Counterpoises, Capacity Hats, and A Standard
for Comparing Antennas Suspected of Radiation from the Feedline

L. B. Cebik, W4RNL (SK)




Investigators have suspected that a number of very small antennas do not themselves have significant radiation. Instead, the so-called antenna structures form non-radiating or very low-level radiating structures, and the main radiation from the antenna assembly as a whole occurs from the outer surface of the braid of the coaxial cable feedline.

Most of the tests so far performed lack one essential ingredient to an unambiguous test result: one or more standards against which to compare the system under study. These notes are designed to suggest a standard against which to compare subject antennas.

At the outset, I shall suggest that 50 MHz may be a good test frequency. It is within an amateur band, allowing the use of legal transmitters. The structures are large enough not to require ultra-finicky adjustments either for tune-up or for measurement. As well, upper-HF construction techniques work well. At the same time, they are small enough to be inexpensive and physically manageable. For example, the suggested mounting height will be 1/2-wavelength. At 50 MHz, a half-wavelength is 2.998 meters, 9.836', or 118.03". A ten-foot mast of non-conductive material--such as PVC--serves well with a home-made tripod mount. Careful backyard testing becomes very feasible.

The immediate problem is that many subject antennas are designed for other frequencies. Therefore, the subject antenna will normally require that the tester construct a 50-MHz version for tests. However, since it is the antenna principles that are under test--and not a specific antenna device--the substitution presents no theoretical problems.

Before setting up the suggested standard, let's examine some candidates for the task. In the process, we can perhaps get rid of a few common terminological problems that may inhibit either good testing or good reader understanding of the test results.

Vertical Dipoles and Ground-Plane Radial Monopoles

Essentially, our basic choice for a test antenna standard will be a vertically polarized antenna. If, as the test suspicion indicates, it is the feedline that is radiating, that line normally proceeds downward from the antenna structure under test. This situation provides another reason for using 50 MHz as a test frequency. With a 1/2-wavelength non-conductive mast, the feedline will be able to drop vertically from the antenna assembly. At low HF frequencies, the feedline may have to bend, twist, coil, or crawl along the ground for most of the first quarter wavelength from the antenna. A definitive test requires that we use a single orientation for the suspected actual radiator.

Fig. 1 shows 3 antenna configurations. The vertical dipole is electrically the simplest structure. However, because we need to feed the antenna at its center, the feedline should run horizontally for a considerable distance from the antenna. In practice, we use such antennas along with as many decoupling devices as a given situation needs to prevent pattern distortion due to unwanted coupling to the feedline.

The center vertical monopole uses 4 radials to form a nearly non-radiating ground plane for the antenna. Largely because the radiation from the horizontal radials is nearly zero, early texts on these antennas introduced two expressions into the antenna lexicon, one more dangerous than the other. The expression "ground-plane" radial system is itself not always accurate, because the horizontal radials do not necessarily form a ground plane, where we take the term "ground" seriously. Common practice is to connect the coaxial feedline braid to the radials and the center conductor to the vertical element. Hence, we have the illusion of the radials somehow being connected to ground. However, those radials function even when the antenna is many wavelengths from the energy source and form a ground conductor only for static build-up on the elements. In this context, we sometimes connect an RF choke between the vertical element base and the radial system in order to bleed static build-up from the vertical element as well. However, the antenna radial system may make no connection to the earth and still perform its function within the antenna perfectly well.

A second term is even more insidious: "counterpoise." This term entered antenna work from the world of mechanics in which some machinery required well-balanced counterweights in order to perform its function. Early thought about antennas led to underground wires paralleling horizontal antennas, buried and elevated radial systems, etc., and all received--for want of an understanding of their actual function--the vague label "counterpoise." Today, we find uses for the term that range from highly refined and defined applications to vague and ambiguous uses. Unfortunately, a large number of readers may not be tuned into the more rigorous uses within an article and carry away the idea that whatever constitutes the counterpoise requires less stringent standards of construction or analysis than the so-called antenna proper. I have read an advertisement for an antenna that uses a very long piece of wire as a "counterpoise," with the advice to kick it around until the antenna achieves resonance. In an article within a respected journal, I read about a portable monopole for use on balconies, and the author advised the reader simply to drop a counterpoise downward, with no concern for where it went or in what environment it operated. I have even seen the term used to characterize the coaxial cable feedline of antennas in which the tester suspected that the cable or counterpoise did the radiating.

