Final answer:
The input impedance 4.5 cm away from the load on a transmission line can be found by first normalizing the load impedance with the characteristic impedance, plotting it on a Smith chart, rotating the point by the electrical length corresponding to 4.5 cm, and then denormalizing the result from the Smith chart to find the input impedance.
Step-by-step explanation:
To find the input impedance 4.5 cm away from the load using a Smith chart, we first need to calculate the electrical length of the 4.5 cm distance at the given frequency. Since the wavelength (λ) is 12.5 cm, 4.5 cm corresponds to 4.5 / 12.5 = 0.36 wavelengths or 0.36×360° = 129.6° of electrical length.
With the given load impedance of ZL = 125-j60 Ω and the characteristic impedance of Z0 = 50 Ω, we can plot the normalized impedance (ZL / Z0) on the Smith chart. We then move clockwise on the Smith chart by the electrical length of 129.6° to find the new point which corresponds to the input impedance at the specified distance. The input impedance (Zin) can then be found from the Smith chart and denormalized by multiplying by the characteristic impedance (Z0).
To use this method, one would need access to a Smith chart and familiarity with how to use it, which includes rotating around the chart to account for the length of the transmission line in terms of the wavelength, finding the corresponding admittance if needed, and converting back to the desired impedance.