EZNEC Primer Introduction: This document was written to cover the very basic functions of EZNEC. It's primarily geared to the use of EZNEC demo programs, specifically the Version 5 demo. While more elaborate antennas than those discussed here can be modeled (and the program will run them), on very complex antennas, the restricted number of segments in the demo version will most likely result in highly inaccurate figures for gain and source impedance. This primer will cover only the very basics of antenna modeling. Several texts are available from the ARRL or the Antennex web site (www.antennex.com) that go into far more detail. The ARRL has a basic text (and an on-line course), while the Antennex site has both basic and intermediate texts available. Basics: Most modeling programs are based on one of two 'cores' (also referred to as engines) that were developed over the past 25 or so years. The first iteration of NEC (Numerical Electromagnetics Code) was written in the early 80s to replace the AMP (Antenna Modeling Program). The program was originally written in Fortran to run on the mainframe computers of the day. As the program was too large to run on the typical PC, a smaller version of the analysis software was written and compiled using a BASIC compiler. This 'core,' named MININEC, was severely restricted in terms of antenna complexity, when compared to NEC, but produced adequate results for basic antennas when run on home computers. Through the years, improvements were made to both cores. The NEC core has remained the most standard (it was written by Lawrence Livermore National Laboratory (LLNL) personnel), while MININEC has undergone more field modifications. Many of the points discussed here will apply to all NEC-based programs. Unless specifically mentioned, do not assume that MININEC programs follow the same constraints (one popular MININEC based program is MMANA-GAL, by Macoto Mori, JE3HHT). This document will be directed only to the workings of EZNEC, an application written by Roy Lewallen, W7EL, to utilize the NEC core. EZNEC, in and of itself, serves as a conduit to pass information to the NEC core. EZNEC varies from some other programs in that Roy's incorporated a version of NEC directly into the application. All versions of EZNEC, with the exception of Pro 4, use the NEC-2 Engine, the latest public domain version. NEC-4 is available, for a fee, from LLNL. Models: 15-meter dipole The NEC core is written to analyze thin wire antennas in a variety of environments. While the core refers to all antenna elements as 'wires,' a wire might be a ½ piece of aluminum tubing. The term 'thin' refers to the long aspect ratio (length to width) of the element. It doesn't literally refer to a specific diameter of wire. To illustrate the way the EZNEC (and the NEC core) works, we'll look at a simple antenna.
Open the file '21 MHz dipole.' This is a model of a 15-meter dipole with a design frequency of 21.275. The model hasn't been optimized. It was made using the standard formula of 468/f to get the total length of the antenna. If you click on the wires tab in the main window, you'll see the coordinates of the antenna wire (in this case it truly is a wire). The antenna stretches along the Y axis, from -10.99 to 10.99 feet, and is 30 feet in height. Not an unreasonable antenna. You'll also notice that the antenna's made from #14 wire, and we've assigned it a dielectric constant of 1, with a thickness of 0 (basically a dielectric constant of free space or dry air, and no thickness, so we're using uninsulated wire). When entering wire diameters, you can either specify a measurement, or use the proper AWG preceded by the #. We've divided the antenna into 19 segments. The way the NEC core makes calculations is by taking the antenna you've broken down into wires, and using the segments you've defined on those wires to calculate the current on those antenna pieces. For calculation purposes, NEC cores place currents at the center of segments. An odd number of segments must be used to put the source at the exact center of the antenna. (Note: MININEC uses 'pulses' at segment junctions, and an even number of segments need to be used to place the source (feedpoint) at the center in a MININEC based program.) If you look at the parameters of the model in the EZNEC main menu, you'll notice a few things. First, under Ground Type, we have 'free space' selected. Our 30 foot height doesn't matter much in free space (there's no ground plane to influence the antenna pattern), but will become important shortly. Second, click on the source button. A source is what the NEC core calls the feedpoint. In this case we're feeding the antenna at its center, and the program shows that the source is indeed located 50% from end 1 of our only wire. Don't worry that the dipole is a single wire with no break in the middle. The break will be assumed by the placement of the source. We've got wire loss set to zero. While most antennas aren't made from superconducting material, this was done to show the effects of the ground, etc. on the antenna, ignoring any effects of antenna material. Let's check the impedance of the antenna. In the first column, there's a button labeled 'Src Dat' for Source Data. Click there. You should get something similar to this (Note: The processor in your computer might have a small effect on the way things are calculated, and you might see slight discrepancies in the trailing decimal places, these are operationally insignificant): EZNEC Demo ver. 5.0 21 MHz Dipole 3/22/2008 9:36:36 PM --------------- SOURCE DATA --------------- Frequency = 21.275 MHz Source 1 Voltage = 1 V at 0.0 deg. Current = 0.0136 A at 22.44 deg.
