Some Basics of Very-Wide-Band Yagi Design
Part 1: A Study of Very-Wide-Band Crossed-Element Yagi Performance

L. B. Cebik, W4RNL

Purpose: The goal of this series is to explore just how far we may extend the operating bandwidth of the Yagi-Uda antenna. Historically, Yagis were initially designed for maximum gain, a phenomenon that seemed to be limited to a narrow bandwidth. Wide-band Yagis--nost notably of the DL6WU VHF/UHF type--appeared in the 80s and 90s, with variations appearing in the HF region. A special variation, called the OWA or optimized wide-band antenna, appeared in the 1990s. Its special features included a tight control of peformance as well as feedpoint impedance across a moderately wide frequency spectrum--as much as 4-5% of the center or design frequency. The DL6WU Yagis, however, are capable of at least 7% bandwidths and possibly up to 10%, depending on design.

Wide-band design does not have a definite border that separates it from very wide band design (VWB). However, we shall use any operating bandwidth over 20% of the design center frequency as falling distinctly within the very wide band region. The question then is simply this one: is it possible to design a Yagi array that provides usable performance over a bandwidth greater than 20% of the design center frequency with a feedpoint impedance that varies within 2:1 SWR limits? The idea of "usable performance" depends, of course, on the particular application for the antenna. Therefore, our initial foray into VWB design will be application-specific.

The initial study examines the fundamental operation of very-wide-band crossed element Yagis antennas, ordinarily designed for satellite communications. I shall use a self-designed 8-element Yagi for 250-317 MHz as a vehicle for exploring both basic operation of the antenna and its performance potential. Included will be a discussion of very-wide-band Yagi design principles. The second part of the micro-series will examine the design of standard planar Yagis in the very wide band mode.

The Test Antenna: Design and Operation: The test antenna is a crossed-element Yagi employing 8 element sets: 1 reflector set, 1 driver set, and 6 director sets. Fig. 1 shows the outline of the final array.

The parasitic elements all meet that their center points, which would normally occur at a boom--whether or not conductive. No performance figure is altered by either joining or isolating the linear parasitic elements at their centers.

The drivers are quadrature fed, that is, fed with roughly equal currents at a 90-degree phase angle by the use of a simple phasing line approximately but not exactly 1/4 wavelength long at the center frequency on the band. The actual length of line specified was adjusted for the smoothest impedance curve.

The individual antennas in the crossed set each have source impedances of about 50 Ohms. Therefore, a 50-Ohm phase line is specified. The net impedance of the driver set is about 25 Ohms. Therefore, a 35-Ohm matching line was added to the feedpoint to raise the impedance to 50 Ohms. Like the phase line, this match line is approximately but not exactly 1/4 wavelength at the center of the operating band, due to adjustment for the smoothest impedance curve across the band.

The operating band for this design is 250-317 MHz, with a center frequency of 283.5 MHz. The operating 67 MHz bandwidth is about 23.63% of the center frequency.

The design of the individual Yagis was derived from highly modified DL6WU wide-band Yagi design criteria. Elements were recalculated for a diameter of 0.5" to achieve the widest natural bandwidth within the range of potentially usable materials. However, the bandwidth might be achieved with elements only half the diameter used, since the principles of true wide-band design apply to the antenna.

Quadrature feed provides one method of increasing the SWR bandwidth, but does not itself improve the bandwidth of such parameters as gain, front-to-back ratio, and pattern shape. Those parameters require careful design of the element sequence in the Yagi.

Crucial to an understanding of very-wide-band design is a survey of the current on the driven element and the first director of each Yagi in the set. In VWB design, the first director is set about 0.075 wavelength ahead of the driver. The actual spacing--as is true for all other element spacing in the design--is a function of the element diameter and the variations in mutual element coupling that occur as a result of varying that diameter. The combination of driver-to-director-1 spacing and driver-to-reflector spacing together set the general operating source impedance for the array. The spacing used is roughly optimal for an individual Yagi source impedance of approximately 50 Ohms.

