Part 4: Rhombic Arrays and Beams

Every step along our path through traveling-wave antennas has led us to new heights of gain per unit of wire length (as measured in wavelengths)--and to narrower beamwidths. The final steps take us to the pinnacle of long-wire development: the rhombic antenna. (We should note that there are some "fishbone" designs that may be able to achieve more gain per acre of ground than the designs with which we are working. However, these antennas use a quite different design and require at least 2 to 4 wavelengths of wire per wavelength of forward antenna dimension. We shall not cover them here. However, the *ARRL Antenna Book* chapter and the Laport volume, both cited in the short list of references, cover the basics of these designs.)

The rhombic antenna derives its name from its shape: the rhombus. In geometry, a rhombus is an equilateral parallelogram, that is, a closed 4-sided figure with all sides the same length, but with all corner angles normally using other than right angles. **Fig. 1**, at the top, shows a basic rhombus, with indications of the key dimensions.

An alternative way to look at the rhombus is to see it as 2 V antennas end-to-end. This orientation makes clear that the centerline is correctly identified, and it gives the elongated shape some sense, assuming that Part 3 of this series has had its impact. The length L, in wavelengths, defines the length of each leg, suggesting that each rhombic antenna that we examine will likely be twice as long overall as a corresponding V antenna with the same leg length.

Also apparent in the sketch is angle A (usually represented by a Greek alpha). When we examined V antennas, we used the angle of the strongest lobe of a single long-wire of length L to determine the value of angle A. We then found that angling each V wire from the centerline by the value of A produced additive lobes along the centerline. Since the far end of any rhombic antenna is a mirror image of the feedpoint end, the lobes for the far-end wires will also be aligned with the center line. Hence, we can expect more gain from a rhombic antenna than from a corresponding V antenna.

The earliest literature, starting with the classic article by Bruce, Beck, and Lowry ("Horizontal Rhombic Antennas," *Proc. IRE*, 1935), began the practice of referring to angle B in **Fig. 1** as the tilt angle. The normal character for this angle is a Greek phi, although I have seen other characters as well. Angle B is simply 90 degrees minus angle A.

Basic rhombic calculations emerge from a situation that is usually not very realistic for the average amateur installation. The premise is that angle A represents 2 different angles in the antenna installation. First, it represents the elevation angle of maximum radiation. Hence,

H_{WL}= [1 / (4 sin A)]

where H_{WL} is the required antenna height in wavelengths. As well, angle A represents the required V'ing angle, the same angle that we used in the V-antennas. To align the major lobe with the elevation angle, we calculate the leg-length as follows:

L_{WL}= [0.371 / (sin^{2}A)]

where L_{WL} is the leg-length in wavelengths. For maximum gain at the chosen elevation angle,

L_{WL}= [0.5 / (sin^{2}A)]

The difficulty faced by amateur installations is that the height is rarely a matter of open choice. As a matter of fact, neither is the length open to selection based solely on calculations. Instead, the maximum height for an installations is usually prescribed by any number of limiting circumstances. All of the examples used in this series have set the antennas at 1 wavelength above ground on the premise that most long-wire antennas will ultimately fall in the upper HF range. 1 wavelength at 14 MHz is about 70'. Property lines usually define the absolute limits of overall array length, abetted by complexities such as the availability and feasibility of supporting very long runs of wire.

Initial and later studies in rhombic antennas provide more complex equations to calculate compromises where the elevation and the V'ing angle do not match. Some of the equations appear in nomographic form. For example, one such nomograph appears in the ARRL chapter on long-wire and traveling-wave antennas, as well as in articles and text devoted specifically to the design of rhombic antennas. (See the Harper volume in the reference list.) Such nomographs are capable of guiding the rhombic designer to excellent results, as we shall see before we close this last segment of our long-wire trek.

However, via NEC modeling, we have an easier route to designing rhombics. The process started in Part 1, with the modeling of end-fed unterminated wires, from which we obtained the values of angle A within the limits of the modeling exercise. We standardized the wire height at 1 wavelength. We might as easily develop a compendium of models using the same (or different) increments of wire length at a number of different heights. For a practical design project, we likely would select a single height dictated by whatever constraints will govern the installation. Then, we can collect data on angle A for any set of wire lengths desired.

