VSWR from power readings — directional coupler example In the setup shown (forward power meter at point A reads 1 mW; reflected power meter at point B reads 110 μW), determine the Voltage Standing Wave Ratio (VSWR) on the line.

Introduction / Context:VSWR quantifies mismatch on a transmission line. Using a directional coupler or dual-direction power meter, one can read forward power P_f and reflected power P_r, convert to the magnitude of the reflection coefficient |Γ|, and then compute VSWR. This is a standard test-bench task in RF labs.

Given Data / Assumptions:

• Forward power P_f = 1 mW at point A.
• Reflected power P_r = 110 μW at point B.
• Meters and coupler are properly calibrated; same reference impedance.

Concept / Approach:The power reflection coefficient is |Γ|^2 = P_r / P_f. Hence |Γ| = sqrt(P_r / P_f). VSWR is defined as (1 + |Γ|) / (1 − |Γ|) for 0 ≤ |Γ| < 1. After computing |Γ| from the given readings, plug into the VSWR formula to get the final ratio.

Step-by-Step Solution:

Verification / Alternative check:Convert |Γ| to return loss: RL = −20 * log10(|Γ|) ≈ 9.58 dB. The VSWR corresponding to about 9.6 dB return loss is ~2:1, which corroborates the calculation.

Why Other Options Are Wrong:

• 1.5: corresponds to |Γ| ≈ 0.2, not 0.332.
• 2.5: implies |Γ| ≈ 0.429, larger reflection than measured.
• 3: implies |Γ| ≈ 0.5, much larger reflection.

Common Pitfalls:Using power ratios directly in VSWR without taking the square root for |Γ|; mixing dB and linear units; misreading μW vs mW.

Final Answer:2