Practical Antenna Theory

Computer Assisted Design
by AD5XJ, Ken Standard
ARRL Technical Specialist

This series of articles deal with the more technical aspects of antennas and the practical theory behind their use. You will find this guide to be a pragmatic approach to antenna theory. The views expressed here are the author’s and are not meant to be the definitive text on the subject. You should also be armed with the knowledge that there may be changes from time to time where technology advances and the author deems it approprate to update the text.

You should do your won research and fill in where there are “learning gaps”.

Much of the material in this series is derived from publications by the ARRL. Namely,

The ARRL Handbook ®


The ARRL Antenna Book ®.

You should consider those publications reference material in this cursory study of a very complex subject. The most recent editions are available from the ARRL Store online and can be seen at many hamfests, but may vary in quality from used to mint condition, over many past versions. Any should be considered a valuable addition to your reference library on antennas.

I hope you enjoy this. Please email me if you have questions or would like to see a particular subject enhanced.

In our series so far, we have discussed the basic theory behind how antennas are designed and how we can exploit that design to our advantage. But suppose we wanted to design our own antenna? A number of questions and requirements surface when entering this area of study. Please, do not try to jump ahead of the previous discussions and dive into Computer Assisted Antenna Design. You will not be satisfied with the result. Automated design assumes you already know antenna basics on more than a casual basis and computer operational basics intimately.

Computer Assistance

In this series we will just touch on the area of Computer Assisted Antenna Design. The choice of words here is with design and purpose. Antenna design is in and of itself very complicated. It is made somewhat easier with the use of computers, in that the computer can do all of the calculations necessary for proper design. But because the computer does the complicated calculations quickly, it does not mean the user is free of responsibility. One must know what the results mean and how to use them.

For illustration we will look at a simple antenna familiar to most hams, and see how the use of the computer can aid us in design of a new antenna of a particular type.

Designing a dipole.

The simple single band flat–top dipole is one of the simplest of all antennas to model on the computer. This will be the subject of our introduction of Computer Aided Design of antennas.

If you read QST or The ARRL Handbook, you will have come across the mention of EZNEC. In fact, a working demo version of it is included in the ARRL Antenna Book. EZNEC is but one of several similar applications used to model and design antenna projects. We will look at the design of our dipole antenna using each and point out the differences.


It’s assumed that you know basic Windows operation, such as clicking, dragging, and selecting, and references will occasionally be made to common Windows tools such as Notepad or the Windows Explorer. Please consult your Windows documentation if you’re not familiar with basic Windows techniques.

...these applications are a tool, not a panacea! Alan R. Applegate, KØ

Just for the record, EZNEC, and most of the other numeric electromagnetic coding (NEC) engines, are marvelous programs. They allow expert, and neophyte alike, to model all–manner of antenna parameters. However, the results are dependent on the data provided! For example, leaving out the feed line when doing an analysis can skew the results. Another common error is miscalculating ground losses. Therefore, assuming and quoting the results verbatim without a thorough understanding of how antennas behave (especially mobile ones), often leads users astray. In other words, these applications are a tool, not a panacea! — Alan R. Applegate, KØ

All programs of this type take into consideration all of the things we have discussed in this series and much more. All Antenna Computer Aided Design (CAD) applications include the ability to specify and save:

EZNEC is no exception. You will find all of the above and more.

EZNEC 6 Demo running with WINE on Linux

You can easily notice the list of parameters EZNEC allows to be configured and stored describing our project antenna. For this discussion we have selected the design frequency of 300MHz. You can select any frequency you wish, but this is our choice for this demonstration.

Essentially, CAD program use is made to be cosmetically similar to manual design. Meaning that the same parameters used to design and model antennas by hand are used in EZNEC. Each parameter is presented in the list displayed on the main window of EZNEC. The results of most will be presented in a separate window, such as the display of the wires in the window just to the right. You will notice that calculations have been made to also display the RF currents along the wires displayed as the curved colored line above the antenna.

Also shown in this pictorial is the window for wire edit and the calculated far–field pattern generated by the antenna currents. All of the windows shown in this pictorial depend entirely on the selections made and the successful calculations of EZNEC.

