Transmission-line terminations: Which of the following terminations makes a line behave like an infinite line (no reflections seen at the input)?

Introduction:
A practical transmission line appears “infinite” when the source cannot tell where it ends, i.e., when there are no reflections. This happens when the load equals the line’s characteristic impedance Z0. Understanding this is fundamental to matching and RF power transfer.

Given Data / Assumptions:

• Uniform line with characteristic impedance Z0.
• Single-frequency steady-state operation.
• Linear, time-invariant, passive load unless otherwise noted.

Concept / Approach:

The reflection coefficient at the load is Γ = (ZL − Z0) / (ZL + Z0). If ZL = Z0, then Γ = 0. With no reflected wave, the input sees a constant Z0 independent of line length, the same as if the line extended indefinitely. Hence, a matched termination makes the line behave like an “infinite” line.

Step-by-Step Solution:

Verification / Alternative check:

Smith chart confirms that a matched termination pins the operating point at the chart center regardless of electrical length, evidencing no reflections.

Why Other Options Are Wrong:

• Pure inductance or capacitance reflects power strongly except at special tuned lengths.
• A “short” line may be convenient but still reflects unless matched.
• Negative resistance creates instability, not “infinite-line” behavior.

Common Pitfalls:

Assuming low reflection is good enough; many systems require Γ ≈ 0 across a band, achieved via broadband matching networks or resistive terminations.

Final Answer:

a line terminated in Z0 (its characteristic impedance)