Impedance = 67.97 - J 28.07 ohms Power = 0.01257 watts SWR (50 ohm system) = 1.758 (75 ohm system) = 1.496 The important thing here is the impedance. It's 67.97 - J 28.07 ohms. The antenna's a bit too short, based on the reactive component of it's impedance being negative (capacitive). At this point, if you click on 'View Ant' in the first column, you can look at the antenna as modeled. The pink line is the current magnitude, produced when you ran the source impedance. You can turn the view, center, zoom, etc. If you zoom in too far, you'll have to click the 'center antenna' button to bring the antenna back into view. I modified the current antenna to be more resonant on the design frequency (resonance in this document will be defined as a reactive impedance <1 Ohm). Open the file '21 MHz Dipole resonant' and click on the 'wires' tab. You'll notice that in doing the modification, I switched the units to inches. You can switch back and forth between units using the 'other' pull-down when in wires editing mode. If you exit wires and click on 'Src Dat' you should get something similar to this: EZNEC Demo ver. 5.0 21 MHz Dipole 3/22/2008 10:02:43 PM --------------- SOURCE DATA --------------- Frequency = 21.275 MHz Source 1 Voltage = 1 V at 0.0 deg. Current = 0.01388 A at 0.1 deg. Impedance = 72.03 - J 0.1292 ohms Power = 0.01388 watts SWR (50 ohm system) = 1.441 (75 ohm system) = 1.041 The antenna now shows very little reactive impedance, and is resonant. The impedance of a half-wavelength dipole in free space is typically given as 73 Ohms. Why does ours vary? The theoretical impedance often cited is for an infinitely thin, lossless conductor. We've used a lossless conductor, but ours isn't infinitely thin it's 14 AWG wire. In the main window, click on 'Plot Type' and change the value to 3D. Now click on the button labeled 'FF Plot.' You should get something similar to that shown in figure 1. This is the free space pattern of a dipole antenna. The radiation pattern is off the sides of the antenna. The 'dimples' observed in the figure occur at the antenna's ends. Close the 3D plot and change the plot type to Azimuth. Make sure the elevation angle (the button right under plot type) is set to 0 degrees, and click on FF Plot. A plot similar to that shown in figure 2 should now be shown. This is an E-field plot of the dipole in free space, showing the gain at the textbook value of 2.14 dbi.
