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Antenna and Radar Engineering

Antenna and Radar Engineering. ECE-005. Radiation Pattern. Radiation Pattern lobes. Field Regions. Kr>>>>>1 Farfield region. Kr>1 radiating near field. Kr<<<<<1 Near reactive field region. Radiation Power Density . Directivity .

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Antenna and Radar Engineering

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  1. Antenna and Radar Engineering ECE-005

  2. Radiation Pattern

  3. Radiation Pattern lobes

  4. Field Regions Kr>>>>>1 Farfield region Kr>1 radiating near field Kr<<<<<1 Near reactive field region

  5. Radiation Power Density

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

  7. Antenna Efficiency or total Antenna Efficiency

  8. Input Impedance Thevenin Equivalent Antenna transmitting mode Input Impedance is given by

  9. Antenna Radiation efficiency Antenna effective aperture(area)

  10. Polarization Rotation of wave

  11. Linear Polarization Circular Polarization

  12. Elliptical Polarization

  13. Front-to-Back Ratio • 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 Radiation Pattern

  14. 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.

  15. Mathematical Analysis Analytical analysis Numerical analysis Requires algorithm , approximations, In short tedious calculation Gives a function (well behaved) easy to differentiate

  16. Tedious integration Simple integration Differentiation is very easy i.e. finding CURL e.g. Auxiliary function Well Behaved function A

  17. Poisson's Equation Charge Source Solution of Poisson's eqn

  18. Solution of the inhomogeneous vector potential wave equation Let us assume that a source with current density Jz which in the limit is an Infinitesimal source is placed at the origin. Since the current density is dire cted along the z-axis Jz, only Az component will exist.

  19. Helmholtz equation for vector potential Assumption : current element as a point source Az = f(r)= Az(r) Assumption : Source free region i.e. J=0 …….(1) Expanding eq.(1) in spherical coordinate system having only radial component of Az

  20. Fig: Source at origin

  21. We have : …..(2) Eqn(2) is differential eqn of order two so its solutions are …..(i) …..(ii)

  22. For transmitting antenna we have eq(i) as soln for time varying case * Only multiplication of to static case Solution for static case becomes 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

  23. …….(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

  24. (This solution is for time varying case) Corresponding Vector potential are

  25. Solution to Vector wave eqns are Generalized equation

  26. Generalized equation for surface integral Generalized equation for line integral

  27. Final expression for Auxiliary vector potential

  28. Retarded Vector Potential The retarded potential formulae describe the scalar or vector potential for electromagnetic fields of a time-varying current . The retardation between cause and effect is thereby 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 or measured.

  29. Field at P have time lag Field radiated velocity c Field radiated from dipole will reach to p with a time lag

  30. Wire antennas It is of three types Finite length dipole Infinitesimal dipole Small dipole

  31. (z) (z) Finite length dipole Infinitesimal dipole Small dipole Current distribution (Z vs I)

  32. Wire antennas It is of three types

  33. (z) Infinitesimal dipole

  34. Calculation of Auxiliary vector potential Conversion of Auxiliary vector potential to spherical coordinate system

  35. Calculation of H from Auxiliary vector potential H= Calculation of H from curl should be in spherical coord. system Similarly from Maxwellseqn Calculation of E from curl of H should be in spherical coord. system

  36. Numerical Since the length is Solution

  37. Directivity

  38. Radiation Pattern 3 D

  39. Radiation Pattern 2 D infinitesimal dipole 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.

  40. Small Dipole Small dipole Current distribution

  41. Soln@ Sangeetasharma EC-E

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