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I don't think that's a valid excuse. The 3 dB rule applies to phased
arrays only when mutual coupling is ignored or in a few special cases. Mutual coupling had to have been known at least at the time of the invention of the Yagi-Uda antenna in 1926, and probably long before that. It was being calculated for geometrically simple antennas at least as early as 1943 (cf. R. King, Proc. IRE). Work proceeded rapidly through the '40s, with papers describing increasingly accurate techniques with antennas of increasing complexity. We now have the means to calculate mutual coupling much more easily than before, and for geometries which were impossible to deal with before we had computers to do the work, but I don't think we've modified our understanding of the phenomenon for many decades (some notable antenna charlatans notwithstanding). Anyone measuring the gain of a short Yagi, the gain of which routinely exceeds 3 dB per doubling of elements by a considerable margin, must have become aware of the shortcoming of the 3 dB rule. I suspect that if we were to read the cited quotations very carefully, we'd see qualifications that explain neglecting mutual coupling. Roy Lewallen, W7EL Ian White GM3SEK wrote: +3dB is a valid generalization, based on sound physics - but it is only a generalization. At the time those Grand Old Men were writing their textbooks, such generalizations were the best that anybody could manage. But they had no way of checking their accuracy - or more important, why and when they start to become INaccurate. 50 years on, we do have a way, and we now know much more than they did. That makes it very dangerous to quote those Grand Old Generalizations as accurate and universal truths. Richard was quite correct to describe the "+3dB rule" as "naive" - because, at today's level of knowledge, it is. But we still need to know that the +3dB generalization exists; and understand the fundamental reasons for it. That fundamental understanding is what protects us against stupid mistakes. |
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