Electrically Small Antennas 2016
Updated 20170818
The subject of antennas is arcane and boring to the crowd. But to anyone trying to talk (or type) to the world from a small plot in crowded England, they’re an interesting headache. Antennas for radiating a signal on HF frequencies will always be quite large. Technology in this area is evolving; the flow of academic papers continues, but radio hams continue to use designs half a century or more old.

A good HF antenna has:
1. High efficiency
2. Small size in any dimension
3. Good bandwidth (or easy to tune)
4. Practical to build and mechanically robust

The issue of directional antennas (e.g., Yagi) is left aside, as it’s something of a separate problem.

An antenna system is
electrically small if it's enclosing sphere is <λ/2π. So a 10m band antenna of under 1.6m long qualifies, for instance. This is the definition of a small antenna from 60 years ago. The biggest problem in small antennas is the Chu-Harrington limit. This defines the minimum Q factor (or maximum bandwidth) a certain size of antenna can ever achieve, with linear polarisation and 100% efficiency:
Screen Shot 2016-06-12 at 15.12.38
Where a (sometimes more logically called ‘r’) is the radius of the smallest sphere enclosing the entire system, and the free space wave number k = 2π/λ. This rule is derived from near-field charge storage around an antenna, and refers to an ideal mathematical situation. Estimating the efficiency factor η is an additional but important problem.

A short dipole has low
radiation resistance and is highly reactive. Practically this makes it hard to match to a transmitter or receiver, and even when matched the bandwidth of operation is small. Over recent decades computer simulation allowed small designs to be optimised, as shown in this paper. There were hopes a few years ago metamaterial would provide a solution, but it's just alternative matching system at HF. These solutions are mechanically complex and don't yield practical designs for longer wavelengths.

Following on from 2015 experiments, the capacitor antenna concept is worth investigating because:
  • Radiation entirely from the feed line was disproved by shortening the cable, with no reduction in performance
  • A field strength meter indicates most radiation is from the high voltage tuned plate

Capacitive Mobile Antenna
A capacitive antenna was constructed for 14MHz to test my implementation of the Landstorfer and Meinke theory. It uses a "paddle" in the break-away field region, and a car body for a ground plane. In this photo the small antenna is seen clearly above the MINI car roof, and the size of the reference antenna is obvious.

Hill - windy antennas
The small antenna is 0.05λ (1.0m) above the roof, and grounded to the vehicle body. It is not a conventional top-loaded mobile antenna, but is fitted similarly the car. The reference antenna is supported by a 10m high fibreglass pole.

A test was performed against a vertical
end-connected windom, which is functionally equivalent to an end-fed half wave, as pictured above. The windom being 10m high is much larger and awkward to setup. To a local station 3 miles away on 14.250MHz, these signal measurements were obtained:

Windom vertical = S8.5 (26dB) to hex beam and S7.5 (22dB) to vertical receive antenna
Small antenna = S9+1dB (28dB) to hex beam and S6 (20dB) to vertical receive antenna

In other words the small antenna is overall equal to the large one. The bandwidth of the small antenna is less, but this is still a good result. The vertical receive was lower and the horizontal higher. In A/B switched tests I preferred the small antenna on receive. With the local station transmitting it was noted the signal strength on receive between the 2 antennas was the same on the KX3 signal bar-graph.

Another station was set-up at a beach, with a 20m long 4-band windom and the small mobile antenna. Over several hours signal strengths on 20m were compared directly. It was found the background noise and signal readings on an Elecraft KX3 were equal or above the long wire antenna. Some videos were made and put on
YouTube here and HERE and HERE.

Then a
helically wound mobile whip was compared. The two antennas operating on 14.250MHz to the same local station who helped me with the first test.

Small antenna = S9+3dB (32dB) to hex beam and S6 (18dB) to vertical receive antenna
Helical whip = S9+2dB (31dB) to hex beam and S6 (18dB) to vertical receive antenna

This result shows how effective the car body is at reducing ground losses, with the AmPro whip coming out slightly better than the full length vertical. It should be noted the whip is 2.5m (0.12λ) vs. the small antenna of 1.1m (0.055λ). A length reduction of 2.3x by conventional means
could be achieved by a capacitive top loading system. The top loading would be more mechanically unwieldy and probably result in impedance changes, necessitating a matching network.

Estimating efficiency is fraught with many variables, but I will begin with the common formula for radiation resistance of a shortened radiator -
Screen Shot 2016-06-17 at 22.57.17
Plugging in the values gives Rrad = 1579 x 0.0144 = 22.73Ω. As the VSWR is close to 1:1 at that frequency, Rloss = 50 - 22.73 = 27.26. Using the efficiency formula Rrad/(Rrad + Rloss) gives 0.55 (55%). Given the similarity in signals, it is reasonably assumed the small antenna is the same efficiency as the longer helical whip.

A calculation with Chu's formula given above gives Q = 19.5, and for the small antenna I take
a = 1.1m (edge of the "paddle") and assuming η = 0.55. A VSWR of 2.6:1 is measured at the -3dB bandwidth of the antenna.

_20m cap antenna VSWR
From the plot, 2.6:1 is at about 280kHz, so Q factor = 0.280MHz/14.250MHz = 51. Comparing to the Chu formula, we see it is 2.6x the limit. As there are so many assumptions in these calculations, I will refrain from comparing this antenna to the theoretical (and often impractical) designs from the academics. But it should be noted that a substantial reduction in height that doesn't lead to a large reduction in efficiency is an achievement, given the square law reduction of radiation resistance vs. height. Height is more important with the lower bands and for mobile operation when passing under low bridges!

It maybe possible to improve the design by optimising the size and shape of the "paddle" and approach 2x the Chu limit. A further test will be to construct a 40m band version, and compare to a 40m AmPro whip. ANTENNA TESTING CAN BE VERY MISLEADING.

Further tests will involve an Internet connected receiver, giving instant results, rather than having to wait a day for the measurement! Tests will involve adding various ground planes under the antennas, and trying to confirm the "breakaway region" theory.

Crossed Field Loop and Maurice Hately
Finally here, some words about the crossed field loop. This was the successor to the crossed field antenna developed by Prof. Maurice Hately (GM3HAT) with great fanfare and controversy about 25 years ago. The CF Loop has US patent US6025813, and I built one to the design as closely as I could, with this result:

Only some cheap parts are required, thick copper wire, a T200 iron dust toroid and two small trimmer capacitors. Performance was >10dB down on a conventional wire antenna, and bandwidth very narrow. This barely merits the word "antenna”, it's almost a non-radiating tuned circuit.

I found it was easy to control common mode current, by moving the coil tap to the centre, and using two turns of the coax thru a clip-over ferrite. Common mode current was always used by opponents of this design to explain its mode of operation. I have a different opinion, and also may explain why Prof. Hately vigorously defended his antenna until his death in 2012.

Any tuned circuit will radiate a small amount, and give an SWR dip when viewed on a network analyser. I think Prof. Hately was deceived by a combination of "if you can put power into it, it must radiate" and the vagaries of HF propagation. As shown above on this page, the effect of ground under the antenna is VERY MISLEADING.