Question

In many land based radar installations, a rotating antenna sweeps a radio beam around the sky. But in a phased-array radar system, the antennas remain stationary and the beam is swept electronically. To see how this is done, consider two radio antennas, both on the y-axis, separated by a distance d, emitting coherent radiation with equal amplitude Eo and wavelength ?. If the radio signal emitted by these two antennas are in phase, they will create an interference pattern at distances large compared to d, with a principal maximum at ? = 0 (that is, in the +x direction, perpendicular to the line of the antennas). If d < ?, this is the only principal interference maximum in the angular range -90o < ? < 90o . Hence this principal maximum describes a beam emitted in the direction ? =0. ?n array of N antennas that are arranged along the y-axis at equal intervals of separation d will serve to narrow and intensify this beam, similar to what is seen when a laser passes through a diffraction grating. The relative phase ? of the emission from adjacent antennas can be varied, however. If the antenna at y = 0 emits a signal that is given by Eocos(?t – kx1), the antenna at y = d emits a signal given by Eocos(?t – kx2 + ?). The superposition of these waves effectively rotates the angular position of the beam ? (i.e. the angle to the location of the principal maximum). Thus, by varying ? from positive to negative values and back again, which can easily be done electronically, the beam can be made to sweep back and forth around ? =0. A weather radar unit to be installed on an airplane emits radio waves at 9000 MHz. The unit uses 15 antennas in an array 30.0 cm long (from the antenna at one end of the array to the antenna at the other end). What must the maximum and minimum values of ? be (that is, the most positive and most negative values) if the radar beam is to sweep 45o to the left or right of the airplane's direction of flight? Give your answer in radians.

Answer 1