For an experimenter, a good theoretical background is a benefit. Although theoretical exercises are more boring than experiments, one usually has to do them both in parallel. Personally, I enjoy experimenting, and a main part of my satisfaction comes from a good agreement (if any) between my experiment and a theoretical prediction. And each disagreement is a reason to think which side was wrong: the experiment, or its theoretical model? Or maybe they are both not perfect? Amateur measurements are mostly restricted by available tools and, more specifically for antenna testing, by available space. This leads to prevalence of A/B comparison tests, thus involving one more unknown: a reference antenna used in the test. Does it really mean that all the amateur tests are useless? Not at all. Even a listening-only A/B comparison test may give a half of S-unit accuracy, or 3 decibels. Is it too bad? You can get a fraction of decibel accuracy from modelling, but only if all your input is absolutely correct, which is usually not the case: all the antenna surrounding is left behind, and a ground model is just a best guess.
This article deals with a feeder radiation phenomenon. This phenomenon is well known, but Hams usually think of it as a small fraction of the total antenna radiation and mitigate it only when it distorts a radiation pattern of an antenna, or causes TVI. All the above is true for big good antennas. For small ones, like the Isotron, the DL7PE-microvert, and the EH antenna, the feeder radiation can exceed the radiation of the antenna itself by two orders of magnitude (20 dB). This leads to claims about a new method of the electromagnetic waves radiation, since the classic theory can't explain that. This leads to some new "theories" and revisions of the classic theory. Here we shall try to look at the radiating feeder phenomenon from the classic theory position; we shall try to model it using a well established software package; and we shall compare our figures against existing experimental data. We restrict our scope to only two "small" antennas: the DL7PE-Microvert and the EH antenna. They are very close to each other in term of creating useful radiation via their feeders, but they have also some difference, which helps us get a better understanding of the problem.
Juergen Schaefer, the author of the DL7PE-microvert, points to theoretical principles discovered by two German scientists and published in the "NTZ" magazine. They have discovered a radiation resistance of 30 Ohms for a very short (0.02 wavelength) monopole, and they explain this by some kind of a "dead" capacitance of short radiators. Unfortunately, Juergen gives only short quotations from this work in his antenneX article, so we can just guess about test conditions where the 30 Ohm radiation resistance was measured.
For the EH antenna, at the time of writing this article, I see only two attempts at a theoretical explanation how it works. The first one belongs to Ted Hart, who has patented this antenna, and the second was made by Lloyd Butler. Ted's theory starts with breaking Kirchhoff's law, since he states that it is possible to change a phase between a voltage and a current of a two terminal network by means of an external phasing network. It states a 30 Ohm figure as a radiation resistance of the EH antenna after a proper "phasing". Lloyd's theory accepts a third terminal of the EH antenna, which is a coax shield. His theory even accepts a common mode excitation of the EH dipole with respect to the coax shield as a possible component of the whole radiation, claiming it as a small fraction only, but with no quantitative results. This theory postulates a radiation resistance of 2*Pi*377 Ohm for a parallel RC network equivalent circuit (approximately 2350 Ohms). For a series RC equivalent, the radiation resistance becomes around a half of kilo Ohm, if you assume C=10pF for the 20 meters band. Both theories try to derive a proper phasing and amplitude ratio of electric (E) and magnetic (H) field components in the near field zone of the EH antenna. Both theories claim that this is the only way such a small antenna can radiate like a full size one, hence rejecting any attempt of classic theory application. We state our goal as explaining the DL7PE-microvert and the EH antenna operation based on the classic theory only.
I must confirm that I am not the first person to try this route. Igor (Gary) Gontcharenko DL2KQ/EU1TT has a good description of his own experiments and thoughts on his personal site http://www.qsl.net/dl2kq, unfortunately in Russian only. He has also results of MMANA modelling, and these models are used as a starting point here. My participation in the Yahoo EH antenna forum discovered that many people do not share Ted's ideas. Speaking a Patent English, everybody skilled in the art can come to the same conclusion.