In fact, in antenna work, there is no such thing as a counterpoise. Every part of the antenna system performs a function that we may directly analyze and calculate--and measure as well. The carelessly dropped "counterpoise" wire was actually the lower half of a vertical dipole. It exhibits a current distribution comparable to the distribution on the upper section, the so-called antenna proper. Radiating coaxial cables are susceptible to measurement and adjustment either to maximize or minimize the radiation. Finally, the radial system of the monopoles in Fig. 1 also show appropriate current distributions along their lengths, and they do radiate. They just happen to be horizontal and their far-field radiation is mostly self-canceling.

Let's compare the 3 configurations as physical NEC-4 models and see what we obtain in free space. Free space has no other object in its universe other than the antenna structure modeled. Hence, there is no ground. We shall note something else that is lacking shortly.

Dimensions of Free-Space Models of Vertical Dipoles and 4-Radial Vertical Monopoles

Vertical Dipole
Element Length WL Inches Millimeters Diameter WL Inches Millimeters
0.474 111.891 2842.04 2.118e-3 0.5 12.7
4-Radial Vertical Monopole (both versions)
Element Length WL Inches Millimeters Diameter WL Inches Millimeters
0.245 57.834 1468.98 2.118e-3 0.5 12.7
Radial Length WL Inches Millimeters Diameter WL Inches Millimeters
0.255 60.195 1528.94 1.059e-3 0.25 6.35

There is a reason for the element diameters used in the model. Ultimately, we want a standard that will reasonably replicate a main element composed of large diameter (low-loss) coaxial cable, that is, a cable whose braid approaches 1/2" in diameter. Also note that the monopole length is slightly greater than 1/2 the length of the vertical dipole. That maneuver results from the fact that the virtual position of a source is in the center of a model segment. The vertical dipole uses 31 segments with the source assigned to segment 16 at the center of the wire. The vertical element in the monopoles uses 16 segments, with the source assigned to the segment nearest the junction with the radials. By lengthening the vertical element about half the length of a segment, the monopole has a source position that is about the same distance from the vertical element tip as in the dipole.

We recognize that the right-most portion of Fig. 1 is simply the center antenna turned upside down. In free space, the orientation makes no difference, so long as we select the correct polar plot to show the resulting pattern. In all cases, I selected E-plane plots, which in modeling terminology means azimuth plots. The results appear in Fig. 2.

The gain of the dipole is 2.13 dBi (using aluminum elements throughout, although that hardly matters, given the large diameter of the elements). Both of the monopoles show a gain of 1.35 dBi. Note that the horizontal structure of each monopole creates no difference in the elevation angle of maximum radiation. It remain perpendicular to the vertical element.

If you explore the current distribution on the antennas, you will easily discover that that vertical dipole current decreases slowly at first as we move away from the source. A similar distribution occurs on the vertical section of the monopoles and is identical for both versions. The radials also participate in the current distribution. However, the current divides into 4 equal components at the junction, with each radial's first segment showing about 1/4th the source current. The radials are active parts of the antenna and critical to its proper operation.

In fact, the radial length was selected to bring the monopoles to near resonance, defined as a remnant source reactance of less than +/-j1 Ohm. Hence, they are slightly longer than the vertical element. Radial length is a function in part of the few radials used. I have elsewhere shown on a number of occasions that the higher the number of radials, the shorter the radial length needed to achieve system resonance. Somewhere in the region of 60 to 70 radials in free space, the radial length closely approaches the radius of a thin solid surface.

The modeled source impedance of the vertical dipole is, as we would anticipate, 72.04 + j0.35 Ohms. A persistent error in much literature would have the monopole impedance be 1/2 half that value, since the vertical element of the monopole is half the length of the dipole. Unfortunately, this easy derivation holds true only if we use a perfect ground, that is, if we mathematically recreate the missing half of the dipole with no radials in the model. When we place the monopoles in free space, we obtain a source impedance of 23.19 - j0.24 Ohms. To arrive at 36 Ohms, we must lengthen the vertical element considerably with a consequential shortening of the radials to return to near resonance. The result is an off-center-fed vertical element with its maximum current well above the feedpoint on the segment that joins with the radials.

