Another way to look at Antennas

I am going to approach antennas from a different direction in this post. At least I think I am! 

I want to start with the assumption that I want as strong a transmitted signal that I can possibly get at one single place in the world.  Where?  Well let’s start with some place like Utah.  That would be a distance of approximately 1900 miles away. Real close to 3000 KM.  This thought process could be for anywhere. 

Next would be to decide which amateur band I want to use. Let’s start with 20 meters. 

Obviously power has a lot to do with signal strength. However the same antenna setup will work for 5 watts as well as 1500 watts. So power really does not need to be mentioned again as we want to concentrate on the antenna. Suffice it to say 1500 watts is 10 dB stronger than 150 watts.

Whatever antenna we use needs to be pointed in the right direction and in this case that is a heading of about 290 degrees. That’s the great circle bearing from me. This is important for any antenna except an omni directional vertical and we are definitely not going to use a vertical if we want a strong signal on 20 meters let alone the strongest possible signal! 

We will want to use a horizontally polarized antenna. We will definitely get more gain with a horizontal antenna. Regardless of which horizontal antenna we decide on it needs to be fairly high above the ground in terms of wavelength. At 20 meters one-half wavelength is about 33 feet and one wave length is about 66 feet. The height above the ground determines the elevation angle of the maximum radiation from the horizontal antenna. 

From any number of sources you can get this information. 

First of all we need to estimate the radiation angle we need. For one hop we would want a very low angle and for two hops it would not need to be so low.  The normal skip distance on 20 meters is frequently 1200 to 1500 miles and that equates to an elevation angle of about 15 degrees more or less depending on the height of the ionosphere. The angle for 1000 miles is about 30 degrees and that lends itself to a horizontal antenna at half wave high or 33 to 35 feet.

For a two hop situation the half-wave high antenna is great for distances around 2000 miles. These numbers are not etched is stone because the ionosphere is constantly changing and moving up and down. For our 3000 mile distance we might want around a 10 degree angle if we can get it.

At the end I will have charts the show angles vs distance for typical ionospheric heights. 

In general there will be a range of angles that are good for a horizontal antenna. 

The half-wave high antenna although centered on 30 degrees is considered to cover angles from 15 to 50 degrees. A horizontal antenna at 3/8 wave likewise covers 40 to 70 degree angles quite good. The 1/4 wave high antenna covers angles of 70 degrees and above quite good. These are optimum angles and I don’t mean to imply they don’t work at other angles but just less than you might want. 

A full wave high 20 meter antenna at 66 to 70 feet will be centered at 15 degrees and optimally cover angles of 7 to 23 degrees. It then has a null centered at 30 degrees. That null is significant or at least noticeable from about 25 to 40 degrees. 

So for our antenna height we would prefer a full wave in height to best cover the 10 degree angle for possibly one long hop or two 1500 mile hops. 

The difference in the half wave high and the full wave high antenna at an elevation angle of 10 degrees is just under 5 dB. It would be expected that the difference between two identical stations, the only difference being one antenna at 33 feet and the other at 66 feet, would be less than 1 S-unit. 

Now that we have a couple possible heights that are good, we need to think about the actual antenna. The standard to compare all antennas to is the high, straight, flat dipole. This is an easy antenna to construct and works great. Point it broadside to the desired direction and at a height of 33 or 66 feet ( really anywhere in between) and you have 7 to 8 dBi of gain to compare all other antennas against.

This following is a list of typical antennas with their gain at 10 degree elevation angle:

Dipole at 1/2 wave   1.35 dBi

Dipole at 1 wave high   6.24 dBi

Note: any half-wave straight wire, end fed or off center fed will be virtually identical to the half wave dipole at the same height.

Two element Yagi at 1/2 wave      5.35 dBi.   ( Dipole 1.35 plus 4 )

Two element Yagi at 66 feet         10.24 dBi.   (Dipole 6.24 plus 4)

Three element Yagi at 1/2 wave.    6.85 dBi.       ( 2el Yagi plus 1.5 )

Three element Yagi at 66 feet.       11.74 dBi.     (2 el Yagi plus 1.5)

Four element Yagi at 1/2 wave.     8.24  dBi.       ( 2 element Yagi plus 3)

Four element Yagi at 66 feet.         13.24 dBi.      (2 element Yagi plus 3 )

Eight element Yagi at 1/2 wave.      11.24  dBi.     (4 element Yagi plus 3)

Eight element Yagi at 66 feet.            16.24 dBi     (4 element Yagi plus 3 )

Two element broadside array consisting of two dipoles spaced 1/2 wave apart will give 3.5 dB over one such dipole. At half wave high that is 4.85 dBi and at 1 wave it is 9.74 dBi

All these gains follow the same pattern. Start with a dipole and add about 4 dB when it is doubled the first time and then add 3 dB each time the size is doubled. There is, however, a limit on how many times you can double the size and still get 3 dB of gain. A four element 20 meter Yagi has about a 26 foot bool and is a large antenna. So doubling that gives you a boom over 50 feet! Usually Yagis are stacked one over the other to get the next 3 dB of gain. 

So the answer to our question should be

1. 4 element 20 meter Yagi at 66 to 70 feet.   13.24 dBi
2. 2 element Yagi at 66 feet.                           10.24 dBi. 
3. Two dipoles broadside spaced 1/2 wave apart 9.74 dBi
4. 4 element Yagi at 33 feet.                             8.24 dBi
5. Dipole at 66 feet (includes end fed and off center fed half wave)   6.24 dBi 

This is a common answer for lots of distances on 20 meters other than maybe extremely short skip.

In practice a 4 element Yagi at 70 feet is a superior DX antenna to everything except the contest super stations that have 130 foot or taller towers.

Without towers, then the broadside array of dipoles is one step above the high single dipole.

For DX at 20 meters and above verticals are not considered. The common 3 element Yagi was not included as it is only marginally better than the 2 elements. If going for 3 elements you may as well just do 4 and get a good ( 3dB) benefit for the trouble and expense.

One more item to consider is propagation. Will the band be open? Typically 20 meters is considered to be a daytime band during most of the solar cycle. As the sunspot number increases 20 

Meters will be open later and later for long distance communication.