Final answer:
To determine the load impedance ZL on a transmission line, calculate the full wavelength using the distance between the voltage maximum and minimum, use the VSWR to determine the impedance at the voltage minimum, and finally calculate ZL by considering the transformation of impedance through the line.
Step-by-step explanation:
In order to find the load impedance ZL on a transmission line with given parameters, we first note that the distance between the voltage minimum and the voltage maximum on the line, which is 6 cm (9 cm - 3 cm), corresponds to one-quarter of the wavelength (λ/4). Therefore, the full wavelength (λ) is 4 times this distance, which gives us 24 cm or 0.24 m.
Since the Voltage Standing Wave Ratio (VSWR) S is given as 2, we can calculate the reflection coefficient Γ as (S - 1) / (S + 1), which yields a value of 0.333. Using this reflection coefficient, we can also find the return loss, which is -20 log(Γ) in dB.
The impedance at the voltage minimum Zmin can be calculated by using the formula Zmin = Zo / S, where Zo is the characteristic impedance of the line, which is given as 150 Ω. Substituting the known values, we find Zmin to be 75 Ω.
In order to find the load impedance ZL, we use the location of the voltage minimum to determine the impedance transformation through the line. If the minimum is λ/4 away from the load, the impedance at the load can be found by ZL = Zmin * S2, which gives us 300 Ω. Hence, the load impedance ZL is 300 Ω.