Because of the complexity of antenna design and the numerous features of the EZNEC program, we will not go into all of the options and methods here. If you are interested in EZNEC and it’s use you can find a printable manual at


MMANA-Gal Basic running with WINE on Linux

Another Windows–based CAD program has almost as long a history as EZNEC. The application is known as MMANA-Gal...a conflation of the original name MMANA, and the maintainers’ initials. The original MMANA was designed and released as freeware by Macoto Mori, JE3HHT. Mori San maintained the application for years before releasing the code to Alex Shewelew, DL1PBD and Igor Gontcharelko, DL2KQ. It is now known as MMANA-Gal Basic as freeware, and MMANA-Gal Pro as a commercial product.

MMANA-Gal attempts to make the user interface simple and easy to use with the employment of integrated tabs instead of separate windows as in EZNEC. It employs extensive use of the "method of moments" calculation technique.

Method of moments element method

The method of moments (MoM) or boundary element method (BEM) is a numerical computational method of solving linear partial differential equations which have been formulated as integral equations (i.e. in boundary integral form). It can be applied in many areas of engineering and science including fluid mechanics, acoustics, electromagnetics, fracture mechanics, and plasticity.

MoM has become more popular since the 1980s. Because it requires calculating only boundary values, rather than values throughout the space, it is significantly more efficient in terms of computational resources for problems with a small surface/volume ratio. Conceptually, it works by constructing a “mesh” over the modeled surface. However, for many problems, BEM are significantly computationally less efficient than volume-discretization methods (finite element method, finite difference method, finite volume method). Boundary element formulations typically give rise to fully populated matrices. This means that the storage requirements and computational time will tend to grow according to the square of the problem size. By contrast, finite element matrices are typically banded (elements are only locally connected) and the storage requirements for the system matrices typically grow linearly with the problem size. Compression techniques (e.g. multipole expansions or adaptive cross approximation/hierarchical matrices) can be used to ameliorate these problems, though at the cost of added complexity and with a success-rate that depends heavily on the nature and geometry of the problem.

BEM is applicable to problems for which Green’s functions can be calculated. These usually involve fields in linear homogeneous media. This places considerable restrictions on the range and generality of problems suitable for boundary elements. Nonlinearities can be included in the formulation, although they generally introduce volume integrals which require the volume to be discretized before solution, removing an oft-cited advantage of BEM.The method of moments was introduced by Pafnuty Chebyshev in 1887. – Wikipedia

We include this rather technical explanation to indicate that all antenna assisted design software is an approximation based on calculation of minute portions of the total antenna. The antenna elements are divided into segments, and the NEC engine calculates against each segment (often based on the previous or connected segment).

4nec2 For Windows

4nec2 running with WINE on Linux

This application is more about the technical aspects of antenna design than user friendliness. It allows the use of several numerical calculation engines such as NEC2d, NEC2d extended, and NEC4d. You can even design and use your own calculation engine following the application programmer interface (API) outlined in the developer documentation.

As shown, 4nec2 displays the wire edit, and calculation output in separate windows. Despite this [relative] user unfriendliness, this is a more than capable application for the antenna designer. Like the EZNEC application, 4nec2 (as the name implies) uses the NEC engines for calculation. The numeric electromagnetic coding (NEC) engine is a popular antenna modeling system for wire, geometric, and surface antennas. It was originally written in FORTRAN in the 1970s by Gerald Burke and Andrew Poggio of the Lawrence Livermore National Laboratory. The code was made publicly available for general use and has subsequently been distributed for many computer platforms from mainframes to PCs.

4nec2 is several times faster than EZNEC on simple designs, and frequency sweeps on designs such as our example. The antenna description is a more familiar NEC file... a legacy format from the Fortran days of early NEC software mentioned above.

However, it should be recalled that each of the highlighted applications uses a different method to calculate the output. EZNEC uses the NEC 2 and NEC 3 methods. The 4nec2 application can use the NEC2d, NEC2d Extended, and NEC4d methods. For this, and several other reasons, there will be differences in the results between EZNEC, MMANA-Gal Basic, and 4nec2.

It is recommended you do your own experimentation against the real world and see which fits your model better. Sadly, many new users opt for appearance and convenience rather than proven accuracy and repeatability.

