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268                                                       ANTENNA BASICS


                       
        Here cos =       and   is the phase shift to be provided. Finally, we obtain
                                
                
                      2
                    � +() 2
                                                                   ||
                            = (ℎ + ) − ||cos = (ℎ + ) −     (5.112)
                                                  
                            
                                                                   2
                                                                 � +()  2
        Step 3. The field intensity in the XZ-plane can be calculated as the fixed sum of fields emitted
        by all radiators
                                (, ) = ∑    −(||cos−  )            (5.113)
                                         =−
                               Σ
        Here cos =  √ +   .
                        2
                            2
                    ⁄
        Step 4. The results of numerical simulation for 2N + 1 = 201,  = 0.1,  = 10, ℎ =
        31.42 are presented in Figure 5.6.9. Note that the intensity data are normalized to the peak (the
        center of red sport). The RF focusing is not great as optical but quite satisfied and can be
        improved by increasing the total number of array radiators.

























              Figure 5.6.9 Beam focusing illustration. Field intensity distribution in XZ-plane.

        A significant advantage of such approach that the focal point position in space can be easily
        changed  electronically without  the mechanical  movement of any part of  the  array.  The
        described so-called near-field focusing, i.e. focusing the beam in the far field area of radiators,
        is a well-known technique used for many applications. Note several of them:
        Non-invasive medical therapy based on the limited non-thermal exposure of the human body
        to  low-level  electromagnetic radiation.  According to  various  types of research, it can  help
        healing cardiovascular disorders  and wounds,  treating  diabetes, dermatitis, gastrointestinal
        disorders, depression, relieving chronical pain, reducing the toxic side effects of chemotherapy,
        etc. A quite the opposite effect is the “skin on fire.” Since the RF energy of higher level can
        rapidly  heat  water molecules  in the  human  skin,  it causes intolerable pain and a burning
        sensation. If so, the focusing microwave array can be used as a ‘gun’ to scatter large crowds of
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