(Developed Jointly with Courtney Duncan, N5BF/6 )
and I have developed band selection and operating procedures that optimize the
probability of successful QSOs between our Iowa and California QTHs. These
procedures call for the use of all bands, 20-10m, because the best band on any
give day varies with propagation conditions. We both needed inexpensive
frequency independent antennas to properly implement these procedures.
This Log Periodic of Another Sort is one of our design solutions.
The goals of this development included (with equal importance):
- Low cost (no tower, rotator or directional array)
- Direct feed from a typical solid-state rig (no matching network)
- Single coaxial transmission line (no coaxial switching)
- Continuous low SWR 13-30MHz
- Constant radiation pattern at all frequencies (comparable to 1/2-wave dipole at 1/2-wave height)
- Horizontal polarization
- Close to omni-directional performance (comparable to 1/2-wave dipole)
A brief review of the ARRL Antenna Book finds chapters on multiband, broadband and log periodic antennas. Numerous time proven designs are offered including random length end-fed wires, end-fed Zepps, center balanced feeders, parallel dipoles, trap dipoles and verticals, and HF discones. All of these designs have proven successful over time by numerous users but they all, in one way or another, fall short of our goals. Many designs require antenna matching. Many create substantially different radiation patterns on different bands. A couple create vertically polarized radiation.
The log periodic dipole array (LPDA) antenna design is more encouraging but, in its typical form, it is oriented toward directive qualities, gain-over-a-dipole and front-to-back-ratio, that do not fit our goals. However, with a stretch of the imagination, designing and installing an LPDA in a new orientation has met all of our expectations.
The ARRL Antenna Book chapter on log periodic antennas provides a complete general discussion and several construction ideas. It includes a complete section on both basic theory and design procedure based on QST articles by Peter Rhodes, K4EWG.  Further discussion of LPDA input impedance and feed suggestions is covered by Jon Bloom, KE3Z.  For further LPDA discussion consider Frequency Independent Antennas by Victor Rumsey  and Antennas by John Kraus, W8JK.  Kraus defines frequency independence as having all parameters, impedance, pattern, polarization and gain, constant over the entire frequency range. Note how close this definition matches our development goals and solution.
A log periodic dipole array is made up of several center-fed dipole antennas fed alternately out of phase from a common balanced feeder. This arrangement creates an active region of adjacent dipoles that accepts power at any given frequency. To meet our goals we take this basic concept and design an LPDA with dipoles roughly horizontal, the feeder vertical, and the shortest highest frequency dipole closest to the ground. By adjusting the height of the highest longest dipole, the number of dipoles and their spacing, we place the active region at any given frequency 1/2-wave above ground.
Rhodes has provided a complete calculative path of LPDA design but, for numerous design iterations, it is arduous enough that use of modern spreadsheet techniques has been a great help. Fortunately Kalevi Hautaniemi, OH3FG/KO4BC, was way out ahead of us and provides an LPDA EXCEL spreadsheet. We have modified the user interface of Kalevi's original work in both input and output but his complete calculative process remains .
User input to this EXCEL spreadsheet includes lowest frequency, highest frequency, tau and sigma (as discussed by Rhodes), and the height of the highest longest dipole. Spreadsheet output is a table of array dimensions, in meters and feet, for the varying total number of dipoles and a table of XYZ coordinates which are imported to EZNEC, a sophisticated yet inexpensive antenna modeling program by Roy Lewallen, W7EL.  The combination of an LPDA design spreadsheet and Roy's antenna modeling program has made the evaluation of numerous model iterations entirely reasonable. All cutting and trying is done on the keyboard with results of unproductive ideas filling only the bit bucket.
Through numerous design iterations we homed in on a configuration that appears to meet all of our goals. This design has ten dipoles and a feeder length of 25 feet. When the highest dipole is at 35 feet, held up either at the center or stretched between two supports, active regions for all bands are placed near 1/2-wave height. In the five Amateur Radio bands, 10-20m, the result is equivalent to five separate dipoles each at 1/2-wave height and fed with individual coaxial transmission lines. A bonus for SWL listeners is that the LPDA produces low impedance dipole-like performance for all frequencies 13-30MHz.