When designing the antenna for VWB service, the drive system makes use of a phenomenon that inter-relates the spacing and relative lengths of the driver and the first director. At the low end of the defined operating band, the driver exhibits a current magnitude that is considerably higher than that of the first director. However, at the upper end of the defined operating band, the first director current magnitude exceeds that of the driver. In effect, the first director becomes the effective driver at the upper end of the operating band. So long as the fed driver can couple energy to the first director, the upper end of the spectrum will operate with usable amounts of gain and front-to-back ratio and with a satisfactory pattern shape. Ordinarily, there is a fairly sharp high-end cut-off point at which the first director is too long to sustain its driver function, and the overall performance of the antenna degrades rapidly. The escalating SWR is often accompanied by a pattern distortion that yields multiple peaks in the forward lobe.

At the upper end of the operating spectrum, the driver and reflector show reduced influence on the Yagi performance figures and pattern shape. So long as the driver is not too long to couple energy efficiently to the first driver, its length becomes optional with respect to upper-end performance. The main element on which to make fine adjustments in upper-end performance becomes the forward-most director: director 6 in the case of the subject antenna. Changes in the length of the reflector have almost no effect on upper-end performance.

At the low end of the operating spectrum, where the driver shows a significantly higher current magnitude than the first director, the driver and reflector tend to control lower-end performance parameters. The driver may be lengthened to extend the lower-end limit to a satisfactory source impedance. Lengthening the reflector in tune to the driver extends the range of acceptable gain and front-to-back performance. Changes in these elements--up to a limit--result in negligible changes in the upper-end performance of the antenna.

By combining the elements of VWB Yagi design (in concert with quadrature feed), it is possible to obtain a crossed-Yagi design that covers the entire subject band of 250-317 MHz. Fig. 2 shows the NEC-4-modeled SWR curve for the test antenna.

The upper portion of the curve shows the 50-Ohm SWR values at 2-MHz intervals between 250 and 318 MHz. The upper-end curve rises very rapidly above 318 MHz. The curve rises somewhat less rapidly below the set lower limit of the operating band.

Notable in the curve are the 5 minimums at 250, 278, 298, 310, and 318 MHz. The broader the operating bandwidth and the greater the element coupling, the higher the number of minimums in the curve, with 5 being the maximum that I have so far been able to obtain. The upper end of the band shows a greater level of fluctuation than the lower end. The lower portion of the figure shows an expansion of the graph between 314 and 316 MHz to confirm that the SWR does not rise above 2.0:1 in this region. The position and level of this curve can be partially controlled by the spacing and length of the forward-most driver.

The objective in any design is to assure as best possible a coincidence between the SWR and impedance curves and the other operating parameters. Initially, these factors include the source resistance and reactance.

Fig. 3 shows the source resistance across the band with the antenna model in 3 different environments used to test the design. One curve presents the modeled free-space source resistance. Another models the resistance with the antenna pointed vertically upward with its reflector about 1 wavelength above the ground at mid-band. The height of about 41.5" is roughly coincident with what might be a standard desk-top operating height. The final curve shows the source resistance with the antenna angled upward 45 degrees, with the center of the reflector at the 41.5" level. This corresponds to desk-top operation for a satellite well below zenith. As with the SWR curve, the source resistance shows increasing fluctuation toward the upper end of the operating spectrum.

Reactance across the entire operating spectrum varies by less than 15 Ohms, as shown in Fig. 4. Above 317 MHz, the reactance rises sharply, effectively cutting off use of the antenna within the 2:1 SWR limits most often used as a standard. The reactance changes more slowly below the lower end of the operating spectrum. Once more, the curves are virtually identical for all three environments. Together with the overlapping resistance curves, these two graphs show why a single SWR curve (actually modeled with the antenna in the vertical condition over real ground) suffices to demonstrate that parameter. The impedance and SWR figures represent the net values presented to the main feedline after all phasing and matching have been implemented at the antenna feedpoint.

These results were obtained with the dimensions shown in the following table.

               Dimensions of the 8-Crossed-Element Yagi for 250-317 MHz

All elements:  0.5" diameter 6063-T832 aluminum.  Dimensions apply to each linear element in each set
of two "wires" making up the crossed element.

