Question $1(20$ points$)$: Linear Array

A phase$-$controlled linear array consisting of $\backslash ($ N$=10\backslash )$ isotropic point sources with an element spacing $\backslash ($ d $\backslash )$ is arranged along the z $-$axis as shown in Figure $1.$

Determine a general expression for the far$-$field pattern of this arrangement in dependence of the element spacing d $,$ the phase progression $\backslash (\backslash$Delta $\backslash$alpha $\backslash )$ and the excitation

$\backslash [$

$\backslash$underline$\{$I$\}\_\{$n$\}=\backslash$left$|$I$\_\{$n$\}\backslash$right$|\backslash$cdot e$^\{$j n $\backslash$Delta $\backslash$alpha$\}.$

$\backslash ]$

Patch Antennas

Microstrip patch antennas are an exciting antenna technology since they are easy to manufacture, cost efficient and have light weight. These kinds of antennas are frequently used in the Global Positioning System $($GPS$),$ wireless, satellite communication systems and the cellular phone industry. They have narrow bandwidth and high metallic losses at upper microwave and millimeter wave frequencies.

One of the most common microstrip radiating elements used today is the rectangular geometry. A simple patch design can be done for the dominant mode by using the transmission line model and with more accurate by the cavity model. In the following part, a patch antenna will be designed using these two methods.