The following notes compile a number of replies that I have given to various theme-related e-mail inquiries on using NEC at or beyond the limits of its capabilities. In a number of cases, I have suggested that NEC (either -2 or -4) may not be the software of choice for various modeling enterprises. In other cases, I have suggested that the user must employ experimental calibration techniques prior to using NEC models, especially when the goal is to design a working antenna, even of ordinary types. Understanding what NEC can and cannot do is critical to making best use of the software. Let's examine a few interesting cases at or beyond the limits of NEC.
Non-Round Elements
One of the most common inquiries in home antenna construction is whether one might substitute non-round wires for round wires that most handbooks suggest for antenna elements. Of course, there are practical reasons for using round antenna elements. For the most part, round elements slip the wind better than most of the alternatives, especially when the elements have a significant radius. As well, many materials accumulate snow and ice faster and thicker than round elements. However, elements with flat surface appeal to home antenna builders for numerous reasons. First, the materials are readily available from various local sources. Second, they have flat surfaces that many less-experienced builders find easier to handle and drill than round elements.
Rather than trying to adjudicate the pros and cons of element materials with flat surfaces, let's confine ourselves to the question of trying to use NEC to design or to refine the design of a typical antenna, perhaps a modest Yagi. Fundamentally, NEC begins with a thin-kernel model of all wires in the antenna geometry. The thin-kernel model presumes a bare round wire in free-space or its equivalent, that is, a vacuum or dry air. As the NEC-2 manual explains, "In the thin-wire kernel, the current on the surface of a segment is reduced to a filament of current on the segment axis. In the extended thin-wire kernel, a current uniformly distributed around the segment is assumed. The field of this current is approximated by the first two terms in a series expansion of the exact field in power of aa [where a is the wire radius]. The first term in the series, which is independent of a, is identical to the thin-wire kernel, while the second term extends the accuracy for larger values of a. Higher order approximations are not used because they would require excessive computation time."
"In either of these approximations, only currents in the axial direction on a segment are considered, and there is no allowance for variation of the currents around the wire circumference. The acceptability of these approximations depends on both the value of a/wavelength and the tendency of the excitation to produce circumferential current or current variation. Unless (2*pi*a)/wavelength is much less than 1, the validity of these approximations should be considered." One potential arena in which the validity of these approximations may be tested is the modeling of a boom connected directly to the parasitic elements of a Yagi antenna. In practice, the connection or the very close proximity of a boom to the parasitic elements alters the required length of the elements to preserve array performance. However, in NEC-2 and NEC-4--when modeled within the other limitations of the software--the boom has no effect upon the parasitic elements.
The NEC-2 manual goes on. "The accuracy of the numerical solution for the dominant axial current is also dependent on [the ratio of segment length to radius or Ls/R]. Small values of [Ls/R] may result in extraneous oscillation in the computed current near free wire ends, voltage sources, or lumped loads. Use of the extended thin-wire kernel will extend the limit on [Ls/R] to smaller values than are permissible with the normal thin-wire kernel." In general, Ls/R must be greater than 8 for errors under 1% for the normal thin-wire kernel. This amounts to a segment length-to-wire-diameter ratio of 4:1, for programs that input wire thickness as a diameter. The manual notes that "reasonable solutions" have been obtained for the normal thin-wire kernel for Ls/R values down to about 2, with equally "reasonable solutions" for the extended thin-wire kernel for Ls/R values down to about 0.5.
In NEC-4, according to its manual, "the thin-wire approximation is now implemented with the current treated as a filament on the wire surface and the boundary condition enforced on the wire axis. With the boundary condition enforced on the wire axes, the openings at wire ends should be closed with end caps. This is particularly important when the ratio of segment length to radius is on the order of 2 or less. Wire ends are closed with flat caps in NEC-4, with the current and charge density assumed continuous from the wire onto the cap." NEC-4 also includes optional caps for use with voltage sources with equally low values of Ls/R. "This approximate treatment was found to be about as effective as the extended thin-wire kernel included as an option in [NEC-2 and] NEC-3. The extended thin-wire kernel option (EK card) has been dropped from NEC-4."
I have repeated these extracts from earlier episodes in the series because every user needs periodically to review the fundamental premises underlying the software. These premises reveal to a large extent the limitations of the software. The thin-wire kernel model of the currents along an antenna element wire provides us with one of those limitations. We cannot automatically transfer the results of a model to a physical implementation that uses non-round elements.
For many substitute elements, we may use NEC models effectively if we carry out for the frequency and material that we propose to use a series of simple experiments. I had occasion to perform such a calibration exercise in connection with the design and implementation of several alternative versions of a 3-element Yagi for 146 MHz. The procedure that I used may be instructive. However, for a specific project, the required effort will be considerably shorter than I needed for a survey that involved numerous materials.
