A resistive microwave load with impedance ZL = 150 Ω is connected to a 50 Ω coaxial line. What will be the standing wave ratio (SWR) on the line?

Introduction / Context:Standing wave ratio (SWR) is a measure of impedance mismatch between a transmission line and its load. It indicates how much of the incident signal is reflected due to mismatch.

Given Data / Assumptions:

• Line impedance Z0 = 50 Ω.
• Load impedance ZL = 150 Ω (purely resistive).
• Formula: SWR = (1 + |Γ|) / (1 − |Γ|).
• Reflection coefficient Γ = (ZL − Z0) / (ZL + Z0).

Concept / Approach:

SWR is always ≥ 1. If ZL = Z0, SWR = 1 (perfect match). If ZL differs from Z0, reflections occur, raising SWR.

Step-by-Step Solution:

Verification / Alternative check:

Measured VSWR in microwave labs for this ratio confirms the theoretical result of 3.

Why Other Options Are Wrong:

• More than 3: incorrect, exact value is 3.
• Less than 3: mismatch is significant, not smaller.
• Either more than 3 or equal: introduces ambiguity not present in calculation.
• Exactly 2: would occur if ZL = 100 Ω, not 150 Ω.

Common Pitfalls:

Forgetting to take absolute value of Γ; misapplying formula.

Final Answer:

Equal to 3