22.1 Antenna Arrays

Lens Antennas1087where the left-hand side represents the optical pathFPAB. Geometrically, we haveRcos +d=FandF=R0+h0. EliminatingdandR0, we find the lens profile:R=F 1 1n 1 1ncos ( )which is recognized to be the equation for an ellipse with eccentricity and focal lengthe=1/nandF1= the above discussion, we considered only the refracted rays through the dielectricand ignored the reflected waves. These can be minimized by appropriate Antenna ArraysArrays of antennas are used to direct radiated power towards a desired angular number, geometrical arrangement, and relative amplitudes and phases of the arrayelements depend on the angular pattern that must be an array has been designed to focus towards a particular direction, it becomesa simple matter tosteerit towards some other direction by changing the relative phasesof the array elements a process shows some examples of one- and two-dimensional Arrays consistingof identical linear antennas.

22.3. Array Pattern Multiplication 1091 [g, phi] = gain1d(d, a, Nph); % compute normalized gain of an array Example 22.3.1: Consider an array of two isotropic antennas at positions d0 =0 and d1 =ˆxd (alternatively, at d0 =−(d/2)ˆx and d1 =(d/2)ˆx), as shown below: The displacement phase factors are: ejk·d0 =1,ejk·d1 =ejkxd=ejkdsinθcosφ or, in the symmetric case:

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