The first step involved constructing a series of round element dipoles for the test frequency. In this step, I was interested in learning to what degree physical antennas using the proposed construction methods might vary from models that included none of the hardware and other appertenances that are required parts of the proposed antenna. Table 1 summaries the results for a range of round 6063-T832 aluminum elements from 1/8" to 3/4" in diameter.
The table itself does not comment on the accuracy of NEC software because it does not show the details of the models, such as the segment density. As well, it does not show the instrument calibration and accuracy. What the table does do is to provide me with a set of expectations relative to correlating other materials to round elements and from there to models.
The nature of the project involved a number of potential element materials with alternative cross-sections. Fig. 1 shows the varieties that I subjected to tests. One might easily expand the shapes to include square tubing and U-channel aluminum stock. This particulkar collection happened to coincide with the project's overall goals.
For each material, I created a dipole and brought it to resonance at 146 MHz by the simple expedient of successively shaving the dipole outer ends in small increments, using a disk sander for the final fine tuning. (Sanding, of course, does not apply to the collapsible whips.) Table 2 summarizes the results and shows the conclusions that I reached regarding the correlation of the material at the test frequency to the nearest commonly available U.S. round element size.
One result that I found somewhat surprising was the close correlation between any of the flat or L shaped materials and round elements when I compared the element width measurement to the tubing diameter. So long as the stock has a significant thickness--1/16" at the test frequency--the width of the stock correlated to the round element with the same value for its diameter. However, for very thin materials, such as the measuring tapes, the simple correlations did not apply. However, the tests did not use techniques that allowed me to separate any effects due to using a very thin element and effects from the ferrous materials used in measuring tapes.
The correlations allowed me to design and build working 3-element Yagis using any of the materials. In fact, I built one version that used a combination of materials as a demonstration. I can find no performance difference between it and its round-element counterpart. The use of calibration methods does allow the antenna builder to employ NEC in developing an antenna design, so long as one uses due caution. The calibration procedure used here applies to materials at the test frequency plus or minus about 20%. Beyond those limits, I would strongly urge a new set of calibration experiments. For example, if one wished to design a beam for the U.S. 223-MHz band or for the FM band, then one should use calibration experiments designed expressly for those frequencies.
The Medium Surrounding a Wire
NEC-4 added the IS or insulated sheath command to the collection of control commands available to the user. A number of implementations of NEC-2 have added codes that either replicate or simulate this command. The command allows the user to specify a wire in the geometry and to encase specified segments in a material having a user-selected set of values that include the material's relative permittivity, conductivity, and outer radius. Thickness is simply the sheath radius minus the wire radius. Numerous inquiries over the years have wondered how far one might extend the sheath to form essentially a special medium for the wire inside. Since the calculations that modify the fields calculated for the wire occur late in the sequence of NEC processes, it is likely that there is a practical limit about how thick one may make an insulated sheath, although I have seen no data on the precise limits.
Of course, modelers can use the command creatively. One such example is the development of a hollow thermoplastic tube near a radiating wire. To create the tube, the modeler added a wire to the geometry and assigned to it the conductivity of air. The wire diameter corresponded to the inner diameter of the tube. The modeler then added an IS command using the values appropriate to the plastic involved. He gave the sheath a radius corresponding to the tube's outer diameter.
The limitation of this technique is that one must need a round surface for the structure. However, most modelers are interested in flat non-conductive materials to which we may bond antenna wires. These substrates come in many forms. The next inquiry wondered if one might use the NEC-4 UM command to replicate the substrate. Unfortunately, the UM command has some limitations that largely preclude its use in this manner. Fig. 2 shows the situation modeled by employing the UM command.
Most substrates have a finite dimension and thickness. The UM command uses a set of constants for the ground and another set for the upper medium. Except for the ground surface at Z=0, each medium is without limit. One may, of course, specify a second medium for the ground, but the depth of each medium will be without limit. Hence, we cannot limit a substrate to its actual thickness using the ground. The antenna environment is the upper medium, which also extends without limit in all directions in the hemisphere above ground. In addition, the UM command is usable only with the reflection coefficient approximation (RCA) ground calculation system, which has limitations of accuracy as the antenna is brought toward the ground surface.
In general, neither the IS nor the UM command provides a means of approximating the situation of antenna elements bonded to a substrate.
Substrates and Strip Elements
A very wide range of antenna applications make use of modified printed circuit board techniques. The essential features of such antennas include the use of relatively wide strip elements having negligible thickness and the use of a substrate to which we bond the elements. The substrate has a certain set of dimensions, along with relevant values of conductivity and relative permittivity. Fig. 3 shows some of the techniques commonly used to form such antennas. The edge views show element ends as an artificially thick line, although the actual strips are very thin.
The most common type of antenna-substrate combination etches elements on one side of the substrate, as shown at the upper left. However, we may use both sides of the board, as shown at the upper right, to create such antenna types as an LPDA. At the bottom are two variants of the theme, sandwiching the elements between two boards or fully encapsulating the antenna within a molded substrate. These latter forms provide the antenna with maximum protection from environmental or user damage.
