antenna-theory.com

[Riaan]

Has anyone been able to quantitively or mathematically show why a spiral antenna radiates in the region where the circumference equals one wavelength? We know that from experimental results and numeric modelling.

PS: I have been in the antenna manufacturing business for 20 years and only recently discovered that there are some aspects of spiral antenna radiation that we (I) probably still do not understand 100%! It is however possible that I missed relevant publications, so any references will be appreciated.

[Schubert]

Well, I can offer my thoughts. At a circumference of one wavelength, the spiral (linear) length will be on the order of a half-wavelength (depending on how tightly or loosely the spiral is wrapped, of course).

Spirals have a lower frequency at which it radiates, and that is when the spiral length obtains a significant fraction of a wavelength. Above this frequency, the spiral becomes electrically larger, and it still radiates, the extra length then just cancels out since the two arms of the spiral carry roughly the same current.

As for the mathematics on this, or references, I don't know. In my opinion, antennas are best understood intuitively. The math tends to be overly complicated and not at all useful for real world antennas. Mathematicians, frankly, don't know anything about antennas.