Text: Remote sensing. N identical z-polarized short dipole antennas are positioned at: Zd = (xn, Yn, z), where 0 < n < N as illustrated in the figure to the right. Let E(r) be a phasor representing the z-component of the field radiated by a dipole at the origin r = (x, y, z). Furthermore, assume that all dipoles of the system above radiate the same amount of average power P at the same oscillation frequency. However, there are no constraints on the phase shifts an of the individual antenna input current In.
a. Derive an expression for E(r) denoting the z-component of the TOTAL field phasor within the far-field of the radiating system. The expression should be given in terms of E(r), r = (x, y, z), and the propagation constant in the medium.
b. If λ = 100 m and d = 2λ = 1 m, what is the value of the Rayleigh distance that separates the far-field of the radiating system from the near-field? The Rayleigh distance is:
c. What is the maximum possible value of the total field component [E(x, 0, 0)] in the far-field? Under what conditions would the maximum be realized?