We may use the selected height and the associated values of angle A to design any number of rhombic antennas. In fact, we can use a simple long-wire as the starting point. NEC allows us, via the GM command, to rotate the wire by the required number of degrees dictated by the value of angle A for a given wire length. (Programs like EZNEC use a different but equally effective method of rotating wires.) Hence, we can easily create a V and find its coordinates. From those coordinates, we can complete the rhombic by doubling the overall length and bringing 2 new wires back together--or almost together. See the lower part of **Fig. 1** for 2 possible versions of an unterminated rhombic configuration.

The use of angle A assures us of lobe direction coincidence and gain addition along the centerline of the antenna. We may then let NEC calculate the gain and actual elevation angle for the selected antenna height over any selected soil. Before we close this series, we shall find that NEC's handling of rhombic design and at least one nomographically based design turn out to be virtually identical. Traditional methods are quite accurate, but in the present age of computerized antenna design, the modeling process is often simpler. As we have seen from our experience with single long-wire and V antennas, the modeling method also provides ready supplementary information, for example about sidelobes, feedpoint impedances, and power dissipation in the load resistance of terminated antennas.

In our exploration of rhombic antennas, we shall simply extend our modeling methods. First, we shall leave the antenna at 1 wavelength above average ground (conductivity 0.005 S/m, permittivity 13). The test frequency will be 3.5 MHz, and the lossless wire will be 0.16" in diameter. Part 1 of the series sampled some of the variations on these choices, so you may readily extrapolate additional losses or gain from selecting different background parameters. Better yet, you may easily model most of the antennas yourself, using your own selection of parameters. Some beginning programs are limited to 500 segments. A few of the longer rhombics may require up to 900 segments if we adhere to our 20-segment per wavelength standard. However, a full 6 wavelength-per-leg rhombic comes in at under the 500 segment mark.

**Unterminated Rhombic Antennas**

The lower portion of **Fig. 1** shows two ways of modeling an unterminated rhombic antenna. We may separate the far end point by a small space. This configuration is perhaps the most common understanding of an unterminated (sometimes called a resonant) rhombic. However, we may equally bring the ends together to short-circuit the gap. The options expose something of a misimpression of the rhombic antenna. If we were given to extreme (and unfortunately, contentious) modes of expression, we might suggest that there is no such thing as an unterminated rhombic antenna.

The single long-wire unterminated antenna and the V array both make good sense of the idea of a wire without a resistive termination. Any form of termination requires extra wires and ultimately a ground connection--although there is a version of the V-beam that does not use ground at the far end of the array. The rhombic returns the 2 wires of the antenna to close proximity. In the models that we shall explore, the gap will be 0.002 wavelength. At 3.5 MHz, that distance is 170 mm, where a wavelength is over 85.6 m long. If we leave the gap open, we can treat the terminating resistance as simply indefinitely large. One modeling technique for rhombics is to use a short wire to bridge the gap. To create a terminated rhombic--as the term is generally used--we place a load resistor of a desired value on the bridge wire. To create an open circuit, we might specify the load resistance as 1e10 Ohms or higher. To short out the gap, we can either remove the load resistor or give it a value of 0 Ohms. Alternatively, we can remove the bridge wire and simply bring the 2 legs to the same point on the coordinate scheme.

Despite the existence of a reasonably plausible claim that all rhombics are terminated to one or another degree, we shall adhere to the common referential terms. Without a mid-range non-inductive resistor at the far end of the antenna, the rhombic will be unterminated in either the open or closed configuration. The chief difference between the open and closed versions of the unterminated rhombic antennas lies in the sidelobes, not in the small differences in gain and inherent front-to-back ratio that is a part of all end-fed long-wire antennas. **Fig. 2** contrasts the structure of the sidelobes for open and closed unterminated rhombics. Note that the closed version shows larger sidelobes than the open version, suggesting less complete cancellation of lobes from the parallel legs.