From the engineering point of view, each piece of information falls into one of the three categories posted as the header. Although this is just a joke, we have to look through all the claims of EH antenna fans very carefully. Unfortunately, not all the claims were confirmed by test results. One of the most important is that the EH dipole itself radiates at the same efficiency as a typical full EH antenna installation having some quarter wavelength coaxial feed line. Participating in Yahoo EH antenna forum made it clear to me that this "fact" should be moved into the "untested claims" group. An attempt made by Conny Winrot, SM5DCO, to test this claim gave rather mixed result, since it was neither an A/B comparison test nor an absolute field strength measurement. Experiments with a current balun situated close to the EH antenna by other people discovered a hot balun and/or a some 10 dB loss of radiation efficiency.
So, what facts do we have to explain? The most important fact is that a typical installation of the EH antenna works just fine. It may behave similarly to a quarter wavelength vertical antenna and even outperform it. This task is already quite challenging, but we hope to get some more side results going our way. For the DL7PE-microvert we have a claimed efficiency -6 to -12 dBd to be explained.
Since we are going to show how much a small antenna can radiate by a common mode current of its feeding coaxial cable, we have to make clear what is this current and where it comes from.
Usually we consider a piece of a coaxial cable as a two port device, like in Fig. 1, part A. This means that we connect some voltage source across its input terminals and we connect some load across its output terminals. Each two terminal port behaves like a lumped circuit: a current going into one terminal is equal to the current going out of the second terminal. This is shown in Fig. 1, part B. Here IDS is a differential current at the source side, and IDL is a differential current at the load side. The same is true for any cross section of the coaxial cable (Fig. 1, part C): a current IDM going to the load through the inner wire of the coax is the same as returning from the load by the coax shield, although this value can be different from the input terminal current. This happens only when the load does not match the characteristic impedance of the cable. Finally, due to the skin effect phenomenon, all the shield current in this mode goes on the internal surface of the shield, and looking onto the coax from outside you can see neither an electric nor a magnetic field outside it. This in turn means that if we wind up the cable to form a coil, no difference will be made for such a signal. Since in this mode an input voltage of the cable is a difference of an inner wire potential and a shield potential, this mode is usually referenced as a differential mode.
Fig. 1. Differential signal in a coaxial cable.
Is it the only way of sending a signal over a coaxial cable? No, of course not. If we connect the two input terminals together, and the two output terminals together, we get just a piece of wire whose diameter is equal to the outside diameter of the coax shield, as shown on Fig. 2, part A. If we apply a voltage source to one end of this wire and a load to its other end (Fig. 2, part B), both with respect to ground, it can carry a signal from the source to the load. Here ICS is a common mode current at the source side and ICL is a common mode current at the load side. Is it a good application for a coaxial cable? Definitely it is not. A simple wire can do this job. But this mode is what causes a radiation from the coax shield, since there is no more shielding around it. This mode is usually referenced as a common mode, because the input signal is common for both input terminals. Although on low frequencies some part of the common mode current goes through the inner wire of the cable, on high frequencies all the common mode current goes through the outer surface of the shield only. Fig. 2, part C illustrate this. Here ICM is a common mode current in the middle cross-section of the cable. We may conveniently think of the common mode current path as completely independent from the differential mode current path, being connected only at input and output shield terminals.
Fig. 2. Common mode signal in a coaxial cable.
In most practical cases, both modes are present in the same coaxial feeder, but they behave in a different manner. The differential signal is not affected by a current balun, while the common mode signal has to go through a common mode inductance of the balun. The differential signal propagates at lower speed, depending on the permittivity of a dielectric material inside the coax, but the common mode current goes at the full speed of light. And as it was mentioned above, the differential current is perfectly screened inside the coax, but the common mode current can easily radiate electromagnetic waves.
This is a good place to recall open wire symmetric transmission lines. They can also have common mode current, but due to their symmetric nature, this current is split into two halves, each going by its wire, in the same direction.
There is a common misbelief among Hams that a radiating feeder should get hot. This is a baseless statement. For a differential signal going inside a typical 50 Ohm cable only 1/4 of total losses occurs at its shield, and other 3/4 on its inner wire. Since a common mode current value is roughly the same as a differential current in most cases, we have a four fold more current handling capability, if we need our cable for common mode current only. If we are going to use the cable for both common mode and differential signals, then we have to derate its current handling capability by 1/4 only.