Element                             Tip-to-Tip              Distance from                       Distance from
                                    Length (")              Reflector (")                       Preceding Element (")
 Reflector                           21.80                   ------                              ------
 Driver                              19.50                    8.27                                8.27
 Director 1                          16.82                   11.10                                2.83
 Director 2                          16.56                   18.19                                7.09
 Director 3                          16.32                   26.65                                8.46
 Director 4                          16.09                   36.48                                9.83
 Director 5                          15.88                   47.50                               11.02
 Director 6                          15.29                   59.30                               11.80
Phase line length:  9.344", 50-Ohm cable, VF=1.0.  Match line length:  8.948", 35-Ohm cable, VF=1.0.

Table 1.  Dimensions of the 8-crossed-element satellite Yagi for 250-317 MHz.

The phase line provides quadrature feed, which in turn provides the antenna with roughly circular polarization. With a fixed phaseline and a potential feed connector at each end, the direction of circularization reverses simply by connecting the match line and main feedline to one or the other connector. Because the phase line is perfect for only one frequency, the strength of the fields will vary slightly as one moves away from the design frequency of the phase line. However, for satellite work, the degree of departure from perfection is below the significance level.

Performance: The standard tests for modeled antennas usually include free-space performance and performance over ground in some single configuration. However, satellite antennas may be used at any angle with respect to ground from nearly parallel with the earth's surface to pointed straight upward. To sample the performance of the antenna over real ground, with the lowest end of the boom about 1 wavelength above ground, I set the antenna in two positions: straight up and angled at 45 degrees. These two orientations yield very interesting differences in performance, especially when contrasted with the free-space performance. When antennas are placed parallel to the earth's surface, whether horizontally or vertically polarized, the patterns obtained--with gain adjustments--tend to match the corresponding free-space E-plane and H-plane patterns. This expectation does not apply to antenna placed in a vertical or angled orientation.

1. Gain: The free-space gain varies from about 9.75 dBi to 12.6 dBi, with the band edges reasonably well matched. Fig. 5 shows the free space gain curve, as well as curves for a vertical and an angled environment above ground. The 45-degree curve closely parallels the free-space curve, but at a strength level well below what we normally expect from ground reflections. The average difference in gain between the angled antenna and the free-space model is about 0.75 dB.

The curve for the vertical antenna has two interesting features. At the low end of the spectrum, the curve flattens. The larger rear lobes at the lower gain levels become part of the forward radiation when reflected off the ground, thus limiting the gain reduction. Higher in the band, the peak gain does not coincide with the peak for the other curves. This, too, is a function of rearward radiation: the peak gain coincides roughly with the peak front-to-back ratio. When vertical, the antenna has less total radiation upward when the forward and reflected radiation are summed.

2. Front-to-Back Ratio: The specification of a front-to-back ratio (in dB) applies only to the antenna when in free space or angled over ground. Because the antenna, when angled, does not operated exactly like the same antenna parallel to the earth's surface, the peak front-to-back level shows a frequency shift owing to the differences in the interception of reflected waves with incident waves. The actual peak is at a frequency somewhat above 269.9 MHz, but well below 303.6 MHz. As well, the effects of ground and the angle of the antenna alter fluctuations that we find in the free-space front-to-back ratio from the lower end of the spectrum to the mid-band frequency. See Fig. 6.

Taking the gain and front-to-back values together, we find an emergent design specification for the antenna over the entire spectrum: a gain for all uses in excess of 10 dBi and a front-to-back ratio of greater than 12 dB. For the application, a high front-to-back ratio is not necessary, and its presentation here is mainly to explain various phenomena associated with vertically oriented and angled antennas. With only 2 band-edge exceptions, the design meets or exceeds these specifications.

