As an extreme example, take mobile HF antennas. These can have very low feedpoint impedances, maybe as low as $6\Omega$. The ideal impedance of a quarter/wave vertical is $36\Omega$, but electrically lengthening it makes the impedance go down. How's that work?
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asked Jun 2, 2014 at 1:51
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$\begingroup$ How long are your radials? $\endgroup$– HarveyBCommented Jun 11, 2014 at 15:31
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$\begingroup$ @HarveyB about 25 feet, I reckon. $\endgroup$– Phil Frost - W8IICommented Jun 11, 2014 at 15:32
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$\begingroup$ That antenna is such a complex arrangement of tuned circuits there's no telling what the cause is. A theoretical analysis of its' big brother is here: [link] (eham.net/articles/21272) (for what it's worth.) $\endgroup$– HarveyBCommented Jun 11, 2014 at 17:55
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$\begingroup$ I've since discovered that the problem in my case was too much inductance in the feed arrangement. I've edited the question to be more narrow, and hopefully, answerable. $\endgroup$– Phil Frost - W8IICommented Jun 19, 2014 at 16:37
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$\begingroup$ I deleted my vague answer to the vague question, because it now has no resemblance to what is being asked $\endgroup$– Scott Earle ♦Commented Jun 20, 2014 at 1:55
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1 Answer
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The ideal $36\Omega$ comes from the fact that a vertical is 1/2 dipole (so 1/2 of $72\Omega$).
If you shorten a dipole (shorter than 1/2$\lambda$, the resistive part of the antenna will lessen, and the antenna will get more capacitive. You could see this on a Smith chart, or from the impedance formulas.
Then, if you eliminate the capacitive part, by adding an inductor in series you get only the resistive part. Remember, a capacitor + inductor in series, at resonance are a short-circuit.
There's a catch though: if the resistive part is so low, the resistance of the inductor (copper!) will start heating up because of the high currents, and you'll loose part of your power through heat, unless you use really thick wire. The same, high, current must also be managed by the ground-plane.
That's also why AM stations, which can only afford a fraction of the tower they'd need, have to use a really effective ground-plane to handle such large currents. ELF stations are build near large - preferably salty - water surfaces to have a reflector able to handle 1000's of A.
This reasoning is slightly simplified to make it clear enough to make it understandable, I hope.
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$\begingroup$ So why does radiation resistance decrease with a shorter antenna? I wouldn't mind some math. $\endgroup$ Commented Jul 6, 2014 at 21:49
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$\begingroup$ I realize this is counter-intuitive :) Have a look at en.wikipedia.org/wiki/Dipole_antenna which does a quite in-depth treatment of dipoles and doublets (elementary dipoles, i.e. very small ones). It doesn't make much sense replicating those formulas. $\endgroup$– jcoppensCommented Jul 6, 2014 at 22:59