Question

The necessary condition for maximum of the first side lobe of n element array is ______

(a) \(\frac{Nᴪ}{2}=±\frac{5π}{2}\)

(b) \(\frac{Nᴪ}{2}=±\frac{3π}{2}\)

(c) \(\frac{Nᴪ}{2}=±\frac{π}{2}\)

(d) \(\frac{Nᴪ}{2}=±\frac{4π}{2}\)

I had been asked this question in class test.

The above asked question is from Radiation Pattern of 8-Isotropic Elements topic in portion Antenna Array of Antennas

Answer 1

Correct answer is (b) \(\frac{Nᴪ}{2}=±\frac{3π}{2}\)

The explanation: The secondary maxima occur when the numerator of the array factor equals to 1.

⇨ \(sin(\frac{Nᴪ}{2})=±1\)

⇨ \(\frac{Nᴪ}{2}=±\frac{2s+1}{2} π \)

⇨ \(\frac{Nᴪ}{2}=±\frac{3π}{2}\) [s=1 for first minor lobe].