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This discussion is an extension of OCF tuning of L-dipoles and is related to multi-frequency applications.

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Center-fed Bent-Dipoles

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Hams associate Off-Center-Feed (OCF) dipoles with multiple bands and RF in the shack. The original 1930's Windom antenna is based on a 1/3 - 2/3 relationship of the dipole arms. There are variants based on different ratios for tuning or angles for impedance adjustment.

As an outgrowth of the 4NEC2 antenna models developed for this web site, a study was done related to the frequencies generated related to the harmonic ratios of off-center feedpoints.

What happens when you feed a dipole off-center?

Starting conditions: 1/2-wave center-fed horizontal dipole of #14 AWG fed at 1/2-wave over ground.  The auto-segmentation function is used because of differing lengths of wire.

Half-wave dipole velocity factorThe first run of the study is to find the center-fed resonant length of wire for the target frequency of 3.8 MHz.  This is: 38.751 meters.  The calculated length is 150/3.8 = 39.474 meters.  The length ratio of 38.751/39.474 = 0.9817 is refered to as the Velocity Factor.  This is primarily due to the metal, radius and covering of the wire radiator and secondarily to its interaction with ground.  This factor is needed to correct the theoretical MHz to match the MHz of the harmonics determined in the computer runs ( see the adjacent table ).

The series of off-center runs of the 4NEC2 computer model are based on feed points at 1/3, 1/4, 1/5, 1/6 of the resonant length. It is interesting to note that, contrary to conventional dogma, the Resonant Length for 3.8 MHz became longer as the off-center runs progressed. 1 inch at 1/3, 3.39 inches at 1/4, 5.06 inches at 1/5, and 7.28 inches at 1/6 for a 127 foot dipole.

At each feed point ratio, a detailed frequency sweep was made in 0.2 MHz steps up to 52 MHz. From this, each resonant harmonic frequency was determined along with its SWR50.  A regular pattern emerged. At 1/3 ratio a pattern of 2 peaks over each 3 harmonics.  At 1/4 ratio, 3 peaks over each 4 harmonics, At 1/5 ratio, 4 peaks over each 5 harmonics. At 1/6 ratio 5 peaks over each 6 harmonics.

Harmonics 80m Half-wave dipoleHarmonics Two-thirds OCF dipoleHarmonics Three-quarter OCF dipoleA half-wave dipole at 3.8 MHz can be tuned to its odd harmonics.
3.   11.6 MHz   SWR 2.4
5.   19.4 MHz   SWR 2.5
7.   27.1 MHz   SWR 2.9
9.   34.8 MHz   SWR 3.2
11.  42.6 MHz   SWR 3.4
13.  50.3 MHz   SWR 4.1
Harmonics Four-fifths OCF dipoleNow you can see why 75/80 meter dipoles are difficult to tune on other bands.

Harmonics Five-sixths OCF dipoleAt 1/3 ratio, a half-wave dipole can be tuned to the first two of each three harmonics. The SWR's are higher.
A 4 to 1 balun is good choice.

The antenna is 0.06% longer.

It can be bent for lower SWR matching but the improvement is very small.

At 1/4 ratio, a half-wave dipole can be tuned to the first three of each four harmonics. A 4 to 1 balun is still a good choice but SWR variance is greater.

The antenna is 0.22% longer.

At 1/5 ratio, a half-wave dipole can be tuned to the first four of each five harmonics. Few are usable.

The antenna is 0.33% longer.

At 1/6 ratio, a half-wave dipole can be tuned to the first five of each six harmonics.  Only the 2nd, 3rd and 4th of each 5 harmonics are usable.

The antenna is 0.47% longer.

Dick Reid, KK4OBI at