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In a directional coupler, which relationship between coupling, isolation, and directivity (in dB) is correct?

Difficulty: Easy

Correct Answer: isolation (dB) equals coupling + directivity

Explanation:


Introduction / Context:
Directional couplers are four-port passive microwave components characterized by coupling (how much power is sampled), isolation (how much the isolated port is suppressed), and directivity (ability to discriminate direction).


Given Data / Assumptions:

  • All quantities are in decibels.
  • Standard coupler port labeling and definitions apply.


Concept / Approach:
Directivity (in dB) is defined as isolation (in dB) minus coupling (in dB). Rearranged: isolation = coupling + directivity. This identity is fundamental in coupler specifications and cascaded design calculations.


Step-by-Step Solution:

Start from D (dB) = Iso (dB) − Cpl (dB).Rearrange to Iso (dB) = Cpl (dB) + D (dB).Hence, isolation equals coupling plus directivity (in dB).


Verification / Alternative check:
Manufacturers’ datasheets present these three figures of merit; calculating any one from the other two follows this identity.


Why Other Options Are Wrong:

Statements that add isolation and directivity to get coupling—or multiply terms—contradict the standard definition.


Common Pitfalls:

Confusing linear ratios with dB; the add/subtract rule applies only in dB.


Final Answer:

isolation (dB) equals coupling + directivity
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