient, also known as the ideality factor. The emission coefficient n
varies from about 1 to 2 depending on the fabrication process and semiconductor material and in
many cases is assumed to be approximately equal to 1 (thus the notation n is omitted).
The thermal voltage VT is approximately 25.85 mV at 300 K, a temperature close to “room
temperature” commonly used in device simulation software. At any temperature it is a known
constant defined by:
where
q is the magnitude of charge on an electron (the elementary charge),
k is Boltzmann’s constant,
T is the absolute temperature of the p-n junction in kelvins
The Shockley ideal diode equation or the diode law is derived with the assumption that the only
processes giving rise to current in the diode are drift (due to electrical field), diffusion, and
thermal recombination-generation. It also assumes that the recombination-generation (R-G)
current in the depletion region is insignificant. This means that the Shockley equation doesn’t
account for the processes involved in reverse breakdown and photon-assisted R-G. Additionally,
it doesn’t describe the “leveling off” of the I–V curve at high forward bias due to internal
resistance.
Under reverse bias voltages (see Figure 5) the exponential in the diode equation is negligible, and
the current is a constant (negative) reverse current value of −IS. The reverse breakdown region is
not modeled by the Shockley diode equation.
For even rather small forward bias voltages (see Figure 5) the exponential is very large because
the thermal voltage is very small, so the subtracted ‘1’ in the diode equation is negligible and the
forward diode current is often approximated as
The use of the diode equation in circuit problems is illustrated in the article on diode modeling.
Small-signal behaviour
For circuit design, a small-signal model of the diode behavior often proves useful. A specific
example of diode modeling is discussed in the article on small-signal circuits.
6. Write a short note about Avalanche diodes
Diodes that conduct in the reverse direction when the reverse bias voltage exceeds the breakdown
voltage. These are electrically very similar to Zener diodes, and are often mistakenly called Zener
diodes, but break down by a different mechanism, the avalanche effect. This occurs when the
reverse electric field across the p-n junction causes a wave of ionization, reminiscent of an
avalanche, leading to a large current. Avalanche diodes are designed to break down at a welldefined reverse voltage without being destroyed. The difference between the avalanche diode
(which has a reverse breakdown above about 6.2 V) and the Zener is that the channel length of
the former exceeds the “mean free path” of the electrons, so there are collisions between them on
the way out. The only practical difference is that the two types have temperature coefficients of
opposite polarities.
Section C
1. write a short note about Diodes
Esaki or tunnel diodes
These have a region of operation showing negative resistance caused by quantum tunneling, thus
allowing amplification of signals and very simple bistable circuits. These diodes are also the type
most resistant to nuclear radiation.
Gunn diodes
These are similar to tunnel diodes in that they are made of materials such as GaAs or InP that
exhibit a region of negative differential resistance. With appropriate biasing, dipole domains form
and travel across the diode, allowing high frequency microwave oscillators to be built.
Light-emitting diodes (LEDs)
In a diode formed from a direct band-gap semiconductor, such as gallium arsenide, carriers that
cross the junction emit photons when they recombine with the majority carrier on the other side.
Depending on the material, wavelengths (or colors) from the infrared to the near ultraviolet may
be produced. The forward potential of these diodes depends on the wavelength of the emitted
photons: 1.2 V corresponds to red, 2.4 V to violet. The first LEDs were red and yellow, and
higher-frequency diodes have been developed over time. All LEDs produce incoherent, narrowspectrum light; “white” LEDs are actually combinations of three LEDs of a different color, or a
blue LED with a yellow scintillator coating. LEDs can also be used as low-efficiency photodiodes
in signal applications. An LED may be paired with a photodiode or phototransistor in the same
package, to form an opto-isolator.
Laser diodes
When an LED-like structure is contained in a resonant cavity formed by polishing the parallel end
faces, a laser can be formed. Laser diodes are commonly used in optical storage devices and for
high speed optical communication.
Photodiodes
All semiconductors are subject to optical charge carrier generation. This is typically an undesired
effect, so most semiconductors are packaged in light blocking material. Photodiodes are intended
to sense light(photodetector), so they are packaged in materials that allow light to pass, and are
usually PIN (the kind of diode most sensitive to light). A photodiode can be used in solar cells, in
photometry, or in optical communications. Multiple photodiodes may be packaged in a single
device, either as a linear array or as a two-dimensional array. These arrays should not be confused
with charge-coupled devices.
PIN diodes
A PIN diode has a central un-doped, or intrinsic, layer, forming a p-type/intrinsic/n-type
structure. They are used as radio frequency switches and attenuators. They are also used as large
volume ionizing radiation detectors and as photodetectors. PIN diodes are also used in power
electronics, as their central layer can withstand high voltages. Furthermore, the PIN structure can
be found in many power semiconductor devices, such as IGBTs, power MOSFETs, and
thyristors.
Varicap or varactor diodes
These are used as voltage-controlled capacitors. These are important in PLL (phase-locked loop)
and FLL (frequency-locked loop) circuits, allowing tuning circuits, such as those in television
receivers, to lock quickly, replacing older designs that took a long time to warm up and lock. A
PLL is faster than an FLL, but prone to integer harmonic locking (if one attempts to lock to a
broadband signal). They also enabled tunable oscillators in early discrete tuning of radios, where
a cheap and stable, but fixed-frequency, crystal oscillator provided the reference frequency for a
voltage-controlled oscillator.