3. Take-Off Angle: With the Yagi angled along its boom at 45 degrees with respect to the earth's surface, the elevation pattern of the antenna shows an angle of maximum radiation that fluctuates only in minor ways from the angle of the antenna itself. Except for the highest frequency sampled, the total fluctuation is only 6 degrees. Even at 317 MHz, the 33-degree take-off angle presents no problems of alignment, since the vertical beamwidth--as measured at -3 dB points away from the bearing of maximum strength--is sufficiently wide so as to require no readjustment. See Fig. 7.

4. Beamwidths: In free-space and pointed straight upward, the differences between the beamwidths of the patterns as measured parallel to each type of element set are too small to require individual treatment. Hence, Fig. 8 graphs only a single beamwidth value for each of these two conditions.

The free-space beamwidth values are almost solely a function of the forward gain of the array. Hence, the beamwidth curve is almost the inverse figure of the gain curve. When the antenna is pointed straight up, there is a variable amount of power devoted to moderate to incipient side lobes. The stronger the side lobe, the narrower the beamwidth for any given gain level. Hence, at the lower end of the operating band, where side lobe formation is generally highest, the beamwidth narrows more rapidly than in free space.

When the antenna is at a 45-degree angle with respect to earth's surface, we must consider both the vertical and the horizontal beamwidth of the pattern. In a general way, both curves follow the free-space curve, with slight adjustments for the effect of the varying front-to-back ratio above the mid-point of the operating band. The presence of the earth's surface restricts the vertical beamwidth to levels roughly comparable to those of the antenna pointed straight up. The 49-degree vertical beamwidth between -3 dB points at 317 MHz points to the reason why the seemingly low 33-degree take-off angle presents no aiming problems for the array. The horizontal beamwidth tends to be higher than we would expect from a horizontally polarized Yagi of the same boom length, but less than that we would expect of a vertically polarized Yagi, if both were parallel to the ground surface. However, the crossed-element beam tends to take on a value intermediate between these two cases.

Patterns: It may be useful in understanding the behavior of the crossed-8-element Yagi to examine selected patterns.

1. 250 MHz: The patterns for 250 MHz include the free-space pattern, the elevation pattern for the antenna when vertically oriented 1 wavelength above ground, and azimuth and elevation patterns for the antenna when the reflector center is 1 wavelength above ground. See Fig. 9. These patterns give us a portrait of antenna behavior at the low end of the operating band.

Although the antenna exhibits only 10 dB of front-to-back ratio in free space, the rearward lobe contributes to good forward gain performance when the antenna is set vertically above ground. The vertical pattern also shows the incipient side lobes that narrow the beamwidth in this mode. When we angle the antenna 45 degrees, the pattern shows a very broad wave front in both the horizontal and vertical dimensions, as well as improved front-to-back performance relative to free space. Because phasing at this frequency is not quite ideal, the azimuth pattern shows elements of non-symmetry.

2. 283.5 MHz: At mid-band, the array shows a well-controlled pattern with forward side lobes about 16 dB below the level of the main forward lobe. When we place the antenna vertically over the ground, the side lobes appear as near-ground-angle lobes. However, the main forward (upward) lobe is very well shaped for its intended application.

When we tilt the antenna 45 degrees relative to the ground, we obtain the patterns at the right of Fig. 10. It is no accident that the azimuth pattern shows good (although less than absolutely perfect) symmetry, since the phasing line is close to its optimal length. As well, the azimuth pattern resembles that of a 2-element horizontally polarized single Yagi with 2 elements. The resemblance goes beyond appearances, since the forward gain of the array is also quite similar to the gain of a 2-element Yagi.

The greatest departure from the 2-element horizontal Yagi pattern occurs with the elevation pattern. The crossed-element Yagi has a strong vertical component and, at about 1 wavelength above ground, it shows the double-lobe structure of a vertically polarized Yagi. The rearward lobes of the array remain quite well-controlled relative to the application of satellite communications.

3. 303.6 MHz: In free space, the 303.6 MHz pattern shows the highest front-to-back ratio--about 34 dB, as is evident in Fig. 11. This particular condition results in an actual reduction of gain (relative to the peak gain that we may obtain from the array) when we place the antenna in the vertical position. There is very little energy for the rear lobes to contribute to the upward forward lobe. The vertically positioned antenna shows a higher gain at a slightly lower frequency (see Fig. 5). The side-lobes, both forward and rearward, in the free space pattern contribute to small sidelobes in the vertical pattern, although these remain both narrow and of low amplitude.

