A 50-MHz generator with Zg = 50 Ω is connected to a load ZL = (50 − j25) Ω. The time-avera...

A 50-MHz generator with Zg = 50 Ω is connected to a load ZL = (50 − j25) Ω. The time-average power transferred from the generator into the load is maximum when Zg = Z*L where Z*L is the complex conjugate of ZL. To achieve this condition without changing Zg, the effective load impedance can be modified by adding an open-circuited line in series with ZL, as shown in Fig. 1. If the line’s Z0 = 100 Ω, determine the shortest length of line (in wavelengths) necessary for satisfying the maximum-power-transfer condition.

Figure 1

Transmission-line arrangement.