UNIT IV
RADAR
Introduction – Block diagram – Classification – Radar range equation – Factors affecting
the range of a radar receivers – Line pulse modulator – PPI (Plane Position Indicator) –
Moving Target Indicator (MTI) – FM CW Radar- Applications.
SECTION A
1. Define PPI?
PULSE POSITION RADAR
2. Classify the RADAR?


CW RADAR
PULSED RADAR
3. RADAR stands for RADIO FREQUENCY DETECTING AND RANGING
SECTION B
1. EXPLAIN THE CW RADAR?
* The simple pulse radar described above was actually preceded in the prewar timeframe
by simpler systems that consisted of a transmitter sending a signal to a receiver on a
continuous basis. For example, the transmitter could be placed on one side of the mouth
of a harbor and the receiver placed on the other, with a ship entering the harbor breaking
the radio beam and announcing its presence. The transmitter and receiver could also be
placed on the same side of the harbor, with the passing ship bouncing the radio beam
back to the receiver. These simple "continuous wave (CW)" systems weren't really radars
since they couldn't realistically give a range to a target, they could only detect that
something was there. They are better described as "CW alarm systems", and they are
really something of a footnote in the history of radar.
However, although a simple CW alarm can't determine range, a direct variation on it can
be used to determine velocities. Suppose a continuous radio signal at a given frequency is
focused on an aircraft approaching head-on; the velocity of the aircraft will actually
increase the frequency of the echo. If the aircraft is going directly away, it will decrease
the frequency of the echo return. This is known as the "Doppler shift". The same effect is
observed with sound waves when an aircraft is flying overhead: as it approaches, the
sound of the aircraft has a high pitch, in other words a high audio frequency, and when it
is going away it has a low pitch, or a low audio frequency.
Derivation of the Doppler shift is a bit beyond this document but can be found in any
simple physics text. For a radar, which generally tracks targets moving much slower than
the speed of light, the shift in frequency, or "Doppler frequency" is roughly:
doppler_frequency = 2 * target_velocity / radar_wavelength
For example, if:


The radar frequency is 100 MHz, corresponding to a wavelength of 3 meters.
The target velocity is 1,000 KPH, corresponding to 278 meters per second.
-- then the Doppler frequency is:
2 * 278 / 3 = 185 Hz
This is the shift up in frequency if the target is approaching and the shift down in
frequency if the target is moving away. Incidentally, the Doppler shift for radio emissions
transmitted from the target itself is only half this, 92.5 Hz; the value is doubled for radar
because the target is moving as the radar arrives, causing a shift, and as the return is
reflected, causing a second shift.
It would be possible to imagine a simple continuous-wave radar Doppler velocity meter,
consisting of a transmitter unit and a receiver unit. Since this device is only intended to
measure velocity, the two units can share the same antenna, with the receiver blocking
out the signal of the transmitter with a "band rejection filter" that blocks signals at the
transmit frequency but allows all others to pass. The transmitter would send a radio beam
at a target. A calibrated dial on the receiver could then be used to adjust a variable filter
until the Doppler-shifted echo was received and lit up an indicator light. The velocity
could be read off the dial. Of course, this scheme only gives the velocity of the target on a
straight-line radial to the detector. At any angle off the radial the perceived velocity is
smaller, until at 90 degrees it falls to zero.
A more practical device would feature a receiver that had sets of fixed filters in a range of
frequencies above and below the transmitter frequency. Each filter would be connected to
a simple circuit that activated a light on the front panel of the receiver, with each light
marked with a particular range of velocities. If the Doppler shifted echo passed through a
specific filter, it would turn on the appropriate light to give the target velocity. The radars
used by police to catch speeders actually operate more or less along such a principle,
though their implementation is much more sophisticated and they will actually give speed
readings.
The essential point here is that, although timing radio pulses can be used to obtain ranges
to targets, it is also useful to obtain information from the Doppler shift to learn about the
velocities of targets. The combination of these two approaches in "pulse Doppler" radars
is an important theme in modern radars.
2.EXPLAIN THE FUNCTIONAL BLOCK DIAGRAM?
Functional block diagram
In the interrogator on the ground:
The secondary radar unit needs a synchronous impulse of the (analogous) primary radar
unit to the synchronization of the indication.



The chosen mode is encoded in the Coder. (By the different modes different questions
can be defined to the airplane.)
The transmitter modulates these impulses with the RF frequency. Because another
frequency than on the replay path is used on the interrogation path, an expensive duplexer
can be renounced.
The antenna is usually mounted on the antenna of the primary radar unit and turns
synchronously to the deflection on the monitor therefore.
In the aircrafts transponder:
A receiving antenna and a transponder are in the airplane.




The receiver amplifies and demodulates the interrogation impulses.
The decoder decodes the question according to the desired information and induces the
coder to prepare the suitable answer.
The coder encodes the answer.
The transmitter amplifies the replay impulses and modulates these with the RF replyfrequency.
Again in the interrogator on the ground:



The receiver amplifies and demodulates the replay impulses. Jamming or interfering
signals are filtered out as well as possible at this.
From the informations „Mode” and „Code” the decoder decodes the answer.
The monitor of the primary radar represents the additional interrogator information.
Perhaps additional numbers must be shown on an extra display.
