A Common-Mode Current Picture Show 
Common-mode currents on transmission lines come in two varieties: good ones and bad ones. Of course, if we do not know what a common mode current is, then we would have a difficult time telling the two apart.
On a normal transmission-line, free of anything other than the energy that we wish to transfer from one end to the other, we find on the 2 conductors (of a 2-conductor transmission line) currents of equal magnitude and opposite phase angle. The field between the conductors ideally prevents the line from radiating any energy. However, if we introduce energy onto the lines that has a common magnitude and phase angle on both lines, then the transmission lines becomes a simple antenna wire that happens to be composed of two wires. Many amateurs have pressed old lengths of 300-Ohm TV ribbon cable into antenna use by joining the wires at each end and using the cables as a single wire. Under these conditions, the wires have only antenna currents. We might also call them radiation currents. Finally, we can call them common-mode currents, since the two wires have a common current magnitude and phase angle.
Now suppose that we could combine transmission-line currents and antenna/radiation/common-mode currents on the same pair of wires. We do so every time we construct or use a folded dipole or a folded unipole (monopole). In "Unfolding the Story of the Folded Dipole", I noted that a folded dipole is also a transmission line, and I showed a method for sorting the radiation from the transmission-line currents. The transmission-line currents turned out to have a phase angle of just about 90 degrees, indicating a non-power-consuming current. Hence, the energy that we supply to the folded dipole becomes radiation just as efficiently as similar energy supplied to a standard dipole. (An identical relationship exists between the two types of current in a folded monopole and a standard or 1-wire monopole.)
Note that we want to call the non-transmission-line currents radiation currents when we have a devise like a folded dipole, where our main interest is in the radiation. We tend to call those very same currents common-mode currents when we have a transmission line that we do not wish to radiate. There is another reason for the name change. Common-mode currents exist all along the transmission line (until we attenuate them sufficiently). The end of the line that enters the house and the operating room radiates these currents into other nearby wires and devices, including the transmitting equipment. These currents can cause some metering circuits, such as the one measuring SWR, to produce erroneous readings. It does not take much current to create problems in solid-state circuitry. We may experience the RF energy on sharp corners of equipment cabinets in the form of small surprising shocks. This "bite" is only a small version of what we might experience if we were to touch the antenna wire itself while transmitting. For all of these reasons, common-mode currents tend to represent the bad side of radiation currents. Nevertheless, the two are in principle the very same when contrasted to transmission-line currents.
Every transmission line has the potential for carrying common mode currents. Common-mode currents occur whenever we have an imbalance between either the magnitude or the phase of the currents along a transmission lines, where we measure such an imbalance at any facing points along the line. The two most common sources of common-mode currents in lines on which we do not want them are an imbalance at the antenna feedpoint and induced currents from the antenna field. Parallel transmission lines show imbalances whenever we feed a wire antenna away from a point of maximum current. This point is normally the center point on a half wavelength antenna. If we move the feedpoint on this wire off-center or to the end, we shall find a current imbalance and resulting common-mode currents (and what we sometimes call feedline radiation). On a parallel transmission line, we can induce common-mode currents by improper routing (that is, routing the line at other than a 90-degree angle to the antenna element). We can sometimes create them by running the line too close to a metallic object, like a down spout. If we have different coupling levels between each wire and the metallic object, an imbalance may result, and so too may common-mode currents.
In a parallel transmission line, we rarely can easily sort the transmission-line from the common-mode currents. (In fact, few amateurs are equipped to even measure the currents on a parallel transmission line.) Even when we use NEC or MININEC to model a transmission line as a set of wires, the program reports a single set of currents, one for each wire at any facing segment or pulse pair. However, in a future episode of my continuing series on antenna modeling (#123), I shall describe the necessary steps to set up a simple spreadsheet or similar calculating aid to do the sorting.
Coaxial cables are another matter when it comes to sorting transmission-line from common mode currents. Since introduced by Walt Maxwell, W2DU, in the early 1980s, we have seen pictures like Fig. 1 in various handbooks. The sketch portrays the junction of a common dipole or other center-fed wire antenna with a coaxial cable feedline.
The sketch shows a cutaway view of the coax so that we have a braid line on each side of the center conductor. Between facing surfaces of the coaxial cable, we have transmission-line currents, as suggested by the arrows that have opposite directions. Since the currents are RF (a form of AC), they change direction periodically, so any arrows indicate the directions at one instant of time. At that instant, the currents in the antenna wire have a direction in common with the conductors of the cable, since the cable and its source are in series with the antenna feedpoint.
