Assignments:

Design a single patch antenna at $2\mathrm{.}4$ GHz based on the structure in Fig. $4$ with the substrate parameter as follows:

Height: $1\mathrm{.}6$ mm

Metal Thickness: $0\mathrm{.}7$ mil $(1/2$ oz$.$ Copper$)$

Dielectric constant, ${}_r$:$4\mathrm{.}6$

Loss tangent, TanD: $0\mathrm{.}001$

Conductivity: $5\mathrm{.}8$E$7$ S$/$m

Show step$-$by$-$step calculations and calculated geometries of the rectangular patch antenna $[5$ marks$].$ Then, simulate the rectangular patch antenna structure with the calculated geometries using ADS, showing the schematic diagram $[5$ marks$],$ layout of the antenna $[5$ marks$],$ simulated S$-$parameters $($return loss$)$ of the single patch antenna $[5$ marks$]$ and show the radiation patterns and basic antenna parameters such as gain, directivity, and radiation efficiency $[5$ marks$].$

$2.$ Design a $12$ linear antenna array, Fig. $7,$ based on the single rectangular patch antenna design in $1.$ First, a $3-$dB power splitter must be designed with the input port impedance of $50[5$ marks$].$ Each output port impedance of the $3-$dB power splitter must be matched to the input impedance of the patch antenna. Use ADS to simulate the calculated geometries of the $3-$dB power splitter, showing schematic diagram $[5$ marks$],$ layout of the power splitter $[5$ marks$]$ and S$-$parameters of the $3-$dB splitter $[5$ marks$].$ Then, use the designed $3-$dB power splitter to connect to the patch antennas as shown in Fig. $7$ and simulate the antenna array using ADS. Schematic diagram $[5$ marks$],$ layout of the antenna $[5$ marks$],$ simulated Sparameters $($return loss$)$ of the single patch antenna $[5$ marks$]$ and show the radiation patterns and basic antenna parameters such as gain, directivity, and radiation efficiency $[5$ marks$]$ must be shown.