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BM, I think maybe a center fed 5/8 wave yagi design (not a GM) could be made and matched that might work as a driven element for a beam, but like someone has already said, I doubt you could tell the difference compared to a 1/2 wave. IMO, the GM has a terrible matching problem to over come, but the GM does it well...when used as intended.

 

My reason being, the CF 1/2 wave has an advantage in that its natural match is much closer to perfect that the match at the middle of the GM. Thus the much lower matching losses for the 1/2 wave radiator might tend to produce a better pattern and RF in this case. IMO, that alone would probably minimize any CF 5/8 wave advantage.

 

I think the GM design is not practical in such a beam setup due to how it uses common mode currents and the choke to handle the proximity problems with the feed line at the bottom of the vertical antenna. IMO the GM is very responsive to stuff near the bottom and needs to be well into the clear, and that might not sit too well with parasitic elements close by.