I recently had a conversation on the radio with another Ham who had built a 6 Meter wavelength band “J” antenna. He was getting some rather strange performance from this design, so I asked him where or how he had come up with the antennas dimensions. He referenced an Internet web page to me where I learned a calculator was provided to obtain dimensions for any desired frequency. I was immediately suspicious!
You see, the dynamics of antenna performance are such that “rounding errors” when scaling an antenna will basically destroy an antennas performance, dependent upon the relative frequency, or actually the percentage of wavelength. It works like this, if we choose some abstract “Constant” or “K factor” to design an antenna, that will work — over only a relatively narrow range of frequency.
This becomes particularly troublesome when the K factor is developed at some relatively high frequency, such as the 2 Meter wavelength band, and then it is used to scale antenna dimensions to lower frequency bands — such as 6 meters or 10 meters. If we used this same technique to scale up in frequency, it would work better, or at least we would not as likely notice any negative results. Here is why.
At a frequency of 146 MegaHertz (MHz) a piece of 3/4 inch diameter pipe is .009271 wavelengths in diameter. At 51 MHz., this same pipe is .0032385 wavelengths in diameter, or only about 1/3 the wavelength diameter. On 223.5 MHz. this same 3/4 inch diameter pipe is .0141922 wavelengths in diameter. You see on the 222 MHz. band this pipe diameter is a pretty big fraction of the wavelength; pretty fat. At 50 MHz. though its pretty skinny! It would look even skinnier at 29 MHz., and consequently have very high impedance, or AC resistance, at this lower frequency!
The larger fatter diameter conductor, relative to frequency, has greater bandwidth, and generally better performance overall. At relatively lower frequencies its skinnier percentage of wavelength makes its performance narrower in frequency response, and we will see general or even dramatically degraded performance. If in addition to this our numbers are not really exact, or are compromised by rounding errors, the performance will be markedly bad!
You can try this out. The constants or K factors for my 6 Meter “J” antenna are *1 8161.5625 for the radiating elements overall length. The K factor for the Q-line is *1 3023.75. These constants would be close enough to allow a “J” antenna to be designed over any part of the 6 Meter band, and probably for a megacycle or so above or below this band. Try to use these same constants to build a 2 Meter wavelength “J”, and also one for 10 Meters. See what happens!
Terms used in this article
Percentage of wavelength: Given conductors, be they pipe, rod, tubing, or wire, represent a relative percentage of the wavelength of the antenna operating frequency. Larger fatter conductors (relative to the operating frequency) have greater surface area, and consequently lower AC resistance. This gives them greater bandwidth, and better efficiency in their radiation performance.
Constant or K factor: A commonly known K factor or constant is the one used to determine the length of a half-wavelength center fed dipole. This constant is 468 / f in MHz. and has appeared on every FCC Ham license exam for better than 30 years. Other constants that can be developed will allow antennas or other constructs to be fabricated from existing designs. Rounding errors, and dynamics of frequency conversion must however be accounted for! You can’t maintain only certain factors such as tubing diameter, or element spacing, and not have them effect the whole!
Scaling: Antennas can be mathematically scaled up or down over relative wavelength but, all factors must be considered uniformly, or errors will accumulate.
Beyond this I would suggest a book written by the preeminent antenna engineer John Kraus W8JK. His book, “Antennas” (ISBN 07-035410-3) published in 1950 is the exalted antenna compendium for nearly all antenna design work, commercial or Amateur. It explains all of the physics associated with how and why antennas work.
*1 I worked out these numbers only for sake of this article! I did not originally use any calculation to build my original design, which I did about five years ago. I built that antenna from approximations, then I dialed its performance in from empiric tests. Now that I know dimensions that work in this frequency range, I can work backwards to develop these “K factor” numbers.
Article by Wa6BFH originally at /www.geocities.com/SiliconValley/2775/