The length of the first section of the transmission line (adjacent to the antenna) is determined using Equation \ref{m0093_eZ}: \[Z_1(l_1) = Z_{01} \frac{ 1 + \Gamma e^{-j2\beta_1 l_1} }{ 1 - \Gamma e...The length of the first section of the transmission line (adjacent to the antenna) is determined using Equation \ref{m0093_eZ}: \[Z_1(l_1) = Z_{01} \frac{ 1 + \Gamma e^{-j2\beta_1 l_1} }{ 1 - \Gamma e^{-j2\beta_1 l_1} } \nonumber \] where \(\beta_1\) is the phase propagation constant for this section of transmission line and \[\Gamma \triangleq \frac{Z_A-Z_{01}}{Z_A+Z_{01}} \cong -0.0059+j0.4142 \nonumber \] We seek the value of smallest positive value of \(\beta_1 l_1\) for which the imaginary…