Simple Vertical Antenna Theory

This page starts with an introduction about vertical antennas with buried radials. When you are done here, (or now, if you want to ) you can jump to . . .

Learn about underground radials. You might be suprised to know this.
Simple SWR Theory.. Not difficult to understand.
Some Vert. antenna noise theory.. From W8JI's serious lab.
Skip the theory and go to the conclusions. You can just go to the answers.
Start here.
Introduction to Vertical Antennas with buried Radials.
In a perfect world, a vertical antenna would be exactly one quarter wavelength long and have a ground system that has NO resistance. Natural laws have determined that this antenna would have 36 Ohms of "radiation" resistance, which means that the vertical conductor will act as a 36 Ohm resistor even though a DC resistance measurement reads practically zero Ohms.
The purpose of this discussion is to explain both "quarter wavelength" and "ground".
First, lets do "quarter wavelength".
If you are one of those who can not remember a darn thing about your high school algebra, fear not. I will do all the math and I will be happy if you just nod your head and say things like " That is what I thought.", or "I knew that", or "Sure, that makes sense." All you really need to do is to remember the conclusion of the discussion, and I will make that clear by using big or dark words.
The formula for finding the length of a quarter wave vertical wire (which is the vertical element of a vertical antenna) is...
Length = 234 / Frequency ( in MegaHertz)
An example for 40 Meters :
The center of the band is 7.150 MHz so that is the frequency to use in the formula.
Length = 234 / 7.150 = 32.7272 Feet.
OK, you say, but what do I do with the .7272 feet? How do I convert that to inches? You can convert parts of a foot to inches by multiplying that part of a foot by 12, and then add the 32 feet later.
0.7272 times 12 = 8.72 inches. Adding the 32 feet back on gives an answer of 32 Feet and 8.72 Inches.( For those who are wondering about the .72 inches, that is almost exactly 3/4ths of an inch)(That is about 0.2% of the length and can be ignored in real life.)
Another example: The 2 meter band.
The center of the band is 146 MHz so that is the frequency to use in the formula.
Length = 234 / 146 = 1.602 Feet.
OK, you say, but what do I do with the .602 feet? How do I convert that to inches? You can convert parts of a foot to inches by multiplying that part of a foot by 12, and then add the 1 foot later.
0.602 times 12 = 7.23 inches. Adding the 1 foot back on gives an answer of 1 Foot and 7.23 Inches. If you would like to convert that 1 foot into inches, you get a total of ( 12 inches + 7.23 inches) = 19.23 inches.( For those who are wondering about the .23 inches, that is almost exactly 1/4th of an inch)(That is about 1.2% of the length and should not be ignored in real life.)
That is the end of the "quarter wavelength" part of this discussion. So far you should be able to use the formula to find the length of a wire that is one quarter wavelength long. This wire is the vertical element of your vertical antenna.
Next, lets talk about "ground".
There are two distinct different meanings of the word "ground". First, there is the connection at the base of the vertical element so electrons can flow into and out of the antenna. Second, there is the requirement for a large area under the vertical radiator that will hold the electro-magnetic field down near the earth. This is the area from the antenna to many wavelengths out from the antenna that is probably in your neighbors field or clear down the block. The conductivity of what is out there is what keeps the signal down along the surface of the earth.
First, lets start with the flow of electrons in to and out of the vertical radiator. It is true that an antenna will radiate a RF field with a very poor ground. That RF field will be far weaker than it needs to be. The thing that creates the RF field is the flow of electrons up and down the vertical radiator. The more electrons that flow, the stronger the field. In order to get the greatest number of electrons to flow up and down the vertical radiator, you need to have a very low resistance storage area full of electrons. When a rig provides a voltage at the antenna, the lower the resistance, the more electrons will flow. The larger the storage area, the more electrons that can be forced up into and back down out of the vertical radiator.
Caution ..... Major controversy ahead.
Now I need to stop right here and warn you about the following information. The following information is one of the most controversial subjects ever discussed by amateur radio operators around the world. The only other subject that is full of incredible controversy is Standing Wave Ratio, or SWR, which I have written about later in this website, but not yet.
The controvery happens because amateurs have built vertical antennas with buried radials, and they have worked pretty well. The usual thought is that " since it works, I did it right." That is not the truth. It is possible that you could have done a much better job if you understood the theory of how a buried radial antenna works. I have a first hand example. Some years ago, I installed a buried radial vertical antenna for my friend Duane (SK). I used heavy copper braid for the radials and used two radials tuned for each band of operation. The antenna worked fine for years, even though I was unaware at that time that buried radials lose all their tuning when buried. I should have put down lots more and longer radials for a more efficient antenna.
So, why not use a large copper ground rod for the ground connection?
Ground rods work better than no ground at all, but even though they have a low resistance, they do not have much storage area for electrons. The ground rod is surrounded by dirt, which is a very poor conductor.
Try this experiment at home. Measure the resistance of the dirt or sod under the grass at your house. I did it at my house, and found that by keeping the ohmmeter probes at one inch apart, and stabbing them into the ground at various places around the house, I got from 1 MegOhm to 100 KOhms of resistance. That was with the probes at one inch apart in the Pacific Northwest where it rains. Dirt seems to be a pretty good insulator, and not a conductor at all.
Ground rods do not help control the shape of the electro-magnetic field that comes from your vertical antenna. You need a large conductive area under the antenna for that. Radial wires that leave the base of the vertical antenna are a wonderful way to provide a ground system. These radial wires will provide the needed electrons to move up and down the antenna, but they do not help hold the signal down along the surface of the earth. Radials are not long enough to do that. The questions are ....
How many radials? ,
How long should they be?, and
Should they be underground or elevated?
These questions are very tricky and many amateurs have a poor understanding on what is needed. The internet is full of different information from different sources. Lots of emotion and arguments have resulted from the lack for good information.