The sketch shows, on the right side for convenience (but actually extending all around the braid) an extra arrow having the same direction as the arrow in the antenna wire connected to the braid. The idea that the sketch portrays is that the coax braid forms a second path for antenna currents, otherwise called common-mode currents. Those new to antennas and feedlines may ask how this can be so. Others may ask whether such currents are always a problem.
Fig. 2 may help us answer the first of the two questions. Within the coaxial cable, we have two surfaces of concern: the outer surface of the center conductor and the inner surface of the braid or outer conductor. We are concerned about surfaces due to skin effect, which holds the current activity very close to the conductor surface. The indicated field allows the cable to act as a transmission line, since the current magnitudes are the same on any facing points along the way, but the phase angles are 180 degrees apart.
Any common-mode or radiation currents have the same phase angle, regardless of how they originate. The same phenomenon--skin effect--holds common-mode current activity on the outermost surface of the conductor, in this case, the outer surface of the braid. (The intervening dielectric or insulation in the cable does not disrupt this process. In fact, the fields that force RF to the near-surface area make any interior region a poor conductor for the RF of the common-mode current. Hence, we use tubes for beam elements rather than solid rods. The same effect also allows stranded wire to serve with equal effectiveness as solid wire in antennas.) Essentially, the near-surface RF currents on the coax braid are separated from the transmission-line currents on the inner braid surface (and the center conductor) by the material between those surfaces. In effect, when we use a coaxial cable feedline, common-mode and transmission-line currents are self-separating.
Getting Ready for a Picture Show
The second question wondered whether common-mode currents are always a problem. Some amateurs have never used an attenuator for them and still not experienced any problems. Others have had major problems. We need to see if we can find some of the probable causes, at least in principle. To provide some preliminary glimpses into the world of common-mode currents, we can either measure the currents on many dozens of antennas or we might try to construct a model of the common-mode situation.
In episode 100 of the antenna modeling series ("The Dipole and the Coax"), I pointed out some of the difficulties in constructing a completely adequate model of a simple center-fed dipole antenna connected to a coaxial cable. The problems are especially acute using NEC, since we must construct the coaxial cable wire a a single wire having the properties of the coaxial cable's outer-surface. Even then we shall not have captured the coax completely, since coax normally has an insulating outer jacket. In addition, the coaxial-cable diameter is normally different from the diameter of the regular antenna element wire, and NEC (both -2 and -4) has accuracy difficulties when we have angular junctions of wires having dissimilar diameters. Finally, the source will not be at the exact point where the antenna wire and the simulated coax wire form a junction. The source is on the source segment, but the junction must occur at the end of the source segment. Moreover, NEC is most accurate when the length and diameter of the source segment is the same as the length and diameter of the segments adjacent to the source segment. If we connect the coax wire to the end of the source segment, we violate this condition, but if we add a segment on each side of the source segment before creating the junction of antenna wire and coax wire, we increase the problem of displacement between the source and the junction of interest.
By comparing models from both NEC and MININEC systems, I reached the conclusion that models may be good enough to show the common-mode phenomenon, but we cannot fully trust their detailed data reports in the absence of a large (and largely unconducted) set of laboratory and/or field measurements. Since our goal is not to evaluate a specific situation involving an antenna element with a certain diameter and a coaxial cable with a certain diameter, we can minimize most of the problems to an acceptable level.
Fig. 3 outlines the conditions of the models that we shall use in our picture show. We shall create a resonant dipole (within +/- j1 Ohm) at 29.97925 MHz, that is, exactly at 10 meters. The wire will be lossless (or perfect) and will have a 5-mm (0.1968") diameter. To avoid angular junctions of wires with dissimilar diameters, the simulated coax wire will also be 5-mm in diameter. (The selected diameter falls between the outer-braid diameter of RG-174 and RG-58. Hence, the set-up may not be normal in the everyday sense of amateur installations, but it falls within the range of possible installations.)
Constructing the antenna will require 3 wires. The first wire has 51 segments and extends beyond the exact center point by half the length of a single segment. (A segment turns out to be 0.047624 m long, about 10 times longer than the wire diameter to ensure good calculating accuracy in NEC.) The source goes on Segment 51 of Wire 1. Hence, it is at the exact element center. Wire 2 extends from the end of wire 1 to the outer end of the element and uses 50 segments. Hence, all segments in the antenna wire have the same length. The coax wire (wire 3) extends downward from the junction of wires 1 and 2. It length will be variable, depending on our demonstration needs, but it will be segmented so that the length of a segment is as close as possible to the length of a segment in the element proper.