For comparison and contrast, **Fig. 2** also presents two azimuth patterns from corresponding unterminated V arrays. The pattern on the lower left uses 3 wavelength legs, the same length as the legs in the rhombics. On the lower right is the pattern for a V array using 6 wavelength legs. These legs give the V array the same overall length as the rhombic with a small margin of difference due to the difference in the value of angle A. (Both rhombics are 5.39 wavelengths, while the long V is 5.71 wavelengths overall.) On the whole, the long V antenna pattern resembles in general sidelobe strength the closed rhombic pattern. However, the V patterns show the combination of many sidelobes that combine to form fewer distinct lobes and nulls. In contrast, the double-V configuration of the rhombic reduces these indefinite lobe formations down to distinct lobes and nulls. In fact, both rhombic azimuth patterns show a total of 20 lobes. The lower strength levels of the lobes at near-right-angles to the 2 main lobes for the open version of the antenna make lobe counting impossible at the scale of **Fig. 2**, but expanded renderings of the plot reveal them all. In contrast, even large renderings of the V-antennas do not permit an accurate count of the lobes and the bulges that form incipient lobes.

Clear lobe definition and numeric limitation together comprise one of the advantages of the rhombic over corresponding V antennas. The other major rhombic advantage is gain. The following table provides modeled data for both open and closed unterminated rhombics with varying leg lengths from 2 through 11 wavelengths. Remember that the overall length of the rhombic is just under twice the leg length. Like all long-wire antennas, the rhombic suffers the blight of diminishing returns as we strive to make it longer. Doubling the leg length from 2 to 4 wavelengths provides nearly 2.5-dB more gain. However, the next doubling to 8 wavelength legs adds slightly under 2 dB of gain.

*Note*: The values of angle A derive from our earlier work with single long-wire antennas. I have not optimized those values to achieve maximum gain. There is a slight difference.

Performance of Unterminated Rhombic Antennas 1-Wavelength Above Average Ground Type Leg Length Angle A Elevation Max. Gain Front-Back Beamwidth WL degrees Angle deg dBi Ratio dB degrees Open 2 34 14 16.41 2.41 20.4 Closed 2 34 14 15.84 2.90 20.6 Open 3 26 14 17.81 2.40 17.2 Closed 3 26 14 17.50 2.66 17.2 Open 4 23 13 18.89 2.58 14.1 Closed 4 23 13 18.61 2.83 14.4 Open 5 20 13 19.57 2.57 12.8 Closed 5 20 13 19.35 2.77 12.8 Open 6 18 12 20.12 2.55 11.6 Closed 6 18 13 19.95 2.71 11.8 Open 7 16 12 20.53 2.48 11.2 Closed 7 16 12 20.39 2.60 11.2 Open 8 14 12 20.82 2.32 11.0 Closed 8 14 12 20.69 2.42 11.0 Open 9 13 12 21.17 2.27 10.4 Closed 9 13 12 21.03 2.38 10.4 Open 10 13 11 21.52 2.37 9.4 Closed 10 13 11 21.39 2.47 9.4 Open 11 12 11 21.73 2.29 9.0 Closed 11 12 11 21.61 2.38 9.0

At the top of the table, the gain differential between open and closed rhombics appears to be significant: nearly 0.6 dB. However, the differential shrinks continuously as we lengthen the legs. By the time the legs are 11 wavelengths, the gain differential is only a bit over 0.1 dB. Elevation angles, front-to-back ratios, and beamwidths all remain very comparable for both types of unterminated rhombic antennas.

All of the closed unterminated rhombics show a modest feedpoint impedance at the integral leg lengths that appear in the table. The resistive component varies between 235 and 290 Ohms, while the reactance ranges from -j160 to -j190 Ohms. In contrast, all of the open rhombics show very high impedance levels, with resistive components running from 2900 to 3300 Ohms. The reactance seems to have a wide range--from +j130 to +j460 Ohms. However, as a fraction of the total impedance, the range is small. The differential between open and closed rhombic impedances is real, but in practical terms of designing a system, it is also illusory. The curves for changes of feedpoint resistance and reactance for the two types of unterminated rhombics are virtually identical, but displaced from each other by about 1/4 wavelength of leg length.