We begin with underground radials.

I will show you a graph of the number of radials and the length of the radials that should be quite acceptable. I found it at the STEPPIR website while researching this topic. It was created by Brian Edwards N2MF and used here with his permission. This graph was originally shown in the June 1985 QST article "Radial Systems for Ground Mounted Vertical Antennas."www.steppir.com/pdf/radial%20systems%20for%20vertical%20antennas.pdf
All these radials may seem mildly exccesive, but a good ground is an essential part of a vertical antenna. It is not possible to have too many radials.
The vertical radiator and the radials in the ground form a giant capacitor which supplies a "flow" of electrons in the antenna system, and it helps keep the Take-Off angle as low as possible. This is essential.
Are you ready for another graph? This one comes from that same Stepper website as above. This one says that the more radials you have, the efficiency goes up. That is a very good thing. I will discuss "efficiency" in a moment.
The question of "efficiency" in a vertical antenna.
The "efficiency" of this antenna can be calculated by a simple algebra formula, but if you are one of those who can not remember a darn thing about your high school algebra, fear not. Remember that I will do all the math and I will be happy if you just nod your head and say things like " That is what I thought.", or "I knew that", or "Sure, that makes sense." All you really need to do is to remember the conclusion of the discussion, and I will make that clear.
The efficiency is found by dividing the radiation resistance by the sum of all the resistances in the antenna and ground. Then this number is multiplied by 100 so efficiency can be calculated in percent.
Efficiency = Radiation resistance * 100 / sum of all the resistances in the antenna and ground.
In the case of the perfect vertical antenna, where all the ground resistances are zero Ohms,the formula will look like this...
Efficiency = 36 Ohms *100 / 36 Ohms + 0 Ohms = 100 percent
A perfect antenna should have an efficiency of 100 % shouldn't it? 100% efficiency means that 100 % of your output power is going into the air where it should be going, and it is not being used to heat the earth. The point of this discussion is that the only way you can have a perfect antenna system with 100 % efficiency is to have a perfect ground system.
Do not skimp on your ground system. Using both of those graphs, to get 80% efficiency from your vertical quarter wave antenna, you need about 55 radials that are about 0.288 wave lengths long. Using these numbers, an 80 meter vertical will need over 4000 feet of wire for the 55 radials that are about 74 feet long. That is a whole lot of wire.
Vertical antennas that have grounded radials are not cheap to build if you want one that is efficient and has a low Take-Off angle. Both efficiency and a low Take-Off angle are the key to having a FANTASTIC antenna. A good quarter wave vertical with buried radials can often out perform a dipole that is way up in the air.

A little about SWR.My world is not perfect, and neither are my antennas, so now it is important to discuss what can go wrong.

No discussion about antennas would be complete without a word or two about SWR. The Standing Wave Ratio will be explained somewhere much later in this site, but I suspect that you have the idea from somewhere that the SWR must be 1:1 for a perfect antenna. Actually, that is not true. It is true that a low SWR is good, but many radio amateurs attempt to match their perfect antennas (with a 36 Ohm impedance) to a high quality coax that has an impedance of 50 Ohms and expect to get an SWR of 1:1. That just should not happen. The problem here is that most rigs and most coax are not manufactured for a 36 Ohm impedance. There should be some manufacturer somewhere in the world who makes a rig with 36 Ohms, but I do not know of any. I only know of the ones who use 50 Ohms, and that does not match a vertical antenna.

The formula for non-reactive SWR has two possible formulas. Choose the one that gives you an answer that is greater than 1.

SWR = Z load / Z coax
or
SWR = Z coax / Z load

Lets find the SWR of a 50 Ohm coax hooked to a 36 Ohm vertical antenna. I will use both of the formulas to show you what happens if you choose the wrong one.

SWR = Z load / Z coax = 36 Ohms / 50 Ohms = 0.72, which is less than 1.

