Figure 1: MMDS Antennas Installed For AO-40 Downlink At N1JEZ, KE4AZN, & KK5DO

While these antennae are optimized for their intended application, they can be improved for amateur satellite S-band downlink. My recent experimentation with helical antennae led me to believe a helix feed may be an excellent choice for the home brewer (1). In pursuing this, I combined several design concepts, each adding incrementally to the antenna's efficiency. This fortunate synergy provided an easy-to-replicate design ideal for AO-40 S-band reception.

Detailed below are some basic parabolic dish design guidelines, some extrapolations of various ideas as they apply to parabolic antennae, and some specific construction details for one of the commonly available grid-style dish antennas. Much of the following discussion also may be applied to surplus offset dishes from the fast-changing DDS (Direct Digital Satellite) industry (2).

Understanding What You Have:
Figure 2, at right, depicts the asymmetrical E-plane and H-plane patterns for a resonant dipole-plus-parabolic-reflector array (using 3 reflectors) at 2401.500 MHz in free space (3). Note how the -3 dB beamwidth pattern for the H-plane is about twice as "broad" as the E-plane: 120 degrees compared to 70 degrees. Considering these patterns for a feed, it is obvious the rectangular shape of the MMDS reflector is by design. The MMDS antenna manufacturers have taken advantage of this inherent dipole characteristic in designing their antennae broader in the H-plane-perpendicular to the dipole's orientation. It appears an optimized design for the dipole feed, providing higher potential gain and lower G/T (Gain / antenna noise temperature), but invariably requires a low f/D ratio in the range of 0.3 to 0.4 in order to capture as much of the low-gain, wide-beamwidth pattern of the dipole array as possible. For a MMDS dish, measuring 38" (97 cm) x 26" (66 cm), the theoretical gain is:

An (optimistic) efficiency of 50 percent is assumed in the foregoing calculation. The focus is where the parabolic shape of the dish concentrates the reflected signal and is determined by:

Thus, the focus/Diameter (f/D) ratio of this "typical" MMDS antenna is approximately 0.6 in the in-plane dimension and 0.4 in the perpendicular dimension, referenced to the dipole array feed.

Wade, in his authoritative on-line text, states the general feed design goal succinctly: "in order to have a very efficient dish illumination we need to increase energy near the edge of the dish and have the energy drop off very quickly beyond the edge" (4). The oft-quoted feed efficiency rule of thumb is illumination power equal to -10 dB at the dish edge, with perhaps -13 or -15 dB for slightly less efficiency but better G/T ratio (5). A little trigonometry shows the E-plane edge-of-the-dish-cutoff (E) is at 46 degrees and the H-plane cutoff (H) is at 63 degrees for the author's surplus dish:

Note the dipole patterns above, at the calculated cutoff angles, are closer to -5 dB and -4 dB, leading to significant spillover loss--thus efficiency is low for this dish, especially in the H-plane dimension. The standard dipole array feed simply does not have enough gain to meet the -10 dB design goal. Given this, the de facto 50 percent efficiency (() used above appears optimistic and was shown to be just that at a recent microwave conference in Texas. A few iterations of these formulae will indicate a f/D greater than 0.5 helps achieve the desirable characteristic by compensating for the antenna's beamwidth pattern; i.e., the prime focus is closer to the edge than the center. For comparison, an f/D of 0.4 requires about 1.4 dB stronger signal at the edge (inverse square law) than at the center of the dish for constant illumination, while an f/D of 0.6 requires only 0.7 dB at the edge (6). These values are derived from applying the classic power equation to the dish geometry:

Less is More:
Common surplus MMDS antennas are designed for linearly polarized terrestrial signals-hence the dipole feed is a natural choice. The signals of most interest to amateur satellite enthusiasts, however, are predominantly circularly polarized; e.g., the S-band signals from AO-40. Using a linear antenna to receive a circularly polarized signal nets a 3 dB penalty for the antenna above, resulting in a phase-corrected expectation of 21 dBi actual gain from this antenna (7). Simply substituting an appropriately circular feed would seem to regain the lost 3 dB: just replace the dipole with a helix feed inside a cup feedhorn (8). If, however, maximizing the antenna gain is also desired, two feed efficiency design issues need be addressed: 1) phase alignment and 2) losses due to feed geometry.

