There has been a lot of discussion lately, much of it just plain incorrect, about the relationship between resonance and antenna efficiency. Many incorrectly claim that resonance has nothing to do with antenna efficiency at all, similarly others incorrectly claim that resonance is a direct indication of efficiency. Neither of these statements is true. The reality is that resonance does have a significant impact on how efficient your antenna is, but the relationship is highly non-linear and depends on many characteristics.

Below I have attached a chart hat plots out the total radiation resistance (R_r) vs the measured input resistance (R_in) of a dipole. Efficiency is just R_r/R_in. In other words an efficient antenna will have 100% of its resistance as radiation resistance, and R_in is **always** larger than R_r (since it is essentially ohmic resistance plus radiation resistance). When these two numbers differ significantly an antenna is inefficient. The source for the chart below is here and it gives much of the math if you want a deeper dive:

nptel.ac.in/content/storage2/c

What is important to note here is that at anti-resonance we see a **huge** R_in value and a small R_r value, this means an anti-resonant antenna will have very high losses. Keep in mind the graph is very hard to read for the values <0.5 in length because the resolution isnt high. But there is significant divergence there as well. Notice at ~5/8ths wavelength antenna would exhibit very significant internal ohmic losses due to heat.

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@freemo @Electronics can we have an antenna with worse resonance that is more efficient than antenna with better resonance?

@fudgel
Yes, particularly if the two antennas are of different design. Consider an antenna that has a resistor as an end terminator (like a rhombic) vs a nonresonant dipole
@Electronics

@freemo @Electronics in that case arenβt we make better resonat antena worse on purpose? I am asking more about the best possible design and not flawed to make a point. Is it possible to have worse resonant antena more efficent than best designed better resonant antena?

@fudgel
If what you want is an antenna as close to 100% efficient as possible then you want a resonant dipole.

The thing is there are desirable factors other than just effiency, like gain. So sometimes you might want to sacrafice a little effiency for some gain. Also you might want a multiband antenna where resonance on all bands is t an option.
@Electronics

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