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Additional questions-- What determines optimum director diameter and how was that derived?
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bandwidth and cost/mechanical load concerns
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When ganging antennas for additional gain, the second adds an additional 2.5 to 3 db of gain.
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A "perfect", no loss combination would yield up to 3 dB of gain, a doubling. Want another (theoretical) 3 dB of gain? Double the antenna again. And so on. In the real world, one soon runs into real size and weight constraints as well as cumulative combining losses that will soon result in a point of diminishing returns.