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

Question

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 [latex] \phi _i(t) [/latex] between adjacent antennas. What then is the direction of the principal maximum of order 0? How should we choose [latex] \phi _i(t) [/latex] in order to have sweeping at an angular speed [latex] \omega [/latex]?

Accepted Answer

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 [latex] \phi =\phi _o +2\pi (d/\lambda ) \sin heta , \ ext {where} \ \phi _o [/latex] is their initial phase shift. The direction of the pth principal maximum is such that [latex] \phi =2p\pi ; \ ext {thus,} \sin heta _p=(\lambda /d)(p-\phi _o/2\pi ). [/latex] If the initial phase shift [latex] \phi _o [/latex] 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 [latex] \sin heta _1=(\lambda /d)=0.5, \ ext {thus} \ heta _1=30 ^\circ . [/latex] The angular half-width of the principal maximum is the direction of the first zero, given by [latex] N\phi /2=\pi , \ ext {that is,} \ \sin(\delta heta )=(1/30)(\lambda /d) \ ext {or} \ \delta heta =0.95^\circ . [/latex]

b) If the consecutive antennas have an initial phase shift [latex] \phi _i(t) [/latex] , the direction of the principal maximum of order 0 is given by [latex] \sin heta _o=-\lambda \phi _i(t)/2\pi d. [/latex] . The sweeping has a constant angular speed ω if [latex] heta _o=\omega t; \ ext {hence,} \phi _i(t)=-2\pi (d/\lambda )\sin(\omega t). [/latex]

Question 8.2: A radar station uses an emitter that consists of 30 rectilin...

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