Phased array

Consider first any one of the dipole radiators shown in Figure 12.10. For a dipole oriented perpendicular to the plane of the page, the radiation is uniform in all directions on the plane of the page. Suppose we want to construct something like a radar that sends out radiation in only a specific direction, an not in all directions. It is possible to do so using a chain of $N$ dipoles with spacing $d < \lambda$. The maxima of the radiation pattern occur at

$$\sin \theta = m \frac{\lambda}{d}$$ (12.24)

and as $\lambda/d >1$ the only solutions are at $\theta = 0$ and $\theta=\pi$ (i.e. for $m=0$). Thus the radiation is sent our only in the forward and backward directions, the radiation from the different dipoles cancel out in all other directions. The width of this maxima is

$$\Delta \theta=\frac{\lambda}{N d}$$ (12.25)

which is determined by the separation between the two extreme dipoles in the chain.

The direction at which the maximum radiation goes out can be changed by introducing a constant phase difference $2 \phi$ between every pair of adjacent oscillators. The phase difference in the radiation received from any two adjacent dipoles is now given by

$$2 \alpha = \frac{2 \pi}{\lambda} d \sin \theta + 2 \phi$$ (12.26)

and the condition at which the maxima occurs is now given by

$$\sin \theta=\left(\frac{\lambda}{d}\right) \left[m+\frac{\phi}{\pi}\,. \right]$$ (12.27)

The device discussed here is called a ``phased array'', and it can be used to send out or receive radiation from only a specific region of the sky. This has several applications in communications, radars and radio-astronomy.