Figure 2 Figure 1
This is all well and good, but a dipole in free space is theoretical. Open the file '21 MHz dipole over ground.' The only difference with this model is that I've clicked on the 'Ground Type' button on the main screen, and selected a Real, High Accuracy ground. Click on Src Dat again to check the impedance of the antenna. You'll see that with the antenna at ~0.65 wavelengths over a real ground, the impedance has changed some from free space. If the plot type isn't set as 3D, change it, and then click on FF Plot. The plot should look like that shown in figure 3. While looking at the 3D plot, you can click on Azimuth or Elevation Slice and view the respective 2D slices on the 3D plot. The program will tell you the angle of maximum radiation. Note that for this antenna, maximum radiation occurs at an azimuthal angle of 0 degrees (along the X-axis) and at an elevation angle of 20 degrees (resolution is limited to 5 degrees in 3D plots, but may be changed by clicking the 'Step Size' button on the main screen). Figure 3 Close the 3D plot and change the plot type to elevation using the main screen's 'Plot Type' button. Make sure the azimuthal angle (the button just under plot type) is set to 0 degrees, and click FF Plot. You should get something similar to figure 4. Here you'll see that the maximum radiation angle is actually 21 degrees (1 degree resolution is the default for elevation plots, but may be changed on the main screen). To view the azimuthal pattern, change the plot type to Azimuth, and select an elevation angle of 21 degrees (the angle of maximum radiation). The resulting plot should resemble that shown in figure 5.
Figure 4 Figure 5 Notice the gain figure for the dipole over real ground. Ground interactions cause it to be significantly higher than that of the dipole in free space.
So far our look at this antenna's only focused on the feedpoint of the antenna itself. Most antennas require some sort of feedline to connect them to a transceiver. EZNEC provides a method of simulating feedlines and their losses and impedance transformation properties. Open the file '21 MHz Dipole with coax.' Next to the 'Transmission Lines' button you'll notice that the program indicates we have a single transmission line. Click on the Transmission Line button to open the editing window. The transmission line we've added is 100 feet of coax with a velocity factor of 0.68, and a loss of 2 db at 28 MHz (obviously, these can be tailored to fit the specifications of your coax). It's connected to wire 1 (our dipole) at the center, and the other end is connected to a virtual wire, V1 (virtual wires act like real wires but do not interact with the antenna and can't influence patterns). If you click on the 'Source' button, you'll notice that I've moved the source from the center of the antenna onto the virtual wire. Using the 'Src Dat' button, we can verify that the impedance has been slightly transformed by adding the coax. Clicking on the various buttons to re-generate the patterns we examined above, we can see that the program has taken coax loss into account and modified gain figures accordingly. G5RV The antenna we call a G5RV was popularized by L. Varney, G5RV (SK) in the 1950's. Varney's design modified the matching section of a previous incarnation, and also allowed for a coax feed (80 Ohm, as used in Britain at the time) from the shack. The basic design consisted of a 102-foot flat top (3 half-waves on 20-meters) center fed with a 34 foot, 450 Ohm impedance transforming piece of open transmission line. Many modifications have been made to the original design, some well conceived, others less so. Let's look at one well thought out example, Bill Orr's (W6SAI -SK) version of the ZS6BKW version of the G5RV (see The W6SAI HF Antenna Handbook, 1996, CQ Communications for construction details). The Orr version uses a 92'6 flat top and a 37'3 300 Ohm (velocity factor 0.82) matching section. RG-58 coax is used to feed the antenna. Open the file 'G5RV Demo.' A segmentation warning should appear because the EZNEC demo version is limited to 20 segments. This means that with the maximum number of segments used, they're slightly shorter than ideal (10 20 segments per wavelength are recommended). Note that 19 segments are used here, an odd number, in order to keep the feedpoint exactly in the center. Our antenna isn't a complex one, and the segmentation issue shouldn't impact our results much. Close the warning (a 'pay' version of EZNEC would allow you to have the program fix the segmentation issues). Here we find the flat top has been constructed at an elevation of 50 feet. Click on the wires tab and note that the antenna's been constructed on the Y-axis, with the X-axis at its center. If you click 'View Ant' on the main window you can verify that this is the case. Check the source impedance (Src Dat) and you'll find it's highly reactive (my computer says 115.1 - J 553.4 ohms). What happens if we add in the 300 Ohm matching section? Open the file 'G5RV Demo with feedline' and again ignore (close) the segmentation warning. The data in the wires tab hasn't changed, but a feedline has been added. Click on the 'Trans
