http://vk1od.net/antenna/G5RV/optimising.htm

And an article about feeding the G5RV at:

http://vk1od.net/antenna/G5RV/index.htm

And the EZNEC model is available for download at:

http://vk1od.net/antenna/G5RV/G5RV.EZ

One of the best courses was originally written by L.B.Cebik W4RNL for the ARRL Online Continuing Education program. It’s pretty much the only game in town at this level. If you go to the right university, you can take courses that will cover it in far more detail, getting into the mathematics and physics much more deeply. The book seems to be out-of-print at the moment. Amazon.com lists it for sale and you may be able to find a used copy. The ARRL Antenna Book also has a very good chapter on Antenna Modeling which is worth referring to.

As we start, you can refer to the 1st Cebik article which you can find at http://www.arrl.org/members-only/tis/info/pdf/0011034.pdf. I’ll also be discussing this in the AntModel antenna modeling discussion list. Hopefully, some people will participate.

My plans are to work through the articles, doing the models and explaining why I’m doing certain things. I look forward to some level of discussion about modeling as we go along.

What is Antenna Modeling

I don’t need to explain to anyone here about the differences between antenna models and model boats and planes, but it IS worth spending some time talking about mathematical modeling and some of the issues relevant to antenna modeling.

If you really want to understand the mathematics and physics behind antenna modeling, one of the classic places to start learning is John D. Kraus’ book Antennas which is the basis for many graduate courses. I learned from an earlier edition of this book during a course in Radio Astronomy. The mathematics us far too complicated for our purposes here, but it’s fascinating to work with if you like building mathematical models.

Mathematical modeling is about creating a model of a system using mathematics as a language. I first got fascinated in mathematical models when we were still working them on slide rules. With my first exposure to computers, I fell in love and went right to work building models. It’s important to understand that models are never exact. Even the best models are limited in some respect.

Consider the simple antenna model for a dipole antenna.

Believe it or not, this is a REAL mathematical model of a 1/2-wave dipole antenna, but how exact is this. The actual speed of light is

186,282.397 0512 miles/second

or approximately

983,568,960 feet/second

AND we know that the wavelength is related to the frequency by the formula

wavelength = speed of light/frequency (Hz)

if we change frequency to MHz (1,000,000 Hz), then

wavelength (feet) = 983.282 960/frequency (Mhz)

and so a half-wavelength would be approximately (I’m using =~ to say ‘approximately equals’)

983/(2 * freq) =~ 491.5/freq =~ 492/freq

Huh? Why 492? Why didn’t we get 468 which is what the thumb-rule model gives us? The number 468 isn’t arbitrary. It has good reasons for being the choice, let’s see if we can come up with something like this working with an antenna model and in the process, learn something about building antenna models.

Consider a propagation model built into a tool like VOACAP or any other tool that can be used to predict or analyze propagation conditions. Too many people seem to handle them as if they could be expected to make good predictions without thinking critically about the nature of models in general or the specific model in particular. At best, this is unwise, at worst, it can lead to serious consequences.

Models, ANY model, always has a number of assumptions in its construction. In most programs I’ve worked with, the assumptions aren’t stated anywhere. Even when you have access to the source code, you may not be able to piece together all of the assumptions made in building the model. For one thing, models are often constructed without any real regard for internal documentation about algorithms. For another, some people seem to be addicted to tricky programming or complicated ways of doing things.

Some years back as a grad student, I was handed such a model which had been built by other grad students and asked to get it running. I found that it had NEVER run successfully. It filled a whole card box and was written in FORTRAN. What a mess. It took me a while, but I finally got it rewritten and running.

My major point here is that I’ve recently had a conversation which I’ve had over and over again with someone who acted as if a computer model had to give them good answers and that they could simply accept what the computer was providing them without question. That’s never the case.

Whenever you’re working with a computer model, whether it’s to predict radio propagation, antenna patterns, telephone call center performance, or whatever, you have to use the model critically and understand as much as you can about it:

• Do you know what assumptions were made in building the model? ()
• What algorithms are used to do the critical computations? (Is this a solid algorithm for what you want to do? There are often more than one way to accomplish any given calculation)
• What units were used to build the model? (Remember the error in landing the spacecraft on Mars?)

This is just a starting point. You need to ask questions and critically think about the model you’re working with to determine whether the answers you’re getting are sensible. Even if you’re getting sensible answers, that might not prove that the program will continue to provide sensible answers under different conditions.

In this case, I’m going to model two wires connected together and fed at the connection point. However, rather than model it as one wire with a source in the center, I plan to rotate a bit around that center point, so I’ll model it with a split source between the two wires.

In actual fact, I’m not very concerned here with the accuracy of the calculation because the point of the exercise is to show that even a simple reorientation of the wires can change the antenna pattern in noticeable ways.

The Simple Dipole over perfect ground

Let’s start with a simple dipole. I’m going to make each leg out of #14 wire, 5 meters for each leg, and 10 meters above a perfect ground. I’ll run my tests at 14.2 Mhz (20 meter band) just for fun.

Here is the initial antenna:

1/2-wavelength Dipole Antenna

The detailed setup and the radiation pattern can be seen by clicking on the image below:

Now it starts to get interesting.