3.EXPLAIN SIMPLE PULSED RADAR?
SIMPLE PULSE RADAR SYSTEM
* The best way to explain radar is to imagine standing on one side of a canyon, and
shouting in the direction of the distant wall of the canyon. After a few moments, an echo
will come back. The length of time it takes an echo to come back is directly related to
how far away the distant canyon wall is. Double the distance, and the length of time
doubles as well. Given that the speed of sound is about 1,200 KPH (745 MPH) at sea
level, then timing the echo with a stopwatch will give the distance to the remote canyon
wall. If it takes four seconds for the echo to come back, then since sound travels about
330 meters (1,080 feet) in a second, the distance is about 660 meters (2,160 feet).
Radar uses exactly the same principle, but it times echoes of radio or microwave pulses
and not sound. Like a wireless telegraphy set, a simple radar has a transmitter and a
receiver, with the transmitter sending out pulses, short bursts, of EM radiation and the
receiver picking them up.
In the case of the radar, the receiver is picking up echoes from a distant target, with the
echoes timed to determine the distance to the target. Early radars simply used an
oscilloscope to perform the timing, with the detected return signal fed into the
oscilloscope as a "video" signal, and showing up as a peak or "blip" on the display.
An oscilloscope measures an electrical signal on an electronic beam that moves or
"sweeps" from one side of a display to the other at a certain rate. The rate is determined
by a "timebase" circuit in the oscilloscope. For example, the sweep rate might push the
sweep from one side of the display to the other in a millisecond (thousandth of a second).
If the display were marked into ten intervals, that would mean the sweep would pass
through each interval in 0.1 milliseconds. While this would be shorter than the human eye
could follow, the sweep is normally generated repeatedly, allowing the eye to see it.
Since EM radiation propagates at 300,000,000 meters per second, or 300,000 meters per
millisecond, then each 0.1 millisecond interval would correspond to 30,000 meters, or 30
kilometers (18.6 miles). If the sweep on the scope is "triggered" to start when the radar
transmitter sends out the radio pulse, and the sweep displays a blip on the sixth interval
on the display, then the pulse has traveled a total of 180 kilometers (112 miles). Since this
is the round-trip distance for the pulse, that means that the target is 90 kilometers (56
miles) away. The trigger signal provides synchronization, so it can be regarded as a type
of "synch" or "sync" signal. The sweep is called a "range sweep" and the output of the
display is called a "range trace".
The display scheme described here is known as an "A scope", and allows the user to
determine the range to a target. A simple representation of an A-scope is shown below,
along with a graph plotting the travel of the pulse with respect to time:
The amplitude of the return also gives some indication of the size of the target, though
the relation between return amplitude and target size is not straightforward, as discussed
later.
* It would also be nice to know what the direction to the target is, in terms of its "altitude
(vertical direction)" and "azimuth (left to right direction)".
This is a bit trickier to describe, but no more complicated in the end. Some early radars,
like the famous British "Chain Home" sets that helped win the Battle of Britain, simply
transmitted radio waves from high towers in a flood over their field of view, and used a
directional receiver antenna to determine the direction of the echo. Chain Home actually
used a scheme where the power of the echo was compared at separated receiver antennas
to give the direction, which astoundingly actually worked reasonably well. Other such
"floodlight" radars used directional receiver antennas that could be steered to identify the
direction of the echo. Incidentally, a radar that uses receive and transmit antennas sited in
different locations is known as a "bistatic", or in the more general case "multistatic",
radar.
Floodlight radars were quickly abandoned. They spread their radio energy over a wide
area, meaning that any echo was faint and so range was limited. The next step was to
make a radar with a steerable transmitter antenna. For example, two directional antennas,
one for the transmitter and the other for the receiver, could be ganged together on a
steerable mount and pointed like a searchlight, an arrangement that is sometimes called
"quasi-monostatic". The transmitter antenna generated a narrow beam, and if the beam hit
a target, an echo would be picked up by the receiving antenna on the same mount. The
direction of the antennas naturally gave the direction to the target, at least to an accuracy
limited by the width in degrees of the beam, while the distance to the target was given by
the trace on the A-scope.
Of course, it was realized early on that it would be more economical and less physically
cumbersome to use one antenna for both transmit and receive instead of separate
antennas; it was possible to do so in theory because a radar transmits a pulse and then
waits for an echo, meaning it doesn't transmit and receive at the same time. The problem
in practice was that the receiver was designed to listen for a faint echo, while the
transmitter was designed to send out a powerful pulse. If the receiver was directly linked
to the transmitter when a pulse was sent out, the transmit pulse would fry the receiver.
The solution to this problem was the "duplexer", a circuit element that protected the
receiver, effectively becoming an open connection while the transmit pulse was being
sent, and then closing again immediately afterward so that the receiver could pick up the
echo. This was done with certain types of gas-filled tubes, with the output pulse ionizing
the gas and making the tube nonconductive, and the tube recovering quickly after the end
of the pulse. More sophisticated duplexer schemes would be developed later. The
receiver was also generally fitted with a "limiter" circuit that blocked out any signals
above a certain power level. This prevented, say, transmissions from another nearby radar
from destroying the receiver.
* After this evolution of steps, the result is a simple, workable radar. It has a single,
steerable antenna that can be pointed like a searchlight. The antenna repeatedly sends out
a radio pulse and picks up any echoes reflected from a target. An A-scope display gives
the interval from the time the pulse is sent out and the time the echo is received, allowing
the operator to determine the distance to the target.
