41. Multiple-Feedpoint Loop Modeling

L. B. Cebik, W4RNL

There are a number of questions that often arise surrounding quad loop modeling. Some of the answers to these question also apply to other antenna models, so it may be worthwhile to spend an inordinate amount of time with the simple quad loop.

For a single quad loop with a single feedpoint, the conventions of modeling shown in Fig. 1 are very convenient. Essentially, we model "around the horn," taking one wire after the other so that End-2 of the preceding wire matches End-1 of the succeeding wire. We can apply the technique to either square or diamond quad loops--or to any other closed polygon.

The technique is orderly, giving us a systematic way of keeping track of the wires in complex arrays of which this loop may be one of many. However, the technique has more to recommend it than simple orderliness.

Fig. 2 shows the current magnitudes and phase angles at selected points around the loop. Each loop side (21.876") for the sample model has 21 segments (in case you want to replicate the exercise). Copper wire and an arbitrary but resonant (+/- j1 Ohm reactance) frequency of 144.4 MHz with #18 wire complete the essential ingredients for the model used here.

Note that as we begin at the source (the dot in the figure) and move in either direction, we have an orderly progression of current magnitudes and phase angles. Because we have a single feedpoint and a wire that is not perfectly conductive, the midpoints of the vertical wires do not show a relative current magnitude of zero or a phase of exactly -90 degrees. At the upper corners, current magnitude is very slightly less than at the lower corners--not enough to affect antenna operation, but enough to prove that copper has a small amount of resistive loss.

The figure that may seem oddest to the beginning modeler is the phase angle at the point directly opposite the feed point. However, in most implementations of NEC, phase angle values are run from -179.99 to +179.99. The sudden shift in the phase angle value to +178.1 degrees is the equivalent of having a phase angle of -181.9 degrees. With that mental adjustment, then, we have a seemingly smooth transition of current levels along the quad wires.

However, appearances--especially when developed by showing only selected values--can be deceiving. Well over half of the current phase transition occurs in the small region around the vertical wire mid-points, where the current magnitude also approaches zero and rises again. This set of transitions is similar to that for a dipole end, except that the dipole end is open.

In fact, one way to think about a quad loop is as two dipoles with the ends bent toward each other until they touch. The touching ends eliminate the shortening of the so-called end-effect, and a quad loop will have a circumference that is longer than the sum of two dipoles. As well, the effects of changing the wire diameter are opposite each other. For resonance, the fatter the wire of a dipole, the shorter its length must be. For a closed loop, the fatter the wire, the larger the loop circumference for resonance. Despite these behavioral differences, it is often useful to look at a 1 wavelength loop with a single feed as two dipole with touching ends.

One result of this orientation to the loop is to think of the halves of the overall quad as being in phase and hence additive in their pattern production. In fact, a quad loop of the specifications used in this exercise has a free-space gain of about 3.3 dBi in contrast to the 2.1 dBi gain of a dipole in free space.

However, if the two halves of the loop, counting from the left side mid-point to the right side mid-point are two dipoles in phase, why does the upper horizontal mid-point show a phase angle about 180 degrees out of phase with the feedpoint? The answer lies partially in the modeling convention we chose and partially in data that we do not see in Fig. 2 (or in any of the usual tables produced by NEC). The wire direction of our continuous loop model is opposite for the upper and lower horizontal wires. Since current values are functions of the End-1 to End-2 orientation of the wires, we find a -180 degree phase angle at the top relative to the zero phase angle at the bottom. What we do not see is that the voltage at the upper mid-point would have a phase angle that is also 180 degrees out of phase with the voltage at the feedpoint. Hence, the combination yields a power that is in phase for the two positions on the wire loop.

A similar phenomenon occurs with a number of other antennas, some of which are not closed loops. For example, a half square fed at one corner can be thought of as two right angle Vees, each with a quarter wavelength leg vertical. The horizontal quarter wavelength sections join at their ends. The standard and correct way of treating the half square is as two quarter wavelength verticals in phase spaced just about 1/2 wavelength apart. The 1/2 wavelength horizontal wire is often called a phasing line because most of the radiation from it cancels.

