GATE EC 2001 Electromagnetics Solution Q 7

GATE EC 2001 Electromagnetics Solution Q 7

In a uniform linear array, four isotropic radiating elements are spaced λ/4 apart. The progressive phase shift between the elements required for forming the main beam at 600 off the end-fire is:__.

(a) -\pi\;radians

(b) -\pi/2\;radians

(c) -\pi/4\;radians

(d) -\pi/8\;radians

Ans :- (c)

Explanation

\psi=\beta d\;\cos\;\theta+\alpha

For an end fire, \psi=0

0=\beta d\;\cos\;\theta+\alpha \therefore \alpha=-\beta d \therefore \;\;\psi=\beta d\left(\cos\theta-1\right) \therefore \;\;\psi=\frac{2\pi}\lambda\times\frac\lambda4\left(\cos\;60^\circ-1\right) =\frac\pi2\times\left(-\frac12\right)=-\frac\pi4radians

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