One possible way to model a dipole and its coaxial cable is to also model a transmission line using the TL facility within NEC. We then place the source on the wire that terminates the feedline. However, we do not know in advance what characteristic impedance to use for the line. Moreover, we have a choice of velocity factor values. We shall return to the affects of a transmission line on the situation before we close. For now, we may simply place the source at the position indicated in Fig. 3.
Unlike our normal concerns for feedlines, which ordinarily require us to pay close attention to the velocity factor, we need only concern ourselves with the physical length of the simulated coax wire in the model. With respect to common-mode or radiation currents, the electrical length of the coax wire is a function of 3 factors: the physical length, the diameter, and the small adjustment for the outer insulating weather jacket. The antenna velocity factor of insulated wire tends to run between 0.95 and 0.98. Since we need not be ultra-precise in selecting coax wire lengths for these demonstrations, we can ignore both the antenna velocity factor and the effects of diameter without losing track of the major shifts in performance.
In fact, using EZNEC software and NEC-4, we can directly vary the lengths of the coax simulation wire in 1/8 wavelength increments. At the test frequency, exactly 10 m per wavelength, we can always determine the length of any line in meters by multiplying the length in wavelengths by 10. As well, EZNEC's graphic facilities allow us to produce some simply-to-read illustrations suited to these exercises.
The exercises will consists of paired tables and graphics. Hence, it will amount to a picture show of sorts. Indeed, the pictures may be more significant than some of the precise data, although we shall pause now and again to comment on where the data is adequate and where it may be more questionable.
Exercise 1: Free Space
Let's begin our examination of potential common-mode currents by placing the dipole in free space. Although this environment is not realistic for the average amateur installation, it will provide us with one advantage. We may record an average gain test (AGT) score for each model in the series. We shall begin with a zero-length coax wire, that is, a simple dipole with no appendage. Then we may add the coax wire dangling "below" the dipole to approximate an ideal right-angle position. (The term "below" is relative only to the Z-axis of the coordinate system. Free-space, of course, has no inherent above or below.)
For each length of coax wire, we shall record several items of data. The feedpoint impedance will be useful to know, as well the maximum gain and the AGT score. In addition, we shall record the relative current magnitude and phase angle on selected segments. The source segment will always have a value of 1.0 at 0 degrees. Our interest will lie in the adjacent segments. On one side, we have a single segment (wire 1). On the other side, we have two segments that join (wires 2 and 3). (The pure dipole, of course, lacks a wire 3.) These current values may seem tedious to gather, but they will turn out to be informative.
The results of our expedition appear in Table 1.
Although the text omits quotation marks, all tables use them around the expression "coax wire" to ensure that we do not forget that the wire is a stand-in for a length of coax that serves as both the feedline and the source of added radiation currents. Within the free-space set-up, the lengths of coax used are convenient measures, even if they do not represent lengths we might encounter in an amateur installation. In fact, the free end of the coax wire might be an actual wire end or it might be the point at which a longer coaxial cable is subjected to one or another type of attenuator so that the remaining coaxial cable length is effectively isolated from the length under test.
Within the data, two coax-wire lengths should attract our attention: 1/4 wavelength and 3/4 wavelength. Of the sampled lengths, only these two show oddly aberrant feedpoint impedance values, lower current magnitude on wire 2, elevated current magnitude on wire 3, less than ideal AGT values, and lower maximum gain levels. The AGT scores are of special note, since they represent a modeling limitation. When wire 3 shows relatively insignificant current levels (less than 0.1 of the maximum value), the AGT score indicates a reliable model requiring no corrective for either the gain value or the reported feedpoint impedance. However, when wire-3 current is significant, the AGT value departs from the ideal by a significant amount, suggesting that the model's numerical data are not reliable. Even if we use the AGT value to correct the gain figure, we find lower than normal maximum gain. Under the prescribed conditions, common-mode currents are sufficient to significantly alter the dipole radiation pattern relative to our expectations.
