Final answer:
The load impedance on a Z_0=75 [Ω] transmission line with Z_in=75+j20[Ω] 2[cm] from the load at a frequency with λ=6[cm] can be found using the Smith Chart by normalizing Z_in, rotating it by the electrical length on the chart, and then denormalizing the result.
Step-by-step explanation:
To determine the impedance of the load attached to a Z0=75 [Ω] transmission line using the Smith chart, we start with the known input impedance Zin = 75+j20[Ω]. This impedance is 2[cm] away from the load at a frequency that gives a wavelength (λ) of 6[cm] on the line. First, we normalize the input impedance by dividing it by Z0, which gives us Zin norm = 1+j0.267. Then, we plot this normalized impedance on the Smith chart.
Next, we must consider the electrical length between the input and the load, which is θ = (2 / λ) × 360°. In this case, θ = (2cm / 6cm) × 360° = 120°. Using the Smith chart, we rotate this normalized impedance by 120° towards the generator (clockwise) to find the normalized impedance at the load. After the rotation, the point on the Smith chart will give us the normalized load impedance, Zload norm, which is finally denormalized by multiplying with Z0 to find the actual load impedance (Zload).