W8WWV - The RDF Metric

Greg Ordy


The goal of being able to rank low-band receiving antennas is probably impossible to achieve. While it might be possible to rank according to single metrics such as forward gain, or physical size, many metrics go into our sense of an antenna. Performance, size, and cost, to name three. Of course the word performance implies many difference aspects. Gain, take-off angle,  RDF, and front to back ratio, for example.

On this page, I would like to compare a number of low-band receiving antennas, and rank them according to the RDF (receiving directivity factor) Metric. I first came into contact with the RDF on the web pages of Tom Rauch, W8JI. I have written about it on many of my pages, including The Challenge, and The Benchmark Beverage.

RDF is a very simple concept. It is defined to be the difference between the forward gain of an antenna (usually the maximum forward gain) and the average gain of the antenna. The difficult term in that equation is the average gain. What is that? Currently, the only way that I know of to obtain this number is to use version 3.0 (or higher) of EZNEC. EZNEC is an antenna modeling package produced by Roy Lewallen, W7EL. When producing 3D antenna pattern plots, the program reports the average gain. It treats the sky as a large set of points, and computes the gain at each point. The gain at the points is used to draw the three-dimensional plot of the pattern.  The gain is also used to calculate the average gain. According to the EZNEC documentation, average gain is defined to be: The average gain is the total power in the far field (determined by integrating the far field in all directions) divided by the power delivered to the antenna by the sources.

The accuracy of this method will be a function of the number of points. More points will provide more accuracy, but it will take longer to compute the result. In most all of my antenna modeling experiments, I use a 3 degree angular spacing between points. The only other possible choice (which would be more accurate) is 2 degree spacing. My experience has been that the computation time nearly doubles, and the average gain result experiences very little change.

This means that the RDF is computed from modeled antennas, not measured from real antennas. That opens up some issues, since we connect our real receivers to real antennas, not modeled antennas. If the models are incorrect, then the results will be incorrect. So, we have to be careful with our models, and the results we obtain, and the interpretation of those results.

I have built and used most all of the antennas described on this page. I did not have all of the antennas up at the same time, however. In the future, I would hope to be able to erect all of these antennas again, perhaps in a large field, and spend an entire winter season comparing them under many different circumstances. It would be interesting to compare the RDF ranking against true head to head comparisons. Of course even that experiment will not produce some perfect ranking. From signal to signal, and time to time, the best  antenna will change. You can always find a case where a given antenna will be the best. Most amateurs do not have the space, time, nor resources to build one of every possible antenna. So, rankings are of some value if you can only build one or two antennas, and you understand the rules used to create them.

[Since RDF uses the average gain across the entire sky, it will be most appropriate when noise tends to be arriving from all directions in the sky.  In other words, the uniformity and distribution of noise matches the uniformity and distribution of the average gain. It is possible to pick another definition for the background or sky, one that does not include the entire sky. Ideally, we would only consider the portion of the sky that is sending us noise, but that is going to change from moment to moment, and is not uniform. In the 4th edition of his Low-band DXing book, John, ON4UN, defines a metric that he has named DMF - the Directivity Merit Figure. The DMF compares the maximum gain to a portion of the sky. For more information, please consult the 4th edition of his book (chapter 7).]

What RDF Means

There are three types of signals that we can receive. The first is the single signal that we want to listen to at that moment. The second class of signals are the other man-made stations that may be covering up the one signal that we desire. The third type of signal is noise. As frequency rises, this third type of signal becomes less important, since the radio spectrum tends to have less and less (background) noise. In my experience, noise is simply not much of an issue at and above 14 MHz. Below that, however, and especially on 1.8 MHz (160 meters) and 3.5 MHz (80 meters), noise is very important, and becomes a serious and usually dominant problem.

Most of the radio receivers in use today are very sensitive. They have no problem receiving very weak signals. So long as you can hear any background noise, it's hard to understand why you would need any more gain. If the signal is masked by noise, it does not matter how strong the signal is. This leads to the conclusion that gain is not as important as the signal to noise ratio. We need to have the desired signal rise enough above the noise so that we can separate it from the noise. RDF is the difference that the antenna itself provides between the favored direction, and all other directions. It is the advantage that the favored direction receives.

