Chapter 2, Problem 42P

A generator with ${\tilde{V}}_{\text{g}}=300$ V and Z_g = 50 Ω is connected to a load Z_L = 75 Ω through a 50 Ω lossless line of length l = 0.15λ.

1. (a) Compute Z_in, the input impedance of the line at the generator end.
2. (b) Compute ${\tilde{I}}_{\text{i}}$ and ${\tilde{V}}_{\text{i}}$.
3. (c) Compute the time-average power delivered to the line, $P_{\text{in}}=\frac{1}{2}\Re e[{\tilde{V}}_{\text{i}}{\tilde{I}}_{\text{i}}*]$.
4. (d) Compute ${\tilde{V}}_{\text{L}}$, ${\tilde{I}}_{\text{L}}$, and the time-average power delivered to the load, $P_{\text{L}}=\frac{1}{2}\Re e[{\tilde{V}}_{\text{L}}{\tilde{I}}_{\text{L}}*]$. How does P_in compare to P_L? Explain.
5. (e) Compute the time-average power delivered by the generator, P_g, and the time-average power dissipated in Z_g. Is conservation of power satisfied?