One area in which the AGT does not disturb the results is in the calculation of the net current magnitude and phase angle on the right side (wires 2 and 3) of the dipole. The vector sum of the currents on that side should equal the reported current on the left side of the source. We may expect a small and systematic difference, since the sum of the surface areas of wires 2 and 3 is double that of wire 1. However, we anticipate a general coincidence between the net current values. Table 2 will inform us of whether or not the models achieve this end.
The columns marked "wE" provide the required calculated net current values, while those marked "w1" record the current for the single-wire side of the dipole. The pure dipole, of course, shows no difference between the two. For every entry in which we have a coax wire, we find a consistent 0.07 to 0.08 degree difference in the phase angle for all entries. For all entries with an AGT value of 1.000, the wire-1 value for the phase angle is slightly higher than for the simple dipole. I have bold-faced the values for coax wire lengths of 1/4 and 3/4 wavelength, because the phase angle values are out of line with the other values in the list.
Despite the questions of data reliability, the general phenomenon of common-mode currents shows well in the table. We may also represent the data in more graphical form. For each tabular entry, we may generate E-plane and H-plane patterns for the free-space model. In addition, we may also represent the pattern of current magnitude along the antenna elements and the coax wire. Fig. 4, Fig. 5, and Fig. 6 provide a catalog of the current and radiation patterns applicable to the entries in Table 1.
Let's first look at the current magnitude portions of each figure. For all coax-wire lengths except 1/4 and 3/4 wavelength, the current all along the coax wire is small. I have magnified the levels so that a definitive curve shows for each coax wire length. However, the peak current is never above about 0.2 of the maximum value. Therefore, the current distribution on the antenna element wire remains virtually undisturbed by the presence of the coax wire. In contrast, with 1/4 and 3/4 wavelength coax wires, the current peak for the coax wire occurs at the junction with the antenna element. Hence, we find a significant current division between wire 2 and wire 3. The current in wire 2 (to the left in the graphical representations) is low enough that we might expect to find considerable alteration of the normal dipole free-space pattern.
The E-plane and H-plane patterns (azimuth and elevation in conventionalized modeling terms) provide us with two types of data. First, the patterns show both the vertical and the horizontal components of the total field patterns. In virtually all cases, most of the horizontal component disappears beneath the line that records the total field. However, the vertical component is instructive. For example, the pure dipole with no coax wire shows no vertical component in free space. When we add the coax wire, we obtain a distinct vertical component to both patterns. For all but two of the pattern sets, the vertical component is about 20 dB or more down from the maximum gain. In addition, the indicated patterns show side nulls that are at least 20 dB or more lower in gain than the main lobes. The two aberrations are the patterns for 1/4 wavelength and 3/4 wavelength coax wires. The peak vertical components in these cases may be less than 10-dB down from maximum gain values, with strong consequences for the total field dipole radiation pattern. The patterns for lengths of 1/4 and 3/4 wavelength differ, but both equally distort what we think of as the normal dipole pattern.
Exercise 2: 1 Wavelength above Average Ground
Before we draw any conclusions about common-mode currents, let's repeat the exercise with a small difference. For the second run, we shall set the dipole exactly 1.01 wavelength above average ground. (The use of 1.01 wavelength as the antenna height ensures that the 1 wavelength coax wire does not touch the ground. We shall look at that option in a separate exercise.) Since we are now dealing with a lossy ground, we cannot make use of AGT score values, since those values require the removal of all resistive losses, using either a free-space or perfect-ground environment. However, we may record the reported gain value and the TO angle (take-off or elevation angle of maximum field strength). In all other ways the models remain intact. Table 3 records the results of this exercise. Remember that the "zero-length" model is a simple dipole with no wire 3.
In this exercise, coax-wire lengths of 1/4 and 3/4 wavelength again show anomalous results compared to the results for other lengths. At all other coax-wire lengths, we obtain about the same maximum gain and very similar feedpoint impedance values. Note that the impedance for the simple dipole entry shows a small reactive component because I did not change the dipole length when moving it from free space to a position above real ground. The impedances for the two sensitive coax-wire lengths are between 20 and 30 Ohms lower than for the other lengths. As well, the maximum gain is more than a dB lower. In the current-value columns, we find the same general pattern of current values on the first segments of wires 2 and 3 that we found in the free-space exercise
We may translate the tabular results into the same sorts of patterns that we developed for the first exercise. We omit the current portions of the graphics, since they are virtually identical whether in free space or over real ground. However, Fig. 7, Fig. 8, and Fig. 9 provide the elevation and azimuth patterns for each of the entries in Table 3.