The transmitter emits pulses on a regular interval, typically a few dozen or a few hundred
times a second, with the A scope trace triggered each time the transmitter sends out a
pulse to display the receiver output. The number of pulses sent out each second is known
as the "pulse repetition rate" or more generally as the "pulse repetition frequency (PRF)",
measured in hertz.
The width of a radar pulse is an important but tricky consideration. The longer the pulse,
the more energy sent out, improving sensitivity and increasing range. Unfortunately, the
longer the pulse, the harder it is to precisely estimate range. For example, a pulse that last
2 microseconds is 600 meters (2,000 feet) long, and in that case there is no real way to
determine the range to an accuracy of better than 600 meters, and there is also no way to
track a target that is closer than 600 meters. In addition, a long pulse makes it hard to pick
out two targets that are close together, since they show up as a single echo.
PRF is another tricky consideration. The higher the PRF, the more energy is pumped out,
again improving sensitivity and range. The problem is that with a simple radar it makes
no sense to send out pulses at a rate faster than echoes come back, since if the radar sends
a pulse and then gets back an echo from an earlier pulse, the operator is likely to be
confused by the "ghost echo". This is usually not too much of a problem, since a little
quick calculation shows that even a PRF of 1,000 gives enough time to get an echo back
from 150 kilometers (95 miles) away before the next pulse goes out. However, as
mentioned propagation of radar waves can be freakishly affected by atmospheric
conditions that create ducting or other unusual phenomena, and sometimes radars can get
back echoes from well beyond their design range.
This can be confusing, because a pulse will be sent out and a return will be received very
quickly, indicating that the target is close. In reality, the target is distant and the return is
from the previous pulse. This is called a "second time around" return. Given a PRF of
1,000, then a target 210 kilometers (130 miles) away will appear to be only 60 kilometers
(37 miles) away. Similar confusions could be caused by returns that arrive from long
ranges after more than one additional pulse, resulting in "multiple time around" returns.
Of course, a simple pulse radar also has "blind ranges" or "blind zones": if our example
radar is trying to spot a target exactly 150, 300, or 450 kilometers away, the return will
arrive when the next pulse is being sent out and the radar will never spot it.
To deal with such "range ambiguities", radars were designed so they could be switched
between different PRFs. Switching from one PRF to another would not affect a "first time
around" echo, since the delay from pulse output to pulse reception would remain the
same, but the switch would make a ghost return from a current pulse jump on the display.
Suppose our radar could be switched from a PRF of 1,000 Hz to 1,250 Hz, and is trying
to track a target 210 kilometers away. At 1,000 Hz, the maximum range is 150 kilometers
and the target appears to be 60 kilometers away, but at 1,250 Hz the maximum range is
120 kilometers (75 miles) and the target return jumps to a perceived range of 90
kilometers (56 miles). The fact that the target range jumps when PRF is changed reveals
the range ambiguity; adding perceived range to the maximum range for each PRF setting
gives the actual range.
* Incidentally, the power of the transmitter pulse is given as "peak power", usually in
kilowatts or megawatts. This may be an impressive value, but it's only the power that
goes into the pulse itself. Suppose we have a pulse width of 2 microseconds with a peak
power of 150 kilowatts. If we have a PRF of 500, then the time from pulse to pulse, or
"pulse period", is 1/500 = 2 milliseconds, or two thousandths of a second. This means
that the average power transmitted by our radar is only:
150 kW * ( 2 microseconds / 2 milliseconds) = 0.15 kW = 150 watts
-- which is about as much as the power draw of a bright old-fashioned household incandescent
light bulb.
* One of the first US early warning radars, the "SCR-27O", provides a good example of
such a simple radar. It was a VHF radar, actually operating at what by modern standards
at a low frequency / long wavelength of 100 MHz / 3 meters. It had a steerable
rectangular "flyswatter" style dipole array of 4 x 8 dipoles, and featured a pulse width of
10 to 25 microseconds, a PRF of 621 Hz, and a peak power of 100 kW.
SECTION C
1. EXPLAIN THE RADAR?
RADAR
Radar is an object detection system that uses electromagnetic waves to identify
the range, altitude, direction, or speed of both moving and fixed objects such as aircraft,
ships, motor vehicles, weather formations, and terrain. The term RADAR was coined in
1941 as an acronym for radio detection and ranging. Radar was originally called RDF
(Radio Direction Finder, now used as a totally different device) in the United Kingdom.
A radar system has a transmitter that emits microwaves or radio waves. These
waves are in phase when emitted, and when they come into contact with an object are
scattered in all directions. The signal is thus partly reflected back and it has a slight
change of wavelength (and thus frequency) if the target is moving. The receiver is
usually, but not always, in the same location as the transmitter. Although the signal
returned is usually very weak, the signal can be amplified through use of electronic
techniques in the receiver and in the antenna configuration. This enables radar to detect
objects at ranges where other emissions, such as sound or visible light, would be too
weak to detect.
Radar is used in meteorological detection of precipitation, measuring ocean
surface waves, air traffic control, police detection of speeding traffic, and by the military.