**Fig. 3** presents the unterminated rhombic gallery of sample elevation and azimuth plots for leg lengths of 2, 4, 6, 8, and 10 wavelengths. By comparing the plots with **Fig. 2**, you can verify that the gallery uses the open version of each rhombic.

The open unterminated rhombic shows excellent sidelobe control compared to the other long-wire antennas that we have surveyed. In general, azimuth sidelobes are 10 dB of more down, with a very good front-to-side ratio for headings near or at the 90-degree mark off the main lobes. Secondary elevation lobes are 10 to 15 dB down, depending upon rhombic length. **Fig. 4** provides a 3-dimensonal radiation pattern in 5-degree increments of the rhombic with 10 wavelength legs. Although the upper elevation angles still bristle with lobes, they are generally all of low strength and therefore untroublesome to antenna performance.

As a way to summarize our meandering through various unterminated bi-directional wire antennas, the following table presents the modeled maximum gain values for each type that we have surveyed. All values are for perfect-wire antennas 1 wavelength above average ground. Remember that the center-fed and end-fed long-wire antennas show maximum gain off-axis to the wire, while the V and rhombic antennas show maximum gain in line with the antenna centerline. In addition, the rhombics overall are twice as long as the single-wire and V antennas listed for the same leg length.

Maximum Gain of Various Types of Unterminated Long-Wire Antennas Leg Maximum Gain dBi Length Center-Fed End-Fed V Closed Open WL Doublet Wire Array Rhombic Rhombic 2 9.36 10.27 13.60 15.84 16.41 3 10.16 11.32 14.65 17.50 17.81 4 10.93 11.99 15.48 18.61 18.89 5 11.47 12.48 15.97 19.35 19.57 6 11.85 12.90 16.25 19.95 20.12 7 12.14 13.24 16.56 20.39 20.53 8 12.43 13.50 16.75 20.69 20.82 9 12.65 13.72 16.99 21.03 21.17 10 12.82 13.96 17.24 21.39 21.52 11 13.01 14.15 17.35 21.61 21.73

Although some of the gain increase that we see with longer and more complex long-wire antennas comes from sidelobe control, most of it emerges at the expense of beamwidth. We have noted this fact in past episodes, but it needs a reminder here. Short V and rhombic antennas (2 wavelength legs) have beamwidths just over 20 degrees. With 10 wavelength legs, the beamwidth is less than half that value. Although the high gain of long Vs and rhombics seems attractive to many, the utility of a fixed position narrow-beamwidth antenna is for point-to-point communications, not for general communications across the horizon. For comparison, a half wavelength dipole has a beamwidth of about 80 degrees, while the beamwidth of a 1.25 wavelength extended double Zepp is about 30-35 degrees. In many cases, the key design question for fixed long-wire antennas is less "With whom do I wish to communicate?" and more "With whom am I willing not to communicate?"

**Terminated Rhombic Antennas**

The terminated version of the rhombic antenna is identical to the unterminated versions with the exception that the far junction of the wires has an intervening non-inductive resistor (or combination of resistors in series and/or parallel connection) with the desired value. **Fig. 5** shows the outline of the general arrangement. Ordinarily, the terminating resistor is somewhat arbitrarily selected in the 600-800-Ohm range. Angles A (alpha) and B (phi) play the same role in the terminated rhombic that they play in the unterminated versions. L remains the leg length measured in wavelengths, and the leg length plus the angles form unique combinations to achieve maximum gain at some prescribed antenna height.