Trying to model these antennas in NEC presents the analyst with numerous problems. First, the strips are very wide compared to the thickness. As our initial experiments using measuring tape showed, when the thickness becomes almost negligible, the material does not perform like a round wire of any predictable diameter. The only way to form any kind of usable correlation is to perform a series of calibration experiments in advance of any modeling.
The existence of the substrate in contact with the strips on one or both sides and the liited size of the substrate in all dimensions presents additional problems. Although one might reach a workable round-wire free-space approximation of the antenna plus substrate, the effort might require the pre-existence of the finished physical antenna before one could claim any utility to the modeled approximation. For simple antennas, such as dipoles, the problem may not seem difficult. However, for parasitic arrays, the substrate may modify the mutual coupling between elements as well as the performance of each element. Hence, the simple calibration procedure that we successfully used for element materials in free space may not be as successful in the presence of a substrate.
Many of the techniques that we have just described also involve UHF and higher portions of the spectrum. At these frequencies, the width of the strip elements and even their round-wire correlates may press the limits of the segment-length to radius (Ls/R) recommendations for accuracy in NEC.
Under these conditions, NEC may not be the software of choice for trying to model the antennas--at least not in detail. There are available hybrid programs, virtually all proprietary, that can handle the modeling situation more directly. In fact, many allow the direct input of CAD drawings, with appropriate translations for antenna calculations. These input potentials allow the user to handle the strip elements directly. In addition, they allow the inclusion of substrates having specific dimensions and properties. Some are also capable of handling an interesting circuit board possibility: the physical inclusion of both antenna and transmission-line strips, as suggested by Fig. 4.
The sketch shows side-by-side phase line strips feeding the two dipoles from a centered location. (In some software, one may include circuitry beyond the limits of the antenna system.) The reality of the physical structure might use transmission-line strips on opposite sides of the board, where strip width and displacement, combined with the dielectric constant of the substrate, together permit a designer-selected characteristic impedance.
Many packages employ FDTD techniques in calculating antenna properties within the complex structural situation described here. Although data is the critical calculation output, many such packages have labored long to present the outputs in very attractive graphical forms.
For modeling enterprises of the sort described here--and others even more complex--hybrid packages are likely the software of choice. In general, these enterprises are not suited to individual efforts, because the investment required is very considerable. NEC users are accustomed to using relatively low-cost software. There are entry-level packages ranging from freeware to commercial implementations with full support at under $100 for NEC-2. NEC-4 requires a license, which is inexpensive for the individual serious user, and commercial NEC-4 packages run well under $1000. Hence, the practicing consulting engineer can easily afford the best of NEC.
Full-featured hybrid packages may require $50,000 or more, in addition to the cost of sales commissions and seminars to ease the very steep learning curve required to use the packages effectively. The hybrid packages tend to be corporate investments, with costs recovered from the mass sale of systems that emerge from their use. Because these packages do much more than just allow one to design and analyze antennas, it is impossible to apportion costs to a single function. Nevertheless, the packages tend to fall well outside the range that most individuals can invest.
I have not been more definite about the specific capabilities of hybrid packages because they also and easily fall outside my ability to afford. A web search or a recent issue of a journal for professional RF engineers will provide contact with the vendors of such packages. Over the last decade, the number of vendors has shrunk due to purchases and mergers. In the process, the capabilities of individual packages have increased for the same reason.
Conclusion
In these notes, we have examined three situations. The first involved the use of non-round shapes for which we can find for a given frequency range equivalent NEC wire sizes to provide accurate models of the physical antennas that use the odd materials. However, as we contemplate the combination of conductive and non-conductive materials in proximity, we may try to use some of the special commands available, especially in NEC-4. This second situation brought us to an understanding of some of the limitations of commands such as IS and UM. In general, these commands are unsatisfactory for use with strip elements bonded to substrates, a common construction technique for a wide variety of antennas used in the UHF and higher portions of the spectrum. This third situation brought us to the general conclusion that the round-wire, axial-current, free-space environment at the heart of NEC may not be the most apt vehicle for the design or analysis of the subject antennas. As versatile and flexible as NEC may be, it is not a universal software modeling system for all possible antennas.
For round-wire antennas, NEC remains the software modeling system in widest use. It is generally very cost effective, especially for amateurs, consulting engineers, and others dealing with the design or analysis of one-of-a-kind antennas or antennas that fit its special capabilities. Indeed, the relatively low cost, even of NEC-4 plus a license, has led to the development of numerous work-arounds for some of its limits. For example, many Yagi designers who use a direct connection or extremely close proximity between antenna elements and a supporting conductive boom introduce short, fat center element sections to account for the boom effects that NEC cannot directly calculate. In these notes, we have seen the relative ease of calibrating materials with an odd cross-section to NEC's round wires. Other episodes in this series have shown additional work-arounds for situations that press NEC's limitations.
Nevertheless, in the field of antenna modeling, NEC cannot do everything.