EZNEC tells us which adjacent dipoles make up the active region at a given frequency by calculating and displaying the magnitude of current flows on every dipole. The active region can be easily seen and the average height of the region's dipoles taken from the LPDA spreadsheet and resulting EZNEC wire list.
21MHz Dipole Currents
The power of spreadsheet design and antenna modeling has required the fabrication of only two LPDA designs. Our first antenna uses eight dipoles on a 19 foot feeder which, like a conventional LPDA, is shorted a few inches beyond the longest dipole. EZNEC confirmed the feed impedance is near 200-Ohms as discussed in cited QST articles. A standard off-the-shelf 4:1 balun is used to allow a 50-Ohm coaxial transmission line. SWR measurements made on this dipole are slightly worse than EZNEC predicted but
nonetheless encouraging. This original model is packed for ARRL Field Day use.
The second antenna was designed with what we learned from LPDA-1. First, to improve the SWR curve, LPDA-2 uses ten dipoles on a 25-foot feeder. Second, LPDA-2 does not have a feeder short just beyond the longest highest dipole. Otherwise construction is the same including the 4:1 impedance matching balun. The broadband SWR curve, both predicted and measured, satisfies our goal of not using an antenna tuner across the entire design frequency range.
LPDA SWR Curve by EZNEC
Antennas are constructed with insulated 14ga stranded electrical wire (500ft for $16, enough for two antennas), 4-inch pieces of 1/2-inch PVC electrical conduit for end insulators (10ft for less than a dollar), 450-Ohm ladder line (100ft for $15, enough for four antennas) and a 4:1 balun ($15-25). It is fair to say that a complete antenna costs less than $50.
Dipole ends are soldered to the ladder line at required spacings. PVC insulators, cut, drilled and countersunk, are attached to the outside ends by looping the wire through and then soldering. The 4:1 balun is attached at the bottom end of the feeder. The ladder line feeder is twisted 180-degrees between each dipole so adjacent dipoles are fed out of phase.
From EZNEC modeling and practical application we now understand that dipoles don't have to be straight and parallel. To allow inexpensive support, dipoles can angle down or sag with no practical radiation or feed problems. My installation uses two 10ft masts spaced 32ft either side of the main support mast and equipped to gather 10 dipole support lines. Get the longest highest dipole as close to 35ft as possible, spread the elements out as best you can (but in the same plane), add a 50-Ohm coaxial transmission line and have at it.
We believe we have met our design goals. The antenna is inexpensive, is directly fed from a solid-state rig, uses only one coaxial transmission line, provides continuous coverage 13-30MHz, yields dipole-like near omni-directional radiation patterns, and is horizontally polarized. QSYing from band to band is as fast as switching from VFO A to B.
 Courtney Duncan, N5BF, 4402 Rockmere Way, LaCanada, California 91011, firstname.lastname@example.org
 Peter D. Rhodes, K4EWG, The Log-Periodic Dipole Array, QST, November,
1973, pp. 16-22 and The Log-Periodic V Array, QST, October, 1979, pp. 40-43.
 Jon Bloom, KE3Z, Input Impedance of LPDA Antennas, Technical Correspondance,
QST, October, 1986, p.51
 Victor H. Rumsey, Frequency Independent Antennas, Academic Press, 1966 (we
borrowed a copy from the Iowa State University engineering library)
 John D. Kraus, W8JK, Antennas, 2nd edition, McGraw-Hill, 1988 (still in print)
 Available from WØRPK at netINS.net as an email attachment
 EZNEC by Roy Lewallen, W7EL, P.O. Box 6658, Beaverton, Oregon 97007,
http://www.eznec.com (also see ad in QST)