In the experiments I have been conducting, the universe of practical RDF values varies by less than 10 dB. This suggests that a single dB is important. I have already expressed some opinions about the value of a dB on another page. In the case of RDF, each dB improvement is conceptually saying that all other signals except the ones in the primary direction are all reduced by a detectable amount, even if a dB is very small. It's one thing if a signal already out of the noise increases by 1 dB. Perhaps that is not too exciting. But, if you are trying to dig a signal out of the noise, reducing all other signals and all noise by 1 dB seems much more meaningful.

Modeling Issues

All of the antennas presented were modeled at 1.83 MHz (unless noted). That is within the DX window of the 160 meter amateur band.

Many of these antennas are located close to the ground, and interact with the ground. That interaction can make it difficult to accurately model an antenna. The antenna modeling software includes a range of ground models. The EZNEC program uses the NEC-2 engine, which includes several different ground models. Please consult the web pages of L.B. Cebik, W4RNL, for excellent background information on the finer points of ground models across the various NEC engines.

In this case, the main issue boils down to using either the MININEC ground model, usually done to simplify modeling vertical antennas (no radials are needed), or using the high-accuracy and real ground model. The common problem is that the MININEC model will compute a gain which is too high. Typical gain errors are under 3dB. While this problem is certainly true, my experience to date in looking at RDF values is that the impact of the gain errors is minimized because both the maximum gain and average gain are incorrectly boosted. Since RDF is the difference between the two values, the fact that they are both slightly high does not change the difference.

When using a real and high accuracy ground model, I use pastoral and good quality soil, which is typical of the soil in my area.

Summary Table #1

I have ranked several antennas according to increasing RDF. In addition to the RDF, I have included the maximum gain, take-off angle (of maximum gain), whether the antenna operates over a broad frequency range, and a size metric. All of this data comes from EZNEC simulations.

RDF Summary Table #1
RDF (dB) Max Gain (dBi) Take-Off Angle (degrees) Broadband Size Description
5.06 1.41 24 no 7  130' Vertical (MININEC ground (no loss))
5.06 -0.09 24 no 7  130' Vertical (MININEC ground (15 Ohms loss))
5.06 0.6 24 no 7  130' Vertical (real ground, 60 radials)
5.26 -15.9 90 no 1  small loop (6-sided, 36' perimeter)
7.52 -15.42 24 yes 4  Big Flag (40'X50')
7.54 -24.35 24 yes 2  K9AY (MININEC ground)
7.67 -20.31 33 yes 5  EWE (15' X 45', MININEC ground)
7.69 -28.75 24 yes 3  Flag
8.10 7.46 90 no 6  Inverted VEE (100'/80')
8.13 4.55 90 no 6  Inverted VEE (40'/20')
8.28 7.34 90 no 6  Inverted VEE (80'/60')
8.30 -18.53 66 yes 8  Benchmark Beverage (250')
8.33 6.68 90 no 6  Inverted VEE (60'/40')
9.05 -16.94 60 yes 8  Benchmark Beverage (330')
10.03 -15.23 48 yes 8  Benchmark Beverage (470')
11.04 -13.48 39 yes 8  Benchmark Beverage (660')
12.00 -11.9 30 yes 8  Benchmark Beverage (890')
13.00 -10.51 24 yes 8  Benchmark Beverage (1160')
14.00 -9.33 21 yes 8  Benchmark Beverage (1460')
14.92 -8.31 18 yes 8  Benchmark Beverage (1800')

Table #1 is designed to contain what I would call single antennas (as opposed to arrays). This is not always technically true. Antennas such as the Flag and EWE are actually compact phased vertical arrays. While that is their principle of operation, they are usually considered to be single antennas.

An antenna is broadband in this table when it will operate across several amateur bands, without need of some form of tuning. Another way to say about the same thing is that what I'm calling a broadband antenna is also a nonresonant antenna.

The size rating is my personal subjective sense of the area/effort required for the antenna. I simply called the small loop a 1, and counted up as each antenna became larger.

The Antennas #1

The following paragraphs describes the models and the results. The 1/4 wavelength vertical and the inverted VEE can be used for transmitting, since they have reasonable gains above 0 dBi. The other antennas are usually used only for reception.