We are now in a position to look more closely at the upside-down monopole. Suppose that we had inserted 2 or 3 segments of vertical wire between the present source segment and the radials. To achieve resonance, we would have shortened the radials to compensate for the added vertical length. As well, we would have dubbed the radial structure a "capacity hat." As long ago as the 1950s, Laport's classic text clearly notes that the name is based not on solid electronic theory, but on an analogy that is useful for approximate calculations of the required hat size based on the capacitive reactance of short vertical monopoles at ground level used in the low frequency region of the spectrum. Nevertheless, the name and idea persisted in amateur circles due to an article in QST in the 1970s, and the article was reprinted often in various antenna books. I have elsewhere shown that the calculations are seriously off in the HF region and above. As well, there is a complex relationship between the vertical element diameter and the diameter of the radials (or spokes, when speaking of hats).

In the end, the so-called capacity hat has nothing to do with capacity. We do not have one plate of a capacitor, the other plate of which is presumed to be the universe itself. Our free-space universe for the model has nothing in it to form the other plate of the so-called capacitor. Rather, the spokes of a top-hat structure provide the element length necessary for a normal current distribution such that the source impedance is whatever the designer needs it to be, normally, near to resonance. Because the hat spokes are at right angles to the main radiator and are symmetrically arranged, they contribute nearly nothing to the overall element radiation. The element end is actually 4 ends: the tips of the radials, not the flat plane created by the right-angle structure.

In point of fact, our upside-down monopole is simply an extreme form of top-hat. If we place the virtual source at the center of the source segment, then the radials are already displaced slightly from the source and constitute a top-hat. However, we have already seen that the free-space operation of the antenna is identical to the right-side up version, for which we are not in the least inclined to apply the term capacity-hat to the radials. In fact, the radials complete the antenna structure--relative to dipole current distribution--and do not form either a ground or a capacitor. Hence, it is likely that calling the structure a "top-hat" (or "end-hat" on horizontal elements) may be preferable to continuing the use of the label "capacity hat."

We can illustrate the relative identity of the ground-plane radials and the top hat by bringing the monopoles closer to earth--dragging the vertical dipole along for the ride. As a first step. let's use the so-called average ground for our earth (conductivity = 0.005 S/m; relative permittivity = 13). Next, let's set the source at 1/2-wavelength above ground. This is not yet a fair test, because the right-side-up monopole extends from 1/2-wavelength upward, while the upside-down monopole extends from 1/2-wavelength downward. If we take elevation plots of the three antennas in their new positions, we obtain the patterns shown in Fig. 3. The figure also shows the maximum gain and take-off angle for each configuration.

The first thing to notice about vertical antennas is that their source impedances do not change much until we bring them very close to the ground. The antennas in Fig. 3 are at the border of this region. The vertical dipole remains within a half-Ohm of its free-space value with an impedance of 69.45 + j0.72 Ohms. The right-side-up monopole shows a modeled impedance of 23.63 + 0.44 Ohms, again within a half-Ohm of its free-space value. Only the up-side-down monopole, with its tip about 1/4-wavelength from ground shows a slightly larger deviation: 22.02 - j2.09 Ohms.

The right-side-up monopole shows a very high TO angle, largely due to the fact that all of its radiating structure is above 1/2-wavelength. If we drop the antenna to a base height of 0.25-wavelength, the gain is 1.16 dBi at a TO angle of 16.2 degrees. The source impedance also changes to 21.59 - j1.77 Ohms. These values closely parallel those of the upside-down monopole, which has very similar top and bottom height values relative to the revised position of the right-side-up version. In short, the two monopoles remain the same antenna, even when we bring the earth into the picture.

I have noted that the radiation from the radials is nearly zero. However, it does not go completely to zero. We may observe remnant radiation from the radials by taking azimuth plots of the vertical dipole and either of the monopoles--and we may use the models in free space or over ground. For each type of antenna, there will be no difference due to the presence or absence of a ground surface. As Fig. 4 shows, the vertical dipole has no detectable horizontal component to the overall radiation pattern. The monopoles, however, have an 8-lobe pattern that shows up at the -40 dB level. For all practical purposes, we can ignore this small horizontal component. Nevertheless, the horizontally polarized component does establish that the radials--whether at the top or bottom of the monopole structure--do radiate. Most of that radiation is self-canceling, taking the symmetrical arrangement into account. But some radiation does emerge.

