Discussion about the far field radiation patterns produced by each harmonic of an End Fed Half Wave antenna in straight form.

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Multi-band Operation Any length of wire has a resonant frequency. Think of a guitar string. If you touch it in the middle you now have two halves at twice the frequency. Touch at one-third you get three sections at three times the resonant frequency. At one-fourth, get four sections at four times the resonant frequency, et cetera. These are harmonics. Starting with a wire that resonates at 80 meters (3.5 mHz), the second harmonic is two halves at 40 meters (7 mHz); third harmonic is three parts at 30 meters (10.5 mHz); 4th is four parts 80/4=20 meters (14 mHz). 5th = 17 meters (17.5 mHz). 6th = 15 m (21 mHz). 7th =12m (24.5 mHz). 8th = 10m (28 mHz). Antenna modeling shows that a resonant half wave wire can be fed at any point (End, Off-Center, Center) without changing gain or efficiency... only impedance. Away from center, impedance is high so a transformer is used to match an antenna to coaxial cable. At 8% from the end is the unique feedpoint where harmonics number 2 to 8 fall into best alignment. At this point the Standard Deviation between those seven resonant length's is only 0.3 meters. TThese can be aligned with the 1st harmonic by using a small inductance and capacitance. The key characteristic that does change is the radiation pattern on each harmonic. What
Happens
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You Transmit on Harmonics of a Straight EFHW Antenna? To answer the question, a wire antenna model was developed* based on data reported by Danny Horvat, N4EXA and E3m (MyAntennas.com), a model by VE3KL and the spherical geometry technique used for the Bent Dipoles "Elevated Radials" study. 4NEC2 Antenna Model: Here The pattern of antenna radiation is dependant on Wavelength Height, the distance in wavelengths above the ground. The general rule is to position an antenna is "as high as wide". This halfwave elevation provides the maximum signal to the sides with minimum signal skyward. No feedline is considered. Click here to see a table of the elevation effects on antenna radiation pattern for these bands: 160m, 75/80m, 40m, 20m, 15m, 10m and 6m Note: Every half-Wavelength Height adds a figure-8 broadside to any half-wavelength of wire. A round reflection dome develops between each half-wavelength. As seen from the table, an 80 meter antenna at half-Wavelength Height should be at 129.5 feet. This is impossible for most amateur radio operators, therefore the modeling data that follows is based on a 12.2 meter elevation (40 feet). This is a practical maximum for commercial masts, telescoping poles and trees. If you must mount an antenna lower, remember that the closer the to ground: (1) the more signal absorbed by the ground; (2) the remaining signal is increasingly reflected skyward. (You can use the above 4NEC2 antenna model to see what happens for specific elevations and bands). Model Data by Harmonic The following data are for the far field radiation patterns and 3D color views of a straight End Fed Half Wave antenna at 40 feet over "Real ground". The direction of radiation is the Blue trace on the polar graphs. Horizontal is 90°. Up is 0°. Red color indicates the stronger radiation on 3D views.
