Theories for the Basis-in-Physics of Small Loop Efficiency

It is axiomatic (self-evident) that the ‘physical’ cross section area of a simple 1/2 wave dipole antenna is far smaller than the effective aperture (Ae), per many notable sources:

http://www.w8ji.com/capture_area_ae_effective_aperture.htm

For example a 1/2 wave long dipole in freespace has a capture area of about .13λ². This means a lossless freespace dipole has an Ae of approximately .13 square wavelengths. This effective aperture is about 100 times larger than the actual physical area of a thin wire dipole antenna. Energy is extracted from an elliptically shaped area slightly longer than the dipole and about 1/4 wave diameter at the center.

and:

http://en.wikipedia.org/wiki/Antenna_aperture

In general, the aperture of an antenna is not directly related to its physical size.

So how do these same thoughts apply to smaller resonant structures like small (magnetic) loop antennas – or atoms or molecules even? Let’s take a look at a few papers to see what researchers have found at really small scales …

How can a particle absorb more than the light incident on it?
C. F. Bohren
Am J Phys, 51 #4, pp323 Apr 1983

http://www.cheniere.org/references/bohren/index.htm

ABSTRACT
A particle can indeed absorb more than the light incident on it. Metallic particles at ultraviolet frequencies are one class of such particles, and insulating particles at infrared frequencies are another. In the former, strong absorption is associated with excitation of surfaces plasmons; in the latter it is associated with excitation of surface phonons. In both instances, the target area a particle presents to incident light can be much greater than its geometrical cross-sectional area. This is strikingly evident from the field lines of the Poynting vector in the vicinity of a small sphere illuminated by a plane wave.

Light Absorption by a dipole
H. Paul and R. Fischer
SOV. PHYS. USP., 26(10) Oct. 1983 pp 923-926

ABSTRACT
In semiclassical radiation theory, the electric dipole moment induced on an atom by a strong incident field absorbs much more energy, per sec, than is flowing through its geometrical cross section. This means that the atom has the capability to “suck up” electromagnetic energy from a spatial region that is by far larger than its own volume. An intuitive understanding of this effect is provided by studying, in the framework of classical electrodynamics, the energy flow in the total field made up by superposition of the incident wave and the field that is generated by the dipole also in the absorptive case.

Resonant energy absorption and the CTF hypothesis
Michael Ambroselli ; Chandra Roychoudhuri
Proc. SPIE 8832, The Nature of Light: What are Photons?
V, 88320T (October 1, 2013); doi:10.1117/12.2024126

http://proceedings.spiedigitallibrary.org/proceeding.aspx?articleid=1747250

Abstract
Antennas in resonant circuits can present an effective energy absorption cross-section much larger than its physical dimensions to the impinging EM waves.

Similarly, atoms can absorb energy from fields with energy densities so low that the atom must have an effective interaction cross-sectional diameter on the order of tens of microns. It appears that resonant energy absorption exhibits a sort of “suction” effect by the absorbing dipole, or a “pushing” effect by the field, or a combination of both. This allows the field energy to converge from a larger volume into a smaller region. We will argue that this effect may actually correspond to the field preferentially directing energy into such resonant systems, and discuss how this provides further evidence for the utility of our proposition of a universal, complex tension field (CTF). We have proposed that CTF can support propagating field gradients, like EM waves, as well as resonant, localized and self-looped oscillations representing various particles. Different gradients in the CTF, generated by different kinds of particle-oscillations, represent the various forces experienced by particles within each others’ physical domain. Even time emerges as a secondary property.

Further discussion:

http://amasci.com/freenrg/sukdynam.html

Loop Calculator not in agreement with Implementation

Playing around with this on-line loop evaluation tool:

http://www.66pacific.com/calculators/small_tx_loop_calc.aspx

Immediately below are the outputs for a 17 gauge (.045 inch diameter) wire just under one-quarter wavelength in length for the 40 meter band loop antenna. Compare what the loop antenna calculator calculated versus what was seen for ‘actual real-world results’ shown further down:

Input Values:
Length of conductor:          32 feet
Diameter of conductor:        .045 inches (17 AWG)
Frequency:                    7 MHz

RESULTS:
Antenna efficiency:           21% (-6.9 dB below 100%)
Antenna bandwidth:            217 kHz
Tuning Capacitance:           149 pF (real world result = 24 pF)
Capacitor voltage:            702 volts RMS
Resonant circulating current: 4.60 A
Radiation resistance:         0.484 ohms (real world = 22.2)
Loss Resistance:              1.87 ohms
Inductance:                   3.46 microhenrys
Inductive Reactance:          152 ohms
Quality Factor (Q):           32.3
Distributed capacity:         26 pF
Antenna "circumference":      32 feet
Comments:

1) The specified conductor length of 32 feet is OK.

2) Conductor length should be between 17.0 and 34.1 feet at 
the specified frequency of 7 MHz.

3) For highest efficiency, the conductor length for a small 
transmitting loop antenna should be greater than 1/8 wavelength 
(greater than about 17.0 feet at the specified frequency of 7 
MHz). 

4) To avoid self-resonance, the conductor length for a small 
transmitting loop antenna should be less than 1/4 wavelength 
(less than about 34.1 feet at the specified frequency of 7 MHz).

- – - - – - - – - - – - - – - - – - - – - - – - - – - - – - - – - - – - - – - - – - - – - - – - - – - - – -

Below are the actual, real-world results obtained:

Antenna efficiency:           ~100% (on a par w/dipole)
Tuning capacitance:           24 pF 
Antenna bandwidth:            50 kHz 1.5:1, 110 kHz 3:1 
Radiation resistance:         22.2 ohms (fed w/transformer next to
                                         tuning capacitor)

AC and DC wire resistance calculations at 7 MHz:

Freq  Gauge  Wire  Len    DCR    ACR  Rrad  Ratio 
----- ------ ----- ---- ------- ----- ----  ----- 
7 MHz 17 ga.   Al   32'  0.265  2.452 22.5  9.17
7 MHz 10 ga.   Cu   32'  0.0318 0.835 22.5  26.9