The first difference to note in the patterns relative to free-space models is that even the simple dipole shows a small vertical component over real ground. When we compare this component with the corresponding components for most of the models with coax wires, we find that the strength of the component does not change. It remains about 20 dB below the maximum gain, although the exact shape of the component changes somewhat with the length of the coax wire. In contrast, the maximum gain for the vertical components for 1/4 and 3/4 wavelength coax wires is only about 10 dB down from the maximum gain value. The consequences for the total field elevation patterns are not dramatic. However, we find distinct distortions in the azimuth patterns for coax wire lengths of 1/4 and 3/4 wavelength. These distortions do not make the antenna unusable, but when combined with the gain reduction, they do make a difference. Note that even with the pattern distortions, the TO angle for all of the patterns remains at 14 degrees elevation.
At this point, we might be tempted to draw some hasty conclusions. One such conclusion is that we can avoid coaxial cable common mode currents by avoiding line lengths that are odd multiples of 1/4 wavelength. However, this conclusion would be warranted only for cases in which the coax end was either free or was isolated by some attenuation device to the degree that it acted like a free end. In most amateur installations, we do not find these conditions at work. We need to set up a model that might more adequately represent installation conditions.
Exercise 3: Coax Wire to Ground, with and without a Ground Rod
In most cases, the coax wire will come to the level of the ground. The route may be direct or indirect. One such indirect route is through the equipment cases to a station grounding system. I cannot represent each possible case. However we might explore some stand-in cases. For example, we might set the dipole at various heights from 3/4 wavelength up to 1-1/4 wavelength, with coax wires that just reach the ground. For this set of cases, we shall expect elevation patterns that show different TO angles, since each entry places the dipole at a different height.
We also have two ways to handle the fact that the coax wire just reaches the ground. One way is to simply let the wire end at Z=0. This type of model may not be wholly reliable, since NEC typically shows an inaccurate source impedance under these conditions. So we might (in NEC-4) create a 1/4 wavelength ground rod, using the same 5-mm diameter wire that we have used in the remainder of the model.
Table 4 records the NEC reports for both type of models. In addition, it also records reference values of simple dipoles (with no coax wire) at each of the heights for the other cases in this exercise.
The table immediately shows some very interesting results. When the coax wire touches the ground, with or without a good ground rod, the sensitive lengths are no longer odd multiples of 1/4 wavelength. Instead, the sensitive lengths become multiples of 1/2 wavelength--in this case, a length of 1 wavelength. Our previous hasty conclusion turns out to have been far from universal.
The second notable feature is the difference in the dipole performance with a 1 wavelength coax wire between having a ground rod and only touching the ground. The no-rod situation shows the greater reduction in the feedpoint impedance and the maximum gain. In comparison, the other coax-wire lengths show only modest differences between a rod and a no-rod condition. Additionally, the gain with a ground rod and a 1 wavelength wire shows the greatest reduction in maximum gain of all the cases when we compare the values with the gain values for a modeled dipole with no coax wire. If we were to carry out the exercise in even smaller increments, we might expect to see the gain differential curve show a non-linear curve to a peak difference at 1 wavelength and then a non-linear downward trend, with repetitions every half wavelength.
We may sample the current magnitude and distribution curves, as in Fig. 10. The curves for coax-wire lengths of 0.75 and 1.25 wavelengths begin at the feedpoint junction with very low current values, and those values remain very low all along the coax wire. The samples use ground rods, which are a constant 0.25 wavelength for each case. The curves for the 1 wavelength coax wire begin at the feedpoint with high current on the coax wire. Indeed, the current magnitude is high enough so that we find unequal current curves on the two halves of the antenna element itself. The current pattern presents two significant peaks at heights of 1 wavelength and 1/2 wavelength: these maximums are strong enough to affect the overall radiation pattern.
Before we turn to the patterns, let's take note of the current distribution on the ground rod. Although the ground rod is physically 1/4 wavelength, its electrical length within the selected ground medium (conductivity 0.005 S/m, permittivity 13) is longer. Hence, the current undergoes 2 peak values. (An underground dipole would not have to be very long physically to be a resonant half wavelength electrically, although the precise physical length will vary with the ground medium.)
Fig. 11 translates the tabular data for the models with ground rods into elevation and azimuth patterns. Despite the half-dB gain loss in the model with a 1 wavelength coax wire, we find nothing unusual in either the elevation or the azimuth pattern. The vertical component of the patterns is only slightly greater than for the other patterns. Indeed, with the well-grounded termination of the coax wire, we find that the feedpoint impedance is not very far off the mark for a dipole at a 1 wavelength height with no coax wire at all.
