(Solved): 4. The scattering matrix for a two-port network is (assuming \( 50 \Omega \) system impedance) \[ [ ...

4. The scattering matrix for a two-port network is (assuming \( 50 \Omega \) system impedance) \[ [S]=\left[\begin{array}{ll} 0.5 & 0.5 e^{\mu+r} \\ 0.5 e^{j 4 s} & 0.5 e^{\mu r} \end{array}\right] \] - Find the return loss at port 1 if \( Z_{0} \) is \( 50 \Omega, \theta=45^{\circ} \), and \( Z_{1}=Z_{0} \) - Find the return loss at port 1 if \( Z_{0} \) is \( 50 \Omega, \theta=45^{\circ} \), and \( Z_{0} \) is a short circuit - Find the return loss at port 1 if \( Z_{0} \) is \( 50 \Omega, \theta=180^{\circ} \), and \( Z_{1} \) is an open circuit 5. Design 3- section binomial and Chebyshev Transformers to match \( \mathrm{ZL}=80 \) to \( \mathrm{Z} 0=60 . \Gamma \mathrm{m}=0.03 \). 6. Find the minimum no. of sections required to match \( \mathrm{ZL}=125 \) to \( \mathrm{ZO}=100 \) such that \( \Gamma \mathrm{m}<0.1 \) within the band 3 to \( 11 \mathrm{GHz} \).