Benchmark Beverage

The Benchmark Beverage is a particular Beverage antenna that I described on another page. By changing the length, you can control the RDF. The shortest Beverage that I modeled, 250', had an RDF of 8.3. While this is slightly higher than most all of the other choices, it has a relatively high take-off angle of 66 degrees. Typical DX take-off angles are 10 to 30 degrees. The gain at a DX take-off angle of 21 degrees is 3.74 dB less than the maximum at 66 degrees. This difference dilutes the strength of the RDF.

From my experience, I would prefer the K9AY, Flag, and probably EWE, over a short Beverage. Those other antennas have much lower take-off angles. The take-off angle of short Beverages is substantially higher then typical DX take-off angles.

1/4 Wavelength Vertical

Some folks define a vertical to be an antenna that radiates equally poorly in all directions. From my experience, with a large number of ground-mounted radials located over rich midwestern soil, additionally located over my septic tank leach field, I find verticals to be outstanding performers - for transmitting that is. On reception, they are indeed quite noisy.

Verticals also have the lowest RDF among the antennas that I modeled. I modeled the same vertical with three variations. When I used the simple MININEC ground, I obtained the highest gain: 1.41 dBi. I then added 15 Ohms of series resistance to the base of the MININEC vertical. This 15 Ohms is designed to represent the loss in an average radial system (ground loss). With the additional 15 Ohms, the gain drops to -0.09 dBi. I then switched to the high accuracy ground model, and added 60 radials, each approximately 1/4 wavelength long. The gain was 0.6 dBi.

Even though the ground model influenced the gain, the RDF stayed constant at 5.06 dB. The take-off angle also remained at 24 degrees. While this is very respectable DX angle, the RDF was the lowest measured. The vertical can be, and often is, used for transmitting.

Small Loop

The small loop in my table is a six-sided hexagon which approximates a circle. The perimeter is 36' in length, and the loop is tuned with a variable capacitor. I usually use a matching transformer in my loops, just to avoid wasting too much of the inherently small signal. The loop is made of coax, and is built after the shielded loop design. My 160 meter loop is not currently described on a web page, but my 80 meter loop is.

The take-off angle of the loop is 90 degrees, straight up. That's not a good DX angle. Other than it's small size, the main virtue of these loops is that they have deep broadside nulls at very low (under 10 degrees) take-off angles. These nulls can be used to remove fixed local interference, such as from street lights or poorly shielded electronic devices. If you build the loop to handle large currents, it can be used for transmitting (but note the low gain). The tuning is quite sharp. The 2:1 SWR bandwidth is on the order of  15 KHz. For receiving this does not matter, although you can hear the output of the antenna fall off as you tune off resonance.

I cannot recommend these loops for DX purposes, but they are great for local work, especially in the noisy summer months. I use one on 160 meters, and a pair of them on 80 meters, connected via a phasing box.


The K9AY terminated loop array was first published in the September, 1997, issue of QST. It is an antenna with a high value, since it is relatively simple to built (one tall support), offers good performance, has a small footprint, and can be easily switched in 4 different directions.

Gary Breed, K9AY, calls his antenna a terminated loop array. Components of the system are available from his web site. A K9AY can be erected in a 30 foot by 30 foot area, and requires a single center support, 25 feet off of the ground. For this modest investment is space you can have a directional antenna that works over many bands. In order to obtain the highest performance, a remotely variable termination resistor can be used. Mark Connelly, WA1ION, has a whole set of very good web pages devoted to receiving antennas and remote termination. (remote termination can be of value on any antenna that uses a termination resistor)

The K9AY take-off angle is 24 degrees, very appropriate for DX.

Since the K9AY has a ground connection, I modeled it with the MININEC ground. This means that the gain reported is probably higher than it really is.


The EWE antenna consists of two vertical wires which are attached at their tops with a horizontal wire. Typical dimensions, and the ones that I used, are 15 feet of vertical wire, and 45 feet of horizontal wire. The EWE is fed at the bottom of one vertical, and the other bottom connects to ground through a termination resistor - 1000 Ohms in this example. The desired antenna is the pair of verticals, and the horizontal wire is a funny form of transmission line that connects the two verticals.

It is claimed the EWEs are ground dependent. As a result, I have never built one, preferring the Flag antenna, which is sometimes described as a ground-independent EWE. The single horizontal wire in the EWE will pick up some unwanted signals that mix with the vertical sections, which are the desired antennas. This causes the take-off angle to move up, and the EWE modeled in this case had a take-off angle of 33 degrees.

