Electrically Small Antennas 2016
Updated 20160630
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 are 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 ham radio stations continue to use designs half a century or more old.

A good HF antenna for ham radio 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, it's 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.

EH Antenna Revisited
The PVA/EH antenna is probably the most controversial design ever published. Analysing it with NEC2 indicates it's a short fat dipole. Accusations of radiation by common mode current have persisted, though I find this mostly untrue. Proponents of the EH claim it requires "extensions" to Maxwell's equations. As shown by the above result I conclude something similar to the EH can give comparable performance to a full length wire antenna under practical conditions. Removal of the lower cylinder of the EH antenna results in similar performance.

Here I advance an alternative theory which
does not require any changes to physical laws which have been accepted by genius level scientists for over 100 years. It does require the acceptance that the NEC2 antenna simulator produces incorrect results.

The classic paper by Landstorfer and Meinke describes electric field lines breaking away from a rod above a ground plane. Only the top of the rod produces "escaping" field lines that manifest as far-field radiation. As the field lines are electric (as opposed to magnetic) their equations suggests higher voltage on the top of the rod will increase the strength of the escaping field. My tests bear out their ideas.

The EH antenna places a high voltage (via step-up transformer) on a cylinder. In practice the cylinder is raised above a "ground plane" which may consist of a car body, house roof, or the actual ground. If the transmitter is connected in any way to ground even by capacitive effects, electric field lines will be formed, and some will escape to be far-field radiation. The losses of such a system will include:

  • Resistive or dielectric losses in the circuit path between the high voltage plate and "ground"
  • Loss by resistive or lossy magnetic/dielectric materials which make up the "ground"
  • Dead capacitance between the lower cylinder and upper cylinder

Therefore by having a reasonably low loss conductive ground plane beneath it, and connected somehow to the transmitter, the effectiveness of the EH antenna is improved. The second point is self-evident and applies to any kind of antenna.

The 3rd point takes us back to the Landstorfer paper. It classifies capacitance into 2 types; radiating and dead-capacitance. The lower cylinder of the EH antenna is dead-capacitance. Its presence reduces the resonant frequency, but does not contribute anything to far field radiation. This can be proved by removing the lower cylinder, and enlarging the upper cylinder to compensate for the increase in resonant frequency. Signals to/from the antenna tend to increase or remain the same. Hence the "Poynting vector synthesis" theory of the EH antenna is disproved.

The realisations here explain why some reports of unexpectedly good performance happen with the EH antenna. When a vehicle body or other metallic plate are introduced under the antenna, the electric field losses are reduced, and the top cylinder radiates effectively as Landstorfer envisaged. If the system is connected directly to the vehicle body somehow, the ground losses are reduced.

The combination of ground loss effects and radiating capacitance explains how a short radiator can have such apparently good performance, even down to the radiator itself being ~5%λ. The height above "ground" and the ground plane itself add to the electric field radiation mode described. Radiated efficiency can apparently match full size antennas as shown by my measurements above.

I am working on how short this concept can be made above the ground plane, and a more definite result proving it's worth against a conventional antenna. Its probable the lower limit is 5% λ. Nowhere near as small as the other controversial designs, but I will repeat: ANTENNA TESTING CAN BE VERY MISLEADING.

MicroVert and PVA
The MicroVert has been around since 2001. The designer, DL7PE, asserts that having a conductive cylinder outside a short fat radiating element produces space capacitance. There will indeed be capacitance between the 2 cylinders. However by admission of his article, the performance of the MicroVert is 10-20dB down on a standard dipole. This because the capacitance between the 2 cylinder is not space capacitance at all, and DL7PE completely mis-interpreted the Landstorfer paper. Also this page goes over the same ground but makes the mistake of analysing with NEC2.

More recently the
Poynting Vector Antenna appeared. In particular this page ignores the graphs given by Landstorfer, and moves the radiating capacitances far too close together. This is why the PVA (despite the charming pig and horse shapes) performs badly. I constructed one (made from 2 plastic bottles plus copper foil) and found it to be very "dead" compared to a conventional wire antenna. I find it difficult to believe these people ever read the original academic paper!

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:
CFL1
There are only some cheap parts required, like 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 very 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.

Unfortunately today is a low point in alternative HF antennas. Anything that doesn't simulate well or easily in NEC2 is dismissed out of hand. This is probably why none, or very few new HF designs have appeared over the last 10 years.