The models for the unterminated rhombics have used only 4 wires, one for each leg. The model source consists of a split source, that is, two sources in series. The sources go on the segments adjacent to the junction of the wires at the feedpoint end of the antenna. As the right side of **Fig. 5** reveals, I used a similar technique to place the terminating resistor. Non-reactive resistive loads go on the last segment of each far-end wire, with each resistance equaling half the total terminating resistance. These techniques of placing sources and loads preclude the need to create a short wire at each end of the rhombic structure. To preserve an equality of segment lengths, the bridge wire would have to be long enough that it would not preserve the value of angle A. Alternatively, to maintain the value of angle A, the source/load wire would be significantly shorter than adjacent leg segments, a condition on the source wire that NEC does not recommend for the most accurate calculations. Split sources and split loads preserve both the geometry of the model and the best conditions for calculation.

Like all other models in this series, the lossless 0.16"-diameters wires use 20 segments per wavelength. All terminated rhombics are 1 wavelength above average soil with a test frequency of 3.5 MHz.

Before we present a table of modeled performance values, we must select a value for the terminating resistor. Many rhombic builders rely on the tradition that the terminating resistor controls the feedpoint impedance. Since 600-Ohm ladder line is readily available or easily built, 600 Ohms has been a popular resistance for the rhombic termination. For spot frequencies in otherwise well-designed rhombics, a 600-Ohm termination produces a low 600-Ohm SWR. However, many rhombics find use over at least a 2:1 frequency range. Therefore, I swept the version of the rhombic with 3 wavelength legs from the design frequency to twice the frequency to observe the likely undulations of resistance, reactance, and 600-Ohm SWR. **Fig. 6** shows the results.

In many ways, the resistance and reactance swings appear to be modest. Indeed, the SWR curve shows low values for 3.5, 5.25, and 7 MHz (which would correspond to 14, 21, and 28 MHz on a properly scaled version of the model). However, the SWR for 4.53 MHz (scale value: 18.118 MHz) is greater than 2:1, and the value for 6.24 MHz (scale value: 24.94 MHz) is approaching 2:1. These values would not be troublesome for a wide-range antenna tuner between the shack end of the feedline and the transceiver. However, they may be high enough to defeat the low-loss use of a wide-range impedance transformation device, such as a transmission-line transformer balun.

Higher values of terminating resistance yield smaller resistance and reactance excursions. The result is a set of smaller SWR swings, all within an acceptable range. **Fig. 7** shows the same frequency sweep using an 850-Ohm terminating resistor, referenced at the feedpoint to 850 Ohms.

Comparing the resistance and reactance lines between **Fig. 6** and **Fig. 7** reveals the smaller swings in these impedance components. The SWR (blue) line swings may appear similar in the 2 graphs. However, note the smaller limit to the Y-axis in **Fig. 7**: its highest value is 1.45:1. Although creating a wide-range impedance transformation device may be more difficult with the higher reference impedance (850 Ohms), the technique will be applicable with low losses across the 2:1 frequency range of the rhombic.

Within the usual range of terminating resistor values, the lower the terminating resistance value, the higher the the array gain--but only slightly so. **Fig. 8** overlays the gain values of the rhombic beam for both the 600- and the 850-Ohm resistors. Throughout the 2:1 frequency range, the 600-Ohm version provides the higher gain, but by no more than 0.01 to 0.02 dB.

In the range of terminating resistance between 600 and 900 Ohms, certain performance parameters remain extremely stable. The elevation angle of maximum radiation and the beamwidth are two values that remain the same throughout the range of terminating resistors, at least for the sample rhombics using leg lengths that change in 1 wavelength increments between models. The impedance is also relatively stable at the test frequency for each model through the 600- to 900-Ohm resistor range. The maximum spread of resistance goes from a low of about 730 at 600 Ohms to a high of 870 at 900 Ohms, although the range is a bit smaller for any one leg-length model. The reactance swing is equally small, ranging from a -j40-Ohm value at 600 Ohms to a +j40-Ohm value at 900 Ohms.

My reason for selecting the 850-Ohm terminating resistor has as much to do with drama than with good electronics. Normal construction variables and the selection of leg lengths that are not perfect integral increments of a wavelength would likely alter the results. However, as the following performance table reveals, 850 Ohms as the termination value yields very high values of 180-degree front-to-back ratio, resulting in radiation patterns in which the main forward lobe and the sidelobes take center stage. The shortest of the rhombics has the lowest front-to-back value because the 40+-dB ratio occurs with an 800-Ohm terminating resistance. In practice, values from 750 to 900 Ohms will likely yield indistinguishable results, although the higher end of the scale will usually result in the smoothest SWR curve. However, we tend to obtain the flattest wide-range SWR curves when the terminating resistance and the feedpoint impedance are as close together as possible.