SWR = Z coax / Z load = 50 Ohms / 36 Ohms = 1.38, which is more than 1.

In this example, you should choose the answer which is greater than 1, which is 1.38. This will become 1.38 to 1 or can be written 1.38:1. 1.38 is almost 1.4, so I will say that this SWR is 1.4 to 1. The conclusion here is that a perfect vertical antenna with a perfect ground connected to a perfect 50 Ohm coax will have a SWR of 1.4 to 1.

This is a critical idea. If your vertical antenna has a SWR less than 1.4 to 1, or more than 1.4 to 1, something is not perfect. A 1:1 SWR is not a good sign.

So, why is a 1:1 SWR not a good sign? To get a 1:1 SWR means that the antenna system has 50 Ohms of resistance and is being used with 50 Ohm coax. The radiation resistance is suposed to be 36 Ohms with a vertical antenna, not 50 Ohms. Somehow the antenna system has gained an extra 14 Ohms. (50 Ohms minus 36 Ohms equals 14 Ohms.) Where can an antenna system get an extra 14 Ohms? The easiest way to increase the resistance of an antenna system is to have a bad connection or a bad solder joint. The next easiest way to get extra resistance in an antenna system is to have a poor ground system.

The efficiency of a vertical antenna system with extra resistance in it will be lower than a perfect system. Lets do the math again.

Efficiency = Radiation resistance * 100 / sum of all the resistances in the antenna and ground.Efficiency = 36 ohms * 100 / 50 Ohms = 72 %

This means that the 1:1 SWR antenna system is losing 28% of its power and transmitting only 72% of its power.

Just a little more math.....

Remember when we looked at both of those graphs, and found that 55 radials each 0.288 wavelengths long would give us 80% efficiency? You can use the 36 Ohms and the 80% to find out what the total resistance is in the whole system. You can use the formula for efficiency and turn it around (transpose it) to find that total resistance, then use that total resistance in the SWR formula.

Efficiency = 36 Ohms / the Total resistance . . . so, Total Resistance = 36 Ohms / 0.8 = 45 Ohms Calculating the SWR of an 80 % efficient antenna looks like this.....

50 Ohms / 45 Ohms = 1.11, or 1.11 : 1 SWR.That sure looks perfect, but it is only 80 percent efficient !

80 %? That really does not look good, but it is not as bad as it looks.

One more look at math.......What is 80% in Decibels?

dB = 10 times log 10 (power ratio)

where the power ratio is 0.8. (because 80% is equal to 0.8)

Decibels = -.969

The Decibel calculation of 80% efficiency turns out to be slightly less than 1 dB ! I think I can live with a 1 dB loss in my ground system.

This is a good place to put it all together.

Actually, you might want to know the value of efficiency VS. decibels so you can make a better estimation of how many radials you really need. This information comes from the same two graphs at the Stepper web site found on another page in this web site.

Efficiency | decibels | # of radials | wave length | SWR

90% | -.457 dB | 120 radials | 0.40 wl | 1.25 : 1
80 % | -.969 dB | 45 radials | 0.24 wl | 1.11 : 1
70 % | -1.54 dB | 22 radials | 0.16 wl | 1.02 : 1
60 % | -2.21 dB | 7 radials | 0.06 wl | 1.20 : 1
50 % | -3.01 dB | 4 radials |0.03 wl | 1.44 : 1
40 % | -3.97 dB | no info | no info | 1.8 : 1
30 % | -5.23 dB | no info | no info | 2.4 : 1
20 % | -6.99 dB | no info | no info | 3.6 :1
10 % | -10.0 dB | no info | no info | 7.2: 1

It is difficult to know if your antenna is really doing a good job from "on the air" reports from other amateurs. The following paragraph is an example of a standard automotive system on UHF orVHF.

You can see that at 50% efficiency an automotive 50 Watt transmitter will be putting out 25 Watts which beats any standard handheld transmitter at UHF or VHF. Using the formulas for efficiency and SWR as shown above, the SWR for a 50% efficient antenna is 1.44, which looks pretty good for an automobile system. While this system is not very good at all, the operator will possibly think that her/his system is doing fine because everyone says the signal gets into the repeater "full quieting".

I hope you can see that a poor antenna can do a OK job and the operator will never suspect that the antenna is not really doing all it can do. In fact, the operator is likely to think the antenna is quite good. This is where bad information gets its start and intelligent people get the wrong idea !

What about NOISE ! Are Vertical antennas noisy?

Yes, vertical antennas are noisy, but that is not a problem at all. It turns out that the earth will filter out some of the horizontally polarized noises (signals) that are generated around the world, so a horizontal antenna will not hear some of that energy, but the earth will also filter out some of the horizontally polarized ham radio signals. If you want to hear what is really out there, a vertical antenna is actually better than a horizontally polarized one.