Problem $4($a$)[($i$)-2$pts; $($ii$)-3$pts; $($iii$)-2$pts; $($iv$)-3$pts$]$ To measure the impedance of an antenna, we measure the voltage standing$-$wave pattern $($VSWR$)$ of the transmission line to which the antenna is connected as a load, shown in the Figure below where the characteristic impedance of the line is $50,$ the reflection coefficient at the antenna $($load$)$ is ${}_L$ and the antenna $($load$)$ impedance is $Z_2.$ Use the given Smith chart on the next page to determine the following:

$($i$)$ Identify the appropriate circle $(A$ or $B)$ for ${}_L.$ Your answer must be backed up with a computed result. Please note that any guessed answers will earn you no points.

$($ii$)$ Find the antenna impedance $Z_r.$ If you guessed your answer in $($i$),$ do not bother to find $Z_2($you will earn no points!$).$

$($iii$)$ Find the shortest distance $d_{\text{s}\text{h}\text{o}\text{r}\text{t}}$ from $z_Z$ to position a shunt susceptance $($shortcircuited stub$)$ to tune the line for a perfect match.

$($iv$)$ Determine $($a$)$ the length and $($b$)$ the shunt susceptance $($in mhos$)$ of the shortcircuited stub positioned at $d_{(shom)}.$

Solution to Problem $4($a$)$: