By L. B. Cebik, W4RNL A Beginner’s Guide to Modeling With NEC Part 4: Loads, transmission lines, tests and limitations

this fourth and final installment cal output data in which the beginning source at the feedpoint is invis- of our series designed to get modeler is interested does not depend on ible to the user. However, by selecting a In you started in modeling with the source values. Gain, front-to-back ra- current source and using the default value NEC, we’ll look at two disparate areas tio and the source impedance will come of 1.0 for the magnitude, we can perform of modeling. The first arena involves a out the same for a single-feed antenna no our survey with ease.1 Our one caution pair of auxiliary facilities built into NEC: matter what source values we use. is to note that while the NEC core and the ability to model reactive (capacitive Sometimes it is convenient to use a NEC-Win Plus use peak values of volt- and/or inductive) loads and the ability to current source. Should you wish to model age and current, EZNEC translates these model transmission lines—both within phased arrays, you’ll need to use current values into their corresponding RMS val- limits. The second area is composed of sources to establish the relative magni- ues. For our work here, the difference will model testing and some of the limits tudes and phases of currents for the not have significance, but for translating within which successful modeling occurs. feedpoint of each driven element. Our voltage, currents and impedances into Some words of caution will be a good beginning project, however, will be much power levels and back again, peak values way to conclude our preliminary survey. simpler: we want to look at the current must be transformed into RMS values. As we have done in the first three parts, levels along a simple dipole. We can do Now let’s build a simple free-space (no we’ll focus on NEC-2 and two commer- this by using a voltage source, but the ground) model, a 20-meter (14.175 MHz) cial implementations: EZNEC 3.0 and typically low current values tend to be dipole using 1-inch diameter aluminum, NEC-Win Plus. hard to interpret without some further 21 segments, and a modeling length along arithmetic. If we only had a way to set Currents and Current Sources the source current at a value of 1.0, then 1Notes appear on page 35. In the very first episode of this series, all of the other values along the dipole we noted that using a voltage source is the would be relative to 1 for easier compre- most normal procedure for simple mod- hension. els with a single feedpoint. We can leave Commercial versions of NEC-2 pro- the source values at a magnitude of 1.0 vide a current source capability. The and a phase of 0.0 degrees (the default network used to transform the natural values) for most models, since the criti- voltage source of NEC into a current

Figure 1—The Figure 2—The NEC-Win Plus basic entry relative current screen for a load consisting of a distribution along resistance and a reactance in series a resonant dipole, (called a “complex load”). using a source current value of 1.0 as a reference.

Figure 3—A comparison of current distributions along equal-length short dipoles using a center-loading and 2 mid- Figure 4—The NEC-Win Plus basic entry element-loading screen for loads consisting of a resistance , and an in series. A series referenced to a capacitor, not used in this example, could source current be added to the mixed load. Note that value of 1.0. parallel combinations of resistance, induc- tance and capacitance are also possible. From February 2001 QST © ARRL the Y-axis of +/Ð198.75 inches. We All loads that we introduce a resonant impedance of about 45 Ω. The should find a source impedance at the are mathematical models, impedance value is higher than with cen- design frequency of about 72 Ω with only ter-loading, but lower than the impedance a fraction of an ohm of reactance. not physical models. of a self-resonant dipole. Our interest lies in Figure 1, a sum- The difference is this: Before we leave the loaded dipoles, mary of the current magnitude on each a physical model, such as let’s look at the current tables (since we segment of the model. NEC provides the antenna wire, used a current source for our runs). Re- these values, and commercial implemen- fer also to Figure 1 for comparison. The tations make them available as one of the contributes to the current level on the antenna wire past the tabular outputs. Figure 1 will be a stan- radiation pattern. loads suddenly decreases relative to the dard for the next phase of our work, but The mathematical current distribution on an unloaded di- for the moment, we can note two key pole. Hence, we would expect either items. First, the progression of values is loads do not. loaded dipole to show somewhat less gain almost, but not quite, a sinusoidal curve. than the unloaded standard. Second, the lowest value is not zero be- We need not always use a center load- There are some cautions to observe for cause the calculation is for roughly the ing coil. Instead, we can place coils in loads. First, the mathematical load as- center of the outermost segment, not the the middle of each antenna leg away from sumes equal currents on both ends of a very end. the feedpoint. If we remove the center coil. As Figure 3 shows, this condition loading coil, we can replace it with a coil only exists for the center loading coil, but Loads 30% from the left end (segment 5) and not for the mid-element coils. Hence, the Next, let’s shorten the dipole to another matching coil 70% from the right calculations you make for mid-element +/Ð144 inches, or 24 feet overall. Reduce end (segment 11). Experimentally, we can loading coils will be slightly less precise the number of segments to 15 so that each adjust the reactance of the two coils until relative to building the coil. Second, us- segment will be about the same length the antenna is once more resonant. For ing the coil’s reactance is good only for as in the original longer dipole. The the 24-foot 20-meter model, values of a single frequency. If you wish to perform shortened antenna, of course, will not be j 212 Ω (reactance) will do the job, and a frequency sweep of the antenna, re- resonant. In fact, it will report a source for a Q of 300, we can assign the resis- enter the coil values, an inductance and a impedance of about 27 Ð j275 Ω. If we tance box a value of 0.7 Ω. Running our resistance in the series RLC option for want to resonate the antenna, we shall new mid-element loaded dipole will yield entry, as shown in Figure 4, a NEC-Win have to compensate for the high capaci- Plus load box for the center loading coil. tive reactance with loading coils some- Standard handbook equations for trans- where in the antenna structure. forming reactance to inductance (or NEC lets us model reactive loads. The capacitance) apply here.2 Some imple- loads can have a resistive as well as a re- mentations of NEC call for µH and pF, active component, as shown by the NEC- while others may call for basic units. With Win Plus load screen in Figure 2. Adding Figure 5—The EZNEC screen for inductive, capacitive, and resistive units, introducing a mathematical a series resistance to the reactance lets into a model. loads will show the correct reactance at us account for the Q of the loading coil. each checkpoint of a frequency sweep, Note the reactance value: 276 Ω, just and the resulting source impedance val- enough to compensate for the capacitive ues (and SWR values, if needed) will be reactance. The resistance value (0.9 Ω) much closer to the reality of the antenna’s reflects a coil Q of 300. The upper left performance. corner of the figure shows that the load has been placed at the center of the an- Transmission Lines tenna, on the same segment as the source. A second mathematical convenience Loads are always in series with a source offered by NEC is the use of transmis- on the same segment. sion lines in a model. Like loads, these All loads that we introduce are math- lines do not enter into the calculation of Figure 6—The NEC-Win Plus screen for ematical models, not physical models. introducing a mathematical transmission radiation patterns. If the pattern influence The difference is this: a physical model, line into a model. of a transmission line is significant to a such as the antenna wire, contributes to model, the modeler must physically the radiation pattern. The mathematical model the line, which is possible for par- loads do not. So any variations (normally allel lines, but not generally feasible for insignificant) in radiation patterns that re- coaxial cables. sult from using large or small coils will Figure 5 shows the EZNEC transmis- not show up in the output of NEC. sion line entry screen, while Figure 6 If we run our model with its load, we’ll shows the NEC-Win Plus equivalent. find a source impedance of about 31 Ω Both show the same line: a shorted stub and a fractional value for reactance. Re- of 600-Ω line having a length of 11.02 member that the inductive reactance of inches or 0.2799 meters. EZNEC provides the load cancelled out the capacitive re- an invisible structure for open and shorted actance at the source by simple addition. stubs, while NEC-Win shows the actual In series circuits, we add resistances and Figure 7—A standard use of a construction. Every transmission line add reactances. The added resistance of transmission line between the antenna must run from one wire to another. In wire and a short, 1-segment terminating the coil shows up in the resistive part of wire that becomes the location of the NEC-Win Plus or raw NEC, we create a the source impedance. antenna system source. new short (1 segment) thin wire that is From February 2001 QST © ARRL far away from the antenna. Its position is not critical, since the line length entered into the proper box on the transmission line screen controls the calculation. A shorted stub requires a high shunt admit- tance. The long numerical entry for 110 (1 to the tenth power) is used to assure a true short circuit at the far end. Note in passing that we can reverse the line between the two terminating wires, es- sentially giving it a half twist—a useful feature for modeling phased arrays. The transmission line entry boxes il- Figure 8—An EZNEC view of the lustrate the critical elements of a NEC 3-element Yagi with a beta-match shorted Figure 10—The NEC-Win Plus report on transmission-line stub (hairpin) at the the results of the average gain test for transmission line. Figure 7 shows the driven element terminals. the 3-element Yagi used for the beta- layout of such a standard sort of model match illustration. using a transmission line used with a di- pole. The dipole wire is one end of the line, while a new short 1-segment line ter- Figure 9—The NEC- Win Plus wires page minates the transmission line. For this for the 3-element Yagi kind of application, we move the source and beta-match stub, from its usual position at the center of showing the remote the dipole and place it on the new wire. terminating wire for the transmission-line We might wish to see what impedance we stub. might obtain at the end of the line using various line lengths. We need only change the line length, perhaps in quarter-wave- length increments, to explore the effects of line length on the system source im- pedance. Note that some programs have a velocity factor entry box, which lets you enter the physical line length. Other pro- grams do not have a velocity factor box, so you must precalculate the of the line and use that figure.3 There are cautions to observe in the use of NEC transmission lines. First, they to illustrate the basic transmission-line array (LPDA) runs from one element to the do not account for line losses. For short setup in Figure 5 and Figure 6 is exactly next with a half twist between each ele- line runs, the source impedance error will what we need to introduce an inductive ment. Such structures are extremely diffi- likely not be significant, but the error will reactance of about 50 Ω across the an- cult to model physically, but the transmis- grow with very long transmission line tenna terminals. Because transmission sion line facility in NEC not only simplifies runs. Second, transmission lines are in lines are mathematical and use remote the process, but as well increases the ac- parallel with sources (in contrast to loads, terminating wires for stubs, Figure 8 does curacy of the array analysis. Used with care which are in series with sources). Third, not show the stub, but indicates its pres- and with their mathematical (non-physical) transmission lines are accurate only ence with a dot. (If the view tried to show nature always in mind, transmission lines where the antenna element current on the terminating wire for the stub, the an- in NEC can be a valuable design tool for each side of the line is equal. Hence, they tenna structure itself would shrink almost many types of antennas. are most accurate at element centers and to invisibility in the graphic.) other low impedance points along an an- Figure 9 shows the NEC-Win Plus Testing Models tenna and become quite inaccurate at low wires page that goes with Figure 6, the I have stressed that both loads and current, high voltage positions. corresponding transmission line screen. transmission lines must be used with care Transmission line runs to a remote Wire 4 is the remote 1-segment thin wire and within their limitations if we are to source are only one use of this NEC fa- that terminates the shorted stub. The units achieve accurate model results that coin- cility. Stubs are also useful for modeling of measure are meters, which coincides cide closely with the physical antennas some kinds of matching networks for an- with the stub length in Figure 6. If we the models represent. This same caution tennas. For example, consider the 20- run the model, we should get a source applies to the physical structure of mod- meter 3-element Yagi in free space, as impedance at 14.175 MHz of about els. There are two general tests that we shown in Figure 8. Before adjustment 51 Ð j3 Ω. You may wish to run a fre- can apply in order to increase our confi- with a matching network, it has a source quency sweep of the antenna across the dence in a given model. impedance of about 24 Ð j25 Ω. The re- entire 20-meter band to check the 50-Ω The first analysis is called the conver- sistance and capacitive reactance are ex- VSWR at the band edges. gence test. In Part 1 of the series, we actly suited to the use of a beta match. Besides their use as standard transmis- noted the minimum number of segments We can implement the match with a small sion lines and as stubs in matching net- to be used on open-ended linear elements. coil across the feedpoint or with a shorted works, transmission lines have other uses However, as the antenna geometry be- transmission line stub (often called a in advanced modeling. For example, the comes more complex, we may need more “hairpin”). In fact, the stub that we used phase-line needed in a log periodic dipole than the minimum number of segments From February 2001 QST © ARRL to assure an accurate model. Moreover, performance trends. For most uses, val- or both tests) does not necessarily mean segment length should ideally be about ues of 0.95 to 1.05 for the average gain that the modeler is at fault. NEC has limi- the same throughout a model. Whether test indicate a very usable model for vir- tations. We saw some of those limitations we have enough segments of the right tually any purpose. in Part 1, when we noted certain guide- lengths is subject to a simple test. However, both the convergence and lines for the minimum segment length to Start by running the original model average gain tests are necessary conditions diameter ratio, segments per half wave- and recording the gain and source imped- of model adequacy. They are not sufficient length of wire, etc. There are others, a ance. Then increase the number of seg- conditions. There are at least a few types few of which are illustrated in Figure 11. ments for each wire by about 50%. Again, of models that can pass both tests and still For example, letting two wires touch at record the gain and source impedance. yield inaccurate results. However, pass- mid-segment points (in contrast to junc- You may wish to give the test a third ing both tests should increase our confi- tions) will trigger the NEC core to reject trial with another 50% increase in the dence that we have a good model. the model. Most of the NEC core number of segments per wire and record rejection messages occur due to simple the results. NEC Limitations mistakes in creating or revising the ge- The level of segmentation at which the A bad model (one which fails either ometry of an antenna model. The solu- output figures for the model do not tion is to find and correct the error. By change significantly is the minimum level using the paper planning techniques of segmentation for the model. The mod- shown in Part 2, we minimize the chances els are said to converge at this segmen- of receiving a core rejection notice. tation level. In some cases, minimum More subtle are NEC limitations that segmentation is satisfactory. In others, es- the core does not signal with a rejection pecially for antennas having a closed message. For example, NEC will nor- geometry (like angular loops), the re- mally yield inaccurate results when two quired segmentation level may be higher. wires of different diameters meet at an A few antennas, such as those with an- angular junction. The difficulty grows gular elements of different lengths ex- more pronounced as we add more seg- tending from the feed point, may not ments to each wire. Consider a folded X- converge until very high levels of seg- beam composed of 1-inch aluminum ele- mentation. And some models will not ments in the facing V sections with thin converge at all because they exceed the wire tails pointing toward each other in limitations of the NEC core or have other each side of the structure. This antenna construction errors. There is no absolute will not converge at any level of segmen- standard of what counts as the borderline tation in NEC.4 between converged and non-converged Likewise, NEC can grow inaccurate models. However, if two successive lev- when two wires of different diameters are els of segmentation produce results that Figure 11—Some NEC limitations, brought close together. Wires of the same indicate differences in antenna perfor- including the prohibition against wires diameter should have their segment junc- mance or structure that go beyond nor- crossing at mid-segment locations, and tions well aligned when in proximity for mal tune-up adjustments, the models are accuracy difficulties with angular highest accuracy, for example, with a junctions of wire having different likely not sufficiently converged. diameters and close-spaced wires of folded dipole. However, even if the seg- A second test is called the average gain different lengths or diameters. ment junctions are aligned, wires of dif- test. If we place a horizontal antenna ferent diameters and lengths will show model in free space or a vertical antenna errors of both gain and source impedance over perfect ground, we can then perform Most of the NEC core as they approach too closely. The degree a 3-dimensional radiation pattern test, of error depends on many factors, includ- using equally spaced checkpoints. To per- rejection messages occur ing the wire diameter, the spacing, the form the test, we omit wire losses and due to simple mistakes in frequency, and the relative element resistive loads. The reason for these creating or revising the lengths. The average gain test will nor- moves is that the average gain of a geometry of an antenna mally catch this overstep of the limita- lossless antenna, taking into account a tions inherent in NEC.5 fair sampling of all possible directions of model. The solution is to The NEC core also has a limitation in radiation, is 1. Resistive losses would find and correct the error. handling tapered-diameter elements, that interfere with this result. For the 3-element Yagi that we used Figure 12—A to illustrate the beta matching stub, we sample, from receive the NEC-Win Plus report shown EZNEC, of the original tapered- in Figure 10. Equal in quality to the 0.999 diameter element average gain value would have been and its uniform- 1.001, since the test is run with a large diameter Leeson but not exhaustive sample of directions substitute. for the radiation pattern checkpoints. Again, there is no absolute standard for what counts as “highly accurate.” The level may depend on whether we are pre- paring to home brew an antenna or whether we are deriving some detailed From February 2001 QST © ARRL is, elements composed of ever-smaller Elements that taper equations for inductance and capacitance and their respective reactance values: diameters of tubing as we move outward toward thinner diameters from the element center. However, com- = XL XLLfL = 2π (Eq 1) mercial implementations of NEC, in- as we move away from 2πF cluding both EZNEC and NEC-Win Plus, the center feedpoint where XL is the inductive reactance in Ohms, L is the inductance in Henries, and f is the offer the modeler a system of carefully require longer physical frequency in Hz. calculated substitute elements having a element lengths for 1 1 uniform diameter. The corrective ele- X == C 2 ππ (Eq 2) ments are based on the work of Dave than do 2 fC 2 fXC 6 where X is the capacitive reactance in Ohms, Leeson, W6QHS (now W6NL). Using a uniform-diameter C C is the capacitance in Farads, and f is the complex set of equations, the program elements. frequency in Hz. In addition, when using ei- precalculates substitute elements. How- ther the series or parallel RLC option, place ever, the equations only work within example, we have not mentioned trap an- a zero in the box for a missing value, for tennas, which can be modeled with good example, the capacitance box of Figure 4. about 15% of the design frequency and NEC interprets the zero as a missing value on symmetrical open-ended linear ele- results. We have not delved into model- and not as 0 pF capacitance. ments with no mid-element loads or ing by equation, which can simplify the 3For reference, transmission lines. Despite these limita- construction and revision of models and L =• =p tions, the correction factor has been a so speed up the design process. And we LVFLLP ee (Eq 3) VF boon to designers of directional arrays for have not touched upon the modeling or where Lp is the physical length of the line, Le the upper HF and lower VHF region. complex structures, such as typical tower is the electrical length of the line (in the same Figure 12 provides a small sample of sections, or the use of substitute models.7 units), and VF is the velocity factor, ordi- the Leeson corrections in action, using What we have attempted to do in this narily 1.0 or less. 4 4-part series is to acquaint you sufficiently Interestingly, MININEC has no difficulty in EZNEC as the source. The upper part of modeling the angular junctions of dissimilar the figure shows the 3-wire dipole used with the fundamentals of NEC modeling wires, although length tapering may be as an example in Part 2 of this series. The so that you can embark on your own ex- needed at the acute angle corners. NEC-4 ploration of the antennas in which you improves on the performance of NEC-2 lower portion of the figure shows the sub- for such structures, but remains shy of stitute elements that replace the tapered have the most interest. Hopefully, there is perfection. diameter model in NEC calculations. enough information in these notes to make 5Once more, MININEC has no problem with Note that the uniform-diameter element your initial efforts successful and make close spaced wires of different diameters the next steps confident ones on your own. and