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    • https://phys.libretexts.org/Bookshelves/Electricity_and_Magnetism/Electromagnetics_I_(Ellingson)/03%3A_Transmission_Lines/3.19%3A_Quarter-Wavelength_Transmission_Line
      The length of the first section of the transmission line (adjacent to the antenna) is determined using Equation ???: \[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 ???: Z1(l1)=Z011+Γej2β1l11Γej2β1l1 where β1 is the phase propagation constant for this section of transmission line and Γ We seek the value of smallest positive value of \beta_1 l_1 for which the imaginary…
    • https://phys.libretexts.org/Courses/Berea_College/Electromagnetics_I/03%3A_Transmission_Lines/3.19%3A_Quarter-Wavelength_Transmission_Line
      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…

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