$6.1.$ Designan E$-$plane horn such that the maximum phase difference between two points at the aperture, one at the center and the other at the edge, is $\backslash (120^\{\backslash$circ$\}\backslash ).$ Assuming that the maximum length along its wall $($ pe $),$ measured from the aperture to its apex, is $\backslash (10\backslash$lambda $\backslash ),$ find the

a$)$ maximum total flare angle of the horn

b$)$ largest dimension of the horn at the aperture

c$)$ directivity of the horn$($ dimensionless and in dB $)$

d$)$ gain of the antenna $($in dB $)$ whenthe reflection coefficient within the waveguide feeding the horn is $0\mathrm{.}2.$ Assume only mismatch losses. The waveguide feeding the horn has dimensions of $\backslash (0\mathrm{.}5\backslash$lambda $\backslash )$ and $\backslash (0\mathrm{.}25\backslash$lambda $\backslash )$