ENGINEERING MATLAB

Documenting and detailing work and answers (explanation of method used, commented Mat-lab code, plotted results, interpretation of results, etc.) Question 1: For a dipole antenna of length l = 3λ/2, a‐ Determine the directions of maximum radiation. b‐ Obtain an expression for Smax. c‐ Generate a plot of the normalized radiation pattern F(θ). Question 2: A two‐element array consisting of two parallel, vertical, Hertzian dipoles with axes along the x‐direction separated by a distance d along the z‐axis is placed in a coordinate system whose z‐axis points eastward and whose x‐axis points toward the zenith. a0 = 1 and a1 = 2 are the amplitudes of the excitations of the antennas at z = 0 and at z = d, respectively, and  is the phase of the excitation of the antenna at z = d relative to that of the other antenna. The power density radiated by a Hertzian dipole is given by Se (θ ′) = S0 sin2 θ ′, where θ ′ is the angle measured from the dipole axis. a‐ Determine the array factor in the x‐z plane for  = /2 and d = /4. b‐ Determine the normalized radiation intensity S(θ) in the x–z plane and plot it. (An alternative way of determining the maximum of S(θ) is by trial and error if you cannot calculate it) Question 3: A uniformly illuminated aperture is of length lx = 20λ. a‐ Plot the normalized radiation intensity F(θ). b‐ Determine the beamwidth between first nulls in the x–z plane. Question 4: A two‐element array with equal excitation and a separation d = 5λ/2. a‐ Plot the array factor. b‐ Estimate the half‐power beamwidth. Question 5: A twelve‐element linear array with λ/π spacing is excited with equal amplitudes. In order to steer the main beam to a direction 30 above the broadside direction, a‐ what should be the incremental phase delay between adjacent elements? b‐ Give the expression for the array factor and plot the pattern.