Question 8.2: A radar station uses an emitter that consists of 30 rectilin...
A radar station uses an emitter that consists of 30 rectilinear parallel wires separated by a distance d = 20 cm between consecutive wires. The station uses a wavelength of 10 cm. a) What are the directions of the principal maximums of order 0 and 1 and what is their angular width. b) Instead of rotating the array, it is possible to use a phase command, which consists of producing a phase shift \phi _i(t) between adjacent antennas. What then is the direction of the principal maximum of order 0? How should we choose \phi _i(t) in order to have sweeping at an angular speed \omega ?
a) If the wave is emitted in a direction making an angle θ with the normal to the array of wires (Figure 8.17), the phase shift between two consecutive waves is \phi =\phi _o +2\pi (d/\lambda ) \sin\theta , \ \text {where} \ \phi _o is their initial phase shift. The direction of the pth principal maximum is such that \phi =2p\pi ; \ \text {thus,} \sin\theta _p=(\lambda /d)(p-\phi _o/2\pi ). If the initial phase shift \phi _o is equal to zero, the principal maximum of order 0 is in the normal direction (θ = 0), while the maximum of order 1 is in the direction such that \sin\theta _1=(\lambda /d)=0.5, \ \text {thus} \ \theta _1=30 ^\circ . The angular half-width of the principal maximum is the direction of the first zero, given by N\phi /2=\pi , \ \text {that is,} \ \sin(\delta \theta )=(1/30)(\lambda /d) \ \text {or} \ \delta \theta =0.95^\circ .
b) If the consecutive antennas have an initial phase shift \phi _i(t) , the direction of the principal maximum of order 0 is given by \sin\theta _o=-\lambda \phi _i(t)/2\pi d. . The sweeping has a constant angular speed ω if \theta _o=\omega t; \ \text {hence,} \phi _i(t)=-2\pi (d/\lambda )\sin(\omega t).
