Easy Birth of VHF/UHF Antennas
Many times throughout the past decades I’ve been asked the question about the creation of antennas, Yagis for the most part, “Where do I start?” Well, there is a myriad of antenna design programs available to us today, some cheap, some expensive. Some of them are so detail oriented that once you have input all the parameters asked for you either forget what you wanted to design or loose interest. Sure, I have available YO and AO and YagiMax and NEC-Win- Pro, but I generally don’t have the time to spend hours massaging some design to come up with ultimate perfection. Besides, once this piece of perfection is created in a computer and placed in the real world all bets are off on its performance anyway.
Those that are aware of the above have asked me, “What do you actually do, when you need to design an antenna for a customers requirements?” The Johnny Carson method (listen to the customer) and KISS is always a good answer. These are very close to my procedure and practice. I usually take a wooden pencil and an old HP-25 Calculator and begin as follows. I know that the reflector of aYagi will be half a free space wavelength of material, which will be 3-5% longer than the driven element. I also know that most materials used in antenna construction will exhibit a velocity factor of about 95-97% the speed of light or for another term, the velocity of propagation. Radio Frequency Energy travels slower in a metallic medium than in air (free space). Therefore if I simply take 300 and divide it by the intended design frequency (in megahertz, MHz) I come up with a value that is twice the required reflector length or a free space wavelength. Yagis have near half wavelength elements e.g. 300/144.2 = 2.0804 meters (M) or 208.04 centimeters (cm). Divide this in two for a free space half wavelength, or 104 cm. To acquire inches, this value is divided by 2.54 as there are 2.54 cm/inch. This gives me a length of material that is 40.9536” (41”). But, what diameter you ask? Well, I suppose a little experience won’t hurt in this instance but a little observation and common sense will go along way also. In order to build a Yagi that will exhibit a +/- 3-5% bandwidth, ¼” to 3/8” diameter aluminum tubing, for a 2-Meter antenna, will serve you well. Oh sure, I can ponder the charts and play with rho (P) factors but why? Just peruse the commercially manufactured antennas on the market and get an idea from that.
Now you need to calculate the length of the driven element, so take 5% of the reflector length and subtract it from the reflector value. You come up with a dimension of 38.95”,
make it 39” long of the tubing you selected or have available. Now, with just two elements you have a beam antenna that will exhibit 3dB gain over a dipole. A little more gain (or directivity) on the 2 Meter band won’t hurt a bit. In order to double the gain (3dB) of the antenna you need to double the size of the antenna, i.e. go to four elements. So now you need a couple of directors. The length of the first director is determined by subtracting 5% from the length of the driven element or 37.05” make it 37”. The second director is simply the first director length minus 5% or 35.15”, make it 35. Now you have Elements that are 41, 39, 37 and 35 inches long. These are enough elements to construct a beam antenna that will give you 6dB gain over a dipole or 8.15dBi. This will provide you with a directional antenna of 60 degrees beam width. This is certainly better than 140 X 140 degrees bi-directionally that you would have with a dipole.
Now that you have all the elements calculated, how about spacing between the elements. You can go to the charts in the Radio Amateur’s Handbook or ARRL Antenna Books and articles to find the best spacing for the most gain between reflector and a driven element. It will be on the order of 0.2 wavelengths. Just in passing let me describe one of the best 6M antennas I ever built was from an article by Joe Reisert – W1JR. The spacing he used between the four elements was “0.2” wavelengths. So just for grins I ran our hypothetical Yagi of four elements and 0.2 wavelength spacing on YagiMax. The result was an antenna 49.5 inches long, has a gain of 9.52dBi and a 13dB front to back ratio (F/B). This is not too bad a quick and dirty, throw together, junkbox antenna. If you wish to play the charts and maybe better the F/B ratio you might do the following. Keep the spacing between reflector and driven element at 0.2 wavelength. Make the spacing between driven element and first director 0.12 wavelength, and the spacing between first and second director 0.15 wavelength. You will wind up with a little shorter antenna (38.5”), loose a half a dB gain but increase the F/B ratio by 1.5 dB (14.5dB).
Now 9dBi gain is a fairly respectable antenna. This is an increase of 8 times in Effective Isotropic Radiated Power (EIRP). In other words this would be like having 80 watts radiated in a 60-degree beam width as compared to 10 watts radiated isotropically (in all directions). If you’d like to have 3 dB more gain or double the EIRP you need to double the size of the antenna (to 8 elements) and keep the spacing of the additional directors to about 0.15 to 0.2 wavelength.
At this point we need to figure out two things, boom material and matching system. A 1” X 1” piece of Redwood makes a fine lightweight boom, it’s fairly impervious to weather and usually won’t warp. If wood is used for the boom or if the elements are mounted above a metal boom (as opposed to through the boom) the element dimensions remain the same as calculated. If a metal boom is used and the elements are mounts through the boom add 90% of the boom diameter to the element lengths. If the elements are mounted through the boom but insulated with shoulder washers, add 20% of the boom diameter to the elements. If you hard mount the elements through a square metal boom add 120% of the boom diameter to the elements.
One of the simplest and most common matching systems for Yagi antennas is the Gamma Match. It consists of a Gamma rod that is 15% the length and 1/3 the diameter of the driven element. A shorting bar that is 2% the length of the driven element and attached to the end of the gamma rod and then attached to the driven element so that the opposite end of the rod is very near the center of the boom. A Gamma capacitor is attached to the Gamma rod near the center of the driven element where the shield side of the transmission line is attached to the boom. The Gamma capacitor is in series with the center conductor of the transmission line and the Gamma rod. The size of capacitor, in picofarads (pF), can be determined by a Rule of Thumb that specifies the capacitance to be 7 times the wavelength value of the band of interest, e.g. 7 X 2M =14pF. A variable capacitor may be use here. Most if not all these dimensions are available in reference books, I bring them to you for illustration of the simplicity of creating a simple usable bean antenna for VHF operation. The calculations are the same for UHF antennas also. Good luck, call, or e-mail if in the construction of one of these you run into trouble.
From: The Rocky Mountain VHF+ Newsletter THINK TANK December 1999
Dave W6OAL –
Olde Antenna Laboratory 41541 Dublin Drive Parker, CO 80138