Principle
The radar dish, or antenna, transmits pulses of radio waves or microwaves which
bounce off any object in their path. The object returns a tiny part of the wave's energy to
a dish or antenna which is usually located at the same site as the transmitter. The time it
takes for the reflected waves to return to the dish enables a computer to calculate how far
away the object is, its radial velocity and other characteristics.
Radar equation
The power Pr returning to the receiving antenna is given by the radar equation:
where







Pt = transmitter power
Gt = gain of the transmitting antenna
Ar = effective aperture (area) of the receiving antenna
σ = radar cross section, or scattering coefficient, of the target
F = pattern propagation factor
Rt = distance from the transmitter to the target
Rr = distance from the target to the receiver.
In the common case where the transmitter and the receiver are at the same location, Rt =
Rr and the term Rt² Rr² can be replaced by R4, where R is the range. This yields:
This shows that the received power declines as the fourth power of the range, which
means that the reflected power from distant targets is very, very small.
2. Explain About Pulsed Radar?
Basic concept
A Doppler radar is a radar that produces a velocity measurement as one of its
outputs. Doppler radars may be Coherent Pulsed, Continuous Wave, or Frequency
Modulated. A continuous wave (CW) doppler radar is a special case that only provides a
velocity output. The advantage of combining doppler processing to pulse radars is to
provide accurate velocity information. This velocity is called Range-Rate. It describes the
rate that a target moves towards or away from the radar. A target with no range-rate
reflects a frequency near the transmitter frequency, and cannot be detected. Due to the
low pulse repetition frequency (PRF) of most coherent pulsed radars, which maximizes
the coverage in range, the amount of doppler processing is limited. The doppler processor
can only process velocities up to ±1/2 the PRF of the radar. This was not a problem for
weather radars.
Doppler Effect
This is most often demonstrated by the change in the sound wave of a passing
train. The sound of the train whistle will become "higher" in pitch as it approaches and
"lower" in pitch as it moves away. This is explained as follows: the number of sound
waves reaching the ear in a given amount of time (this is called the frequency) determines
the tone, or pitch, perceived. The tone remains the same as long as you and the train are
not moving relative to each other. As the train moves closer to you the number of sound
waves reaching your ear in a given amount of time increases. Thus, the pitch increases.
As the train moves away from you the opposite happens.
Continuous Wave RADAR(CW RADAR)
Continuous-wave radar system is a radar system where a known stable
frequency continuous wave radio energy is transmitted and then received from any
reflecting objects. The return frequencies are shifted away from the transmitted frequency
based on the Doppler effect if they are moving.
The main advantage of the CW radars is that they are not pulsed and simple to
manufacture. They have no minimum or maximum range and maximize power on a
target because they are always broadcasting.
They also have the disadvantage of only detecting moving targets, as stationary
targets (along the line of sight) will not cause a Doppler shift and the reflected signals
will be filtered out. CW radars also have a disadvantage because they cannot measure
range. Range is normally measured by timing the delay between a pulse being sent and
received, but as CW radars are always broadcasting, there is no delay to measure. .
3.DRAW THE BLOCKDIAGRAM OF PPI RADAR?
BASIC RADAR SYSTEMS
BASIC RADAR SYSTEMS
Radar systems like other complex electronic systems are composed of several major subsystems
and many individual circuits. Although modern radar systems are quite complicated, you can easily
understand the concept by basic diagram of pulsed radar
FUNDAMENTAL RADAR SYSTEM
Since most radars used today are some variation of the pulse-radar system, this section discusses those
used in a pulse radar. All other types of radars use some variation of these units. Refer to the block
diagram in figure 1-4.
Modulator You can see on the block diagram that the heart of
the radar system is the modulator. It generates all the necessary timing pulses (triggers) for use in the radar
and its associated systems. Its function is to ensure
that all subsystems of the radar system operate in a
definite time relationship with one another and that the intervals between pulses, as well as the pulses
themselves, are of the proper length.
Transmitter
The transmitter generates powerful pulses of electromagnetic energy at precise intervals. The required
power is obtained by using a highpower microwave oscillator (such as a magnetron)
or a microwave amplifier (such as a klystron) that is supplied by a low- power RF source.
4. EXPLAIN THE BASIC PRINCIPLE OF RADAR?
Radar Technology
The basic principle of operation of primary radar is simple to understand. However, the
theory can be quite complex. An understanding of the theory is essential in order to be
able to specify and operate primary radar systems correctly. The implementation and
operation of primary radars systems involve a wide range of disciplines such as building
works, heavy mechanical and electrical engineering, high power microwave engineering,
and advanced high speed signal and data processing techniques. Some laws of nature
have a greater importance here.
Radar measurement of range, or distance, is made possible because of the properties of
radiated electromagnetic energy.
1. Reflection of electromagnetic waves
The electromagnetic waves are reflected if they meet an electrically leading surface. If
these reflected waves are received again at the place of their origin, then that means an
obstacle is in the propagation direction.
2. Electromagnetic energy travels through air at a constant speed, at approximately the
speed of light,
o 300,000 kilometers per second or
o 186,000 statute miles per second or
o 162,000 nautical miles per second.
This constant speed allows the determination of the distance between the reflecting
objects (airplanes, ships or cars) and the radar site by measuring the running time of the
transmitted pulses.
3. This energy normally travels through space in a straight line, and will vary only slightly
because of atmospheric and weather conditions. By using of special radar antennas this
energy can be focused into a desired direction. Thus the direction (in azimuth and
elevation of the reflecting objects can be measured.
