If a traveling-wave travels along a loss-free overhead line does not result in any reflection after it has rea

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If a traveling-wave travels along a loss-free overhead line does not result in any reflection after it has reached the far end, then the far end of the line is

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Option C: Terminated into a resistance equal to surge impedance of the line

Explanation & Concepts:
When a transmission line is terminated with a resistance equal to its surge impedance (characteristic impedance $Z_c$), the reflection coefficient becomes zero. This condition ensures that the entire incident wave is absorbed by the load, preventing any reflection back toward the source.

Working Principle: The reflection coefficient $\rho$ is defined as $\rho = \frac{R_L - Z_c}{R_L + Z_c}$. When the load resistance $R_L$ is equal to the surge impedance $Z_c$, the numerator becomes $Z_c - Z_c = 0$, resulting in a reflection coefficient of zero. Consequently, the reflected voltage wave $V_r = \rho V_i$ becomes zero, signifying a matched condition where power is fully absorbed by the termination.

Key Formulas: $Z_c = \sqrt{\frac{L}{C}}$ — Surge impedance of a loss-free line; $\rho = \frac{R_L - Z_c}{R_L + Z_c}$ — Reflection coefficient at the load

Key Points: Surge impedance $Z_c$ for an overhead line is typically between 400\u03a9 and 500\u03a9.; A matched termination (load = surge impedance) eliminates standing waves in the transmission line.; Reflection coefficient $\rho = 1$ for an open circuit ($R_L = \infty$).; Reflection coefficient $\rho = -1$ for a short circuit ($R_L = 0$).

Advantages: Elimination of reflected waves prevents overvoltage stress on insulation.; Optimal power transfer and absence of standing waves on the line.

Disadvantages: Requires dissipation of energy in the termination resistor if used for high-power transients.; Physical resistors capable of handling high-voltage surge energy are bulky and expensive.

Applications: Terminating surge diverters or protective equipment.; High-frequency radio frequency (RF) transmission lines to prevent signal distortion.

Additional Info: An open-circuited end reflects the voltage wave with the same polarity, causing voltage doubling.. A short-circuited end reflects the voltage wave with opposite polarity, resulting in zero voltage at the end.

Answer: C is correct — Terminating the line with a resistance equal to its surge impedance results in a reflection coefficient of zero, meaning no energy is reflected back to the source.

Exam Tip: Always remember that for power systems, $Z_c$ is resistive for loss-free lines, making it easy to match using standard resistors to prevent traveling wave reflections.

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Option A: Open circuited

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Option B: Short circuited

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Option D: Terminated into a capacitor

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