There are lot of photographs showing successful EH antenna installations available on the Internet. Since Ted Hart recommends elevating his antenna to a quarter wavelength height, this usually leads to a coaxial feed line of the similar length. The feeder often goes down from the antenna, then has a significant length running horizontally. Some installations include a current balun close to the transceiver, and a separate grounding to prevent RF energy coming into the shack. This makes creating a single model almost impossible. To simplify the task of building a model, we shall first try making it for a DL7PE-microvert and then extend it for the EH antenna.
First, look at the Microvert carefully. The left part of Fig. 3 shows it. Unlike the EH antenna, its feeder consists of two parts, delimited by a current balun. We suspect the part of the feeder closer to the Microvert itself can radiate, but we have only one source of RF energy, and this source is connected to the feeder in a truly differential way. So our first task is to find an equivalent common mode source in this system.
Fig. 3. DL7PE-Microvert and its model.
A technique that we use for this transformation of a differential source into a common mode one can be described as pulling out the source toward the load. If we have a matched antenna system at some frequency, the source "sees" a perfect resistive load. It will see the same load if we add some additional length of coax, or if we make it shorter. This does not affect a differential current in the coax. Since our intention is to keep a common mode current path untouched, we can't cut or paste our feeder directly. Instead, we can cut our cable somewhere in the middle, connect our source to the part going to the load, and also keep the shield of the other part connected. Going this way we can put our source at the load side of the feeder, thus making the feeder only a common mode current path. Fig. 4 shows this transformation. Its part A is a piece of a coaxial cable with a grounded source connected to its left end and a semi-symmetric load (like a dipole) connected to its right end. On the part B, the source is shown half the way to the load, while on the part C, the source is at the load end.
Fig. 4. Moving source toward load.
Is the resulting circuit fully equivalent to the circuit we started with? Actually not. In the initial circuit the differential signal is attenuated and delayed by the cable. The attenuation is usually small on RF bands, and we can also account for it by adjusting the source voltage properly. The delay also can be taken into account, but if we have the only RF source in our system, and the only way from this source to the load, then we don't even need this absolute phase.
Applying this technique to the Microvert, we get its model shown on the Fig. 3, middle. What do we have in our equivalent circuit of the Microvert? Well, I guess everybody recognizes just an asymmetric vertical dipole. Its top half is short, but has a coil in series, which can be adjusted to a resonance at a frequency of interest. The bottom half of the dipole contains a balun somewhere 0.2 wavelength down. If its inductance is infinitely high, we can cut the cable at this point. If it is just high, we have to account for a balun value and a residual part of the feeder. In our case we can make this 0.2 wavelength part a bit longer. Now the bottom half of the dipole is close to a quarter of wavelength.
Can we estimate an input impedance of the Microvert just looking at the model we have? This is shown as an equivalent circuit on the Fig. 3, right. The source "sees" a series connection of two radiation impedances, one of the top monopole, and another of the bottom monopole. We may expect some fraction of Ohm (RRAD) in series with some picofarads (CRAD) for the top monopole. If we add a coil (LCOIL) to get a resonance, we compensate the capacitance, but add some coil losses (RCOIL), say units of Ohms. On the other hand, a radiation impedance of the bottom monopole (RCP) can be almost resistive and some 25 to 30 Ohms. In case of some reactive component, it can be easily compensated by adjusting the top coil. Now we can conclude that a claimed 30 Ohm radiation resistance is a property of Microvert's counterpoise, not of the Microvert itself. At this point I have to disagree with Prof. F.Landstorfer and Prof. H.H.Meinke. However it is still very interesting for me what was written in their article published in the "NTZ" magazine.
Although we did not get precise figures from the estimation above, we got an idea about an overall efficiency of this antenna system. We have a series connection of coil losses and a radiation resistance of a long enough counterpoise, while we can safely ignore a very small radiation resistance of the Microvert itself. This already gives us a thought that most radiation comes from the counterpoise, and the overall efficiency is rather high.
