Re: VLF: 1.6 Hz from Kiruna?

[Markus Vester <markusvester@aol.com>]

Hi Clemens, David,

not sure if scalar wave proponents would accept that their antenna efficiencies are restricted by the Chu-Wheeler limit...

To my understanding, the reason for this fundamental Q limit is the energy stored in the 1/r^3 near field, which necessarily has to exist in the space between the outer dimensions of a small antenna and the far-field boundary lambda/2pi. The assumption is that twice per cycle, the capacitive energy of an electric antenna has to be converted to magnetic energy in the loading coil, and vice versa. The same applies for the magnetic energy of a resonanted loop antenna connected to a tuning capacitor. 

Recently  someone in the LF Group mentioned a possible DARPA grant for the development of small VLF transmitters, based on mechanical movement (vibration or rotation) of permanent magnets or polarized dielectrics. Of Course, a rotating magnet would also need to be surrounded by same near-field energy as a loop (or in this case a pair of orthogonal loops for circular polarisation). But it wouldn't necessarily need to convert the magnetic energy to elecrtric energy. In the double-loop analogy, the magnetic energy from one coil would be directly transferred into magnetic energy in the other coil. So would the Chu limit still apply? 

It seems that the only bandwidth limit would be related to the mechanical mass and inertia of the rotating structure, which could be made arbitrarily small (e.g. a rotating superconducting DC coil). Or would we need to consider the mass of the stored energy itself, m=E/c^2 ?

Best 73,
Markus (DF6NM)

-----Ursprüngliche Mitteilung-----
Von: Clemens Paul <cpaul@gmx.net>
An: rsgb_lf_group <rsgb_lf_group@blacksheep.org>
Verschickt: Sa, 10. Feb 2018 20:43
Betreff: RE: VLF: 1.6 Hz from Kiruna?

Hi David,

>>Maybe you can disclose at least the the 3dB BW of this kind of antenna?

>Hi Clemens, I'm not sure I understand your question.

The 3 dB bandwidth is f0/Q and Q is defined as X/R
where X is the reactance of the inductor and the capacitor at the
resonant frequency.

The lossless-Q of a small antenna is a useful academic quantity, and is
the reactance divided by the radiation-resistance. It gives the maximum
theoretical Q for any given small antenna, and then the actual Q can be
measured on the real antenna. The radiation efficiency is the lossless Q
divided by the actual Q, by the equations:

Qlossless = X/Rrad,

Qactual = X/(Rrad+Rloss),

Qactual/Qlossless = Rrad/(Rrad+Rloss) = radiation efficiency.

An interesting limit for small antennas is the minimum lossless Q that can
be achieved, and was derived by Chu in 1948 from only the frequency and
the size of the antenna.

73
Clemens
DL4RAJ


>-----Original Message-----
>From: owner-rsgb_lf_group@blacksheep.org
>[mailto:owner-rsgb_lf_group@blacksheep.org] On Behalf Of David Hine
>Sent: Saturday, February 10, 2018 7:13 PM
>To: rsgb_lf_group@blacksheep.org
>Subject: Re: VLF: 1.6 Hz from Kiruna?
>