A transmission line has a load reflection coefficient Γ = 0.2 ∠45°. What is the standing-wave ratio (SWR) on the line?

Introduction / Context:The standing-wave ratio (SWR) is a key performance metric of transmission line matching. It is computed directly from the magnitude of the reflection coefficient at the load.

Given Data / Assumptions:

• Reflection coefficient Γ = 0.2 ∠45°.
• Only |Γ| affects SWR; the angle does not enter the SWR formula.

Concept / Approach:

The SWR on a line is SWR = (1 + |Γ|) / (1 − |Γ|). This follows from the ratio of maximum to minimum envelope of the standing wave formed by incident and reflected waves.

Step-by-Step Solution:

Verification / Alternative check:

As a quick check, |Γ| = 0 yields SWR = 1 (perfect match), and |Γ| = 0.2 should yield a modest mismatch above 1, consistent with 1.5.

Why Other Options Are Wrong:

• 0.8, 1.1, 1.2: Do not satisfy the formula for |Γ| = 0.2.
• 2.0: Would require |Γ| = 1/3, not 0.2.

Common Pitfalls:

Using angle of Γ in SWR computation; mixing return loss (in dB) with SWR; forgetting to use magnitude only.

Final Answer:

1.5