Now we need more solid figures. We have a model, which contains only two wires of different diameters, a single source, and a single load. For the 20-meter band we have a 0.31-m radiator (20 mm outside diameter) and a 5.4-m counterpoise. Putting this model into MMANA is simple and easy (DL7PE_2.MAA), and computation time is less than a second. The resulting current distribution is shown on the Fig. 5. For a real ground with 1 mS/m conductivity and dielectric constant DK=5, situated 2 m below the bottom end of the counterpoise, we need an inductance L=22.75 uH (assume Q=200) to get an almost active input impedance 38+j0.3 Ohms and Ga=-2.6 dBi at 22.6 degrees elevation angle. Is this what we expected? Well, this is what one may expect for a quarter wavelength radiator. Is there any difference from Juergen's figures? He claims -6 to -12 dBd, but he also claims that there is only very low electromagnetic field found around the counterpoise, and that hiding a part of the counterpoise behind a steel enforced concrete wall makes no difference to the signal strength. I think Juergen's figures are true for a far from perfect counterpoise location, like partially lying on the floor, and paying more attention to the counterpoise one can get better results. His conclusion about a very low electromagnetic field around the counterpoise was probably made by looking on the electric field component only. Due to a series connection, a current value in the top end of the counterpoise is the same as in the bottom end of the Microvert, and the counterpoise is by an order of magnitude longer.
Fig. 5. MMANA model of the DL7PE-Microvert
Can we get anything else from the Microvert before switching to the EH antenna? Yes, we can. Above we saw an example of a common mode feeder radiation phenomenon for a particular arrangement of the feeder. The radiating part of the feeder was made as a quarter wavelength vertical radiator, isolated by means of balun at its bottom end and fed from its low impedance top end. Now we will try an opposite arrangement. If we ground the bottom end of a quarter wavelength radiator, we expect to get some thousand ohms radiation resistance on its top end. Hence we need a matching network there. A sketch is shown on Fig. 6, left. For a model, we take the matching network as a part of an equivalent source, leaving only a single coil at the bottom side of the Microvert's radiator (Fig. 6, right). Note that in the MMANA model DL7PE_2a.MAA we have to make the only change: lower the model to connect the counterpoise to ground. Now for L=36.2 uH (Q=200), we have Rin=1957 Ohm and Ga=-2 dBi at 29 degrees elevation angle. The maximum of the current is at the grounding point now, as Fig. 7 shows. Due to much higher radiation resistance, the coil losses are even less important now, but we have to account for additional losses in the matching network and also for losses at the grounding point. If we add 50 Ohm losses to the grounding point (DL7PE_2b.MAA), we have Rin=1227 Ohm, Ga=-6 dBi at L=27.9 uH.
Fig. 6. Microvert with grounded counterpoise.
Fig. 7. MMANA model of the grounded counterpoise.
Eventually we try an L-shaped counterpoise consisting of two quarter wavelength parts, the first part going vertically toward ground, then the second part running horizontally and grounded near a transmitter (DL7PE_3a.MAA). Fig. 8 presents its MMANA model with current distribution. This counterpoise has both its ends at low impedance. The result of modelling, presented in Fig. 9, is not surprising. Beside a good radiation of a vertically polarized electromagnetic wave (Ga=0 dBi at 25 degrees elevation), we get also a good amount of horizontal polarization. There is also a preferred direction with a front to back ratio F/B=4.2 dB. Other figures include 32+j0 Ohm input impedance at L=23 uH. Just keep these results in mind, and switch to the EH antenna.
Fig. 8. L-shaped 1/4+1/4 wavelength grounded counterpoise.
Fig. 9. Radiation pattern for 1/4+1/4 WL grounded counterpoise.
