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antenna bandwidth

If an element is at a center resonant frequency, it will show a negative gain gradient as one moves off its resonant frequency, is this 'area under the curve' broadened with the diameter of the element? ie assume I somehow have a gain of 10dB at its resonance with a 1/8" D element, and drop 5dB's as I move up or down frequency from it's resonance, will I have a slower decrease of gain over change of frequency?

Thanks