Constructing The Model

So, we have an idea for an antenna and we wish to model it on the computer. From this point on in our discussion, we will arbitrarily use the MMANA-Gal application to construct our model. It easily, and best illustrates, all the points we will be making in this discussion. Of course, the same model could be made in any of the programs shown here with slightly varying results.

Making the wire model

When modeling an antenna design, all modeling programs use a description file that tells the application what to calculate against. They may differ in the input methods, but all require the antenna to be described as a series of wires (even if it is constructed of pipe) connected together in a fix way.

The model is just that — a model. author AD5XJ

In our illustration, MMANA-Gal does this with a table of figures on the Geometry Tab (see the pictorial above.). The entry of figures in this tab should be familiar to anyone who has used a spreadsheet application. Each column represents different aspects of the antenna element(s). In our model, we have one element with two sections. So, there is only one line in the table that describes the antenna elements. All elements of an antenna model are described by X,Y, and Z coordinates. The X and Y coordinates are in the horizontal plane, and the Z coordinate is the vertical plane.

Our model is represented by a wire that is in the Y plane a given distance to either side of the center (Y=Ø). The minus indicates a distance in one direction, and a positive value is a distance in the opposite direction. Any Z value would position the elements above the antenna center position. To make the design simple we are using Z=Ø for the element description and adding additional height above ground when doing the calculations.

There are several things to note on this view. First the calculations are done with the dimensions in metric values. This is a characteristic of the NEC engine. Even if the user interface (e.g. EZNEC) can accept English measurements, they will be converted to Metric when calculating. In our model, the elements are only millimeters long. You should remember in our earlier discussion, size always matters when we are talking about antennas. Our design frequency is an arbitrary 300 MHz. You should also recall from our earlier discussion that resonate dipoles are usually ½ λ long. Calculating the total length of our antenna would look something like:

   300 / f(e.g.300 MHz) = 1 meter

This is one wavelength (1λ). Our dipole should be half that or ½λ(= .5 meters in our design). Each element segment should approximate one half of the dipole or ¼λ (or apprx. .25 meter = 250mm). As you can see environmental parameters have affected the theoretical length. Our actual calculation indicates a slightly shorter practical length of .2361 meters (236.1mm) due to proximity above ground.

Knowing that proximity to ground and frequency will affect what impedance our antenna will display at the feedpoint, changing any of these factors will dramatically change impedance. We have arbitrarily chosen a physical height of 12 meters above ground for our model.

The diameter of the element influences impedance as well – more so at higher frequencies than lower HF frequencies. In our model, we have used ¼ inch copper pipe for the elements (.25 in = 6.25mm / 2 to find radius of 3.125mm). You can find a good conversion calculator on the web at

The length makes physical construction measurements and tuning a matter of precision. An error of one millimeter could yield a very unexpected result. When thinking about the physical construction, methods of construction should include the ability to add and subtract length to elements for fine tuning.

If we use the CAD view window to look at the design view of our model, it does not appear any different than a wire antenna for frequencies much lower...until we examine the wire lengths shown in the box to the lower right of the view window. Our elements have a physical length of far less than one meter. In fact this one is only .472 meters total length. Less than half of one meter (.472 mm = 18.582 inches). Our model spans only 18 1/2 inches end to end.

The relatively small size and ease of construction are some of the attractive qualities of the VHF / UHF frequencies. You will also notice that our “wire” has a diameter of about ¼ inch. We view this with the knowledge that 25.4mm / inch and radius = 1/2 diameter. So, ( (25.4mm [per inch] / 4 = 6.35) / 2 = 3.175mm). The reasons for the large diameter should be apparent if you have read the previous lessons. But lets look at how well we did with the calculations.

In our previous lessons we were concerned about two things:

  1. the feedpoint impedance – R +jX and
  2. the resonate frequency

If our antenna is resonate (i.e. the “imaginary” value = +jX = Ø) then the “real” part should be the same as the characteristic impedance of our feedline.

So how do we know if our model has reached that goal? Observe the next illustration. This graph is of the calculation results of our input to the MMANA-Gal Basic wire description. We obtained the plot by clicking the Start button to get a calculation then the Plot button on the Calculation page. The graph has three legends, on the left the “real” part of the impedance, and on the right the “imaginary” values. At the bottom you will see a range of frequencies used to plot this graph.