What is different in the EH antenna compared to the DL7PE-Microvert? First, its feeder has no dedicated counterpoise. Second, it contains a phasing and matching network between its feeder and its radiating elements. And third, it has a bottom radiating element, thus forming a short symmetric dipole. How can we handle this? We can model some simple feeder layouts as we have modelled for the Microvert. The latest of them, having a total feeder length of a half wavelength and an antenna height of a quater wavelength, is a typical EH installation. There are two possible phasing/matching networks for the EH antenna, and one of them (the so-called "L"+"Tee" network) has a common terminal for its input and output ports. This means we can use the same technique as we have used for the Microvert with a matching network added. And initially we have to present the bottom half of the EH dipole as a wire mesh model, since there are two other wires inside it. The wire mesh model raises a question about its accuracy and makes the calculation time much longer, so we may try also replacing it by a single wire going in parallel with the coaxial feeder.
We start with a wire mesh MMANA model prepared by DL2KQ: EH_2mesh_0.maa; it is shown on Fig. 10. The model consists of two cylinders, each 2 inches diameter and 6 inches long, spaced by a two-inch gap. With no additional components, it shows Zin=0.017-j1700 Ohm input impedance and Ga=1.76 dBi gain in free space and with no wire losses. Such a dipole is almost a perfect capacitor with a quality factor of Q=Xc/R=100000. Adding a real coil (Q=200) for reactance compensation results in poor efficiency: for L=19.7 uH the same dipole shows Zin=9+j0 Ohm and Ga=-25 dBi. This is what one can expect from a "no feeder" EH antenna test.
Fig. 10. Wire mesh model of EH dipole.
Replacing the top radiator with a single thick wire makes almost no change: EH_1mesh_0.maa requires L=20.15 uH and has an input impedance Zin=9.2+j0 Ohm and a gain Ga=-25.2 dBi for the same conditions: free space and no wire losses. Since the results are very close, we may conclude there is not much difference between a wire mesh model and a thick wire model.
Now we are ready to add a piece of coaxial cable to our EH antenna model. Since Ted Hart recommends a half wavelength feeder or a whole number of half wavelength units and this cable is grounded at the transmitter end, we may expect a low common mode impedance at the antenna end. Similar conditions present themselves for a quarter wavelength coax isolated at the transmitter end by a large balun. We will try this cable layout first. Fig. 11 shows an initial "L+T" EH antenna diagram (left) and its equivalent model (right) derived by pulling a differential source toward the top end of the feeder.
Fig. 11. "L+T" EH antenna and its model.
Adding a single wire to the last MMANA model we get a new one: EH_LT1qf_0.maa, shown in Fig. 12. Tweaking a series coil inductance, we have 14.2+j0 Ohm input impedance and Ga=-3.5 dBi gain for L=15 uH and a real ground 1.5 m below the bottom end of the counterpoise. Comparing to a single EH dipole (-25 dBi), we got more than 20 dB increase in radiation efficiency. Compared to our results for DL7PE-Microvert, we may find them very close to each other. The greatest difference is in the input impedance. Looking in depth onto the EH antenna "L+T" diagram, we may suggest a possible reason of that: a part of a series coil is situated close to the top radiator. Moving the whole coil there, we get a slightly different model EH_LT1qf_1.maa and a new figure for input impedance Zin=28+j0 Ohm at L=21.9 uH. The gain did not change significantly: now we have Ga=-3 dBi.
Fig. 12. EH antenna with 1/4 wavelength non-grounded counterpoise.
Now we can construct a typical EH antenna installation. If the antenna itself is at a quarter wavelength elevation, we may have roughly 1/4 wavelength piece of cable going down, then some more 1/4 wavelength going horizontally to the shack. Assume the transceiver end of the feeder has a proper grounding. Fig. 13 shows this arrangement and its equivalent model.
Fig. 13. EH antenna with 1/4+1/4 wavelength grounded counterpoise.
Its MMANA model ( EH_LT2qg_0.maa ) looks similar to the model we have on Fig. 8 for the DL7PE-Microvert. Since their main radiating parts are almost the same, we expect similar figures from their models. The EH model shows 23 Ohm real impedance for L=22.2 uH and Ga=-0.67 dBi gain at 25 degrees elevation angle. Its radiation pattern is shown in Fig. 14, and it is very close to one shown in Fig. 9 for the Microvert.
Fig. 14. Radiation pattern of EH with L-shaped feeder.
