Slide 1

Cylindrical coordinate systemhe distance from the axis may be called theradial distanceorradius, while the angular coordinate is sometimes referred to as theangular positionor as theazimuth. The radius and the azimuth are together called thepolar coordinates, as they correspond to a two-dimensionalpolar coordinatesystem in the plane through the point, parallel to the reference plane. The third coordinate may be called theheightoraltitude(if the reference plane is considered horizontal),longitudinal position,[1]oraxial position.[2]Cylindrical coordinates are useful in connection with objects and phenomena that have some rotationalsymmetryabout the longitudinal axis

The three coordinates (,,z) of a pointPare defined as:The radial distanceis theEuclidean distancefrom the z axis to the pointP.The azimuthis the angle between the reference direction on the chosen plane and the line from the origin to the projection ofPon the plane.The heightzis the signed distance from the chosen plane to the point P.

Cylindrical coordinate systemThecoordinate surfacesof the cylindrical coordinates (,,z). The redcylindershows the points with=2, the blueplaneshows the points withz=1, and the yellow half-plane shows the points with=60. Thez-axis is vertical and thex-axis is highlighted in green. The three surfaces intersect at the pointPwith those coordinates (shown as a black sphere) in one direction, and

Conversion:Z = z = tan-1 (y/x)In situations where one needs a unique set of coordinates for each point, one may restrict the radius to benon-negative(0) and the azimuthto lie in a specificintervalspanning 360, such as (180,+180] or [0,360).Spherical Polar coordinate system

To define a spherical coordinate system, one must choose two orthogonal directions, thezenithand theazimuth reference, and anoriginpoint in space. These choices determine a reference plane that contains the origin and is perpendicular to the zenith. The spherical coordinates of a pointPare then defined as follows:Theradiusorradial distanceis theEuclidean distancefrom the originOtoP.Theinclination(orpolar angle) is the angle between the zenith direction and the line segmentOP.Theazimuth(orazimuthal angle) is the signed angle measured from the azimuth reference direction to the orthogonal projection of the line segmentOPon the reference plane.r 00 180 ( rad)0 < 360 (2 rad)

Spherical Polar coordinate system

Antenna ParametersFundamental Parameters of Antennas (Contd..)RADIATION PATTERNS

Fundamental Parameters of Antennas (Contd..)Radiation patterns usually indicate either electric field, E intensity or power intensity. Magnetic field intensity, H has the same radiation pattern as E related by 0. The polarization or orientation of the E field vector is an important consideration in an E field plot. A transmit receive antenna pair must share same polarization for the most efficient communication.

Fundamental Parameters of Antennas (Contd..)

Coordinate SystemFundamental Parameters of Antennas (Contd..)Since the actual field intensity is not only depends on radial distance, but also on how much power delivered to antenna, we use and plot normalized function divide the field or power component with its maximum value. E.g. the normalized power function or normalized radiation intensity :

Fundamental Parameters of Antennas (Contd..)

So,In contrast with isotropic antenna, a directional antenna radiates and receives preferentially in some direction. If the antenna radiates EM waves equally in all directions, it is termed as isotropic antenna, where the normalized power function is equal to 1.Fundamental Parameters of Antennas (Contd..)

The normalized radiation patterns for a generic antenna, called polar plot. A 3D plot of radiation pattern can be difficult to generate and work with, so take slices of the pattern and generate 2D plots (rectangular plots) for all at =/2 and =3/2Polar plotRectangular plot (in dB)

Radiation pattern lobesRadiation pattern lobes

In most radar systems, low side lobe ratios are very important to minimize false target indications through the side lobes (e.g., -30 dB).

Fundamental Parameters of Antennas (Contd..)

Fundamentals of Electromagnetics With Engineering Applications by Stuart M. Wentworth Copyright 2005 by John Wiley & Sons. All rights reserved.

Figure 8-4a (p. 392)General far-field antenna radiation pattern: (a) polar plot; (b) rectangular plot.

Fundamentals of Electromagnetics With Engineering Applications by Stuart M. Wentworth Copyright 2005 by John Wiley & Sons. All rights reserved.

Figure 8-4a (p. 392)General far-field antenna radiation pattern: (a) polar plot; (b) rectangular plot.