Phase alignment is simply assurance the polarity characteristics of the desired signal are mirrored in the reflector+feed so as to minimize losses. Unfortunately, the linear grid pattern of the subject surplus antennas will not effectively reflect a circularly polarized signal. The simplest solution is to cover the reflector surface with a reflective grid. I found aluminum screen wire (mesh) inexpensive and easy to fashion and support on the grid using small conductor wire interlaced in the grid.

Losses due to feed geometry include under-illumination, spillover, and feed blockage. Under-illumination and spillover are addressed by selecting an efficient circularly polarized feed matched to the f/D of the reflector. Feed blockage can be minimized with a coaxial support through the center of the helical feed. Since a helical feed element has symmetrical E- and H-plane patterns, there is no need for the dish's rectangular shape. I cut the grid reflector down to 26" (66 cm) square, which also lowers the wind loading, the visible profile, and the weight of the antenna-all good things. Since I now had a uniform 0.6 f/D and planned to improve the illumination efficiency considerably, I felt justified in modestly increasing the efficiency (() factor to 55 percent in the gain calculation:

This smaller antenna with a circular feed actually has more net gain than the (larger) original one. If a circular feed horn is used, it may be appropriate to ignore the "corners" of the now-square dish and treat it as a circular paraboloid, using the traditional (r2 area factor instead of the substituted length*width. A "dish equivalent" gain of 21.75 dBic results-still marginally better than the larger original dish.

Figure 3: Before (38" x 26") and After (26"x 26")

Helix Feed Design:
With the reflector portion of the antenna now defined, attention is turned to the feed. I integrated several antenna design concepts, each incrementally contributing to an overall efficient design: 1) an end-fire monofilar helices to achieve circular polarization; 2) a cupped reflector to improve forward gain while simultaneously reducing the side lobes to maximize reflector illumination; and 3) design of the cupped feed reflector as a feedhorn to limit/eliminate spillover losses beyond the dish's edge.

A critical component of the antenna's overall performance is determined by the accuracy of the placement of the feed's phase center at the prime focus of the dish (9). I tested a number of helices from 4-turns to 10-turns, using local MMDS video signals as my test source, and found the signal peaked from about the 180 degrees to 450 degrees (1/2-turn to 1-1/4 turn) points of the helix. The drop in signal is slight in moving the feed so the focus is located all the way towards the back of the cup, but is quite pronounced when moving the cup so the focus is located beyond the 450 degree point (towards the dish). Installing a cupped reflector had no measurable impact on this phenomenon. This is in general agreement with other references specifying a range of (/6 to (/8; a range of 0.6 - 0.85" (15-22 mm) for a nominal 2.401 MHz helix (10).

Kraus describes a cupped ground plane as having "supergain" properties, but does not quantify this benefit (11). K&W modeled such a construct and report a consistent 2 dB gain (12,13). My own empirical testing confirms a notable gain, as much as 1 dB, for even a short helix. Kraus defines the parameters as: Diameter = 0.75 lambda and depth = Dia/2 (14). These parameters produce a nominal S-band cup with 3.75 - 4" (10 cm) diameter and 1.75" (4.8 cm) deep.

But, I wanted to also use this cup as a feedhorn, and specifically to construct it so as to limit the spillover from the dish's edge. My idea was to place the helix phase center at the prime focus and then use the previously calculated edge-of-dish-cutoff (( E) of approximately 45 degrees as the (convenient) geometric limit for the depth of the cup; in effect, a helical feedhorn. Figure 4 depicts this geometry. Note how the 45 degree angle goes through the helix's first turn--the phase center--and intersects the edge of the dish.

