The reading material I’ll be referring to is L.B. Cebik’s QST article series ‘A Beginner’s Guide to Modeling with NEC’. I plan to discuss a number of antenna modeling programs here, so this will go on considerably longer than the original articles.
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.
length = 468/wavelength
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
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.
December 28, 2009 2:30 pm
I first got interested in models and modeling when I was at University. I learned to build them mathematically, to do them by hand, and I learned to build them using a computer. I did a lot of modeling for departments as a way to support myself while at school. Since leaving school, I’ve built systems models, propagation models, antenna models, and many more. What always disturbs me is how little people seem to understand about models and modeling.
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.
A question I often have to deal with is just how important the geometry is to the antenna radiation pattern. Most people with some experience know that it IS important, but they don’t know just how important. Let’s consider a very simple model.
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
SIDE1² +SIDE2² = HYPOTENEUSE²
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:
2 x SIDE² = HYPOTENEUSE²
SIDE = √( HYPOTENEUSE² / 2 )
SIDE = √( 5² / 2 )
SIDE = √( 25 / 2 )
SIDE = √( 12.5 )
SIDE = 3.54
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:
Happy Square Root Day!
Today is 3/3/9 … 3 X 3 = 9 … √9 = 3
Square Root day and other mathematically oriented dates happen occasionally. There was 2/2/4 and there will be 4/4/16 coming up and more through the end of the century. There’s even a contest associated with the day run by a teacher in Redwood City with a prize of $339 to the winner.
Square Root day (and similar mathematically oriented dates like π (Pi) day - 3/14) are primarily of interested to mathematicians, but math is so important to Antenna Modeling, that we should remember on a day like this that knowing your mathematical tools is important for good modeling.
I’m finally back online and able to post again, so I’ll be starting again in the next several days as I catch up with things. What amazes me most while I’ve been offline is the volume of spam posts there have been to the blog. So many attempts to get something posted! All of the attempts were so obvious, yet they keep coming in. I sometimes wonder why, but I’m sure I know. It doesn’t require any effort. Adding one posting address to a list and everything else is automatic. What a waste.
February 12, 2009 11:14 am
In responding to a recent question, I spent some time thinking about the objectives in building an antenna system. Unless you’re just playing around (which of course is its own objective) you probably have some reason to put up the antenna. When making decisions about your antenna system, you need to understand these reasons.
|… What is it you are interested in doing? Operating on 160 meters is mentioned, but are you trying for DXCC or chatting with friends or participating in nets or what? How do you intend to use the antenna? Who are you hoping to talk to?
The reason for all the questions is that building an antenna is an exercise in optimization. We need to know what we’re optimizing for or we don’t know what tradeoffs to make. For example, if you want to use an antenna to work DX from many directions, you might want to work towards a reasonably omni-directional pattern which the major lobe centered at a relatively low angle. If your goal is to participate in regional nets you may want to emphasize NVIS if the coverage is appropriate.
The questions concern more than just the antenna, but also propagation. If you launch a signal what will it take to get it where you want?
The most frequent cause of antenna failure is not technical, it’s not knowing what you want the antenna to do when you put it up. Many hams buy a dipole or a vertical or some other antenna just to ‘get on the air’. That’s fine in and of itself if that’s all you want and if you don’t care who you talk to. However, if you have a reason like attempting a DXCC or some other award, or contesting, or something else, you need to know what it is or you’re likely to put up an inappropriate antenna.
No antenna does everything, but some antennas are more general purpose than others. When you know what you want to do with it, you’ll know what antenna to put up.
February 10, 2009 9:30 am
I’ve created a new menu item above called ‘Downloads’ where I’ve placed all of the files uploaded to the AntModel group by Tom Holden VE3MEO in his investigation of the Miracle Whip. I’ll add more structure to the area and more files to download after things get settled with my move.
February 5, 2009 11:34 am
We’re in the process of packing and moving right now (I expect to actually move in about a week), so while I’ll try to post some updates during that time, problems with Internet access and such will likely cause difficulty getting online. I’ll be picking up again for sure once we’re settled in our new location.
We had a question posted to the Antenna Modeling group which presents an interesting modeling problem.
—————– Message ——————————–
I am using EZNEC+ 4.0 and I am trying to model the effect of
increasing the spacing between the inside ends of a simple split dipole.
I can’t figure out how to place the source so it feeds the first
segment of each of the inside ends of the two wires that constitute
the dipole. I thought this was what a split source was, but after
trying that and reading the help file, I see I had that all wrong.
Is there a way to do this?
I replied (with some editing):
—————– Message ——————————–
|With the NEC2 engine, there are only approximations for this instance. You can do four things:
- Put a source on each segment - which puts it always in the middle of the segment
- Use a split source - which does the same for you except that it assumes that the two legs are connected.
- Put a short wire between the two dipole wires and put the source on that wire. The source will be in the middle of this added wire.
- Make the number of segments high enough that the sources are very close to the actual wire end. You DO have to make sure that you don’t make them TOO short. Some recommendations suggest that segments should be at least 4 times the radius of the wire used.
NONE of the options does precisely what you want, but you should be able to get some feeling for the impact. The biggest problem to me (beyond NEC2’s placement of the source) is that the individual segments are likely to be large enough to mask the impact of separating the two legs of the dipole.
Remember, the whole thing is an approximation to the solution of the
integral equations governing the creation of the radiation field. The
assumptions are good in general for most large scale antenna problems, but the effect of changing the gap might very well differ from the calculation results because the scale of the change is too small.
One other possibility is to model the antenna fed by a balanced feed line from a source at a distance from the antenna. Even that’s not guaranteed to give you good answers, but they should be comparable.
What you might try is use several of these options and compare the results. If you try option 4, try increasing the number of segments and running the model at smaller and smaller segment sizes and see what happens to the solution. Does it converge? At some point does making the segments smaller lead to a divergence in the results?
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.