Helical Feed Antennas Paul Wade W1GHZ ©2002 [email protected]

Helical Feed Antennas Paul Wade W1GHZ ©2002 [email protected] Helical antennas have long been popular in applications from VHF to microwaves requiring circular polarization, since they have the unique property of naturally providing circularly polarized radiation. One area that takes advantage of this property is satellite communications. Where more gain is required than can be provided by a helical antenna alone, a helical antenna can also be used as a feed for a parabolic dish for higher gains. As we shall see, the helical antenna can be an excellent feed for a dish, with the advantage of circular polarization. One limitation is that the usefulness of the circular polarization is limited since it cannot be easily reversed to the other sense, left-handed to right-handed or vice-versa. Helical Antennas John Kraus, W8JK, is the originator of the helical-beam antenna; as he puts it1, “which I devised in 1946”. His 1950 book, Antennas2, is the classic source of information. The recent third edition3, Antennas for All Applications, has significant additional information. A sketch of a typical helical antenna is shown in Figure 1. The radiating element is a helix of wire, driven at one end and radiating along the axis of the helix. A ground plane at the driven end makes the radiation unidirectional from the far (open) end. There are also configurations that radiate perpendicular to the axis, with an omnidirectional pattern. The familiar “rubber ducky” uses this configuration; we all know that it is a relatively poor antenna, so we shall only consider the axial-mode configuration. Typical helix dimensions for an axial-mode helical antenna have a helix circumference of one wavelength at the center frequency, with a helix pitch of 12 to 14 degrees. Kraus defines the pitch angle α as: − s α = tan 1 πD where s is the spacing from turn to turn and D is the diameter, the circumference divided by π. The triangle below illustrates the relationships between the circumference, diameter, pitch, turn spacing, and wire length for each turn: S = Turn Spacing α = Pitch Angle α = arctan (S/πD) Circumference = π D L = Wire Length Of Turn The ground plane diameter is typically 0.94λ in diameter at the center frequency, but many other configurations have been used, including square plates, wire grids, cavities, and loops1. The 3 dB beamwidth for a helix with n turns is approximately2: = 52 BW3dB degrees , where the circumference, Cλ, and the turn Cλ n ⋅ sλ spacing, sλ, are in wavelengths. The gain of the helical antenna is also proportional to the number of turns. The gain curves in Kraus’ 1950 book2, and many others, show the gain increasing with helix length with no apparent limit. However, experiments with long helical antennas are invariably disappointing. Darrel Emerson, AA7FV, made a series of NEC2 simulations of various length helical antennas and showed4,5 that the gain approaches a limit of about 15 dB, for a length of around 7 wavelengths. The 2002 Kraus book3 shows similar experimental data. For higher gains, arrays of multiple helixes are needed, or other types of antennas. Almost all helical antennas have been made with uniform diameter and turn spacing. K2RIW once suggested that long helical antennas might require variations in diameter and spacing over the length of the antenna, just as optimized long Yagi-Uda antennas require variable element lengths and spacings for very high gain. Some of the AMSAT satellites and others require more than 15 dB gain with circular polarization for good reception. Until someone finds an optimization that yields higher gain from a long helix, some other antenna type is needed; a parabolic dish is often a good choice. While a large dish can provide gains upward of 30 dB, a small dish can easily provide the 20 to 25 dB gain needed for many satellite applications. The beamwidth of a small dish is broader than the beam of a large dish, making tracking less difficult. Of course, the dish needs a feed antenna, and a short helix is a good choice for circular polarization. A small offset dish is very attractive, since the feed blockage, which degrades small dish performance, is greatly reduced. Helical antennas are relatively broadband, typically useful over a range of frequencies relative to the helix circumference of 3/4λ to 4/3λ, or roughly a 60% bandwidth. Most of the microwave ham bands are spaced by about this much, so there might be the possibility of covering two bands with one helical antenna, one band at the lower limit of the antenna bandwidth and the other at the upper limit. However, we shall see that for a feed antenna, the radiation patterns are much more useful near the center of the range. Thus, the main advantage of the broadband characteristic of the helical antenna is that the dimensions are not critical. Helix