Figure 4: Dish Geometry

Design of helix feed itself was the last "paper" task in this antenna design exercise. As noted above, gain greater than a dipole array was required, but not so high as to concentrate too much energy at the center of the dish. The ideal helical pattern would be 90 degrees at -10 dB, with as wide a -3 dB (half power beamwidth) as possible. I built some simple computer models of this ideal helix and the -10 dB point for a 3-turn helix appears greater than 120 degrees, progressing to 90 degrees for a 4-1/2 to 5-turn helix.

Figure 5: End-Fire Monofilar Helices Without and With A Cupped Ground Plane

Several more complex models were built-both with and without a cup-to analyze the free space behavior of the helices. These are depicted above in Figure 5, with the model on the right constituting more than 450 wires and more than 3,000 pulses. This exercise was started with a 1.5( (6-turn) helix. Much of the literature is in dispute regarding the gain of longer helices, but the preponderance of the data converges on 1.5( (roughly 6-turns) with 11.5 dBi maximum gain (15).

Figure 2, at right, depicts I modeled helices from 3-turns through 7-turns. Figure 6, at right shows the free space NEC patterns for helices of 4, 5, and 6-turns Inside A Cup. Note the small, progressive changes in the gain and -3 dB and -10 dB points for each successively longer helix. The -3 dB points align well with the idealized patterns, but the -10 dB points, particularly noted in the sidelobes, are quite different. These patterns indicate a longer-than-ideal helix is needed to achieve the specified -10 to -13 dB cutoff. It appears from these patterns the 6-turn, or possibly even a 7-turn, helix is a better choice. I found this development surprising and disappointing, because I could not determine which data were correct. Review of the literature was unsatisfactory, as little is documented on helices this short. Since I could not resolve this discrepancy through research, I decided to do my own field testing. I hoped to either validate the NEC models or discard them as inaccurate. The test was conducted using a 2.4 GHz signal source (inside a coffee can), a test fixture to rotate the subject helix in 5 degree increments, and a semi-calibrated receiver--via a converted MMDS downconverter (16). I tested helices with a 0.8 lambda diameter reflector from 3-turns to 7-turns and then repeated the tests with a 0.4 lambda deep cup.

Figure 7: The Signal Source, The Test Fixture, and The Receiving Gear

Things kept getting worse. These empirical data indicate the helix patterns from the tests are generally representative of, but the half-power-beamwidth and rear lobes of the actual antennae are much worse than, the NEC models predicted. In consultation with Paul Wade, W1GHZ, it became apparent I had considerable reflections in my "test range" (also known as my patio). I then moved the test apparatus out to a vacant field and repeated the tests-braving the hot Houston sun and fire ants in August!

This subsequent testing produced more believable results, although still considerably below the performance predicted by the NEC models. I took all three data sets and ran the W1GHZ feed pattern program against them and produced an illumination/spillover analysis/graph for each case (17). The results are summarized below. I now had three disparate "optimum" helix sizes: a 4-turn based on an "ideal" helix; a 7-turn based on NEC modeling; and a 6-turn based on my testing. Which one was correct? I needed to build it to find out.

Figure 8: Patterns For 4, 5, 6, & 7-turn Helices w/Cup	Figure 9: Maximum Possible Efficiency Per W1GHZ Feed Pattern Program

Construction:
Now the design was complete-except for the number of helix turns-- and building it was a matter of finding materials conforming to the design requirements. The helix itself was crafted from common copper house wiring-repeating a prior successful design (18). This design utilizes a smaller-than-optimum diameter and close spacing of the first turn to effect a close match to 50 Ohms. Figure 10 shows the helix construction details.

Next, I searched for a suitable feedhorn. My previous use of a coffee can feed was convenient, but my ability to keep them from rusting was in serious doubt. I spotted an old MDS antenna in my junk pile that had a near-perfect 4" (10 cm) diameter aluminum feedhorn. I cut it down to a 2" depth and started the search for a coaxial support mechanism. I discovered 1/2" EMT fittings with a threaded connection on one end and a compression fitting on the other end. A pair of these and a short section of 1/2" EMT conduit is all that is required for support. This hardware is common and inexpensive, and provides both support for the feed and a cable route without creating additional aperture blockage.

