Final answer:
The question asks for the input impedance of a lossy transmission line with a given characteristic impedance, loss factor, and terminated with a specific load impedance. It's an engineering problem that requires knowledge of transmission line theory and the use of a Smith chart.
Step-by-step explanation:
The student's question relates to finding the input impedance of a lossy transmission line when terminated with a different load impedance. Using the given line characteristic impedance (Zo) of 50 ohms, a loss factor (α) of 1.5 dB/m, and a wavelength of 2 meters, we can establish that the input impedance needs to be calculated at a point 1.0 meter away from the load impedance (ZL) of 100 ohms.
Normally, to solve for the input impedance on a Smith chart, we would first normalize the load impedance with respect to Zo, then apply the effects of the transmission line length to find the input impedance. However, this problem requires considering the line losses, which makes the Smith chart method less straightforward.
For the scenario with an audio amplifier and a low-impedance loudspeaker, we are asked to match impedances using a transformer. Assuming an amplifier's output impedance (Z) of 500 ohms and a speaker impedance of 8 ohms, we would need a turns ratio in the transformer that equals the square root of the impedance ratio. This ensures that the power transfer between the amplifier and speaker is optimized and efficient, minimizing reflections and losses.