You will notice the red “imaginary” value line crosses zero very near our design frequency of 300 MHz while the “real” value crosses that frequency at the same time with a value of about 72.2 ohms. This is a very graphic illustration of one of the principals laid out in earlier lessons. Without changing anything but the frequency, the feedpoint impedance makes a dramatic change. If this is confusing to you, review the lessons again until it becomes more clear.

Now we know that our model is resonate (the +jX value is zero at the design frequency) and the “real” part of the impedance is 72.2 ohms. We can match that with 75 ohm coax easily. What is the SWR since we know a impedance mismatch is one source of SWR?

The SWR tab of the Plots window will display the estimated SWR for the same range of frequencies as before. OK! This is more like what we are after. Within the narrow range of frequencies used for calculation, we have a SWR range of well below the 1.10:1 values. And at our design frequency, we have a 1.04:1 SWR. Any loss of signal using 75 ohm coax in this design will be negligible at this frequency (given the use of good quality coax like RG-214 or RG-6x). Notice that the frequency span is 4 MHz. Very broadband for this frequency given our choice of dimensions (i.e. use of 1/4 pipe instead of wire).

Could we use a balun to connect RG-8/U or LMR-400 to our antenna? Sure, but the mismatch would be much greater and the resulting SWR would be also. Not a desirable situation. Most baluns are constructed as 4:1 (200 ohms : 50 ohms) or 1:1 (50 ohms : 50 ohms) transformers. Doesn’t help much. We would need a 1.5:1 balun. The use of a coaxial match is likely since the ¼λ is inches instead of feet. A short length of higher impedance coax in line with our 50 ohm coax will transform the impedance for us.

The use of a traditional wire transformer balun is possible. They are available, but hard to find. There are homebrew instructions on the Internet if you want to make one for yourself (which is highly advisable for this model).

courtesy ARRL Antenna Book 20th Edition pp.18-5

A simpler, and more flexible, and effective solution, may be to use what is known as a stub match. A stub match is designed with a wire that forms a ½λ “U” shaped connection between the two halves of the antenna. Our 50 ohm coax is connected at the spot where the match stub presents a 50 ohm load. If you recall, in our previous lessons we presented the case of the “J–pole” antenna. It is unique in its use of the ¼λ stub as the bottom portion of the antenna. The coax is connected at the 50 ohm load point. Our diplole presents the same matching problem easily solved with such a device. However, instead of the stub having one side open as with the “J–pole”, we connect the other side of the stub to the second portion of our dipole as shown.

The last aspect of antenna design we want to look at is the pattern of radiation our antenna is expected to have. To see what has been calculated, click on the Far–Field tab to see what to expect from our design. Shown here is the calculated far–field radiation values in the horizontal (azmuth) plane and in the vertical (elevation) plane.

This short tour is only the surface of what is capable with the software mentioned. If you are interested in further study using CAD software, we recommend:

Computerized Antenna Modeling
Continuing Education Online Course and accompanying student handbook
American Radio Relay League Publications Newington, CT

One word of caution to those of you who try to model antennas. The model is only as good as the data given it. It is possible to provide what looks good, but yield misleading results. Consult your Elmer before attempting to construct a physical device. Experienced Elmers know the difference and can help correct any apparent errors before you spend your hard earned dollars on construction.

You may find yourself doing repeated caculations and adjustments to various parameters of the antenna description to reach your goal. It is a procedure that taxes the patience and perseverance of the model maker.

The model is just that. It is a model. You can construct a precise physical duplicate of the model and when it is placed in a real world environment, it will display different values on an analyzer than calculated. That is because we can only estimate what it will be. Hopefully, the modeling software you used will be dependably accurate and not have significant differences. All computer modeling has that same flaw. Never expect perfect results. The CAD program will get you very close, but there is no substitute for actuality.

This model has been using MMANA-Gal Basic for our illustration. Does that mean that EZPAL is significantly different? Not at all. In fact EZPAL will need exactly the same parameters to describe the antenna as MMANA-Gal. The same is true for 4nec2. What is different is how the user interface provides for this input and the ultimate results offered by the model. For specifics on each CAD application, refer to the user documentation on the particular CAD program you wish to use.

Have fun designing and building your antenna.



Rev. 1.10 2018-03-14 AD5XJ