I used a borrowed impedance bridge to adjust the feedpoint impedance match of the helix inside the cup (19). Note the insulation was left on the #10 AWG wire for the first 1/4 turn. By pushing the helix coil's insulated first 1/4-turn against the back of the cup, a perfect 50 Ohm match was obtained. Figures 11 and 12 depict construction details. As mentioned above, the cut-down reflector was covered with aluminum screening cloth and secured with a weaving of small conductor wire.

The completed prototype was installed and immediately tested on UO-11, which provides an excellent, repeatable test signal (20). Later tests on AO-40's S2 telemetry beacon provided very positive feedback on the antenna's performance: at 30,000 km the signal was 9 S-units above the noise on the author's system and telemetry was still solid at apogee (62,000 km) with signals at 5-7 S-units above the noise. You can see the completed prototype below. Note the preamp connects directly to the feed and the preamp's output cable is routed through the 1/2" EMT conduit.

Figure 11: Tuning Using W4MVB's Bridge and the Helix Feed Connection

Figure 12: N-Connector / EMT Fittings and Reflector Plate Modification for EMT Fitting

Figure 13: The Prototype Installed (barely) Between the Rotor and 70 cm Yagi

Final Testing:
I still needed to determine the optimum number of turns for the helix feed. I did another round of tests with the completed antenna separated 100 meters from the signal source; this time using a G0MRF 2.4 GHz oscillator kit in a coffee can (21). The results of this final testing compared favorably with the NEC models, but show no discernable performance difference between 5-1/4 turns and 6-1/4 turns. A 6-1/4-turn helix, with approximately 11.5 dBi gain and -10 dB beamwidth of a little over 90 degrees, was chosen for the final design. The 7-turn helix has additional gain and would be a good choice for a shallower dish with an f/D of 0.75, or if a better G/T was desired at the sacrifice of a little efficiency. Figure 14 depicts results of the final testing.

The results of the final testing shown above also include a rough measurement of circularity. All of the primary readings were taken with the antenna in the horizontal plane (original grid) and the antenna was manually rotated to vertical and readings taken again. These circularity readings are relative delta values (from the horizontal reading) and were quite limited by the resolution and range of the S-meter on my test radio. Still, a strong positive correlation to number of turns is indicated.

As can be seen in Figure 15, FEEDPATT.exe comparison of 6-1/4-Turn Helix With Cup (NEC Model v. Tested), achieving a 55 percent efficiency in "the real world" seems unlikely. The author's dish, with an f/D of 0.6, has the edges 85 percent of the distance to the center. An f/D greater than 0.5 compensates somewhat for the decreasing illumination at the dish's edge, called taper (22,23). Table 1 offers guidelines for helix+cup lengths based on dish geometry. If a conventional reflector plate is used in lieu of the cupped reflector, add 1/2 turn to these recommendations. I followed K9EK's recommendation to add 1/4-turn to all helices to improve the return-loss figure (24).

Conclusions:
The author's first home-brew dish antenna was built without much analysis, but proved successful enough to warrant further thought. This subsequent effort focused on analysis first and construction second. Careful consideration was given to designing an antenna easy to replicate with common hardware materials. The integration of several ideas--a circularly polarized feed, a smaller size reflector suited to that feed, a feedhorn matched in geometry to the reflector, and a helix matched in gain to the dish's geometry--all contributed incrementally to producing a high performance, low profile antenna system. All indications are this antenna system performs well, even if not to the "paper" design specifications. The transponder noise floor is detectable at 40,000+ km. Success!

Potential improvements lie in the area of reducing the feed's aperture blockage-perhaps by reducing the size of the cup or using a back-fire helix with no cup (25). In the end, the author concludes the helix is an easy-to-build and effective, if unimpressive, feed for an S-band dish. Much more work, with better test equipment and methodology, is required to develop this concept further. The helix feed's strongest point of recommendation is ease of construction, not its performance attributes.

