Antennas with Area
The CFA May be a Driver for a Patch Antenna!

David Jefferies G6GPR
Dr. David J. Jefferies
School of Electronic Engineering,
Information Technology and Mathematics
University of Surrey
Guildford GU2 7XH
Surrey
England

Fat Rods, Patch Antennas, and NEC2
our publisher, Jack Stone, has kindly given me this slot to air a few thoughts on the subject of antennas which are constructed from areas of metal rather than from thin wires.

Suppose we want to use some version of the Numerical Electromagnetic Code (NEC) software to model an air-spaced parallel-plate capacitor, all of whose dimensions are very much less than a wavelength at the frequency of interest. (As my experience of running NEC is confined to the software marketed by Nittany Scientific, my remarks must be taken to be limited to their versions of NEC2.)

We might set up a grid of thin, or not-so-thin, wires with perimeter co-terminous with the rims of the capacitor plates, and use a segmentation arrangement so that the individual segment lengths were no smaller than the wire diameters, and no larger than the minimum distances between nodes.

We might then feed the capacitor across the mid points of each grid. Would the capacitance be accurately reported? Would it depend on the "packing fraction", or ratio of the area of the metal in the wires to the total area inside the perimeter of the plates?

There is a brief report of our experimental measurements of what happens in this scenario at
http://www.ee.surrey.ac.uk/Personal/D.Jefferies/perfcap.html

To see what we are talking about, consider the capacitor below with one perforated plate (blue) and one solid plate (red).

Figure 1: A capacitor with one perforated plate

In summary, what we found was that the measured capacitance depended on the total area inside the perimeter, if the hole sizes were smaller than, or comparable with, the plate spacing; whereas the capacitance depended on just the area of metal in the wires (total) if the hole sizes were much larger than the plate spacing.

If NEC is to model capacitative coupling accurately, then it should reproduce these findings. I have not had the time (nor do I have the experience) to try out the NEC simulations; this would be a good task for a keen antenna modeller.

Now there is a graph in John D Krauss's book "Antennas" (Edition 2, ISBN 0-07-100482-3, figure 9-12 page 376) which compares a Hallen calculation (Erik Hallen, "Admittance diagrams for antennas, and the relation between antenna theories", Cruft Laboratory technical report #46, Harvard University, 1948) of the driving point impedance of a resonant dipole antenna with measurements, as the cylindrical rod radius/length ratio is increased.

Figure 2: A dipole with fat rods
and capacitative coupling between the rod-ends.

There are significant discrepancies between theory and measurements reported (A Dorne, "Very High Frequency Techniques", RRL staff, McGraw-Hill NY 1947, chapter 4) for fat rods. A NEC4 simulation, reported to me by Dan Handelsman, also does not reproduce the measured fall and subsequent rise (to nearly 80 ohms) in radiation resistance, as the rods are thickened. NEC predicts a substantially constant resonant radiation resistance close to 72 ohms for all thicknesses of rod. This disagrees sharply with calculated values of resonant radiation resistance, which show a fall to around 60 ohms as the rods thicken. This calculation, in turn, disagrees sharply with the measurements.

I did some initial calculations taking into account the effects of the capacitance between the ends of the fat rods comprising the two halves of the dipole. This of course would put shunt capacitative susceptance across the feed terminals; we are however only interested in the driving point impedance at resonance, so to compensate, the rods must be lengthened. This lengthening puts up the series inductive impedance, and it also puts up also the calculated radiation resistance, which now, because of the effect of the C-L matching section is further transformed up to the measured driving point terminal resistance. Most amateurs would understand the driving point terminal resistance to be what they call the radiation resistance of an antenna. It differs from the "radiation resistance" as calculated from electromagnetic theory. This is because the current supplied by the feed is not the same as the current injected into the antenna rods, as there is an impedance transformation due to the L-C matching section formed from the shunt capacitance of the fat rods, and the residual inductance of the slightly-lengthened antenna. The reason the currents are not the same is because some of the feed current goes to setting up circulating resonant currents in the L-C matching section. If you like, the feed supplies the difference current between the opposing quadrature currents in the shunt capacitance, which is balanced (mostly) by opposite-phase quadrature current in the L-Rrad section. Now it is the current in the L-Rad antenna section that contributes to the radiation, and this current can be larger than the residual difference current drawn from the feed, if the Q factor is not small.

The situation is illustrated in this simple figure.

Figure 3: The dipole antenna is cut a bit long,
and is inductive. Rrad is the classical radiation resistance.
C tunes out the residual rod inductance.

We can estimate the size of the current enhancement, and therefore the step-up in the antenna resonant resistance over Rrad, by considering the quality factor or Q. To a good degree of approximation, for reasonably large Q factors (3 or more) the enhancement in resistance is by the square of the Q factor. For smaller Q factors we need to do the calculation more carefully.

When we take into account this rod-end capacitance, most of the problems of the discrepancy between theory, simulation, and experiment, for the measured driving point impedance of fat rod antennas compared to the theoretical radiation resistance, are significantly lessened. It leaves me wondering whether any version of NEC accurately models capacitative coupling between antenna elements.