Transforming the Upside-Down Monopole into a Testing Standard

The upside-down monopole represents an example of an antenna wherein the top structure radiates as little as possible, and for practical measurements, not at all (unless the measuring equipment is capable of detecting -40 dB radiation relative to the main field). Hence, it is suitable as a standard of comparison with antennas suspected of feedline radiation as the main source of far fields. However, the radials are 5' long and may sag a good bit in their top position. Therefore, we should try to shrink the assembly without changing its basic operation.

One way to shrink the top hat assembly is to add more radials. However, we may use a more efficient means. We can add a perimeter wire from radial tip to radial tip. Fig. 5 shows the general outline. Note the lines that indicate the path of current distribution. Now they extend from the radial hub to the center of each perimeter wire. For the 50 MHz monopole using 0.25" radial assembly wires, the total path length is about 0.253 wavelength, in contrast to the radial-only length of 0.255 wavelength. The slight shortening of the path is due to the sharp corner at the radial tips.

Fig. 6 compares the relative current magnitudes in the standard 4-radial top-hat and the version that uses a perimeter wire in an EZNEC graphic that overlays the current curves on the outline of the models. If you place a ruler on the graphic, you will see on both outlines that the distance between the radial hub and the current line is about 1/4 the distance between the vertical monopole and its current maximum. In the version using the perimeter wire, the current at the tip of each radial is about twice the current in the connecting perimeter wires. Of cources, we have at those points a second splitting of the current paths. The decrease of the current to zero at the exact centers of the perimeter side shows clearly.

The radials themselves have decreased to a length of 0.148 wavelength (34.93" or 887.39 mm). The overall hat assembly is only 58% as large as the radial-only version. The modeled free-space performance data shows a gain of 1.59 dBi, with a source impedance of 21.47 - j0.49 Ohms. With the top-hat 1/2-wavelength above average ground, the gain is 1.20 dBi at a TO angle of 15.5 degrees, with a source impedance of 20.43 - j1.83 Ohms. The horizontal component has shrunk to the -50 dB level relative to the main elevation lobe of the antenna.

It is likely that any version of the standard top hat antenna using a perimeter-wire top-hat will employ a perimeter wire that is considerably thinner than the radials: perhaps AWG #12 or #14 or 2-mm wire. Because NEC (even NEC-4) becomes less accurate when we have non-symmetrical junctions of wires having different diameters, it is not possible to provide a precise design. However, modeling suggests that for AWG #12 perimeter wire, the radials should be about 0.156 wavelength (36.82" or 935.35 mm).

The entire purpose of setting up a standard is to measure it on the test site using all available test equipment. The measurements include--besides the obligatory source impedance record--near-field and ground-wave measurements at distances clearly marked for replication. Do not use hand-held instruments, but devise mounting brackets so that each measurement uses an identical position. You may also generate current probes using a multi-turn winding around a toroidal core and letting the antenna element form the other 1-turn winding of the resulting transformer. By rectifying and filtering the induced voltage or current, you may derive relative current readings along the length of any portion of the array. All of these readings together form the base-line of data for further comparisons. In this set-up, the feedline should operate only as a feedline. If necessary (due to the odd angle of departure from the assembly top), add a choke-balun (common-mode choke) at the feedpoint.

Fig. 6 shows the basic top-hat monopole along side an adaptation to determine the radiating properties of coaxial cable. The cable serves as both the feedline and the main vertical radiator. It is similar in principle to feeding the cable through the center of the driven element tube, except that the role of the tube is played by the outer surface of the coaxial braid. The cable should be at least 1/2-wavelength long, that is, long enough to reach from the top of the 1/2-wavelength non-conductive mast to the ground.

The diagram shows two possible ways to connect the cable: with the center conductor to the hat or with the braid to the hat. In theory, with a perfectly balanced line, there should be no difference in any measurements applied to the system, since any imbalance created by the hat on one side of the line will couple through to the outer surface of the braid. However, practice may show otherwise. The diagram also shows the presence of a ferrite bead choke. At 50 MHz, you may use about a dozen FT-43 toroid cores that have an inner diameter just large enough slide over the coax jacket. Because toroids are available in different lengths, about 6-8 inches of cores is about right for 6 meters. The so-called bead-balun choke is most useful in this application because you can move its position to one in which a. you obtain the maximum radiation and b. you obtain the minimum radiation from the cable. The diagram shows various positions for the coax line on the source side of the bead-balun. Varying the line position below the vertical length needed for maximum radiation is a good way to find out if other forms of coupling to the line may occur.

