Topic: Electromagnetics
In a uniform linear array, four isotropic radiating elements are spaced $\lambda/4$ apart. The progressive phase shift between the elements required for forming the main beam at $60^{\circ}$ of the end fire is
- A. $-\pi$
- B. $-\pi/2$
- C. $-\pi/4$
- D. $-\pi/8$
Answer: C. $-\pi/4$
Explanation: We have, $\varphi=\beta d~cos~\theta+\alpha$. For forming the main beam at $60^{\circ}$ ($0 = \beta d\cos 60^{\circ} + \alpha$), at $\theta=60^{\circ}$ and $d=\lambda/4$, $\varphi=\frac{2\pi}{\lambda}\times\frac{\lambda}{4}[\cos 60^{\circ}-1]$ (if relative to end-fire maximum calculation difference, source states $\alpha=-\beta d$, then $\varphi = \beta d (\cos\theta - 1)$ resulting in $-\pi/4$ radians).