References:
1. Brown, Gerald R., "YAHE (Yet Another Helix Experiment)," Proceedings of the AMSAT-UK Colloquium 2001, July 2001, pp. 89-94, http://members.aol.com/k5oe.
2. Long, Howard, "Modify an Analogue Sky TV Dish for AO-40 S-Band," http://www.g6lvb.com/60cm.htm; and "Entry Level AO-40 Capable Satellite Station," Proceedings of the AMSAT-UK Colloquium 2001, July 2001, pp. 67-80; "Build an Entire AO-40 Ground Station for Under $500," http://www.g6lvb.com/el/index.htm.
3. A model was built with a resonant dipole and three equidistant reflectors using NEC4Win95: http://www.orionmicro.com/n4w95/n95page.html.
4. Wade, Paul, N1BWT (W1GHZ), Online Microwave Antenna Book, Chapter 4, "Parabolic Dish Antennas": http://www.qsl.net/n1bwt/contents.htm.
5. Ibid, Chapter 11, "Parabolic Dish Feed-Performance Analysis."
6. Ibid, Chapter 4, "Parabolic Dish Antennas, Practical Dish Antennas, Feed Patterns."
7. Davidoff, Martin, The Radio Amateur's Satellite Handbook, ARRL, 1998, pp. 9-4 - 9-7.
8. Brown, Ibid.
9. Wade, Chapter 6.0.3 Antenna Efficiency.
10. Martin, Sven, "Antenna Diagram Shaping for Pseudolite Transmitter Antennas..." Institute of Flight Guidance and Control, Technical University of Braunschweig, Germany. Also see the author's additional phase center testing with a local noise source at: http://groups.yahoo.com/group/AmsatTech/files/phase_center_09.JPG.
11. Kraus, John D., Antennas, 1988, Figure 7-16c, p. 281.
12. King & Wong, "Characteristics of 1 to 8 Wavelength Uniform Helix Antennas," IEEE Transactions, AP-28, No. 2, March 1980, pp. 291-296.
13. Trueman, Kubina, & Slater, "Modelling Helix Antennas with NEC4," IEEE Transactions, 1997, pp. 1584-1587.
14. Kraus, Ibid.
15. Emerson, Darrel, "The Gain Of An Axial-Mode Helix Antenna," Antenna Compendium Volume 4 (ARRL), 1995, pp. 64-68; also: http://ourworld.compuserve.com/homepages/demerson/helix.htm.
16. ICM Manufacturing, 5 MHz crystal oscillator: http://www.icmfg.com/osc.html.
17. Wade, Paul, W1GHZ, feed pattern program, FEEDPATT.exe, available for download at: http://www.qsl.net/n1bwt/contents.htm. 18. Brown, Gerald R., "16-Turn Helix Antenna," http://members.aol.com/k5oe.
19. Koehler, Jim VE5FP, & Rawson, Eric KN6KC, "Putting Together a L/S Band Antenna System for the Phase 3D Satellite," The AMSAT Journal, Sep/Oct 2000, pp. 13-19.
20. Wallis, Clive. G3CWV, OSCAR-11 Satellite, http://www.users.zetnet.co.uk/clivew/index.htm.
21. Bowman, David, G0MRF, http://www.g0mrf.freeserve.co.uk/source2.htm.
22. Nelson, Robert A., Antennas, "The Interface with Space," Via Satellite, Sept. 1999, pp. 6-7, also: http://www.aticourses.com/antennas_tutorial.htm.
23. EW & Radar Systems Engineering Handbook, see: http://www.ewa-australia.com/handbook/ANTENNA%20INTRODUCTION%20-%20BASICS.htm.
24. Krome, Ed, K9EK, Mode-S, The Book, pp. 114-121; also "Dish Feeds For Mode S Reception," The AMSAT Journal, Sept/Oct. 1994.
25. Nakano, Yamauchi, & Mimaki, "Backfire Radiation from a Monofilar Helix with a Small Ground Plane," IEEE Transactions on Antennas and Propagation," Oct. 1988, pp. 1359-1364.

(C) 2001, Gerald R. Brown, K5OE