Design exercise: an 80-foot 75-m dipole antenna
by Dick Smith, W4ZQV
I attended a meeting of Buncombe County ARES (BCARES) recently, and realized the importance of the 75-m SSB Tarheel Emergency Net, which meets daily at 7:30 pm at 3.923 MHz. "Uh-oh," I thought, "I've got a problem." No 75-m antenna. My house is on a small lot, and the neighborhood Homeowners Association is pretty strict about what can be installed outside. Not much chance of raising a 119 ft halfwave dipole outside. So I began the design process to squeeze a center-fed dipole into the attic, using loading coils to shorten the dipole legs to fit the 84-foot available space. The antenna will install at only 15 feet (1/16 ??) above ground level, so it'll operate as a Near Vertical Incidence Skywave (NVIS) radiator. For an antenna so near the ground, radiation is launched nearly vertically and on reflection reaches the ground out to a radius of maybe 400 miles. Bad for DX operation, but perfect for use with the Tarheel Net.
INCREASING THE ELECTRICAL LENGTH
I chose 80 feet for the length of the shortened dipole, allowing a few feet for insulators and attachments. This physical length is shorter on 80 m than the resonant half-wave length of ??/2=119 ft, and the antenna impedance at the center feed point is capacitive, as discussed in the ARRL Antenna Book, 22nd Edition, Ch.2. The impedance can be moved toward the pure resistance characteristic of a resonant antenna by adding a compensating inductance in each leg of the dipole. This inductance is called a loading coil, and by transforming the feedpoint impedance from capacitive to pure resistive, the antenna becomes resonant at the driving frequency. The transmitter thinks it is driving a resonant 119 ft antenna!
HOW MUCH INDUCTANCE?
The amount of inductive reactance to be added increases as the loading coil is moved away from the feed point. At the same time, it's desirable to maximize the Q (ratio of reactance to resistance) of the coil so as to reduce the amount of RF power in the antenna which goes into heat and not into radiation. With all these variables, it's helpful to use a comprehensive calculation program such as the one found at http://www.k7mem.com. Using this program and an operating frequency of 3.900 MHz, the midpoint of the General Class 75-m band, I chose a coil installation point 28.0 ft from the center feed point, at which point the required inductance is 39.7 ??H. Identical coils are to be inserted into both dipole legs.
DESIGNING THE COILS
There are many combinations of coil length, diameter and number of turns which will produce an inductance of 39.7 ??H. I was interested in choosing a combination which would maximize the Q of the coil, as noted above. Such a coil is obtained when the length of the loading coil is half the diameter, L/D = 0.5 (ARRL Antenna Book, 22 Ed., p 21-8). The K7MEM website cited earlier also includes a good coil design program, the results of which are: D= 2-3/8" (2" PVC), N=26 closed-packed turns of #16 AWG enameled wire, resulting in a coil length of L = 1-7/16".
FEED POINT IMPEDANCE
The feed point impedance of a halfwave dipole in free space is 72 ohms when driven at its resonance frequency. Thus if it's fed with 50-ohm RG-8X coax, the mismatch is only moderate, resulting in a SWR of only 72/50 = 1.4, a figure which can easily be lowered through use of an antenna transmatch at the transceiver. But the resonance is fairly narrow, resulting in need for retuning when the operating frequency departs significantly from its design point.
It is apparent that antennas are one big hairy challenge, and I've only scratched the surface here. There is a huge amount to learn about loading coils and their effect on current flow in the antenna. Also, I'm particularly interested in understanding the role of baluns and common mode chokes when a coax feedline is connected to a balanced dipole. I hope to describe these studies in a future edition of Smoketest.
I'm grateful to Carl, N4AA, for a very useful discussion on this subject.
*Reprinted by permission from SmokeTest, February 2012
The Official Publication of The Western Carolina Amateur Radio Society, Inc.