Antenna and Radar Engineering

Goodwill @ , Department of Electronics & Communication Engineering,Sharda University, India

School of Engineering & Technology

Antenna & Radar Engineering

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Antenna and Radar Engineering

ECE-005




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Radiation Pattern




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Radiation Pattern lobes




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Field RegionsKr>>>>>1Farfield region

Kr>1 radiating near field

Kr<<<<<1Near reactive field region




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Radiation Power Density




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Directivity

Gain

It is the ratio of Radiation intensity in a given direction to radiation intensity radiated by test or isotropic antenna.

It is the ratio of Radiation intensity in a given direction to radiation intensity radiated by test or isotropic antenna , having no transmission line and antenna loss.




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Antenna Efficiency or total Antenna Efficiency




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Antenna transmitting mode Thevenin Equivalent

Input Impedance

Input Impedance is given by




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Antenna Radiation efficiency

Antenna effective aperture(area)




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Polarization

Rotation of wave




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Linear Polarization

Circular Polarization




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Elliptical Polarization




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• The direction of maximum radiation is in the horizontal plane is considered to be the front of the antenna, and the back is the direction 180º from the front

• For a dipole, the front and back have the same radiation, but this is not always the case

Front-to-Back Ratio

Radiation Pattern




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We begin our analysis of antenna by considering some of the oldest, simplest and most basic configurations. Initially we will try to minimize antenna structure and geometry to keep mathematical details minimum.




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Mathematical Analysis

Analytical analysis Numerical analysis

Requires algorithm , approximations, In

short tedious calculation

Gives a function (well behaved) easy to

differentiate




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AUXILIARY FUNCTION

Well Behaved function A

Differentiation is very easy i.e. finding CURL e.g.

Tedious integration

Simple integration




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Poisson's Equation

Solution of Poisson's eqn

Charge Source




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Solution of the inhomogeneous vector potential wave equation

Let us assume that a source with current density Jz which in the limit is anInfinitesimal source is placed at the origin. Since the current density is directed along the z-axis Jz, only Az component will exist.




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Helmholtz equation for vector potential

Assumption : Source free region i.e. J=0

Az = f(r)= Az(r)

Assumption : current element as a point source

Expanding eq.(1) in spherical coordinate system having only radial component of Az

…….(1)




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Fig: Source at origin




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We have :

Eqn(2) is differential eqn of order two so its solutions are

…..(2)

…..(i)

…..(ii)




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For transmitting antenna we have eq(i) as soln for time varying case

Solution for static case becomes

Only multiplication of to static case

gives soln for time varying case, we will first calculate soln for static case than by multiplying by we will get soln for time varying case

*




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…….(3)

Similarly for eqn (3) we have soln as

This soln is for static case now to get soln for time varying case multiplying by




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(This solution is for time varying case)

Corresponding Vector potential are




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Solution to Vector wave eqns are

Generalized equation




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Generalized equation for surface integral

Generalized equation for line integral




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Final expression for Auxiliary vector potential




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RETARDED VECTOR POTENTIALThe retarded potential formulae describe the scalar or vector potential for electromagnetic

fields of a time-varying current . The retardation between cause and effect isthereby essential; e.g. the signal takes a finite time, corresponding to the velocity of light, to

propagate from the source point origin of the field to the point P, where an effect is produced ormeasured.




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Field radiated velocity c

Field at P have time lag

Field radiated from dipole will reach to p with a time lag




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WIRE ANTENNAS

It is of three types

Infinitesimal dipole Small dipole Finite length dipole




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Infinitesimal dipole Small dipole Finite length dipole

(z) (z)

Current distribution (Z vs I)




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WIRE ANTENNAS

It is of three types




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(z)

Infinitesimal dipole




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Calculation of Auxiliary vector potential

CONVERSION OF AUXILIARY VECTOR POTENTIAL TO SPHERICAL COORDINATE SYSTEM




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Calculation of H from Auxiliary vector potential

H=

Calculation of H from curl should be in spherical coord. system

Calculation of E from curl of H should be in spherical coord. system

SIMILARLY FROM MAXWELLS EQN




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Numerical

SolutionSince the length is




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Directivity




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Radiation Pattern 3 D




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In this figure the antenna is in the vertical axis and radiation is maximal in the plane of the wire, and minimal off the ends of the antenna.

Radiation Pattern 2 D infinitesimal dipole

http://en.wikipedia.org/wiki/File:RadPatt-lin.png




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Small Dipole

Small dipole Current distribution




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Soln@ Sangeeta sharma EC-E




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Numerical

SolutionSince the length is λ/20

Calculate the power radiated by λ/20 dipole in free space and find out Radiation resistance

Since It’s a case of small dipole

=0.493

=




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Finite length dipole(z)

Current distribution(Sinusoidal) (Z vs I)




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Taking small elemental length dz , z distance from origin considering it infinitesimal dipole

Now taking Farfield approximation Kr>>>>>>>1




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We have:




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written

Taking small elemental length dz , z distance from origin considering it infinitesimal dipole using Electric field of infinitesimal dipole for Farfield region we can write:




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Considering one more assumption for farfield region

For whole length , we integrate dE:




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Final expression




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FOR HALF WAVELENGTH




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We have to use this integration value directly




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MONOPOLE

Using Image theory

We are considering Half wave dipole using image theory for a Monopole antenna so the powerRadiated will actually be half, Radiation resistance will also be Half.

73/2=36.5




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THANK YOU FOR YOUR KIND ATTENTION !

Questions




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Near Field Region




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Intermediate Field Region




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Farfield Region

Antenna and Radar Engineering

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