Page 162 - Satellite Communications, Fourth Edition
P. 162

142  Chapter Six

                              of propagation. The vector relationship is shown in Fig. 6.4b, where E
                              represents the electric field, H the magnetic field, and k the direction
                              of propagation. These vectors form a right-hand set in the sense that
                              when one looks along the direction of propagation, a clockwise rotation
                              is required to go from E to H. An important practical point is that the
                              wavefront can be assumed to be plane; that is, E and H lie in a plane
                              to which k is a normal.
                                In the far field, the electric field vector can be resolved into two com-
                              ponents, which are shown in relation to the coordinate system in Fig. 6.5a.
                                                       is tangent at point P to the circular arc of
                              The component labeled E
                              radius r. The component labeled E is tangent at point P to the circle of

                              radius r sin
centered on the z axis (this is similar to a circle of latitude
                              on the earth’s surface). Both these components are functions of 
 and
                              and in functional notation would be written as E (
,  ) and E (
,  ). The


                              resultant magnitude of the electric field is given by
                                                               2    2
                                                       E   2E 
   E                       (6.1)
                              If E and E are peak values, E will be the peak value of the resultant,


                              and if they are rms values, E will be the rms value of the resultant.
                                The vector E shown at the origin of the coordinate system represents
                                           0
                              the principal electric vector of the antenna itself. For example, for a
                              horn antenna, this would be the electric field vector across the aper-
                              ture as shown in Fig. 6.5b. For definiteness, the E vector is shown
                                                                              0
                              aligned with the y axis, since this allows two important planes to be
                              defined:
                                         The H plane is the xz plane, for which     0
                                         The E plane is the yz plane, for which     90°

                                Magnetic field vectors are associated with these electric field compo-
                              nents. Thus, following the right-hand rule, the magnetic vector associ-
                              ated with the E component will lie parallel with E and is normally


                              denoted by H , while that associated with E will lie parallel (but point-


                              ing in the opposite direction) to E and is denoted by H . For clarity, the


                              H fields are not shown in Fig. 6.5, but the magnitudes of the fields are
                              related through the wave impedance Z . For radio waves in free space,
                                                                 W
                              the value of the wave impedance is (in terms of field magnitudes)
                                                        E     E
                                                  Z                120                    (6.2)
                                                    W
                                                        H 
  H
                              The same value can be used with negligible error for radio waves in the
                              earth’s atmosphere.
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