If we replace a wire grid bottom half of the EH dipole by a single thick wire (EH_LT2qg_1.maa), we get almost the same result as above: 22 Ohm real impedance for L=22.7 uH and Ga=-0.56 dBi gain at 25 degrees elevation. One benefit of this simplified model is much less computation time; another benefit is a clearer current distribution picture, which is presented on Fig. 15 (only a top part).
Fig. 15. Current distribution for simplified L+T EH model.
From Fig. 15 it is clear that a bottom half of the dipole takes much less current than the top half or the feeder. A low impedance top end of the feeder takes most of a common mode current. This gives us a thought about a value of a balun we can use to reduce the cable radiation. The value of the balun must be high enough compared to a bottom half input impedance, which is roughly -j2000 Ohm. A typical "+j500" Ohm balun makes no difference in the common mode coax current. A model with balun added is EH_LT2qg_2.maa. Running it with various balun values, each time readjusting a series coil at the top radiator, we get data presented in Fig. 16. This table shows that baluns less than j2000 Ohm do not suppress feeder radiation. The exact j2000 Ohm balun resonates with an EH dipole capacitance, which is close to -j2000 Ohm, resulting in an enormous input impedance. The j5000 Ohm balun suppresses feeder radiation by some 10 dB, and the j10000 Ohm balun isolates the EH antenna from its feeder completely.
Fig. 16. Balun influence.
All the above results were obtained for a so-called L+T matching network. It is claimed that an L+L network brings the same efficiency to an EH antenna as the L+T network. Since we have our method already tested, we get an equivalent model shown in Fig. 17 easily. Here an EH dipole is represented by its capacitances (top radiator, bottom radiator and mutual) only, since radiation resistance is very small.
Fig. 17. L+L equivalent model.
To get these capacitance figures, we have to test our EH dipole in both common mode and
differential connections. We expect a common mode capacitance is equal to 2*CR,
because CM is shorted in this connection. For a differential connection we
expect (CM+CR/2). Constructing two MMANA models (EH_LL_0.maa and EH_LL_1.maa) we get 2*CR=8.87 pF and (CM+CR/2)=3.4
pF. Solving that, we have CR=4.435 pF and CM=1.1825 pF. With all
these figures in hands, writing a SPICE model is quick and easy: LL_0.sp. Starting with both coils of 4 uH and sweeping capacitors from
5 to 35 pF, then sweeping inductors from 3.6 to 4.2 uH, we eventually get C1=31.8
pF, C2=25.5 pF, L1=3.85 uH, L2=4.14 uH. Under these
conditions, the L+L circuit shown on Fig. 17 provides a -3 dB transfer from a 50
Ohm source to a 30 Ohm load. Although the -3 dB figure is just a half of S-unit, it means
a half of input power is dissipated in the coils (at their Q factor of 350).
Is a small antenna small? Looking at both the DL7PE-microvert and the EH antenna, we can point now to their real size. For the Microvert it is roughly 0.22 wavelength; for the "typical" EH antenna it is at least 0.25 wavelength. Do we see anything unusual in their radiating properties taking into account their real size? Not at all. Routinely applying the classic theory to these antennas we have developed a "unified approach" for common mode current analysis in the coaxial feeder. Running antenna modelling software, we have obtained numerical results that are in a reasonable agreement with experimental data. We have seen a part of the feeder as a radiating element in the various configurations and we may think of the intentional use of this radiation in our own antenna designs. -30-
BRIEF BIOGRAPHY OF THE AUTHOR
I was born in a small town situated in Ural Mountains, Russia, in 1962. During my
last years in school I joined UK9FFO club station. Then, being a student of a former
Leningrad Electrical Engineering Institute, I was an active operator of its UK1ADR club
station. Often I joined a local mountain hiking club as a radio operator of their rescue
team, once we were operating UK1CAC/U6E in West Caucasus mountains (3000 meters above see
level). After graduating from the Institute as a Radio Engineer, I worked mostly in
digital circuit design, embedded systems programming, then also in analog and high-speed
digital design. Now I am looking for a real estate suitable for not-so-small antennas.
~ antenneX ~ May 2003 Online Issue #73 ~
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