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Although this article is based on 11m antenna calculations, the theory and calculations relates to any antenna or frequency.
Radio energy waves are waves of energy that are similar to light waves. In fact signals (radio waves) travel through the air at the speed of light. To understand how an antenna works you must first have a basic idea of the makeup of a radio wave. A radio wave can be visualized as a sine wave, shown in figure 1. The distance a wave travels to complete one cycle is known as the wavelength of the signal. A CB signal completes a cycle as it travels through the air at roughly 36 feet. For every 36 feet the wave travels it has completed one cycle. Since we have defined wavelength as the distance a wave travels to complete one cycle, we now know that one wavelength on CB frequency is approximately 36 feet. So, radio waves are similar to light? What is the wavelength of visible light in feet? Smaller than two inches! Figure 2 show the relationship of CB frequencies to other bands.
Figure 1 - A good way to visualize a signal as it travels through the air. We can now visualize an actual distance that a wave must travel to cycle. This distance is around 36 feet. If you convert 36 feet to meters you get approximately 11 Meters. This is why the CB band is sometimes called 11 Meters!
Figure 2 - A chart to show the relationship between the CB band and others. On the left the chart starts out with power line frequencies (60 Hz), AM Broadcast (1MHz), the CB band (27MHz) and goes all the way up through TV,FM Radio, Cellular Phone, Microwave to visible light frequencies. Lower frequencies have long wavelengths and high frequencies have short wavelengths.
How Antennas Work
When your transmitter puts a current (Radio Frequency (RF) energy) into an antenna, your antenna responds by producing a magnetic field surrounding the antenna (this is the signal). When this magnetic wave strikes another antenna (the receiving station antenna), it induces a current on the receiving antenna surface (that current is then converted by the receiving stations receiver to sound).
The length of the antenna structure plays an important role.
The magnetic field that your antenna puts out will produce an electric current on any metal surface that it strikes, however if the metal that the signal strikes has a length relation to itself the induced current will be much stronger on the object. We stated before that as a CB signal travels through the air, it completes a cycle in approximately 36 feet. For instance, if the object that the magnetic wave strikes is 18 feet long (1/2 wave length), 9 feet long (1/4 wavelength) or 36 feet long (1 full wavelength), then the induced current will be much higher than if the signal struck a metal object that was not some appreciable fraction of the wavelength of the signal. If you have ever heard people say they want to "tune" their antenna, they usually mean make it have a length relation to frequency they are trying to receive.
This has a special name, it as known as antenna resonance. Every antenna has at least one exact resonance point.
Antenna resonance is the frequency (in MHz) where the antenna is in a state of electrical balance, which is determined by the length of the antenna (every antenna has an exact frequency it is resonant on). To use some numbers to demonstrate what we are explaining here, let us look at a very simple formula. You can calculate the distance of a wavelength in free space for any frequency using this formula:
One Wavelength, in feet = 984 / Frequency in Megahertz (MHz)
Lets look at an example:
CB Channel 40 uses the frequency 27.405MHz.
One Wavelength for 27.405, 35.906 Feet = 984 / 27.405
So we want to make a antenna that is resonant on channel 40 and not too large in size. Lets cut a straight piece of aluminum rod to be 1/2 a wavelength long. One Wavelength for 27.405 is 35.906 feet (from the formula above), and we want 1/2 of that, or 17.593. So, we cut our piece of aluminum rod to 17.593 and we have made an antenna that resonates on 27.405 (or close to that). This piece of rod should pick up (receive) on channel 40 (27.405Mhz) well.
Ok, now lets look the most basic antenna most CBers are familiar with, the 102" whip, also known as the 1/4 wave whip. Why is it known as the 1/4 wave whip? As we can see if we get out our calculator, 102 inches is approximately 1/4 of 35.906 feet (1 wavelength). This antenna should also perform well on the CB band because its length relates to that 36 foot wavelength signal we are trying to receive!
To further simplify things, we have been speaking strictly about receiving - but these same principles apply to transmitting. Our antenna also transmits a strong signal if the antenna we are transmitting through is resonant on the frequency on which we are transmitting.
This brings us to our next topic - Bandwidth. Most of us use multiple frequencies when we use out radios. So, does this mean our antenna only works good at one frequency, the resonance frequency? No! Our antennas actually perform well over a range of frequencies. Most commercial CB antennas are designed to operate well over the 40 channels (that is a frequency range from 26.965 - 27.405 MHz). So, if you use your radio on all those frequencies it would be best to make it resonant in the middle around channel 20 or so (27.205 MHz). If you talk only on a certain channel then set it up for the frequency that you use most. The term that is important here is bandwidth or how much band your antenna works well over. For example if your antenna works well over the 40 channels then your bandwidth is 27.405 - 26.965, or .44 One method of judging how well (efficiently) your antenna is working is by measuring SWR.
To understand SWR or Standing Wave Ratio, we must first understand a few other properties all antennas have. You may have heard the terms radiation resistance, impedance, input impedance, feed point impedance. These terms are all referring to the same property of an antenna. When we think of the term resistance we usually think of some type of force that acts (or impedes). Do not confuse DC resistance with with radiation resistance. This is a totally different concept. You can not measure your antenna's impedance by using a Ohm meter on it! Impedance in antenna terms refers to the ratio of the voltage to current (both are present on an antenna) at any particular place on an antenna. This ratio of voltage to current is different on different parts of the antenna - which means that the Impedance is different on different spots on the antenna if you could pick any spot and measure it.
In formula terms:
Impedance of antenna = Voltage Field / Current field flowing within antenna.
This is great, but how does this relate to SWR? As you may or may not be aware of, most antennas are usually designed (and intended) to have an impedance at their feed point of 50 ohms. CB radios that are sold have antenna jacks on them that require they be hooked up to a 50 Ohm load (load - usually your antenna). This is why we use a 50 Ohm line (usually coax cable) to connect to the antenna. If we have an antenna not properly tuned close to 50 ohms or we used 75 ohm coax instead of 50 ohm coax a mismatch condition occurs. Basic laws of electronics dictate that if these impedance's (antenna jack, coax and antenna impedance) do not match then maximum power is not transferred. There are all kinds of situations that could cause a mismatch beside what I gave as an example. Smashed coax, bad connections, incorrect antenna assembly, mistuned antenna (incorrect antenna length) and objects too close to antenna are some other common causes.
What happens if there is a mismatch? At this point, lets just say that the antenna isn't tuned right, at the connection of the coax to the antenna, part (or all) of the wave is reflected back down the line. The amount of the wave reflected back depends how bad the mismatch is. The combination of the original wave traveling down the coax (towards the antenna or opposite during receive) and the reflecting wave is called a standing wave. The ratio of the two above describe waves is known as the Standing Wave Ratio (aka SWR). Generally you want a low SWR, preferably less than 2:1. In some mobile installation note that it is not possible to get the ratio lower than this without using a special matching device. This is because the impedance of most mobile antennas are lower than 50 ohms. In general, an SWR of 1:5 is fine! This is an area of battle for most antenna experts. Some strive to achieve a 1:1 ratio that indicates a maximum power transfer through their antenna system.