Since the EWE has a ground connection, I modeled it with the MININEC ground. This means that the gain reported is probably higher than it really is.

Floyd Koontz, WA2WVL is considered to be the inventor of the EWE. Several variations have been developed by different authors.


The Flag antenna gets its name because its outline looks like rectangular flag. There is a variation that has similar performance called the Pennant, that is in the shape of a triangular baseball pennant. I have built a number of Flags. It is not as small as the K9AY, and serving multiple directions is difficult. For that reason, I have built a bi-directional version described on another page.

The history of the flags appears to be based upon an attempt to remove the ground quality dependence of the EWE. A lower horizontal wire is added to the other three sides. The entire antenna is usually located a few feet (typically 6 feet) off of the ground. Important contributors to the Flag and Pennant include Hideho, JF1DMQ, Jose, EA3VY, and Earl, K6SE. A good web site for the Flag is maintained by K3KY. K6SE and EA3VY have pages located at www.topband.net.

The Flag take-off angle is 24 degrees, very appropriate for DX.

The Flag is my personal favorite for relatively small receiving antenna. I think that it performs a little better than a K9AY and an EWE. It is more work to erect, and it is unidirectional. The K9AY can easily switch directions, and in its classic form, you have 4 switchable directions in a very small form factor. Personally, I think that every station should have a K9AY, just because of its small size, multiband operation, and switchable directions. I have taken mine down to reuse the space for another antenna, but I really need to put it back up. It's a very good all-around receiving antenna. It makes a good reference for comparison.

I did build a bi-directional Flag, and that gives me two directions, at the expense of 3 relays and a few more parts. If you only need two directions, and you have the space, that's a very good receiving antenna too.

The Flag is very easy to model, and it has no ground connection, making it possible to use the real/high accuracy ground model.

The table includes an antenna I call the Big Flag. The Flag size can be scaled. The typical size is 14' X 29'. Another size that provides a similar pattern is a Flag which is 40' tall, and 50' long. The bottom of the antenna is 10' off of the ground, as opposed to 6'. As the table indicates, this version of the Flag has substantially more gain (approximately 12dB), but the RDF is nearly identical to the smaller Flag.  The pattern is also very similar. Suspended from high trees, this could be a very good portable DX antenna.

Inverted VEE

I decided to model an inverted VEE since it is a common antenna in practice. Like the vertical, it can be used for transmitting. The antenna initially appears to be a good performer, since it has substantial gain, and a relatively high RDF. Unfortunately, the take-off angle is 90 degrees - straight up. At lower angles the gain drops by as much as 10 dB. Like a short Beverage, this dilutes the RDF number for DX purposes. For NVIS (near vertical) operation, however, the inverted VEE is a fine choice.

The two numbers associated with my inverted VEE model indicate the center height, and the height of the two ends. The inverted VEE is approximately 240 feet long. It is not a small antenna on 160 meters. The height above ground influences the gain, but does not change the RDF substantially.

Improving RDF

What can we do to improve the RDF? For a Beverage, we can simply make the antenna longer. For other antennas, the usual answer is to combine additional element to form a phased array. Actually, this technique works for Beverages as well. I modeled a number of different array configurations. There are many variations. The next table presents several that I modeled.

For the purposes of this page, I have defined three categories of phasing. Broadside phasing locates separate elements across a line perpendicular to the primary direction. The phase difference between elements is 0 degrees. End-fire phasing locates the elements along the axis of the primary direction. While the optimum phase shift can vary, the value of 180 degrees is attractive because it is easy to generate via a coupling transformer. Mixed phasing is what I will call any situation which is neither broadside nor end-fire. Usually there are more than two elements, and they are not located along a single line. Phase shifts other than 0 and 180 degrees may be used (and usually are).

Summary Table #2

I have included all of the entries from Table #1 into this table, to act as a reference. New entries are shown in boldface. The size column has been removed.