These principles can basically be implemented in a radar system, and allow the
determination of the distance, the direction and the height of the reflecting object.
(The effects atmosphere and weather have on the transmitted energy will be discussed
later; however, for this discussion on determining range and direction, these effects will
be temporarily ignored.)
5.EXPLAIN THE DIRECTION FINDING OF RADAR?
Direction-determination
The angular determination of the target is determined by the directivity of the antenna.
Directivity, sometimes known as the directive gain, is the ability of the antenna to
concentrate the transmitted energy in a particular direction. An antenna with high
directivity is also called a directive antenna. By measuring the direction in which the
antenna is pointing when the echo is received, both the azimuth and elevation angles
from the radar to the object or target can be determined. The accuracy of angular
measurement is determined by the directivity, which is a function of the size of the
antenna.
Radar units usually work with very high frequencies. Reasons for this are:



quasi-optically propagation of these waves.
High resolution (the smaller the wavelength, the smaller the objects the radar is able to
detect).
Higher the frequency, smaller the antenna size at the same gain.
The True Bearing (referenced to true north) of a radar target is the angle between true
north and a line pointed directly at the target. This angle is measured in the horizontal
plane and in a clockwise direction from true north. (The bearing angle to the radar target may
also be measured in a clockwise direction from the centerline of your own ship or aircraft and is referred to
as the relative bearing.)
Figure 2: Variation of echo signal strength
Figure 2: Variation of echo signal strength
The antennas of most radar systems are designed to radiate energy in a one-directional
lobe or beam that can be moved in bearing simply by moving the antenna. As you can see
in the Figure 2, the shape of the beam is such that the echo signal strength varies in
amplitude as the antenna beam moves across the target. In actual practice, search radar
antennas move continuously; the point of maximum echo, determined by the detection
circuitry or visually by the operator, is when the beam points direct at the target.
Weapons-control and guidance radar systems are positioned to the point of maximum
signal return and maintained at that position either manually or by automatic tracking
circuits.
In order to have an exact determination of the bearing angle, a survey of the north
direction is necessary. Therefore, older radar sets must expensively be surveyed either
with a compass or with help of known trigonometrically points. More modern radar sets
take on this task and with help of the GPS satellites determine the northdirection
independently.
6.EXPLAIN THE RADAR RANGE EQUATION?
Transmitted Power
Not every transmitting vacuum tube is equally good. Minimal production tolerances can
influence the obtainable transmit power and therefore also the theoretical attainable
range.
Remember: the most important feature of this equation is the fourth-root dependence!
Other then the transmit power we assume all other factors are constant.
Calling all of them the coefficient k, so the maximum range equation becomes:
Now it is easy to see that:
In order to double the range, the transmitted power would have to be increased by 16fold!
We can explain how such deviations change the maximum range values: if e.g. the
transmitted power of the russian Radar “Spoon Rest” is permited to fluctuate from
160 kW to 250 kW, will the maximum range values be correct for distances between 250
to 270 km?
From the relationship shown, we can state that 250km(160 kW)· 1,118 = 279.5 km(250 kW) so
the maximum range value would be correct between 250 and 270 km!
In practice results were reached between 180 kW and 240 kW since the transmitted
power of the planar vacuum tube was frequency dependent.
The inversion of this argument is also permissible: if the transmit power is reduced by
1/16 (e.g. failure into one of sixteen transmitter modules), then the change on the
maximum range of the radar station is negligible in the practice < 2%.
Sensitivity of the Receiver
While evaluating the minimal received power we follow a different procedure:
It's also under the 4th root, but in the denominator.
Well, a reduction of the minimal received power of the receiver gets an increase of
the maximum range.
For every receiver there is a certain receiving power as of which the receiver can work at
all. This smallest workable received power is frequently often called MDS - Minimum
Discernible Signal in radar technology. Typical radar values of the MDS echo lie in the
range of -104 dBm to -110 dBm.
Antenna Gain
The antenna gain is squared under the 4th root (Remember: the same antenna is used
during transmission and reception).
If one quadruples the antenna gain, it will double the maximum range.
Here is a concrete example from VHF- radar technology: Sometimes the P-12 (yagi
antennae array: G = 69) was mounted at the antenna of the P-14 (same frequency,
parabolic dish antenna: G = 900). This combination was often mentioned jocularly to “P–
13”. In accordance with our radar equation the maximum range should increase:
(Please note the fourth root was simplified against the square in the numerator and in the
denominator at once.)
It would be beautiful, if the maximum range could be tripled so simply. But bigger
antennas use much longer supply cables. Losses on the incoming feeding lines and losses
due to the mis-adjustment of the antenna give away half of what is invested.
Nevertheless: 1.6 times the maximum range isn't degraded either. But there are more
disturbances now: too many ambiguous targets (overreaches).
UNIT 5
Section A
1. The outermost layer of the optical fiber cable sheath or jacket
2. Define a fiber optic system.
An optical communications system is an electronic communication system
that uses light as the carrier of information. Optical fiber communication systems
use glass or plastic fibers to contain light waves and guide them in a manner
similar to the way electromagnetic waves are guided through a waveguide.
3.Define refractive index.
The refractive index is defined as the as the ratio of the velocity of propagation of light
ray in free space to the velocity of propagation of a light ray in a given material.