However, if we model two 1/4 wavelength verticals independently, we must provide two sources, each of which have the same current magnitude and phase angle. Only in this way can we obtain a pattern similar to that of the half square. However, if we look at the current tables for the half square, then we find that the current at the corner away from the feedpoint has a phase angle about 180 degrees different from that of the source. Once again, the voltage phase angle at the far corner would also be 180 degrees different from that of the source, establishing an in-phase relationship between the two points.

For single feed systems, these small mental adjustments make almost no difference in the ways in which we handle loops and half squares in the design or analysis efforts to construct arrays with them. However, the adjustments required begin to make a larger difference--with more room for unseen errors--whenever we begin to look at multiple feedpoints on a single wire structure. For example, we can feed a quad loop at both the upper and lower wire center-points. We might use equal lengths of parallel feedline with a junction to the main feedline directly between the upper and lower loop wires. To feed the loop wires in phase, we would physically run the wires in straight lines, with no twist to either the upper or the lower section from the junction.

However, our model--if it uses the convention of wire structuring that we started with--will not reflect reality if we feed it as we would when building the physical antenna. Fig. 3 shows two source points, one at the center of each horizontal wire. Both sources are specified for a current magnitude of 1 and a phase angle of 0, as revealed by the designation "No-Twist" on the figure. Relative current magnitude and phase angle values are shown for the same points as in Fig. 2.

The current magnitude and phase angle values are very much different from those in Fig. 2. In fact, the no-twist sourcing of this model has in fact placed two sources that are 180 degrees out of phase on the model, since a source is in series with its wire. Moreover, the source follows the End-1 to End-2 orientation of the model. Hence, the source on the upper wire is set in the opposite direction as the source on the lower wire. However, we cannot change the voltage phasing, so that the two feedpoints are now out of phase relative to each other.

A similar situation would occur if we simply placed a second source on the half square at the "other" corner of the array. (In fact, if one draws the open wire ends of a half square together, letting the horizontal wire bend at its center, the result would be a diamond-shaped quad loop.)

Note that there is no error within NEC in this regard--only an error caused by our not keeping track of the wire directions and making the sources coincide with those directions. Physically, the difference between feeding the two wires in phase and out of phase makes a big difference to the resulting pattern. Fig. 4 shows the patterns for a normal quad with an in-phase dual feed and one that is dual fed out of phase. The "normal" in-phase feed results in pattern lobes broadside to the plane of the loop. In contrast, out-of-phase feeding results in lobes off the edges of the loop--a situation not designed to bring out the best in a multi-element quad beam.

If we adhere to the initial modeling convention with which we started--remembering that it is most useful for single feedpoint loops--then our model only (and not the physical antenna) will have to place a half twist in one (but not both) of the two sections of feedline from the junction to the antenna wire. Now the model will yield a correct radiation pattern and a set of correct feedpoint values for a dual in-phase feed quad loop.

However, not everything regarding the model will be in best order. Our artifice, while correcting certain elements of the modeling--the ones of highest interest to most casual modelers--has still left some data out of good order.

Fig. 5 sketches the dual feed situation with one source set at 0 degrees and the other set at 180 degrees. Around the perimeter are the relative current magnitude and phase angle readouts yielded by NEC for the model. Note initially that each outer corner has a phase angle that is -2.5 degrees relative to the source phase angle. However, their values are very different.

We may also wish to look at the side mid-point values. Although the current magnitude has gone so close to zero as to not record in limited decimal places, the phase angle is not an anticipated +/-90 degrees. The values differ and depart from 90 degrees by what seems to be a significant amount. However, remember that the closer to the exact mid-point we get, the more rapid is the change of current magnitude and phase angle. At these point--as well as at the open ends of a dipole, NEC calculations may depart by considerable amounts from what we presume (rather than calculate) from theoretical considerations. For the model at hand, the spatial displacement between the calculated +/- 70 degree angles and a true 90 degrees would amount to a very small fraction of an inch at the frequency in question.

You may establish the correctness of the in-phase feeding as requiring no half twist in reality. Simply construct a small quad loop within the frequency range of whatever antenna analyzer you may have. Use equal lengths of parallel feedline from the two source points to a common junction--and then a length of line about 1 wavelength long to the meter. If you give one section of line a half twist, your source impedance will have a very low resistive component--a few Ohms. With correct in-phase feeding, the resistive component will be moderate to high, depending the length of the two sections of line and where you draw the line between "moderate" and "high."