We may fairly ask at this point what all of the pictures might be telling us with respect to common-mode currents on the outer side of a coaxial cable' braid. We have examined two sorts of cases, one in which the coax wire had a free end and another in which the coax wire terminated at ground. Both cases have used straight coax wires projecting at a 90-degree angle from the junction with one side of the feedpoint of the dipole antenna element. Within these conditions, we discovered two different situations in which common-mode currents appeared to be significant. With a free end to the coax wire, sensitive coax lengths appeared to be odd multiples of 1/4 wavelength. With the coax terminated at ground, sensitive lengths appeared to be multiples of 1/2 wavelength.
One initial impression might be that under one or the other condition, we have a good chance of not incurring common-mode currents to any significant degree. However, as we noted near the beginning of our picture show, we do not require common-mode current levels that distort the radiation pattern to experience unwanted coupling into equipment or household devices making use of solid-state circuitry. Since we do find some common-mode currents on coax braids in nearly all circumstances, the potential for problems exists under nearly all coax-wire conditions.
The picture show also suffers severe restrictions. It does not cover a myriad of cable routings that are typical of almost any antenna installation. Cables may travel horizontally for considerable distances at a variety of heights ranging from underground to a considerable distance above ground. Cable routing and switching may make the calculation of the total cable length to a ground connection nearly impossible. As well, we may not be certain of the quality of the cable ground, since a good ground for lightning protection may or may not also be a good ground for RF at the operating frequency.
On top of all this, we have not investigated whether non-ideal cable routing may have an affect on a cable's susceptibility to common-mode currents.
Exercise 4: Coax Wire to Ground with a Ground Rod But Sloping Under the Antenna Element
We have long believed that improper or non-ideal routing of a coaxial cable may increasing the potential for incurring common-mode currents due to coupling between the antenna element fields and the outer surface of the cable. (A similar situation would also induce common-mode or radiating currents on a parallel transmission line.) We can gather some idea of the level of interaction by a simple demonstration. We must note from the start, however, that the variations on the situation that we shall set up are nearly endless. So the exercise will show only that some influence does exist, but it will not go any further.
Let's use a model in which the coax wire reaches the ground and terminates in a 1/4 wavelength 5-mm diameter ground rod with average ground. The coax wire will slope at a 30-degree angle directly under one of the dipole legs. When the angled portion of the coax is at the end of the antenna element, the coax will drop straight down to the ground. The total length of the coax wire is 1 wavelength. Since the sloping leg is 1/4 wavelength, the sloping end is 1/8 wavelength below the end of the dipole. With the remaining 3/4 wavelength of coax wire, the antenna height will have to be about 0.875 wavelength to satisfy the overall geometry.
The top portion of Fig. 2 shows the antenna model geometry and also shows the current magnitude and distribution. The lower portion of the figure shows a straight coax run with an equivalent total length of coax-wire, that is, 1 wavelength. Since the antenna heights differ, the total field elevation pattern differences do not reflect any effects of the different coax-wire routings. Any dipole at a height of 7/8 wavelength will show the large upward lobe structure.
More significant is the vertical component within the pattern. The peak value for that component appears to be somewhat higher with the sloping coax wire than with the straight one. A similar condition appears on the current distribution section of the graphic. Indeed, the two current portraits seem somehow anomalous. Both raise the peak current value to as close to the same level as feasible. The sloping coax wire appears to show higher current peaks than the straight 1 wavelength coax wire, although as we discovered in the preceding exercise, a coax-wire length of 1 wavelength showed the highest coax-wire current peaks of any of the sampled lengths. In contrast to this appearance, the straight-wire model shows a reduced current magnitude on the dipole leg sharing a connection with the coax braid. However, the sloping-coax model shows a seemingly smooth curve of current magnitude across the feedpoint junction.
To resolve the visual situation, we may turn to the data in Table 5. The table lists the modeled data for the sloping case and for two straight-coax cases, the 0.875 and the 1 wavelength coax runs. All three cases use a ground rod.
