GATE EC 1990 Electromagnetics Solution Q 4

GATE EC 1990 Electromagnetics Solution Q 4

Two isotropic antennas are separated by a distance of two wavelengths. If both the antennas are fed with currents of equal phase and magnitude, the number of lobes in the radiation pattern in the horizontal plane are_____.

(a) 2

(b) 4

(c) 6

(d) 8

Ans :- (d)

Explanation

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

Putting d=2\lambda\;and\;\alpha=0

\psi=0+\frac{2\pi}\lambda\cdot2\lambda\cdot\cos\theta=4\pi\;\cos\theta

2 cos \left(\frac\psi2\right)=2\cos\left(2\pi\;\cos\theta\right)

\theta varies from 0 to 2\pi

Maximum will be at \theta=0,\frac\pi3,\frac\pi2,\frac{2\pi}3,\pi,\frac{4\pi}3,\frac{3\pi}2,\frac{5\pi}3

So, number of lobes in the radiation pattern in the horizontal plane = 8.

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