The tabular data shows the value of angle A (alpha), the elevation angle of maximum radiation, the maximum forward gain, the 180-degree front-to-back ratio, the half-power beamwidth, the modeled feedpoint impedance, and the 850-Ohm SWR. For reference, the far-right columns provide the maximum gain values for the corresponding unterminated open rhombics, along with the gain differential between the terminated and unterminated versions of the antenna.

*Note*: The values of angle A are not optimized for maximum rhombic gain, but derive from earlier work with single long-wire antennas.

Performance of Terminated Rhombic Beams (R = 850 Ohms) 1-Wavelength Above Average Ground Unterminated Rhombics Leg Length Angle A Elevation Max. Gain Front-Back Beamwidth Feedpoint Z 850-Ohm Max. Gain Difference WL degrees Angle deg dBi Ratio dB degrees R +/- jX Ohms SWR dBi dB 2 34 14 14.60 30.40 20.6 862 + j23 1.03 16.41 1.81 3 26 14 16.04 41.16 17.2 864 + j23 1.03 17.81 1.77 4 23 13 17.27 43.97 14.4 869 + j27 1.04 18.89 1.62 5 20 13 17.97 44.71 12.8 867 + j23 1.03 19.57 1.60 6 18 13 18.51 44.78 11.6 863 + j24 1.03 20.12 1.61 7 16 12 18.85 42.78 11.2 861 + j24 1.03 20.53 1.68 8 14 12 18.98 43.63 11.0 856 + j24 1.03 20.82 1.84 9 13 12 19.27 43.90 10.4 854 + j24 1.03 21.17 1.90 10 13 11 19.73 44.52 9.4 855 + j23 1.03 21.52 1.79 11 12 11 19.86 43.84 9.0 852 + j24 1.03 21.73 1.87

As we move from a single long-wire antenna to a V-beam and finally to a rhombic, the gain differential between the unterminated and the terminated versions has decreased. The differential was 3.5 to 4.5 dB for the single long-wire terminated antenna. The V-beam showed a range of 2.7 to 3.7 dB differential. In both cases, the differential decreased as the length of the legs increased. For the rhombic, the differentials range from 1.6 to 1.9 dB, a tight range for which there is no apparent correlation between gain differential and leg length.

The gallery of sample elevation and azimuth patterns of the terminated rhombic beam appear in **Fig. 9**. The gallery includes patterns for leg lengths of 2, 4, 6, 8, and 10 wavelengths. Because the arrays are twice as long overall as corresponding V-beams and single terminated long-wire antennas, the transitions in pattern shape are smaller from one increment to the next in the series. Hence, we may use fewer plots to show the evolution of rhombic radiation patterns.

Careful inspection of the sidelobe structures will show that the strength of the forward-most sidelobes--and also the strongest sidelobes--is somewhere between the corresponding sidelobes for the open and the closed versions of the unterminated rhombics. See **Fig. 2** to estimate the limits and where between them the terminated rhombic sidelobes fall. The phenomenon suggests that there is a continuity in sidelobe strength across a range of termination values ranging from an open circuit through a mid-range resistance and ending at a short circuit.

**Fig. 10** provides a 3-dimensional pattern for the rhombic with 10 wavelength legs. It reveals that the terminated rhombic exerts the most control over the morass of small lobes that populate the overall radiation pattern. You may directly compare this pattern with the one in **Fig. 4** for the unterminated rhombic to correlate various lobes and their relative strengths. As well, you may compare it with corresponding patterns for other terminated long-wire arrays in earlier parts of this series.

One quick comparison that we may tabulate is the maximum gain of each of the 3 types of terminated beams that we have encountered along the long-wire pathway. Remember that the maximum gain value for the single terminated long-wire is an off-axis value, that is, not in alignment with the wire itself.

