A NEW CLASS OF DIRECTIVE ANTENNAS R. P. Haviland, W4MB Improve Yagi performance with curved 1.5 wavelength elements In the May. 1983 issue of Transactions on Anten- nas and Propagation, Chang and Cheng introduced a new class of antennas that appear to offer much promise for VHF use. Based on concepts developed earlier by F. M. Landstorfer,2 these antennas feature curved elements, each longer than a wavelength and shaped to compensate for the reversals in phase that occur each half wavelength along an element. With the 1.5 wavelength elements in the classic reflector-driven-director configuration used in the original experiments Landstorfer claimed gains of 11.5 dBi. The same gain in a conventional Yagi using straight half-wave elements would require about nine elements and a much longer boom. While the new design requires greater width, the combination of gain, short boom length, and mounting simplicity form the attractive features of the design. Principle of Operation The general concept and plan of these antennas is shown in fig. 1. The center part of the elements resembles a V radiator. The phase center of the V radiation lies along the center axis, and some distance from the apex of the V. A wave radiated from this sec- tion will arrive at the other element parts after a time a delay that corresponds to a phase rotation. As a result, even though the outer sections are out of phase with respect to the center section, the delayed wave will be at least partly in phase with the waves radiated by the outer sections. This addition of wave components accounts for the increase in gain over a conventional straight-element Yagi. The design problem presented by these antennas is to determine the shaping of the elements for max- imum gain. This subject was addressed by Chang and Cheng in their article.' They approximate the current distributions on the array elements by the method of moments, dividing each element into 22 sections and analytically determining the shaping for maximum gain. The computations are extensive, involving a 63 by 63 complex matrix manipulation (a solution requires approximately 40 minutes of DEC-10 computer time). The problem is far beyond the capability of home computers. Fortunately, Chang and Cheng have summarized their results in such a form that makes it possible to duplicate their optimized design for a three-element Yagi array. For convenience, the results have been ar- ranged as a computer program, fig. 2, written in Simon's BASIC for the Commodore 64. The program is written for easy translation to other versions of BASIC; only the graphic generation section may re- quire a complete rewrite. The program first determines whether hard copy is needed, then requests its only input, the design fre- quency. Element length and diameter are then out- putted, followed by a table of X, Y values that define the center-line position of each element. The feed- point, or center of the radiator is taken as the coordi- nate origin. Figure 3A shows the screen presentation (the ending O's indicate that the end of the element has been passed). Pressing the space bar produces a plot of the lines defining the element centers, as shown in fig 3B. Pressing the space bar again either initiates a hard copy or terminates the program. The general resemblance of this type of antenna to a conventional Yagi is apparent in the figures. The ele- ment shaping causes a taper towards the forward direction, even though the elements are the same length. And the deep V of the director gives an effec- tive wide spacing for the director. The performance of this optimized design is very good. According to Chang and Cheng,l gain calcu- lates to be 11.8 dBi. Beamwidth is 32 degrees in the element plane, and 62 degrees at right angles to it. Front-to-back ratio is just less than 15 dB in both planes. Feed impedance of the 3/2 wavelength radiator is calculated to be 14 + j33 ohms. It should be noted that the design values are opti- mum only for the element diameter given. This was arbitrarily set at 0.01 wavelength by Chang and Cheng. Performance should not be greatly affected by a rea- sonable change in element diameter. Because of the complexity of the required calcula- tions, and the many hours of mainframe computer time necessary to perform them, it is unlikely that there will be much further analysis of the type. Further work will have to be experimental. None has been attemp- ted by the author, but it would seem that additional gain could be secured by placing additional directors of similar shapes in front of the present single direc- tor, using appropriate spacings. It would also seem that any of the common matching methods would be usable. Stacking spacing rules of high-gain Yagi type would appear necessary. Conclusion Those who do not have a computer available, or who wish to avoid the tedium of typing in the program, can use these results by simple frequency scaling. All table dimensions should be multiplied by the ratio, 147/new frequency, since the table was calculated for 147 MHz. Element diameter and length vary in the same way. References 1. Chang-Hong Liang and David K. Cheng. "Directivity Optimization for Yagi- Uda Arrays of Shaped Dipoles." IEEE Transactions on Antennas and Propagation AP-31, Volume 31. No. 3. May, 1983, pages 522-525. 2. F. M. Landstorfer. "A New Type of Directional Antenna." Antennas and Propagation Society International Symposium Digest. IEEE. 1976. pages 169-172.