Simple dipole with one leg rotated up 45°

In order to rotate a leg up, I need to compute the end point coordinates for the leg. Right now, I have leg 1 going from (0,0,10) to (0,5,10) … in other words from X=0,Y=0, Z=10 (all in meters) to X=0,Y=5, Z=10. Leg 2 is the same except that we take it in the negative Y direction, so it goes from (0,0,10) to (0,-5,10). You can see that in the wire table above.

To rotate the leg up 90°, I can do this pretty easily since I’ll take the 5 meters off the Y coordinate and add it to the Z coordinate, so Leg 2 will then go from (0,0,10) to (0,0,15). This makes it look like this:

Dipole Leg rotated up 90°

The results from re-running the model with these coordinates can be found by clicking on the image below:

Pretty Simple really. SO how about 45°?

Simple dipole rotated 45°

Rotating 45°requires a bit more calculation.It’s simple enough if you know a little trigonometry or a little geometry.Let’sdo it geometrically.

If the three sides of aright triangle are SIDE1, SIDE2, and HYPOTENEUSE(the long side), then we know that

Since we’re rotating the leg up by 45°.SIDE1 and SIDE2 will be equal and HYPOTENEUSE will be 5 meters.So we have the simple equation to solve where we’ll let SIDE = SIDE1 = SIDE2:

So the new end point of the second leg will be 3.54 in the negative direction and 3.54 upwards, or (0,-3.54,13.54). The antenna looks like this now:

And the model results in this output:

—————– Message ——————————–

I replied (with some editing):

—————– Message ——————————–

Let’s take some time and play with the model segmentation and see what impact it has on the model. We’ll also try some of the sourcing options as well.

We’re going to take a look at a very simple vertical antenna in free space and use the features of EZNEC to add radials to the model. Note that the radiator is along the Z axis starting at the origin (0,0,0).

FIRST … I’ll add the single simplest radial I can to the model. in this case, I chose to add one along the Y axis from (0,0,0) to (0,50,0) or a 50 foot radial wire.

In the WIRES window, I can now use the ‘CREATE’ menu item and select ‘RADIALS’

This bring up the ‘CREATE RADIALS’ window. I get to specify the prototype group. In this case, I’ve selected just a single wire, but I could have had more than one. I also tell the program what the TOTAL number of radials is.

IMPORTANT: We’re entering the total number of radials, not the number of new ones we want to add. I’ve seen a number of students make this mistake thinking they are entering the number of radials to generate and not the total number that will be present when generated.

When I click OK, the program automatically creates additional radials to match the prototype spread out around the zero point. With 4 radials, this is pretty simple since each now goes along an axis:

The antenna now looks like this:

If I’d said that I wanted 8 total radials, I would have gotten this wire table:

You’ll notice that it automatically adjusts coordinates so that the radials come out properly. If you computed the length of each radial (numbers 3, 5, 7, & 9), you’ll find they’re all 50 feet long. So the radial system is now spread out around the antenna like this:

An inverted L works against a ground circuit. You COULD put up the antenna and just pound a rod into the ground to complete the circuit, but for most of us, bare ground is a pretty poor conductor. We add a ground radial system in order to provide a good return path and minimize ground losses.

Ground losses reduce the efficiency of our antenna, in other words, power is lost to heating in the ground part of the antenna circuit. We have a problem here though. The antenna we’re modeling actually has buried radials (there are some pieces above ground, but the bulk consists of below ground wires. OOPS … NEC2 doesn’t handle wires below the surface of the ground.

NEC4 can handle buried radials and computer the results from using them properly, but NEC4 costs around $1000 to be licensed to use it, not including the front end for it. That takes it out of the range for most of us, so how can we come up with an acceptable model? Simple, we add another approximation! We’ll start with a very simple radial pattern and then experiment with it to see how sensitive our results are to changes in the radial pattern. If, for example, we change the number of radials or their length or their conductivity and we get no change in measurable parameters of the antenna, then we can be pretty sure that our model is ‘good enough’ to use.

FIRST … I added a simple radial pattern to see it’s effect. In this case, I modeled 8 50-foot wires spaced evenly around the feed point



Here is the wires table …


This is the 3D and elevation pattern which results

As you can see, results are approximately what we saw before. In the next post, we’ll take some time to look at actually creating the radials in the software.

NOTE: If you cannot read the figures, you should be able to see the larger ones by RIGHT CLICKING on the image and choosing VIEW IMAGE. If that doesn’t work, try going to the images directly:

Antenna & Radials
Wire Table
Elevation Pattern

You can see some of what’s going on, but the takeoff angle seems to be pretty broad. HOWEVER we’re not done with this yet. The model is far from complete, so we’re not ready to rely on the output. Right now, consider what we’re seeing a qualitative and not quantitative representation of our antenna’s performance. Are we getting the general pattern right? Once we get the actual model correct, the numbers will mean something, but again not very much. They’ll be pretty good, but unaccounted for effects might also mean that the numbers aren’t accurate.

With all of our updates, we can now rerun the model ( which remember is still incomplete) and get this for the maximum azimuthal pattern:

As you can see, it shows the main lobe centered on 20 degrees of elevation. That’s consistent with my own experience for vertical radiators like this, so I’m sure it’s somewhere close to the actual take off angle.

Next, let’s take a look at what happens when we add a radial system to this model.