Lines' tab to view the feedline. Here a 300 Ohm feedline's been added to the center of our wire. The feedline is 37.25' long, with a velocity factor of 0.82. Since twin lead isn't very lossy, no loss data was entered. Note that again we've used a virtual wire to terminate the end of the feedline not attached to the antenna. The source has also been moved off the antenna and onto the virtual wire at the end of the feedline. If you check the source data, you'll find that the antenna's impedance is now a more modest 25.99 - J 43.89 ohms, and the ~3.7:1 SWR could easily be handled with an antenna tuner. Before we look at the SWR on other bands, or even the whole 20-meter band, let's finish the antenna. While it shouldn't change much, let's add in our 50 Ohm feedline, taking into account losses. The values we use will be somewhat arbitrary (but realistic) in order to illustrate what happens in typical installations. Open the file 'G5RV Demo Done' and again close the segmentation warning. You'll now notice that there are 2 transmission lines. The first is the one discussed above. The second is an 80-foot piece of RG-58 with a velocity factor of 0.66 and 1 db of loss at 14 MHz. The coax runs from our first virtual wire (V1) to a second virtual wire (V2) which now is the location of our source. If you check the source data you'll find that we're now looking at an impedance of 27.63 + J 31.85 ohms. With a resulting SWR of ~2.7:1, the antenna shows promise. So far we've only looked at the antenna's impedance at one frequency. We've done nothing with regard to pattern, and haven't even determined if this version of the G5RV is a respectable multi-band performer. Before we check a few patterns, let's see if it's even going to work on multiple bands, or even all of 20-meters. Open the SWR graph function by clicking on the 'SWR' button. Enter 14.0 MHz for the start frequency, and 14.35 MHz for the stop frequency, and use a frequency step of 0.05 MHz. This will show the SWR of the antenna across the entire 20-meter amateur band. Click on 'run' and a graph like that shown in Figure 5 should appear. Note that you can use your arrow keys to move the green dot around on the graph. When you do, the data will update to the frequency of the dot. Also note that the SWR is very respectable. At the high end of the band, the antenna could probably be used without a tuner over the entire General Phone segment. Plots were discussed in the section on dipoles, so no detail will be provided here. I will make one cautionary note that the G5RV is not a simple dipole, and has a very different pattern. On 20 meters, the radiation pattern is 6-lobed, as shown in figure 6. If you're looking at elevation plots of antennas with unknown azimuthal patterns, but very careful to select an angle with a lobe rather than a null. If you make a mistake, you might think the performance of your antenna is like that shown in figure 7 (the G5RV at 30 degrees azimuth) rather than figure 8 (the same antenna at 0 degrees azimuth). Let's look at 40-meter SWR performance. Open the SWR box, but this time use 7.0 and 7.3 MHz as the start and stop frequencies. You can re-use 0.05 MHz as the step. Run the sweep, and you should get an SWR graph like that in figure 9 (data omitted on my plot). You can now repeat the plots on 40-meters, and do the same for SWR and patterns on any other frequency you desire.
Figure 5 Figure 6
Figure 7 Figure 8 Figure 9
Summary: This document has stepped through only a few of the basic functions of EZNEC. Through the use of the Loads, Transformers, and L-networks functions, entire antenna systems can be modeled and evaluated. There are several constraints that need to be adhered to when using NEC or inaccurate results may result (the program will dutifully report the results without indication that they may be in error). These include, but are not limited, to the following recommendations: Use 10 to 20 segments per wavelength. Join wires only at their ends (with identical coordinates). Segment length-to-diameter ratio should be at least 4:1. Avoid closely spaced wires of dissimilar diameters. Avoid angular junctions of dissimilar diameter wires. Separate parallel or crossing wires by several diameters. The 'Help' section of EZNEC is very well written and should be consulted often when beginning to model antennas. This work is licensed under the Creative Commons Attribution 3.0 United States License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/us/ or send a letter to Creative Commons, 171 Second Street, Suite 300, San Francisco, California, 94105, USA.