When we place the antenna at a 45-degree angle, ground reflection effects result in a front-to-back ratio that is less than the peak value. The azimuth pattern shows a small rearward lobe. As well, the azimuth pattern is again nearly symmetrical, since the frequency is also close to optimal for the phase line. Because the antenna is now higher than 1 wavelength above ground, the vertical pattern shows a decrease in the strength of the lower of the two main forward vertical lobes. The pattern actually shows an incipient third forward lobe developing. Hence, the take-off angle is about 5 degrees above the aiming angle. However, the signal strength at the 45-degree angle is down by well under 0.3 dB compared to the maximum possible strength.

4. 317 MHz: The patterns for 317 MHz appear in Fig. 12. The free-space pattern remains well-behaved, with the main rearward lobe at least 17 dB lower than the main forward lobe. For this reason, when we set the antenna vertically above ground, the pattern is quite satisfactory for the application. The incipient side lobes have risen in elevation on the forward lobe, but create no unacceptable pattern distortions.

The azimuth and elevation patterns for the antenna, when tipped 45 degrees, are especially interesting. First, the azimuth pattern shows some degree of non-symmetry in the side lobes, since the phase line is long for this frequency. However, the forward lobe remains aligned within 1 degree of the desired bearing and hence presents no operational problems whatsoever.

The elevation pattern requires some special comment. The angle of maximum radiation is 33 degrees above the horizon, although the antenna is pointed 45 degrees above the horizon. A secondary lobe occurs at 49 degrees, with a strength of 10.26 dBi, compared to the main lobe value of 11.01 dBi. At a 45-degree angle, the gain still exceeds 10.0 dBi, thus exceeding the minimum standard set for the antenna design.

The elevation pattern also shows considerable low-angle lobing. This phenomenon indicates a growing imbalance of horizontally polarized radiation over vertically polarized radiation. Although not yet harmful to the intended use of the array, the ripples are a clear indicator that the antenna is approaching the upper frequency limit of being serviceable in the intended application.

Indeed, the fall-off of gain and front-to-back ratio at the lower end of the operating spectrum and the pattern decay at the upward end of the spectrum suggest that the present design is stretch close to the limits for the overall bandwidth covered. Subjecting the design to further optimization--whether manual or automatic--might increase the usable bandwidth a bit further and indeed might improve one or more of the operating parameters across the band spread. However, it is not anticipated that such improvements would yield operationally significant improvements over the present design.

Conclusion: The 8-crossed-element Yagi design with quadrature feed provides about 10 dBi or more gain from 250-317 MHz, with adequate beamwidth for easy satellite aiming and with an acceptable 50-Ohm SWR across the entire spectrum. However, its chief merit as a design lies in its ability to help us understand the design and operation of VWB Yagis. The fundamental mechanism of VWB Yagi design lies in the relative independence of adjustments for upper and lower end performance enhancement due to the function of the first director as a secondary driver. The independence of the adjustments allows the designer to arrive at a closer coincidence in band-edge performance. Even with quadrature feed, arriving at a 23.6% operating bandwidth with acceptable performance--taking into account the need for aiming the antenna at different angles relative to the ground--is an interesting and potentially useful result.

The crossed-element Yagi design achieves part of its operating bandwidth from the use of quadrature feed. If we extract from the array a planar Yagi using the same element lengths and spacing, the net bandwidth between 2:1 SWER points shrinks from greater than 67 MHz down to 55 MHz. Although this bandwidth is on the cusp of truly VWB design (19.4%), we may inquire into whether the planar Yagi array is capable of covering the same 250-317 MHz spread that we demanded for our satellite communications design. The inquiry may also reveal some additional principles of VWB Yagi design. Hence, we have reason enough to create Part 2 of this investigation.

Updated 11-01-2002. © L. B. Cebik, W4RNL. This item originally appeared in antenneX (Sep., 2001). Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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