RDF Summary Table #1
RDF (dB) Max Gain (dBi) Take-Off Angle (degrees) Broadband Description
5.06 1.41 24 no  130' Vertical (MININEC ground (no loss))
5.06 -0.09 24 no  130' Vertical (MININEC ground (15 Ohms loss))
5.06 0.6 24 no  130' Vertical (real ground, 60 radials)
5.26 -15.9 90 no  small loop (6-sided, 36' perimeter)
7.52 -15.42 24 yes  Big Flag (40'X50')
7.54 -24.35 24 yes  K9AY (MININEC ground)
7.67 -20.31 33 yes  EWE (15' X 45', MININEC ground)
7.69 -28.75 24 yes  Flag
8.02 -21.34 24 yes  2-element Broadside K9AY Array, 0 degree phasing, 100' spacing
8.10 7.46 90 no  Inverted VEE (100'/80')
8.11 -26.01 24 yes  2-element Broadside Flag Array, 0 degree phasing, 100' spacing
8.13 4.55 90 no  Inverted VEE (40'/20')
8.13 2.81 27 no  EZNEC demo 2-element End-fire vertical (real ground)
8.28 7.34 90 no  Inverted VEE (80'/60')
8.30 -18.53 66 yes  Benchmark Beverage (250')
8.33 6.68 90 no  Inverted VEE (60'/40')
8.52 -24.48 24 yes  3-element Broadside Flag Array, 0 degree phasing, 100'X100' spacing
9.05 -16.94 60 yes  Benchmark Beverage (330')
9.34 -19.23 60 yes  W8JI Parallelogram Array (370'X70')
10.03 -15.23 48 yes  Benchmark Beverage (470')
10.42 5.29 24 no  EZNEC demo 4-Square (MININEC ground, 7.15 MHz)
11.04 -13.48 39 yes  Benchmark Beverage (660')
11.12 -25.28 18 yes  2-element End-fire K9AY Array, 180 degree phasing, 117' spacing
11.35 6.01 24 no  EZNEC demo 4-Square, WA3FET, Jim Breakall phasing
11.39 -31.38 18 yes  2-element End-fire Flag array, 180 degree phasing, 100' spacing
11.73 6.3 24 no  EZNEC demo 4-Square, 120 degree phasing
12.00 -11.9 30 yes  Benchmark Beverage (890')
12.47 7.16 21 no  W8WWV hex array (165 degree phasing, MININEC ground)
13.00 -10.51 24 yes  Benchmark Beverage (1160')
14.00 -9.33 21 yes  Benchmark Beverage (1460')
14.92 -8.31 18 yes  Benchmark Beverage (1800')

The following sections will describe the additional antennas.

The Antennas #2

2,3-Element Broadside Arrays

Broadside arrays locate their elements in a line which is perpendicular to the primary direction of the array. All of the elements are combined in-phase. If there are two elements, the current amplitude should be equal in each element. If there are more than two elements, a Binomial  current amplitude distribution often makes sense. I modeled broadside arrays of both  K9AY and Flag elements.  I used an element to element spacing of 100 feet. This is a somewhat arbitrary distance. If the distance is too close, the possible effect of the array will be lost. A spacing of 100 feet is practical for many amateur backyards. If you really want to optimize the effect of spacing, you should model the desired antenna and vary the spacing to obtain the best possible result. If you are interested in multiband operation, however, spacing may end up being a compromise.

The value of broadside spacing, with respect to RDF, was small, measuring approximately 0.5 dB. Forward gain increased by approximately 3 dB, which is a reasonable and expected amount. 100' broadside spacing on 160 meters is rather small. Wider spacing should help the RDF. In one example, I increased the spacing to 300'. The RDF increased to 10.76 dB. The gain stayed nearly constant.

I recorded a 3-element array composed of Flag elements.  The improvement to RDF was again on the order of 0.5 dB (with the 100' spacing between elements).

2-Element End-fire Arrays

K9AY and Flag end-fire arrays were modeled. The spacing was 117' and 100', respectively. The 117' number is simply a value near 100' that I had in an existing model.

The behavior of these arrays was interesting in that RDF increased by approximately 3.7 dB, while forward gain actually dropped. At the same time, the forward take-off angle dropped to 18 degrees.  While the loss of gain is never a good situation, the large increase in RDF is exciting.