The table entries for the sloping-coax model indeed show that the current magnitude of wire 2 is very close to the magnitude on the single-wire side. What the graphic did not show was the very significant difference in phase angles between the two current magnitudes. As a consequence, the current magnitude on wire 3 is about 30% higher than we find on the same segment in the case of a 1 wavelength straight coax wire. Because the graphic omitted the phase-angle data (a necessity for me to provide 2-D representations), it only appears anomalous. With the phase-angle data added, we can see that the sloping-coax situation increases the common-mode current magnitude on the coax braid. In addition, the situation in the model reduces the maximum gain of the dipole at a 7/8 wavelength height by about 0.6 dB relative to the straight coax dipole at the same height.
The single demonstration does not provide a comprehensive picture of how non-ideal cable routing may affect both antenna performance and the level of common-mode currents. However, it does tell us that non-ideal routing can alter antenna performance and provide increased common-mode current levels. We have already seen that we may have difficulty in determining whether we have a sensitive coax length due to problems in measuring the length of the coax between the antenna and ground and uncertainties about the quality of the ground. The safest procedure is to install some form of attenuation for common-mode currents as a standard operating procedure with all coax-fed antennas.
Exercise 5: Coax Wires with Attenuation
Common-mode current attenuation generally comes in two forms: the 1:1 balun or transmission-line transformer and the ferrite-bead choke. Simulating a 1:1 balun is beyond the capabilities of the EZNEC implementation of NEC-4. However, the W2DU-type ferrite bead choke is quite simple. It provides an inductive reactance on the outside of the coax braid without disturbing what occurs inside the coaxial cable. Hence, it does not affect transmission-line currents, but it attenuates common-mode currents.
With a properly constructed bead balun for the frequency used, it is possible to obtain at least j750 Ohms of inductive reactance. (See the current ARRL Antenna Book, p. 26-25. As well, see Bill Sabin, W0IYH, "Exploring the 1:1 Current (Choke) Balun," QEX, July, 1997, as well as Chapter 21 of Walt Maxwell, W2DU, Reflections II, for background on the ferrite bead choke.) Therefore, we shall use a simple load on the coax wire consisting of j750 Ohms.
In the first part of our new exercise, we shall use the model of a coax wire with a free end. We found that when the coax wire was 3/4 wavelength long, it showed a high sensitivity to common mode currents. We may install the load (that is, the bead choke simulation) anywhere along the wire. Let's place it at the feedpoint and then at 0.25 wavelength intervals, including the far or open end of the coax wire. Table 6 shows the numerical results of the exercise.
The table includes values for the case without the bead choke for comparison. When we place the choke 0.25 and 0.75 wavelengths away from the feedpoint, it has virtually no effect on the common mode current values. However, when we place it either at the feedpoint or at a point 1/2 wavelength distant from the feedpoint, it reduces the current on the coax wire to nearly equally low levels. To see this situation graphically, we may examine Fig. 13.
The current distribution graphics for no-load and for loads at 1/4 and 3/4 wavelength positions are virtually indistinguishable from each other, except for the square marking the load location. When we place the load at the feedpoint, common mode current drops to near-zero. When the load is 1/2 wavelength from the feedpoint, the current level between the feedpoint and the load is not quite zero. But, it is very much attenuated compared to the no-load or the misplaced load conditions.
We may repeat the experiment using the model with a ground rod and a straight 1 wavelength coax wire. This model showed the greatest sensitivity to common mode currents in its series of samples. Once more, we shall use a j750-Ohm load and move it from a position at the feedpoint along the line in 0.25 wavelength increments. Hence, the last position will be just about at ground level. Table 7 gives us the outcome of the modeling exercise.
With the load positioned at the 0.25 and 0.75 wavelength points along the coax wire, we obtain little or no benefit. The impedance reflects the value for a no-load (that is, a no-attenuator) condition. However, when we place the load at the feedpoint or at multiples of 1/2 wavelength from the feedpoint, the antenna impedance and gain values return to the levels that we expect of a dipole at 1 wavelength above average ground with no coax wire in the model. Fig. 14 provides a set of current distribution portraits that reflect these conditions.
The portraits reveal the same general patterns as the portraits in Fig. 13. When the choke is at the feedpoint or at a distance that is a multiple of 1/2 wavelength from the feedpoint, we obtain maximum attenuation of common-mode currents. When the choke is at a distance, the common-mode currents do not go to zero between the feedpoint and the load, but they are very much attenuated relative to their value with a no-load or a misplaced-load condition.