lengths. Hence, it yields quite accurate is not simply the average of the two di- results for folded dipoles that use wires of ameters in the tapered-diameter version. Think of NEC as a precision tool. Even different diameters. For further details of As well, the uniform-diameter version is as I write, various improvements to the NEC limitations, especially as they appear modeling process—some general, some in NEC-4, see L. B. Cebik, “NEC-4.1: Limi- shorter than the physical dimensions be- tations of Importance to Hams,” QEX (May/ ing modeled. Elements that taper toward for specific applications—continue to June, 1998, pp 3-16). The limitations of thinner diameters as we move away from develop. However, even though NEC-2 is NEC-4 also apply to NEC-2. the center feedpoint require longer physi- nearly two decades old, it remains far 6David B. Leeson, W6QHS, Physical Design of Yagi Antennas (Newington: ARRL, 1992), cal element lengths for resonance than do more precise than older calculation Chapter 8. Once more, MININEC does not uniform-diameter elements. Finally, note methods. It is superior by far to those have difficulties in dealing with tapered-di- that the length dimension affects not only rules of thumb by which we measure ameter elements and is used as a compara- dipoles and quads, and it is a distinct ad- tive standard by Leeson. (However, the outer ends of the element, but the MININEC 3.13—the public domain version— length of the inner element piece as well. vance in antenna pattern and gain analy- does have numerous limitations of its own, The Leeson corrections have made the sis compared to aperture-area calcula- such as a very slow-running core, limitations tions that were popular in the middle of on the total number of available segments, design of Yagis and similar directional no transmission line facility, a relatively poor arrays routine. Of course, the corrections the 20th century. In short, NEC is a good system for calculating ground effects, must be used within the limitations that tool for the student of antennas to master source impedance calculated only over per- as we move into the 21st century. fect ground, etc. These limitations have we noted above. The upshot is that there made NEC-2 the more preferred modeling are arrays which are difficult (if not im- However, like every precision tool, core among radio amateurs, although possible) to model within NEC. None- NEC requires care, practice, patience, and MININEC still has important uses. NEC-4 theless, despite the limitations, NEC is focus to master well. What we learn about requires a license and advanced software, both of which have placed this improved capable of accurately modeling an almost antennas along the way will be the reward NEC core beyond the economic reach of endless variety of antennas for frequen- for our efforts. most hams.) cies ranging from below the AM broad- 7Those whose interests in antenna modeling cast band into the upper UHF region. Notes grow deeper are invited to look at the series 1Users of raw NEC can achieve a source cur- of AntenneX columns that I do monthly, all of rent of 1.0 in the following way. For a reso- which are at my Web site (www.cebik.com) Conclusion nant antenna, use the voltage source at its under the “Antenna Modeling” heading, or to default values to obtain the source imped- the text Basic Antenna Modeling: A Hands- We have explored NEC-2 modeling On Tutorial, available from Nittany Scien- with the eyes of a beginning modeler, ance. Then use the source impedance as a revised voltage magnitude and phase- tific, Inc (www.nittany-scientific.com). starting from the basic language of the values, and rerun the model. The source The original NEC-2 manuals remain the modeling enterprise and ending with current should be 1.0, since current equals most authoritative references for under- standing the operation of the core. The some fairly advanced cautionary notes the voltage divided by the impedance. Like- wise, one can explore the actual current for on-line or paper manuals accompanying about the limits of NEC-2. We have not a given power level by using the initial run commercial implementations of NEC-2 are exhausted all of the possibilities for com- source impedance and the desired power also authoritative for the respective software bining the features of the NEC core and level. Select a voltage equal to the square packages. root of the power times the impedance. See You can contact the author at 1434 High its commercial interfaces to improve the the main text for cautions concerning NEC’s precision of our analyses or to ease the use of peak voltage and current. Mesa Dr, Knoxville, TN 37938-4443; work involved in creating models. For 2As a reminder, here are the transformation [email protected]. From February 2001 QST © ARRL