A transmission line with Z0 = 300 ∠ 0 Ω is open-circuited at the far end. What is the resulting VSWR on the line?

Introduction:Voltage standing wave ratio (VSWR) quantifies mismatch on a line. An open circuit is a complete mismatch and produces maximum standing waves. This question checks your understanding of reflection magnitude and its effect on VSWR.

Given Data / Assumptions:

• Characteristic impedance Z0 = 300 Ω (purely real).
• Load is an open circuit ⇒ ZL → ∞.
• Lossless line assumption for clarity.

Concept / Approach:

Reflection coefficient at the load: Gamma_L = (ZL − Z0) / (ZL + Z0). For an open circuit, |Gamma_L| = 1. VSWR is (1 + |Gamma|) / (1 − |Gamma|).

Step-by-Step Solution:

Verification / Alternative check:

At current nodes/voltage antinodes, the measured voltage can be much larger than the incident amplitude; the infinite VSWR idealizes this behavior in the lossless limit.

Why Other Options Are Wrong:

• 0 or 0.5: VSWR cannot be less than 1.
• 1: indicates perfect match, not an open circuit.
• 2: corresponds to |Gamma| = 1/3, not a complete mismatch.

Common Pitfalls:

Mistaking infinite VSWR for infinite power; in reality, losses and source limitations cap voltages/currents, but the ratio idealizes to ∞.

Final Answer:

∞