The feedpoint is the most common location for the installation of a common-mode current attenuator. In fact, commercially made devices often combine the attenuator and a dipole center insulator assembly in one. In terms of reducing common-mode currents on coax braids to a minimum, the feedpoint position is universally the best. However, the demonstration has only covered cases of straight-line coax runs. It has not covered the case of a sloping or otherwise erratic coax run. For this reason, it is not unwise to install a second bead choke at the point where the coax enters the house or equipment room. A good earth ground running from the braid on the equipment side of the attenuator is an additional method to maximize the supplemental attenuation.
Exercise 6: Coax Wires and Transmission Lines
One of the markers that we have used to initially spot a coax-wire length that was sensitive to common-mode currents is the feedpoint impedance. In virtually all cases where common-mode currents have been high, the feedpoint impedance has dropped significantly from a more normal dipole value. We have been using the feedpoint impedance as modeled at the center segment of the dipole element. The potentially misleading idea that this situation may suggest is that a normal dipole impedance at the equipment end of the coaxial cable indicates relative freedom from common mode currents, while a lower-than-normal impedance may indicate their presence.
Unfortunately, this idea does not necessarily play out in real situations. The electrical length of the coax outer braid is a function of its physical length and its diameter. The outer jacket may contribute an antenna-level velocity factor that might range from 0.95-0.98, depending on the jacket material and its thickness.
In contrast, the transmission line currents and the impedance transformation that may occur between the center conductor and the inside of the coax braid have very different velocity factors. For 50- and 70-Ohm cables, we find two common velocity factor values: about 0.66 for solid dielectrics and about 0.78 for foam dielectrics. As a result, a given physical length of a coaxial conductor will have an electrical length in practice that is considerable loger than the electrical length of the outer braid for common-mode currents.
Table 8 provides a simple example using the dipole and a 3/4 wavelength coax wire with a free end. To the model we can add a 3/4 wavelength 70-Ohm transmission line, with a short terminating wire on which we place the source. The table shows a reference line with the values for the same model but with the source located on the center of the dipole. If we arbitrarily assign the transmission line a velocity factor of 1.0, we discover that the line transforms the 52-Ohm impedance up to about 94 Ohms.
With realistic values for the velocity factor, we obtain different values for the source impedance, values that are not likely in isolation to give us clues to the common-mode current situation. In an actual situation, we are faced with perhaps two alternatives. One direction in which we can go is to devise means by which to measure the level of common-mode currents. If we lack proper measuring equipment, we might rely upon other signs, such as the presence of interference with communications equipment functions of other household devices.
The other alternative is to install common-mode current attenuation devices, such as bead chokes, during the installation of the antenna system. The antenna system includes both the antenna and the transmission line. As we noted earlier, the most use position for a common-mode attenuator is the junction of the coaxial cable and the antenna element. However, a secondary attenuator at the house or equipment-room entry point can provide additional protection against potentially harmful effects from even low levels of common-mode currents.
Conclusion
Our common-mode-current picture show has reached its end, even though it has surveyed only a few of the possible combinations of antennas and feedlines that might make up an amateur installation. Along the way, we discovered that the level of common-mode currents depends upon several factors, including the length of the coaxial cable and the nature of its termination. Cables with free ends have sensitive lengths that differ from cables that terminate at the ground. Cables that do not leave the antenna feedpoint at right angles tend to be more susceptible to common-mode currents.
Although the tabular data is indicative of actual conditions, we should remember that the models used are subject to some restrictions. We had to use a single wire diameter for both the antenna element and the coax wire to minimize model inadequacies. Even with this departure from the reality of most antenna installations, we still encountered non-ideal AGT values when common-mode currents were relatively high. The chief cause for the deviation from an ideal AGT value is the position of the junction between the coax wire and the element wire immediately adjacent to the source segment. Such models fail to implement the conditions under which NEC calculates most accurately the current on the source segment. The problem does not show up when common-mode currents are very low and most of the source current appears on the antenna element with almost none on the coax wire.
Notwithstanding the limitations that the situation imposes on the numerical data, the general portrait of common-mode currents shows generally accurate patterns of currents and the conditions that tend to either promote or suppress their development. However, in most amateur installations, we have no accurate method for determining the exact electrical length of our coaxial cable as it proceeds from the antenna to the equipment and then via an earth ground line to the actual ground. For the average amateur antenna installation, the safest strategy relative to common-mode currents is prevention. Adding a common-mode current attenuator to the system should be a standard part of any installation involving a coax-fed antenna.
Updated 08-21-2006. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
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