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3.16: Input Impedance for Open- and Short-Circuit Terminations
https://phys.libretexts.org/Bookshelves/Electricity_and_Magnetism/Electromagnetics_I_(Ellingson)/03%3A_Transmission_Lines/3.16%3A_Input_Impedance_for_Open-_and_Short-Circuit_Terminations
Multiplying numerator and denominator by $e^{+j\beta l}$ we obtain $Z_{in}(l) = Z_0 \frac{ e^{+j\beta l} - e^{-j\beta l} }{ e^{+j\beta l} + e^{-j\beta l} } \nonumber$ Now we invoke the following ...Multiplying numerator and denominator by $e^{+j\beta l}$ we obtain $Z_{in}(l) = Z_0 \frac{ e^{+j\beta l} - e^{-j\beta l} }{ e^{+j\beta l} + e^{-j\beta l} } \nonumber$ Now we invoke the following trigonometric identities: Z_{i n}(l) &=Z_{0} \frac{1+\Gamma e^{-j 2 \beta l}}{1-\Gamma e^{-j 2 \beta l}} \\
3.16: Input Impedance for Open- and Short-Circuit Terminations
https://phys.libretexts.org/Courses/Berea_College/Electromagnetics_I/03%3A_Transmission_Lines/3.16%3A_Input_Impedance_for_Open-_and_Short-Circuit_Terminations
Multiplying numerator and denominator by $e^{+j\beta l}$ we obtain $Z_{in}(l) = Z_0 \frac{ e^{+j\beta l} - e^{-j\beta l} }{ e^{+j\beta l} + e^{-j\beta l} } \nonumber$ Now we invoke the following ...Multiplying numerator and denominator by $e^{+j\beta l}$ we obtain $Z_{in}(l) = Z_0 \frac{ e^{+j\beta l} - e^{-j\beta l} }{ e^{+j\beta l} + e^{-j\beta l} } \nonumber$ Now we invoke the following trigonometric identities: Z_{i n}(l) &=Z_{0} \frac{1+\Gamma e^{-j 2 \beta l}}{1-\Gamma e^{-j 2 \beta l}} \\

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