Mathematically, the refractive index is
n = c/µ
where c = speed of light in free space
µ = speed of light in a given material
4. Define critical angle.
Critical angle is defined as the minimum angle of incidence at which alight ray may
strike the interface of two media and result in an angle of refraction of 90°or greater.
5.Define single mode and multi mode propagation.
If there is only one path for light to take down the cable, it is called single mode. If there
is more than one path ,it is called multimode.
6. Define acceptance angle.
It defines the maximum angle in which external light rays may strike their/fiber interface
and still propagate down the fiber with a response that is no greater than 10 dB below the
maximum value.
7. Define numerical aperture.
Numerical aperture is mathematically defined as the sine of the maximum angle a light
ray entering the fiber can have in respect to the axis of the fiber and still propagate down
the cable by internal reflection.
Section B
1. EXPLAIN THE REFRACTIVE INDEX?
Refraction of light
As a light ray passes from one transparent medium to another, it changes direction; this phenomenon
is called refraction of light. How much that light ray changes its direction depends on the refractive
index of the mediums.
Refractive Index
Refractive index is the speed of light in a vacuum (abbreviated c,
c=299,792.458km/second) divided by the speed of light in a material (abbreviated v).
Refractive index measures how much a material refracts light. Refractive index of a
material, abbreviated as n, is defined as
n=c/v
In 1621, a Dutch physicist named Willebrord Snell derived the relationship between the
different angles of light as it passes from one transparent medium to another. When light
passes from one transparent material to another, it bends according to Snell's law which is
defined as:
n1sin(θ1) = n2sin(θ2)
where:
n1 is the refractive index of the medium the light is leaving
θ1 is the incident angle between the light beam and the normal (normal is 90° to the
interface between two materials)
n2 is the refractive index of the material the light is entering
θ2 is the refractive angle between the light ray and the normal
Note:
For the case of θ1 = 0° (i.e., a ray perpendicular to the interface) the solution is θ2 = 0°
regardless of the values of n1 and n2. That means a ray entering a medium perpendicular
to the surface is never bent.
The above is also valid for light going from a dense (higher n) to a less dense (lower n)
material; the symmetry of Snell's law shows that the same ray paths are applicable in
opposite direction.
2.EXPLAIN THE NUMERICAL APECTURE?
Optical Fiber’s Numerical Aperture (NA)
Multimode optical fiber will only propagate light that enters the fiber within a certain
cone, known as the acceptance cone of the fiber. The half-angle of this cone is called the
acceptance angle, θmax. For step-index multimode fiber, the acceptance angle is
determined only by the indices of refraction:
Where
n is the refractive index of the medium light is traveling before entering the fiber
nf is the refractive index of the fiber core
nc is the refractive index of the cladding
How to Calculate Number of Modes in a Fiber?
Modes are sometimes characterized by numbers. Single mode fibers carry only the
lowest-order mode, assigned the number 0. Multimode fibers also carry higher-order
modes. The number of modes that can propagate in a fiber depends on the fiber’s
numerical aperture (or acceptance angle) as well as on its core diameter and the
wavelength of the light. For a step-index multimode fiber, the number of such modes,
Nm, is approximated by
Where
D- is the core diameter
λ -is the operating wavelength
NA- is the numerical aperture (or acceptance angle)
3.DRAW THE STURCTURE OF THE FIBER OPTIC CABLE? The Structure of
an Optical Fiber
Typical optical fibers are composed of core, cladding and buffer coating.
The core is the inner part of the fiber, which guides light. The cladding surrounds the core
completely. The refractive index of the core is higher than that of the cladding, so light in
the core that strikes the boundary with the cladding at an angle shallower than critical
angle will be reflected back into the core by total internal reflection.
For the most common optical glass fiber types, which includes 1550nm single mode
fibers and 850nm or 1300nm multimode fibers, the core diameter ranges from 8 ~ 62.5
µm. The most common cladding diameter is 125 µm. The material of buffer coating
usually is soft or hard plastic such as acrylic, nylon and with diameter ranges from 250
µm to 900 µm. Buffer coating provides mechanical protection and bending flexibility for
the fiber.
4. EXPLAIN THE TOTAL INTERNAL REFLECTION?
Total Internal Reflection
When a light ray crosses an interface into a medium with a higher refractive index, it
bends towards the normal. Conversely, light traveling cross an interface from a higher
refractive index medium to a lower refractive index medium will bend away from the
normal.
This has an interesting implication: at some angle, known as the critical angle θc, light
traveling from a higher refractive index medium to a lower refractive index medium will
be refracted at 90°; in other words, refracted along the interface.
If the light hits the interface at any angle larger than this critical angle, it will not pass
through to the second medium at all. Instead, all of it will be reflected back into the first
medium, a process known as total internal reflection.
The critical angle can be calculated from Snell's law, putting in an angle of 90° for the
angle of the refracted ray θ2. This gives θ1:
Since
θ2 = 90°
So
sin(θ2) = 1
Then
θc = θ1 = arcsin(n2/n1)
For example, with light trying to emerge from glass with n1=1.5 into air (n2 =1), the
critical angle θc is arcsin(1/1.5), or 41.8°.
For any angle of incidence larger than the critical angle, Snell's law will not be able to be
solved for the angle of refraction, because it will show that the refracted angle has a sine
larger than 1, which is not possible. In that case all the light is totally reflected off the
interface, obeying the law of reflection.
