Some folks might think that if they spend $3000 on a top of the line transceiver that they should be able to talk to just about anyone around the world. Not So! It sure will help, but those folks are forgetting the vital importance of a good antenna. I believe that a station should be 25% radio and 75% antenna. This doesn't mean go out and spend 3 times as much on an antenna either... there's alot of things you can do in designing and building an antenna that is for less expensive than any radio. It just takes time and a little know-how.
The answer to this question can be summed up in one word - "resonant". An object may physically resonate - e.g. a piano string, or a guitar string. Each of those musical instruments has a string that is either struck or plucked - and the string physically vibrates at one specific frequency.
An antenna is similar in many ways to that musical string. It resonates best at one particular frequency. It can resonate a little above and below that frequency, and sometimes at multiples of that frequency, but it usually does best at that one frequency.
A radio signal is based off of an alternating current. A direct current is the type of current that comes from a battery. A direct current (D.C.) flows in only one direction. An alternating current (A.C.) flow first in one direction, then it gradually slows down and flows backwards, then it slows down and flows back the first way. The number of times each second that it makes a complete cycle is the frequency of the A.C. Radio frequency is typically above 20,000 cycles per second (or 20,000 Hertz). Power line frequency is typically 60 Hertz (Hz) in the U.S.
Radio signals have waves. The length of those waves is dependant upon the frequency of the radio signal. A higher frequency will have shorter waves. A lower frequency will have longer waves. Think of a harp. A harp has many strings lined up from shortest to longest. The shortest strings when plucked sound high pitched, and the longest strings when plucked sound low pitched. The same with antennas and wavelength. Low frequencies will need longer antennas, and high frequencies will need shorter antennas.
There are about as many different kinds of antennas as there are cars, but there are a few basic designs you can remember the next time you want to make a resonant antenna.

This antenna is one of the most popular antennas used for transmitting and receiving. It is easy to figure out the length of a dipole antenna. Simply take 468 and divide it by the frequency (in MHz - MegaHertz, or Millions of Hertz) you intend to use it for transmitting. If you were making a dipole for 40 meters - 7.1 MHz, then the length would be 65.9 (feet). I failed to mention that this equation gives you the length in feet. If you want the answer in inches, then you would need to multiply the answer given in feet by 12. For example - you wanted an antenna for the 2 meter band - 146.0 MHz; the length would be 3.2 feet or 38.4 inches.
Here you
can see how the coaxial cable hooks up the antenna wires. Usually an insulator
is placed between the two wires and the coaxial cable in order to give
this junction more physical support and to take some strain off of the
wires and the cable. One day, I put up a quick antenna without such an
insulator, and it worked great for that day, but the next day I found that
the wires somehow shorted out which explained why I couldn't hardly hear
anything compared with the day before.
A half-wave dipole can be raised up between two trees (as high off the ground as you can get it... higher is better). It can also be raised in the middle and the ends of the antenna can be tied off closer to the ground (not so close that people can contact the wires). This configuration looks like an upside-down V. It is commonly called an inverted-Vee.
A half-wave dipole works best broadside to the wires. If the wires go North to South, then you will have best results with stations to the East and West of you.
An inverted-Vee has less broadside action than a normal flat dipole.
Height is the key to getting out and being heard. If your 40 meter dipole is too close to the ground (e.g. 10-20 ft), then most of the signal will go up. If it is further up away from the ground (30-50 ft), more of the signal will go out closer to the distant horizon (resulting in being heard farther away). This height will vary with the frequency/wavelength you are using - 80 meters will be twice will work best twice as high as a 40 meter (unless you want most of your signal purposefully going nearly straight up in the sky and coming down around your general vicinity - excellent for close range communication 50-200 miles).
If you would like to use your antenna on many different frequencies, then there are several options. One is to connect several antennas to the same piece of coax (just be sure to spread the antenna ends out from each other to improve the resonance of each antenna). On one piece of coax, I have successfully used an 80 and 40 meter dipole antenna. I've read elsewhere that it is possible to do 4 bands on one antenna, but I've had a little bit of difficulty in doing that (I'm not saying that it doesn't work, I've just had a hard time getting it to work).
There is another antenna that is almost as easy to make, but a little harder to put up. It is a full wave loop. It hooks up to the coaxial cable the same as with the dipole, except that you use about twice as much wire and there are no loose ends.