Measure the same set of parameters as for the basic antenna. Include relative current readings from both the main vertical length of coax that forms the prime radiator and from positions beyond the choke-balun to determine if there is coupling to the line by direct radiation. In theory, it should be possible to obtain just about the same performance from the coax + hat assembly as from the basic antenna in which the feedline operates solely as a feedline. Not shown in either case is the matching network that you may need to raise the low impedance of the assembly (20-25 Ohms) to the 50-Ohm level required by the coax. A quarter-wavelength section of parallel 70-75-Ohm cable (taking the line's velocity factor into account) is a simple way to match the top-hat monopole to the line, although a simple L-circuit will also work well.

Now you may take the third step and replace the hat assembly with any desired test antenna assembly that you suspect may rely on the feedline for radiation. Since many of these top assemblies may not allow easy measurement of their radiation or their current levels due to the shape of their parts. you may estimate better the degree to which they radiate and to which the feedline radiates by comparing measurements with the two base-line antennas. As well, you may compare near-field and ground-wave readings with the choke in various positions on the coax, after ensuring that there is no significant coupling by direct radiation to the coax beyond the choke.

The hat assembly is an example of a half dipole that radiates only about 40-50 dB below the level of the vertical radiator--plus whatever radiation may occur from the feedpoint connection mechanical components. Its very low level of radiation is partly a function of the symmetry of its construction and its size, where the "right" size is determined by resonance when using a vertical main element that is 1/2 the length of a resonant dipole. It is part of the antenna assembly--as determined by the current distribution along its radials and perimeter wire--but unlike some other assemblies that call themselves antennas, the hat is not supposed to radiate significantly.

If the current distribution along the coax feedline substitute for the main vertical element matches the current distribution with a test antenna and if the near-field and ground-wave measurements also match up, then we have strong evidence that the test antenna is little more than a "hat-substitute" and has about the same radiation properties. If the current distribution along the coax outer surface is different for the test antenna, but the near-field and ground-wave readings are the same, then it is likely--subject to more detailed analysis--that the test antenna presents the feedpoint with a different set of impedance conditions, but does not contribute significantly to radiation. If the radiation levels increase with the subject antenna, then it is likely that the antenna assembly is radiating to some degree. (For further comparisons, you may wish to make reference near-field and ground-wave readings with a vertical dipole.) If the overall near-field and ground-wave readings are lower with the subject antenna in place, it is likely that the subject antenna is creating a resistive load that is converting some supplied energy into heat rather than radiation. The comparative measurements do not provide definitive final answers, but they do provide both probable answers and pointers toward the system elements that may need further analysis.

Conclusion

I have dwelt at a bit of length establishing that the top-hat monopole as simply a different but highly usable standard for comparing test results with antennas suspected of relying on feedline radiation for their far fields. It seemed necessary to clear the field of potential misconceptions attaching to notions like "ground plane," "counterpoise," and "capacity hat." The top-hat monopole and its smaller cousin that uses a perimeter wire to shrink the top-hat spread are simply inverted ground-plane monopoles and operate in exactly the same manner.

As a test standard, the top-hat monopole is useful because the hat structure--whether only radials or radials plus a perimeter wire--is designed to minimize radiation. Hence, it provides a standard of comparison by which one can obtain data to determine if a subject antenna radiates better or worse. I have suggested a battery of tests that include ground-wave, near-field, and relative current readings to provide a sufficiently complete portrait of antenna operation by which to reach conclusions supported by evidence with a minimum of assumptions. Refined test equipment is desirable, but rudimentary test instruments based on handbook designs are likely satisfactory if well constructed and if the test set-up is carefully handled to provide consistent results. Moreover, the test set-up requires very little more than a roomy backyard at 50 MHz.

Although a calibrated test range or chamber is superior, the test set-up described that includes standards of comparison as well as a reasonable compliment of measurements should go a long way to determining whether some of the suspected antennas in fact rely wholly, partially, or not at all on feedline radiation as their main mode of operation. If the reliance on the feedline is sufficiently strong, then we can save much effort and money by simply creating a hat to replace the complex and often expensive non-radiating antenna.

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