In a directional coupler, which relationship between coupling, isolation, and directivity (in dB) is correct?
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Aisolation (dB) equals coupling + directivity
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Bcoupling (dB) equals isolation + directivity
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Cdirectivity (dB) equals isolation + coupling
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Disolation (dB) equals (coupling) (directivity)
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Ecoupling (dB) equals isolation − directivity
Answer
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