It is typically made into the shape of a square, or a nearly square shape rectangle. If you make it too narrow of a rectangle, it begins to represent and act like a dipole antenna. Sometimes you can make it into the shape of a triangle. It will perform best if you can get the most amount of area inside of the loop (which is a circle).
Some people like to put a full wave loop up so that it is parallel with the ground (i.e. the whole antenna is at the same height). Others like to put it up on one side so that it stands upright. I prefer the latter design. It, like the dipole, tends to radiate and receive broadside, so if you put it in the first configuration (parallel with the ground), most of the signal seems to go either up into the sky, or down in the the earth. The latter configuration has most of the signal go out lower in the sky - closer to the distant horizon.
A full wave loop's length is found by dividing 1005 by the frequency in MHz. For example, a loop for 40 meters - 7.1 MHz would be 141.5 feet long. I put one of these up between two trees that were about 45 feet apart - I think the top was somewhere around 40 feet, and the bottom around 6-8 feet. It worked well on 40 meters. It's not up anymore because I made the antenna out of 24 gauge speaker wire from Radio Shack (very inexpensive), and certain wire joints broke when the wind blew - so it all came down. With a little better reinforcement and the ability to have some give for when the trees sway, and it would make a perfect permanent antenna.
This antenna is almost as popular as the dipole. The center lead of the coax (short for coaxial cable) goes to a conductor (pipe/wire) that is one quarter-wave long (half as long as the whole half-wave dipole). The equation for this conductor is 234 divided by the frequency in MHz. That's only half of the antenna. The other half consists of two or more wire radials that hook up to the shield of the coax. These are also the same length as the first conductor. If this antenna is placed on the ground with the first member pointing straight up (perpendicular with the earth), then the other members are laid upon the ground. If you want to permanently install them, then you should bury those elements a few inches below the surface of the ground so as not to hamper your ability to mow the yard.
Another name for this antenna is the 'ground plane antenna'. It doesn't have to sit down on the ground, although it does okay there. Since the radials represent ground, the whole antenna could be raised up into the air (either mounted to a tower or mast, or hung from a tree if made from wire). The antenna may perform better if the radials are hung at a 45 degree angle below horizontal. Two radials is enough to make it work, but more can be added if desired.
I've made a quarter-wave ground plane antenna for the 2-meter band. Using 12 gauge solid copper wire, a small piece of plywood or plexiglass, and some lightweight RG-58 coax (with the type of connector you need for your radio - PL-259 or BNC attached to the end). The elements were about 19". The center conductor goes to the vertical element. Instead of two separate wires for the ground radials, I took one wire and made it a little bit longer (about 1/4 inch). I bent that wire so that it was 90 degrees/square in the middle. After removing the insulation at the bend, I soldered the shield of the coax to that wire. To give the whole antenna a little bit of support, I placed the coax and the wires on top of a small 3x3 piece of plywood or plexiglass. With a drill, I drilled out small holes on each side of the wires and coax so that I could tie some strings through the board and around each of the wires and coax. The I took a hot glue gun and ran a bead of hot glue up and down each wire and the coax between them and the board/plexiglass.
To raise this antenna in the air, you can either put a small loop in the top of the radiating element and tie a string to it that goes through your favorite tree, or you can attach it to a mast or piece of wood that puts it up higher than the roof of your house.
The ground plane antenna is easy to make, and it does a good job. When it transmits, it sends most of it's signal down near the distant horizon in all directions. Some folks like to say that it radiates poorly in all directions. That's also true. It does not have the directivity that the dipole and full wave loop have.
If you want to put up an antenna for listening only, then you can try a resonant antenna, OR you could just try a random length wire antenna. This seems to work especially well for Shortwave receivers. This may not help out as much with a VHF/UHF scanner (those usually need an antenna that is resonant - much shorter than those used for 'shortwave').
For example - a shortwave random length antenna could be an antenna that is strung from the side of your house (near a window close to your radio) out to a tree. It could be 20-100 feet... or it could be longer... MUCH LONGER. We've run a 300 foot antenna that is up anywhere from 4-10 feet off the ground in places, and with it we can pick up just about any shortwave station out there (as long as conditions permit), plus we've always improved our AM reception tremendously. While we could only pick up a couple of local stations before (<40 miles), now we can pick up stations up to 100 miles away during the day time on AM.
If you'd like more info on antennas for AM/Shortwave Listening, check out the folks at www.nordicdx.com. They also have a special section just on antennas.
Basic Antennas
Daniel Reynolds - AA0NI - September 23, 1998