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

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Solve this multiple-choice question and choose the correct option.

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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

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

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