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216                                                       ANTENNA BASICS


        The constant phase factor  −  is omitted as nonessential. The factor   is defined in such way
                                                                 0
        that at the peak |( ,  )| = 1 where  ,   are the angular coordinates of the emitted field
                            0
                         0
                                            0
                                         0
        maxima. In practice, the  far field  vector of the electric field  may comprise  more than one
        component. If so, the measurements must be repeated for each of them and included in the
        database of antenna test.  There are numerous  variants of antenna pattern  |(, )|
        representation.
        3D pattern (see Figure 5.2.8a, b) is the works of art but not very informative. Evidently, it
                                              defines the variation of E-fields (typically)
                                              emitted or received by an antenna in space as a
                                              function of spherical angles    and   at some
                                              fixed distance in far field area. A pattern can be
                                              plotted  in relative  units  (normalized  to  the
                                              boresight or total radiated power)  on a linear
                                              scale or preferable in decibels (dB) and allows
                                              visualizing how and where an antenna transmits
                                              and receives EM energy. Usually, the antenna
                                              pattern is frequency dependable. If so, each plot
                                              might be marked with a specific frequency or
                       a)                     b)  range of frequencies.

                                              Multiple 2D slices of 3D pattern in Cardinal
           Figure 5.2.8 Illustration of 3D pattern   cuts such as E- or H-plane, vertical (like Figure
                                              5.2.8b)  or  horizontal planes, azimuth  or
        elevation planes and many other cuts might represent an antenna performance much better
        depending on pattern shape complexity. Any of such 2D pattern slices can be drawn in Cartesian
        coordinates as shown in Figure 5.2.8c (normalized in  logarithmic  scale) or  cylindrical
        coordinates in Figure 5.2.8d (normalized in linear scale). The main beam is the part of antenna


                    [dB]
                                       - 3 dB Level
                                                   c)
                               Main
                               Beam

                  Sidelobes               Sidelobes



                                                                             d)

            Figure 5.2.8 Illustration of c) 2D pattern slice and d) pattern in cylindrical coordinates

        pattern where maximum emitted power is concentrated. Beamwidth (BW ) or Half-Power-
                                                                    −3
        BeamWidth (HPBW) of an antenna pattern is determined by the angular separation of the half-
        power points (i.e. -3 dB) of the radiated pattern as shown in Figure 5.2.8c. To better control the
        antenna pattern shape, the beamwidth may be additionally specified at the level -10 dB (BW −10 )
        and sometimes at the level  like  -20dB  (BW −20 ).  All other  beams  of the  pattern  belong to
        sidelobes representing the energy radiated in or received from typically undesired directions.
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