On 80 meters, 40 feet elevation is over a quarter of the 129.5 feet half-Wavelength Height so some broadside directionality begins to develop. Being this close to ground, signal adsorption reduces the 7.32 dBi normally seen at one-half wavelength elevation down to 6.06 dBi. The remaining RF is mostly reflected upward in the oblong pattern seen in the 80 meter 3D view. Within the pattern are both vertical and horizontal polarizations. The vertically polarized signal aligns with the wire; the horizontal signal is broadside to the wire. This means that the the figure-8 dipole radiation pattern that we visualize is within the pattern but signal strength drops away rapidly at lower angles. At 15° signal strength broadside for distance communication (DX) is down to -3 dBi with nulls off the ends of the wire. Very weak. Because maximum signal strength is skyward, the antenna is more suitable for short range NVIS communication. On 40 meters, the wire acts as two in-line, half-wave dipoles radiating broadside to the wire. Each half-wave has a horizontally polarized figure-8 lobe and a vertically polarized lobe in the middle to form the two long lobes seen in the 40 meter 3D radiation pattern above. Notably, the nulls are now broadside to the wire and maximum signal is off the ends. The 6.12 dBi signal strength at 40 meters is about the same as on 80 meters. At 40 feet elevation the antenna is approaching a 65 foot half-Wavelength Height so the radiation is more directional. The result is a radiation angle at 50° down from vertical. Half power is 70° from vertical. (20° Take-Off-Angle). At 15° for DX the signal is 2.8 dBi off the ends the wire. On 30 meters, the wire radiates broadside as three half-waves. Each of the three half-waves have horizontally polarized lobes on each side (total of six lobes) and two vertically polarized lobes at each end of the wire. These polarizations merge to make the three long, angled shapes seen in the 30 meter 3D radiation pattern above. Even with the broadside help of the directional middle radiation pattern, communication is better in-line with the wire... not to the side. The antenna at 40 feet now has a more directional pattern because it is so close to the half-Wavelength Height of 46 feet. (Reminder: each half-Wavelength in Height is where horizontal radiation is maximum and vertical radiation is minimum). Distance communication (DX) is improved compared 40 meters because the end lobes are angled lower at 60°. Half power is at 75° which equals a 15° Take-Off-Angle. Gain is 7.37 dBi at +/- 30° off the right end, 5.8 dBi broadside from the narrow middle lobe and 4 dBi at +/- 30° off the left end.. The two sharp nulls are +/- 20° from broadside to the antenna.
On 20 meters, the wire radiates as four half-waves. Each has a horizontally polarized figure-8 giving 8 lobes and 8 nulls. A vertically polarized lobe is at each end of the antenna wire.These combine to make the strong, broad patterns seen on the ends of the 20 meter 3D view above. The two small skyward domes in the middle are from ground reflection that is beginning to appear because the antenna, at 40 feet, is a little higher than a half-wavelength (35 feet). The radiation pattern is less directional and more complex. The strong four corner lobes are 7 to 9 dBi gain angled +/- 60° from the wire. The two smaller lobes an each side are +/- 15° from broadside to the antenna at 4 to 5 dBi gain. Compared to 30 meters at 60°, DX radiation is now angled lower at 70° from vertical. Half power is at 75° (15° TOA). On 15 meters, the wire radiates in six half-waves. Each has a horizontally polarized figure-8 with vertically polarized lobes filling in the middle. These form the long radiation patterns seen in the 15 meter 3D view sbove. A second set of higher lobes is almost completely developed because the 40 feet high antenna is almost at a second half-Wavelength Elevation (46 feet). There are twelve lobes and twelve nulls in an increasingly complex radiation pattern. The four corner lobes are +/- 65° from broadside to the antenna at 8 to 10 dBi gain. For distance communication the low angle radiation is now at 75°. Half power is at 85° (5° up from horizontal). However, the corner lobes have only a 20° beam width and the side lobes only 10° beam width which complicates comunications. On 10 meters, the wire radiates in eight half-waves. Each of the eight radiation patterns has a horizontally polarized figure-8 with vertically polarized lobe filling in the middle. The second ring of higher lobes is completely developed because the 40 feet high antenna is over two half-wavelengths high (35 feet). The vertical radiation lobes developing on top are caused by ground reflection because the antenna's elevation is between two half-waves. There are sixteen lobes and sixteen nulls in an exceptionaly jagged, omni-directional, porcupine-like, radiation pattern. The four corner lobes are +/- 65° from broadside to the antenna at 10 dBi gain with a beam width of 20°. The twelve narrow, side lobes are in the range of 6 to 8 dBi gain at 10° beam width.. For DX the low angle radiation is now at 80°... 10° up from horizontal. The patterns for 17 meters and 12 meters are not included to simplify visualiation. All 3D views are from the same angle and compass heading. * Note: In the antenna current diagram (top) there is a simulated counterpoise and small inductance (blue square) at the feedpoint (purple circle). Presumably this causes the model's predicted signal to be slightly stronger at the opposite end. |

Dick Reid, KK4OBI at QSL.net