A transmission line has an attenuation constant of 0.054 Np/m. What is the corresponding attenuation in decibels per meter (dB/m)?

Introduction / Context:
Attenuation constants for transmission lines may be reported either in nepers per unit length or decibels per unit length. Converting correctly between these units is essential for link budgets and cable length planning.

Given Data / Assumptions:

• Attenuation α = 0.054 Np/m.
• Need to express attenuation in dB/m.
• Standard conversion: 1 Np = 8.686 dB.

Concept / Approach:

The conversion relies on the identity: amplitude ratio in dB = 20 * log10(e) * nepers. Since 20 * log10(e) ≈ 8.686, multiply α (in Np/m) by 8.686 to obtain dB/m.

Step-by-Step Solution:

Verification / Alternative check:

Reverse check: 0.47 dB/m ÷ 8.686 ≈ 0.0541 Np/m, consistent with the original value.

Why Other Options Are Wrong:

• 4.7 dB/m and 5.4 dB/m: Off by a factor of 10 or 100 relative to 0.47 dB/m.
• 0.54 dB/m: Not the correct product of 0.054 and 8.686.
• 0.0054 dB/m: Incorrect by a factor of ~100.

Common Pitfalls:

Using 10 * log10 instead of 20 * log10 for amplitude ratios; mixing power and field conversions; rounding too early.

Final Answer:

0.47 dB/m