If we wish all of our values to be correctly aligned and thus to require no mental adjustments from the modeler, then multiple feed quad loops must employ a different convention from the one with which we started. In short, we must model them as two bent in-phase dipoles. Fig. 6 provides some guidance.

For a diamond-shaped quad loop, we need add no wires to the model. Instead, we simple model both the upper and lower Vees from left to right, with junctions at the far left and at the far right. (Of course, we might as easily have gone from right to left in both cases, but these notes follow the western convention of reading from left-to-right in most matters.) Now both source points will follow suit and be in phase. However, remember that for highest accuracy, sources at model corners or junctions of wires should use either a short 3-segment wire on which to place the source or use a split source.

What the square loop gains in simplicity of feeding, it loses in the need to add wires relative to the standard way in which we model quad loops. We must start at the far left mid-point at a junction of two wires, one of which goes down, the other of which goes up. The horizontal wires can be single wires with an odd number of segments in order to center each of the two sources. At the right, we again need two wires, one from the bottom horizontal and the other from the top horizontal--with a junction at the exact center pint between the horizontals. Thus has our 4-wire model of a quad loop grown into 6 wires.

Segmenting the model also calls for attention. If our horizontal wires have 21 segments apiece, then each of the verticals should use either 10 or 11 segments so that segment lengths will be approximately equal throughout the model. Unfortunately, I still encounter many models that simply give every wire the same number of segments, regardless of the wire length. Sometimes, this practice causes no harm; sometimes it yields significantly flawed modeling results. So I have simply tucked in this reminder.

Fig. 7 shows the current magnitudes and phase angles that result from the revised model. All four corners of the model are now synchronized. However, do not be fooled by the nicely balanced current values at the mid-points of the sides. The region at the very center of the sides--corresponding roughly to the ends of a dipole--undergoes a very rapid change in current magnitude and phase. You can see this in action by using 100 segments for each of the vertical wires and 201 segments for the horizontals--or as close to this as a software limitation in total segments may permit. Explore especially the current magnitudes and phases for the segments at End 1 of wires 1 and 4 and at End 2 of wires 3 and 6.

Getting into the habit of modeling dual-feed quad loops (and similar closed polygons) in the way suggested here may not be easy. Of course, since square quad arrays and diamond quad arrays do not differ significantly in performance, you can always simply use diamond-shaped elements and avoid having the 2 extra wires per loop. Or, you can simply model in the old way and make mental adjustments as you go. Or you can simply tell yourself that the current magnitude and phase angle data makes no difference to anything and model in any old way that gets all of the wires roughly in place. None of these options is advisable, although reality tells us that they will be used by some modelers.

One way to get into the habit of using better conventions in modeling is to annotate models thoroughly. Virtually all software allows for the use of the CM entry--the comment card in the Fortran deck. Besides using this facility to give basic information about the antenna which the model replicates, you should also give yourself a record of any features of the model process that might be subject to memory loss later.

In addition, if the dual fed quad loop is to be used in an array of loops, it is useful to model each other loop in the same manner as the driven element. This practice will ensure that current magnitude and phase values on the parasitic elements track those on the driver in accurate ways.

What applies to the quad loop also applies to other types of antennas. Fig. 8 shows the conventional single-feed half square, modeled in typical fashion. However, for a dual feed model that establishes an in-phase feed system, something like the alternative convention should be followed. The vertical wires, as radiators, should be parallel with respect to their End-1 to End-2 orientations. This creates horizontal legs that project toward each other and meet in the middle. Now, when we place separate but in-phase sources at the two corners, the model will perform as it would in reality (apart from the field of sappy pine trees in which we were forced to erect the actual antenna and which are not part of the model).

Less likely to be done is the alternative method of modeling a folded dipole, as shown in Fig. 9. Note that even with a single feedpoint, the current magnitudes and phases will read differently according to the convention of modeling that we select.

From these examples, you should have acquired an appreciation for the differences that modeling conventions can make in the data--and sometimes, the pattern--outputs from NEC. In all cases, models should avoid shortcuts. Instead, the conventions adopted for a kind of antenna or array should be those which yield the most correct outputs across the board, whether we intend initially to use some of the data or not. We may often later find occasion to look into the tabular data, and its usefulness without mental or paper conversions--or remaking the initial model--will depend upon the care we use in constructing the initial model.

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