Feed 4 turns 12.5˚ with 0.94λ GP diameter at 2.4 GHz Figure 2 90 E-plane E-plane 67.5 H-plane 45 22.5 0 0 dB -10 -20 -30 -22.5 -45 -67.5 Feed Phase Angle -90 0 10 20 30 40 50 60 70 80 90 Feed Radiation Pattern H-plane Rotation Angle around specified Dish diameter = 10 λ Feed diameter = 0.94 λ Phase Center = 0.21 λ in front of GP MAX Possible Efficiency with Phase error MAX Efficiency without phase error AFTER LOSSES: 90 REAL WORLD at least 15% lower Illumination Spillover 80 1 dB Feed Blockage 70 2 dB 60 50 3 dB 40 4 dB 5 dB 30 6 dB 20 7 dB Parabolic Dish Efficiency % 8 dB 10 0.25 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Parabolic Dish f/D W1GHZ 1998, 2001 Helical feed antennas A parabolic dish reflector typically requires a feed antenna with a rather large beamwidth, 90º or more. From the beamwidth formula above, only a short helix of a few turns is needed. Figure 2 shows the radiation pattern provided by a typical short helix, 4 turns with a 12.5º pitch and a ground plane of 0.94λ diameter. The calculated dish efficiency with this helix as a feed is very good, about 77%, at a center frequency of 2.4 GHz, with best f/D around 0.69, just about right for an offset-fed dish. Thus, we might expect a real efficiency >60% feeding a reasonably sized (>10λ) offset dish. A three-dimensional view of the radiation pattern, in Figure 3, shows a reasonably clean pattern with relatively small sidelobes; adjacent shades of gray have a difference in amplitude of 2 dB. The backlobes of most helical antennas, like the one in Figure 3, seem to have a twisted asymmetric shape. Helix 4 turns 12.5˚, 0.94λ GP, at 1.8 GHz Helix 4 turn 12.5˚, 0.94λ GP, at 2.0 GHz Figure 4a Figure 4b 90 90 E-plane E-plane E-plane E-plane 67.5 67.5 H-plane H-plane 45 45 22.5 22.5 0 0 0 dB -10 -20 -30 0 dB -10 -20 -30 -22.5 -22.5 -45 -45 -67.5 -67.5 Feed Phase Angle Feed Phase Angle -90 -90 0 10 20 30 40 50 60 70 80 90 0 10 20 30 40 50 60 70 80 90 Feed Radiation Pattern H-plane Feed Radiation Pattern H-plane Rotation Angle around specified Rotation Angle around specified Dish diameter = 10 λ Feed diameter = 0.94 λ Phase Center = 0.04 λ in front of GP Dish diameter = 10 λ Feed diameter = 0.94 λ Phase Center = 0.08 λ in front of GP MAX Possible Efficiency with Phase error MAX Possible Efficiency with Phase error MAX Efficiency without phase error AFTER LOSSES: MAX Efficiency without phase error AFTER LOSSES: 90 90 REAL WORLD at least 15% lower Illumination REAL WORLD at least 15% lower Illumination Spillover Spillover 80 1 dB 80 1 dB Feed Blockage Feed Blockage 70 70 2 dB 2 dB 60 60 50 3 dB 50 3 dB 40 4 dB 40 4 dB 5 dB 5 dB 30 30 6 dB 6 dB 20 7 dB 20 7 dB Parabolic Dish Efficiency % Parabolic Dish Efficiency % 8 dB 8 dB 10 10 0.25 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.25 0.3 1.00.4 0.5 0.6 0.7 0.8 0.9 Parabolic Dish f/D Parabolic Dish f/D W1GHZ 1998, 2001 W1GHZ 1998, 2001 Helix 4 turns 12.5˚, 0.94λ GP, at 2.2 GHz Helix 4 turns 12.5˚, 0.94λ GP, at 2.6 GHz Figure 4c Figure 4d 90 90 E-plane E-plane E-plane E-plane 67.5 67.5 H-plane H-plane 45 45 22.5 22.5 0 0 0 dB -10 -20 -30 0 dB -10 -20 -30 -22.5 -22.5 -45 -45 -67.5 -67.5 Feed Phase Angle Feed Phase Angle -90 -90 0 10 20 30 40 50 60 70 80 90 0 10 20 30 40 50 60 70 80 90 Feed Radiation Pattern H-plane Feed Radiation Pattern H-plane Rotation Angle around specified Rotation Angle around specified Dish diameter = 10 λ Feed diameter = 0.94 λ Phase Center = 0.12 λ in front of GP Dish diameter = 10 λ Feed diameter = 0.94 λ Phase Center = 0.40 λ in front of GP MAX Possible Efficiency with Phase error MAX Possible Efficiency with Phase error MAX Efficiency without phase error AFTER LOSSES: MAX Efficiency without phase error AFTER LOSSES: 90 90 REAL WORLD at least 15% lower Illumination REAL WORLD at least 15% lower Illumination Spillover Spillover 80 1 dB 80 1 dB Feed Blockage Feed Blockage 70 70 2 dB 2 dB 60 60 50 3 dB 50 3 dB 40 4 dB 40 4 dB 5 dB 5 dB 30 30 6 dB 6 dB 20 7 dB 20 7 dB Parabolic Dish Efficiency % Parabolic Dish Efficiency % 8 dB 8 dB 10 10 0.25 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.25 0.3 1.00.4 0.5 0.6 0.7 0.8 0.9 Parabolic Dish f/D Parabolic Dish f/D W1GHZ 1998, 2001 W1GHZ 1998, 2001 Helix 4 turns 12.5˚, 0.94λ GP, at 2.8 GHz Helix 4 turns 12.5˚, 0.94λ GP, at 3.0 GHz Figure 4e Figure 4f 90 90 E-plane E-plane E-plane E-plane 67.5 67.5 H-plane H-plane 45 45 22.5 22.5 0 0 0 dB -10 -20 -30 0 dB -10 -20 -30 -22.5 -22.5 -45 -45 -67.5 -67.5 Feed Phase Angle Feed Phase Angle -90 -90 0 10 20 30 40 50 60 70 80 90 0 10 20 30 40 50 60 70 80 90 Feed Radiation Pattern H-plane Feed Radiation Pattern H-plane Rotation Angle around specified Rotation Angle around specified Dish diameter = 10 λ Feed diameter = 0.94 λ Phase Center = 0.58 λ in front of GP Dish diameter = 10 λ Feed diameter = 0.94 λ Phase Center = 1.05

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