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Restricted Space Antennas

by Walt Fair, Jr., W5ALT

Electromagnetic Waves

Since antennas radiate energy in the form of electromagnetic waves or radio waves, it is important to understand what they are and how they propagate or travel. We wonít get too far into the subject of radio propagation, though. Thatís a whole separate field of study.

Frequency. Radio waves are characterized by an oscillation. In a wire, one can think of electrons moving back and forth at a certain rate. The electric current flows in one direction for some period of time (half a cycle) and then reverses and flows in the opposite direction for the same amount of time (the other half of the cycle). Thus the motion can be characterized by a frequency measured in cycles per second. Nowadays we use the unit of Hertz (Hz), which is equivalent to cycles per second.

The electrical power grid normally uses a frequency of 60 Hz. However, radio frequencies are much higher so it is more convenient to express frequencies in kHz (1000 Hz), MHz (1,000,000 Hz or 1000 kHz) or even GHz (1,000,000,000 Hz or 1,000,000 kHz or 1,000 MHz). Notice that frequency tells us nothing about the strength of a radio wave. It only tells how fast the electromagnetic field is changing.

Wavelength. In a conductor the moving electrons travel a certain distance during a cycle. It turns out that the velocity of motion does not depend on the frequency, but is a constant that depends on the material. This characteristic velocity is normally written as c and is equal to the speed of light in the medium. In free space, c is about 300,000,000 m/s. Now, if the current flows for F cycles per second, then the time for 1 cycle is 1/F sec. And since the speed is c m/s, we can calculate that the current moved a total distance of c/F meters during the time of 1 cycle. This distance is called the wavelength.

Notice that there is a direct relationship between frequency and wavelength. It doesnít depend upon the strength of the current flow at all. It only depends on the characteristic velocity of the medium in which the current is flowing. In free space, as well as in the earthís atmosphere, the velocity is about 300,000,000 m/s. In copper or aluminum wire the velocity is a little less than 300,000,000 m/s, however. Since the wavelength expresses a natural measurement unit for electromagnetic waves, most measurements in antennas are expressed in terms of wavelengths.

Wavelength is normally represented in equations with the Greek lambda symbol λ. In terms of meters, or feet the relationships are

c = 300,000,000 m/s = 984,000,000 ft/s = 186,364 mi/s
λ(m) = 300/F(MHz)
λ(ft) = 984/F(MHz)

For reference purposes, here is a table of approximate frequencies and wavelengths for the amateur HF bands. Remember that it is possible to calculate the wavelength for any frequency from the equations.

BandFrequency (MHz)Wavelength (m)Wavelength (ft)
160 meters1.8166.7546.7
80 meters3.683.3273.3
75 meters3.878.9258.9
60 meters5.455.6182.2
40 meters7.142.3138.6
30 meters10.128.797.4
20 meters14.121.369.8
17 meters18.116.654.4
15 meters21.114.246.6
12 meters24.912.039.5
10 meters28.110.735.0

Here's a good question: What is the wavelength that radiates from the 60 Hz power lines?

Propagation Modes.

The study of radio propagation is a fascinating and complex subject, but we wonít go into detail here. The most important thing to remember is that for most purposes there are 3 major modes of radio propagation that may be important for short wave communication.

Line of Sight. In this mode radio waves essentially travel in a straight line. So if you want to communicate by line of sight mode, you must be able to see the other station from your antenna. Obviously, that means the higher the antennas, the longer the distance that can be reached. Although line of sight propagation works at almost any frequency, it is of importance at VHF, UHF and microwave frequencies when other modes donít exist. On the HF frequencies, it really isnít very useful, since we are generally interested in communicating over much great distances.

Ground Wave. In this mode the radio wave follows the ground. Since part of the wave slightly penetrates the earthís surface, it is attenuated and travels slightly slower than the part of the wave above the earth. That causes a ďdragĒ that allows the wave to bend somewhat and follow the curvature of the earth. Of course the constant ďdragĒ causes the wave to lose power, so it eventually fades away. Ground wave propagation is most important at LF and MW frequencies and allows us to hear broadcast medium wave stations over the horizon during the daytime. It may be important for local communication, but not for working DX.

Ionospheric Propagation. In this mode radio waves travel in a more or less straight line until they reach the ionosphere above the earth. Due to the ionization, the waves are refracted and when the ionization is sufficient, they will bounce back toward earth. When conditions are right, there can be multiple reflections with the signal bouncing between the ionosphere and the earth several times. That is how itís possible to propagate signals over the entire world. This mode is mainly responsible for most DX contacts on the HF amateur bands.

As a result of the geometry, it is easy to see that to communicate at large distances, the radio wave needs to leave the antenna at a relatively low angle. That allows it to move the farthest distance before bouncing off the ionosphere. Obviously, if the signal goes straight up, then it will bounce straight down and not go anywhere. As a consequence, we generally want low angle radiation for DX, but somewhat higher angles for closer communications. This will be important when we evaluate antenna designs. Unfortunately itís much easier to install an antenna that propagates straight up due to reflections from the earth.

The answer to the 60 Hz wavelength question is: λ = 300,000,000/60 = 5,000,000 m = 3106 miles!