Directional Coupler with 10 dB Coupling: Compute Coupled-Port Power A 4-port directional coupler has a specified coupling factor of 10 dB. If 100 mW is applied at port 1 (matched, ideal lossless device), what power appears at the coupled port (port 3)?

Introduction / Context:
Directional couplers sample a defined fraction of the input power to a secondary port while maintaining directionality. The coupling factor specifies how much lower the coupled power is relative to the input.

Given Data / Assumptions:

• Coupling C = 10 dB.
• Input power Pin = 100 mW at port 1.
• Matched, ideal, and lossless coupler.

Concept / Approach:

By definition, coupling in dB is C = 10 * log10(Pin / Pcoupled). Solving for Pcoupled gives Pcoupled = Pin / 10^(C/10).

Step-by-Step Solution:

Verification / Alternative check:

Expressed as percentage, a 10 dB coupler samples 10% of the input power. 10% of 100 mW is 10 mW, consistent with the calculation.

Why Other Options Are Wrong:

15 mW, 20 mW, and 25 mW correspond to 8.2 dB, 7 dB, and 6 dB coupling respectively. 1 mW corresponds to 20 dB coupling, not 10 dB.

Common Pitfalls:

Confusing coupling with insertion loss; mixing amplitude ratios (in dB for voltage) with power ratios.

Final Answer:

10 mW