Design an ordinary endfire uniform linear array with only one maximum so that its directivity is $20$ dBi. The spacing between the elements is d$=$$/4$d $=\backslash$lambda$/4$d$=$$/4,$ and its length is much greater than the spacing. Determine:

$($i$)$ Number of elements

$($ii$)$ Overall length of the array $($in wavelength$)$

$($iii$)$ Approximate Half Power Beamwidth $($HPBW$)($in degrees$)$

$($iv$)$ Amplitude level of first minor lobe maxima $($in dB$)$

$($v$)$ Progressive phase shift between the elements $($in degrees$)$

$4$o