PARABOLIC REFLECTOR

PARABOLIC REFLECTOREarly use : radar application in World War II, radio astronomy, microwave communication, satellite tracking, deep space communication.Plane Reflector Corner Reflector

11PARABOLIC REFLECTOROverall radiation characteristics is upgraded.Focal Point : Parallel beam converges at this point after reflection and vice versa.Vertex : Symmetrical point on the surface Axis : Line joining the focal point and the vertex

2 Different types of FeedFront-fedTransmitter/receiver is at focusLong transmission line

Cassegrain-fedPrimary reflector is a parabola and the secondary is a hyperbolaFeed is placed along the axis of the parabola near vertex; some times behind the primary reflectorUsed for pattern control

3 Different types of parabolic reflectorParabolic Right CylinderEnergy is collimated at a line parallel to the axis of the cylinder through the focal point of the reflector. Source feed- linear dipole, linear array or a slotted waveguide.

ParaboloidFormed by rotating the parabola around its axis. Feed- pyramidal/conical horn Produce high gain pencil beam with low side lobes and good cross-polarizationWidely used for low-noise

4Difference between cylinder & paraboloidThe amplitude taper, due to variations in distance from the feed to the surface of the reflector, is proportional to (1/p) in a cylinder compared to (1/r2) in a paraboloid.The focal region is a line-source for a cylinder and a point source for a paraboloid.When the fields of the feed are linearly polarized parallel to axis of the cylinder, no cross-polarization happens; but that does not happen for paraboloid.Cylinders are mechanically simpler to build and also give larger aperture blockage, but they do not possess attractive characters of a paraboloid.

5Surface geometryThe surface is formed by rotating a parabola about its axis.OP + PQ = 2f since OP = r and PQ = r cos Hence,

for

Again from Snells law, = = /2

6Surface geometryIn terms of rectangular co-ordinates,

with

If is the subtended angle, then - distance along axis from focal point to the edge of the rimPutting , we get -

7Induced current densityTo determine the radiation characteristics (pattern, gain, efficiency, polarization etc.) of a parabolic reflector, the current density induced on its surface must be known, which is given as-

If the reflecting surface is in the far-field of the source generating the incident waves, then the equation can also be written as ------(1)Where is the intrinsic impedance of the medium, are radial unit vectors along the path of reflected wave and is the reflected electric fields.

8Gain function & electric fieldIf a y-polarized source with a gain function of is placed at the focal point of a parabolic reflector, the radiation intensity of the source is given by : total radiated power.The incident field, with a direction perpendicular to the radial distance, can be written as

where is the unit vector perpendicular to and parallel to the plane formed by and .

9Reflected electric field & Current densityThen the reflected field at r(the reflection point), due to the reflector currents, is given by ----(2) : unit vector along the polarization of the reflected fieldThen, putting value of in equation (1) and , it can be written as ----(3) where -----(4)

10Analysis of radiation characteristicsTwo techniques for analyzing the performance Aperture Distribution Method Current Distribution Method In 1st method, the field reflected by the paraboloid surface is first found over a plane normal to axis. Equivalent sources are then formed over the plane and these are used to compute the radiated field.And in 2nd method, induced current density Js is formulated over the illuminated surface of the reflector and then this Js is integrated over the surface of the reflector to yield the far-zone radiation fields.

1111Approximations The following approximations are made-The current density is zero on the shadow side(S2) of the reflector.The discontinuity of the current density over the rim(T) f the reflector is neglected.Direct radiation from the feed and aperture blockage by the feed are neglected.

12Current distribution methodUsing the potential function method, the E and H fields radiated by the sources J and M for far field can be written as -

If the current distributions are introduced by electric and magnetic field incident on a perfect electric conducting surface, the fields created by those currents are known as scattered fields.

13Current distribution methodIf the conducting surface is closed, then the far zone fields can be reduced by letting M =0 and reducing the volume integral to a surface integral with the surface current density J replaced by a linear current density Thus,

14Geometrical arrangement of surfaceThe total scattered fields would be the sum of surface currents over the illuminated area(S1)surface charges over the illuminated area(S1)line charge distribution over boundary T(effect zero in far zone)The total fields can be obtained by a superposition of the radiation from the primary source in directions greater than and that scattered by the surface as obtained by current distribution method.

15Radiated field componentsThe far zone electric field of a parabolic reflector, neglecting the direct radiation, has two components

where

Now, putting values from eqn (2),(3),(4) into eqn(5)

16Current distributionsWhere

The radiated field components obtained from current distribution method and aperture distribution method lead to similar results when component is neglected. becomes negligible for = region.

17Directivity & aperture efficiencyLet us assume that the feed pattern is circularly symmetric (independent of ) and for Assuming , (as for =) the total E-field in the direction of (=) is given by either or -

Then the power intensity (power/unit solid angle) in the forward direction of (=) reduces to -

18Directivity & aperture efficiencyThen the antenna directivity in the forward direction can be written as

The focal length is related to the angular spectrum and the diameter d by

Then aperture efficiency is defined as

It is a function of the subtended angle and the feed pattern of the reflector.

19applicationsThe most common modern applications of the parabolic reflector are in satellite dishes, reflecting telescopes, radio telescopes, parabolic microphones, and many lighting devices such as spotlights, car headlights, PAR cans and LED housings.Liquid mirror telescope is prepared using the concept of forming paraboloid. Parabolic reflectors are a popular alternative for increasing wireless signal strength.

20Advantage & disadvantageIt is an ideal collimating device. It brings the energy to the focal point from a distant source; similarly, it can be used to project energy source present at its focus.In contrast with spherical reflectors, which suffer from a spherical aberration(d/f ratio becoming larger), parabolic reflectors can be made to accommodate beams of any width. However, if the incoming beam makes a non-zero angle with the axis, parabolic reflectors suffer from an aberration called coma.It is severely handicapped in angular scanning. By contrast, spherical reflector is better of use.21