When bandwidth increased, then antenna (or part of it) can not resonate at full power at some frequency. I think relationship is something near formulas about oscillation modes and wavelengths.
In general, there is no direct relationship.
Although, for some particular type of antenna and bandwidth-enhancement technique, it can be true.
Regards
The gain is frequency depend, so you can get from the same antenna more gain at a higher frequency than at a lower.
This could lead to different gains at different frequency points, and perhaps decreases the antenna gain from an antenna with a very large bandwidth.
By the way, what gain is stated from an antenna with large bandwidth? The lowest?
I believe you are wrong. There is a theoretical limiting relating the Q (which is related to bandwidth), gain, and the volume of a sphere enclosing an antenna
**broken link removed**
That said, I think there is no practical way to get near this maximum theorectical value.
I believe you are wrong. There is a theoretical limiting relating the Q (which is related to bandwidth), gain, and the volume of a sphere enclosing an antenna
It't true that there exists such a limitation between antenna size and bandwidth. But what I said is that In general, there is no direct relationship between antenna gain and bandwidth. I.e., there is no a general rule that can be applied to all cases.
Regards