In any tuned antenna installation, it is the actual current(s) circulating in the radiating structure that contribute to the far field radiation. These can be quite different from the net current supplied by the feed. The actual currents on the structure may be significantly larger than the feed-current if the structure is resonant. It is, of course, also possible for the radiating currents on the structure to be less than the feed current.

It is generally accepted now that NEC is extraordinarily successful in modelling thin wire structures. Professor Jim James, of the Royal Military College, Shrivenham, tells me that in dealing with his surface mounted patch antennas he uses FDTD (Finite difference time domain) software rather than NEC. I am here raising the issue that NEC may not model capacitative coupling between adjacent antenna elements having significant area. Thus, Yagi-Uda arrays with plate elements rather than wire elements may behave (in practice) quite differently from their NEC simulations.

There is a recent set of measurements by Mike Underhill at Surrey on small loop antennas, whose inductive impedance component is tuned out by a shunt capacitance, so that the driving point impedance is purely resistive. Now it is known from electromagnetic theory that the radiation resistance of a small loop antenna falls in proportion to the [(radius of the loop) divided by the wavelength], all raised to the fourth power. However, because of the impedance transformation discussed above for short fat dipoles, it is found empirically that for a tuned small loop, the driving point resistance (which is what amateurs would call the "radiation resistance") varies as the [(radius of the loop) divided by the wavelength], all raised to the second power. It is probable that part of this enhanced driving point resistance is in fact loss, transformed by the same mechanism. But that leaves a significantly higher current in the loop (than drawn from the feed) to provide radiation. Field strength measurements on small tuned loop antennas do indeed seem to indicate that they work much better than the simple theory would have us believe. A definitive measurement would be to compare the phase of the radiation with the phase of the feed current, allowing for the transit distance phase shifts.

The Intriguing CFA Question
Elsewhere in an issue of antenneX (Critique of CFA Experiments & Papers by Ralph Holand, VK1BRH) is a critique of the evidence on the CFA. The CFA clearly falls into the category of antenna considered above; the plates are formed from large areas of metal. Perhaps modelling them with NEC may not be entirely satisfactory.

We recall that the originator's theoretical proposal of the mechanism by which the CFA is said to work, is flawed. To recap, the E and D plates are fed in phase quadrature, which results in the displacement current from the D plate producing a magnetic field which is in phase with the electric field produced by the E plate. This is because there is a phase difference of 90 degrees between the D field and the displacement current (dD/dt, the first time derivative) to which it gives rise. However, the D plate produces a strong E field and the E plate produces a D field and hence its own displacement current. These combine to give an inward contribution to the Poynting vector. When the Poynting flux is integrated over an entire surface ( any entire surface) surrounding the structure, there will be as much total inward-directed power as outward-directed power. If you like, this is like a vehicle traffic flow in Washington trying to get to New York, but driving all the time round the block. At any point on the road from Washington to New York there is a large flow of traffic, but it takes four successive right hand turns and doesn't get anywhere, just recirculating all the time. On the other hand, if the E field produced has a component at 90 degrees to the H field no power propagates anywhere; the instantaneous E^H oscillates twice a cycle and the average over a cycle is zero. Thus there is no method of adjusting the phasing which gives rise to a plausible radiation mechanism, other than that of direct radiation from the small CFA structure by the usual processes. In fact, Jack Belrose has found that if anything, the structure works better when the plates are fed in phase (and therefore the directly generated E and H fields are in phase quadrature) than by the method suggested by the inventors.

Thus there is no foundation in fact for believing that the CFA can possibly work "as advertised"....and yet there seems to be supporting evidence for the notion that some of these installations are surprisingly effective. We therefore have to cast around for an explanation as to why this might be the case.

So, here I wish to propose yet another theory, or "worm to add to the can". It is possible that the large area plates of the CFA, handling high voltages (because the Q is high [Jack Belrose]) couple capacitatively to the ground. They therefore may be expected to inject strong currents into any conducting ground which may be present, whether or not there are ground plane radials laid. In the Nile delta we might consider the (supposed wet) ground to be a kind of conducting "patch antenna", possibly extending radially outwards from the drive point as far as a quarter wavelength or more.

Figure 4: The CFA injects currents into a surface patch antenna

The currents in this patch may couple rather nicely to an outward radiating "ground or surface wave". Thus my (and Jack Belrose's) objections that the antenna is small, and therefore necessarily very inefficient or of high Q, are neatly met. And the fact that in Egypt this antenna type works, whereas elsewhere it does not when on a different kind of ground, is neatly explained.

Therefore, when people report CFA experiments I would like to see more attention paid to the kind of mounting over ground, and the character of the ground surrounding the antenna.

Of course, instead of a "worm to add to the can" this proposal may turn out to be just a "red herring", but then Jack Stone does advertise this slot as his "soapbox".

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Last modified: December 27, 2003