Maximum Gain of Various Types of Terminated Long-Wire Antennas Leg Maximum Gain dBi Length Single V Rhombic WL Long-Wire Beam 2 ---- 9.88 14.60 3 7.11 11.41 16.04 4 7.99 12.35 17.27 5 8.65 13.03 17.97 6 9.15 13.50 18.51 7 9.57 13.86 18.85 8 9.92 14.07 18.98 9 10.20 14.29 19.27 10 10.47 14.59 19.73 11 10.70 14.74 19.86

The gain of the single terminated long-wire would not justify its narrow-band use, since we can obtain similar gain levels from antenna ranging from dipoles to extended double Zepps at a great savings in both wire and supporting structures. The single terminated long-wire acquires its usefulness from the relative constant feedpoint impedance, allowing great frequency agility. The terminated V adds about 4-dB of gain, while maintaining a broad SWR operating bandwidth. However, any angle used as the basis for the array has frequency limits for a good pattern: outside those limits, the forward pattern breaks into multiple lobes. As we change frequency, the antenna legs change length as measured in terms of a wavelength at the new operating frequency. Hence, the wire angles are no longer optimal to add in a forward direction.

The rhombic shares the frequency limits of the V-beam. To sense its truer gain advantage, you may wish to compare the rhombic with a given leg length to a V beam with twice the leg length. For example, a rhombic with 5 wavelength legs and neqrly 18 dBi gain is roughly equivalent in overall length to a V-beam with 10 wavelength legs and a 14.6-dBi gain level. Like the V beam, the rhombic is capable of good performance over a 2:1 frequency range with good gain and a relatively constant feedpoint impedance. In fact, before we end out trek through long-wire antennas, we should take one more look at the ARRL rhombic from Chapter 13 of the 20th Edition of *The Antenna Book*. But not today.

**Conclusion to Part 4**

In this episode, we have moved beyond the V array and beam to examine what some call the highest development in long-wire antennas: the rhombic. We learned how to close the V with another V, using the same technique of aligning lobes from each wire to form a rhombus. Modeling allowed us to develop effective rhombic antennas without reference to classical equations by setting the intended height and the leg-lengths that we might use. We explored both open and closed forms of unterminated rhombic arrays, and then we turned to the most common rhombic form, the terminated beam.

By splitting both the source and load, we found a very economical way to model the terminated rhombic beam. We also uncovered some relationships between the value of the terminating resistor and the feedpoint impedance that bear on the smoothness of SWR curves that cover a 2:1 frequency range. Indeed, there is more to be said on this subject. . .

Indeed, I had planned to close the series at this point. However, we have a significant amount of unfinished business with the rhombic.

1.

The Multi-Band Rhombic: We have not yet evaluated theARRL Antenna Bookrhombic for 14-28 MHz. This design has is roots in nomographic design data from Harper's well-known book. (See the list of references at the end of each Part.) The antenna gives us a chance to compare modeling design techniques with classical methods.2.

The Multi-Wire Rhombic: One common method of trying to improve rhombic beam performance is to use more than 1 wire for each leg. The usual arrangement consists of 3 wires that come together at the rhombic points and spread in the middle by relatively arbitrary distances. The arrangement presents both theoretical and modeling challenges, and careless modeling of a 3-wire rhombic can lead to erroneous results.3.

The Multi-Element Rhombic: In the 1950s, Laport developed the multi-element rhombic beam to improve both gain and sidelobe suppression. Since the antenna has seen use on the UHF amateur bands, the design bears at least an initial exploration to look at both design and modeling issues.

With so many outstanding rhombic ideas, I would be remiss if I did not extend the series one more episode. Even then, we shall not have examined every variation on the long-wire, V, and rhombic arrays. However, perhaps we shall have encountered enough designs along our pathway so that you may continue the trek on your own.

*Updated 09-01-2006. © L. B. Cebik, W4RNL. The original item appeared in* AntenneX *for Aug, 2006. 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.*