A dipole antenna, with a triangular current distribution, is used for communication with submarines at a frequency of $150$ kHz$.$ The overall length of the dipole is $200$ m$,$ and its radius is $1$ m$.$ Assume a loss resistance of $2$ ohms in series with the radiation resistance of the antenna. $($a$)$ Evaluate the input impedance of the antenna including the loss resistance. The input reactance can be approximated by Xin $=120[$ln$($l$2$a$)1]$ tan$($l$$$)($b$)$ Evaluate the radiation efficiency of the antenna. $($c$)$ Evaluate the radiation power factor of the antenna. $($d$)$ Design a conjugate$-$matching network to provide a perfect match between the antenna and a $50-$ohm transmission line. Give the value of the series reactance X and the turns ratio n of the ideal transformer. $($e$)$ Assuming a conjugate match, evaluate the instantaneous $2$:$1$ VSWR bandwidth of the antenna.