5.Describe The Advantages Of Fiber Optic Systems?
Advantages of Fiber Optics:
 Less expensive - Several miles of optical cable can be made cheaper than
equivalent lengths of copper wire. This saves your provider (cable TV, Internet)
and you money.
 Thinner - Optical fibers can be drawn to smaller diameters than copper wire.
 Higher carrying capacity - Because optical fibers are thinner than copper wires,
more fibers can be bundled into a given-diameter cable than copper wires. This
allows more phone lines to go over the same cable or more channels to come
through the cable into your cable TV box.
 Less signal degradation - The loss of signal in optical fiber is less than in copper
wire.
 Light signals - Unlike electrical signals in copper wires, light signals from one
fiber do not interfere with those of other fibers in the same cable. This means
clearer phone conversations or TV reception.
 Low power - Because signals in optical fibers degrade less, lower-power
transmitters can be used instead of the high-voltage electrical transmitters needed
for copper wires. Again, this saves your provider and you money.
 Digital signals - Optical fibers are ideally suited for carrying digital information,
which is especially useful in computer networks.
 Non-flammable - Because no electricity is passed through optical fibers, there is
no fire hazard.
 Lightweight - An optical cable weighs less than a comparable copper wire cable.
Fiber-optic cables take up less space in the ground.
 Flexible - Because fiber optics are so flexible and can transmit and receive light,
they are used in many flexible digital cameras for the following purposes:
o Medical imaging - in bronchoscopes, endoscopes, laparoscopes
o Mechanical imaging - inspecting mechanical welds in pipes and engines
(in airplanes, rockets, space shuttles, cars)
o Plumbing - to inspect sewer lines
 Because of these advantages, you see fiber optics in many industries, most
notably telecommunications and computer networks. For example, if you
telephone Europe from the United States (or vice versa) and the signal is bounced
off a communications satellite, you often hear an echo on the line. But with
transatlantic fiber-optic cables, you have a direct connection with no echoes.
6.Explain The Fiber Optic Communication Model?
Above the figure shows the basic fiber optic communication model
It consists of
 Source- voice,audio,digital data or encoded data
 Transmitter- it consists of modulator &transmitter(here intensity modulation is
used)
 Channel-fiber optic cable
 Receiver-it consists of demodulator
 Destination-user end
7..Explain multimode fiber?
An optical fiber (or fibre) is a glass or plastic solid rode that carries light
along its length with the help of the total internal reflection.
It consists of core and cladding. The refractive index of the core is
greater then the cladding.. They can be either single mode or multimode fibers.
Multi-mode Fiber:
Fiber with large core diameter (greater than 10 micrometers) may be
analyzed by geometric optics. Such fiber is called multi-mode fiber,
from the electromagnetic analysis In a step-index multi-mode fiber, rays
of light are guided along the fiber core by total internal reflection. Rays
that meet the core-cladding boundary at a high angle (measured relative
to a line normal to the boundary), greater than the critical angle for this
boundary, are completely reflected. The critical angle (minimum angle
for total internal reflection) is determined by the difference in index of
refraction between the core and cladding materials. Rays that meet the
boundary at a low angle are refracted from the core into the cladding,
and do not convey light and hence information along the fiber. The
critical angle determines the acceptance angle of the fiber, often reported
as a numerical aperture. A high numerical aperture allows light to
propagate down the fiber in rays both close to the axis and at various
angles, allowing efficient coupling of light into the fiber. However, this
high numerical aperture increases the amount of dispersion as rays at
different angles have different path lengths and therefore take different
times to traverse the fiber. A low numerical aperture may therefore be
desirable.
In graded-index fiber, the index of refraction in the core decreases
continuously between the axis and the cladding. This causes light rays to
bend smoothly as they approach the cladding, rather than reflecting
abruptly from the core-cladding boundary. The resulting curved paths
reduce multi-path dispersion because high angle rays pass more through
the lower-index periphery of the core, rather than the high-index center.
The index profile is chosen to minimize the difference in axial propagation
speeds of the various rays in the fiber. This ideal index profile is very
close to a parabolic relationship between the index and the distance from
theaxis.
Single mode Fiber:
The most common type of single-mode fiber has a core diameter of 810 micrometers and is designed for use in the near infrared. The mode
structure depends on the wavelength of the light used, so that this fiber
actually supports a small number of additional modes at visible
wavelengths. Multi-mode fiber, by comparison, is manufactured with core
diameters as small as 50 micrometers and as large as hundreds of
micrometres. The normalized frequency V for this fiber should be less
than the first zero of the Bessel function J0 (approximately 2.405).
Single mode fiber has the least dispersion and hence are used for longer
distances.
8.Discuss the quantum efficiency of Led?
Quantum Efficiency of LED:
9. Explain The Modulation Of LED ?
10.. Explain The Optical Fiber Modes And Configuration?
SECTION C
1. Explain avalanche photodiode?
2.Explain the elements of optical fiber communication link?
3.Explain the single mode fiber optic cable?
4. Discuss the Losses of Optical Fiber?
Absorption Loss
Scattering Loss
Bending Losses
5.EXPLAIN LED?
LED structures
6.Explain LASER DIODES?
Laser Diodes
7. EXPLAIN PIN DIODE?