Matched transmission line example: A line with characteristic impedance Z0 = 400 Ω is terminated by a pure resistance of 400 Ω. What are the reflected quantities (voltage, current, and power) at the load?

Introduction:This problem checks recognition of a perfectly matched transmission line. When the load equals the characteristic impedance, reflections vanish. Understanding this is essential for power transfer and VSWR control in RF systems.

Given Data / Assumptions:

• Characteristic impedance Z0 = 400 Ω.
• Load resistance RL = 400 Ω (purely resistive).
• Assume a linear, time-invariant, lossless or low-loss line.

Concept / Approach:

The reflection coefficient at the load is Γ = (RL − Z0) / (RL + Z0). If RL = Z0, then Γ = 0, leading to zero reflected voltage and current. Consequently, all incident power is delivered to the load (neglecting line loss), and VSWR = 1.

Step-by-Step Solution:

Verification / Alternative check:

On the Smith chart, the matched point is the exact center; any rotation due to line length does not move the impedance because reflections are absent. Measurements with a directional coupler would show forward power only and reverse power at the noise floor.

Why Other Options Are Wrong:

• Equal/half/double: imply a nonzero Γ; inconsistent with RL = Z0.
• Zero voltage but nonzero current reflection: impossible for passive linear lines at match; both are zero when Γ = 0.

Common Pitfalls:

Confusing load match with conjugate match in reactive cases; here the impedances are purely real and equal, guaranteeing no reflections.

Final Answer:

zero