The phasing between front and rear elements was 180 degrees. That is an easy to achieve phase shift. Whenever you see a 180 degree shift in a vertical array, you can be certain that the response at 90 degrees (straight up) will be greatly reduced. A signal (or noise) coming straight down will arrive at the elements at nearly the same time. The only phase difference between them will be the 180 degrees in the system. Two (identical) signals, 180 degrees apart, cancel each other.  These end-fire arrays, with a 180 degree phase shift, will have good rejection of high angle signals and noise. I suspect that this factor is tied to the loss of gain, and the reduction in take-off angle. A spacing of other than 100 feet would probably restore some of the gain. In fact, I set the spacing to 200'. Forward gain increased by 4.59 dB, but the RDF decreased by 0.51 dB. While those may be acceptable trade-offs, the patterns on 80 and 40 meters were unacceptable with 200' spacing. With 100' spacing, the array could be used on 160, 80, and 40 meters. Life is always trade-offs...

The gain loss for 180 degree phase shifts when the elements are close together is due to the fact that more of the sky comes close to a complete phase cancellation within the antenna system. While this hurts gain, it does make sense that it would potentially help RDF, since RDF is related to the average gain. An interesting set of simulations would be to vary the spacing (for a given frequency), and see where the RDF peaks. These simulations could also follow the gain trend. I found this interesting enough that I did run a set of simulations with varying end-fire spacing.

Effect of Spacing on End-Fire RDF and Gain

Given the interesting results in the last section, I decided to take a quick look at the effect of spacing on a pair of Pennant antennas in an end-fire configuration. These simulations were run at 1.83 MHz. Each individual Pennant antenna is 29 feet long. The minimum end-fire spacing I tried was 30 feet. That means that the distance between the end of the first antenna and start of the second was 1 foot. That seemed like a practical minimum. I then made simulations at various separations. The separation distance is measured between the first elements of each antenna. So, for the example I just gave, the spacing would be listed as 30 feet, although the first antenna extends 29 feet towards the second.

Here are the results that I obtained.

Effect of Spacing on 2 Antenna Pennant Array
Spacing (feet) Gain (dBi) RDF (dB) Take-Off Angle (degrees) 3 dB Beamwidth (degrees)
30 -40.71 11.32 18 80.0
40 -38.86 11.49 18 78.1
50 -37.04 11.50 18 77.8
60 -35.51 11.48 18 78.2
70 -34.26 11.46 18 78.2
90 -32.21 11.42 18 79.0
110 -30.65 11.36 18 79.8
130 -29.43 11.28 18 79.8
150 -28.44 11.19 18 82.4
170 -27.66 11.08 18 84.2
190 -27.04 10.95 18 86.2

As expected, gain drops as the two antennas get closer and closer. The gain difference is approximately 12 dB between 30 and 190 foot spacing. RDF, however, peaks near the 50 foot separation, at 11.5 dB. The overall variance in RDF was 0.55 dB. The beamwidth is narrowest when the RDF is maximum.

What this tells us is that if you are willing to give up gain, you can push up the RDF. It does appear to cost a lot of gain, however. Perhaps the best news from this information is that even very close spacing produces good results, except for the loss in gain. For multiband use, however, the smaller spacing works well, since the array appears electrically further apart as the frequency rises. The means that the end-fire array will produce good results on 80 and 40 meters.

2-Element End-Fire Vertical Array

The EZNEC software is supplied with several example models. One was a 2-element vertical array, with 90 degree spacing and 90 degree phasing. This model had an RDF of 8.13 dB at a respectable take-off angle of 27 degrees.

W8JI Parallelogram Array

W8JI's web site is an absolute must-read if you are interested in low-band receive antennas. This model is taken from his pages. Please consult them for details.

EZNEC Demo 4-Square

Some sources have compared the receive quality of a 4-Square to that of a 2 wavelength Beverage. It appears from the numbers that it has an RDF more in line with a 1 wavelength Beverage, but with an improved take-off angle (24 degrees as opposed to 40 degrees). The RDF difference is on the order of 2.5 dB. I would suspect that when the noise is above average, the Beverage, with increased RDF, might be the best. Under lower noise conditions, the gain of the 4-Square would be useful.

It is possible to improve the 4-Square RDF. The ON4UN book, in section 4.9.4, describes an improved phasing specification designed by Jim Breakall, WA3FET. The current magnitude across the 4 elements is specified as 0.969 : 1 : 1 : 1.11, and the phase specification is -107 : 0 : 0 : 111. The RDF and gain for this phasing specification does increase. Another alternative, which I find to be much simpler to implement, is to leave the current magnitudes equal, and change the end phasing to 120 degrees. This further increases the RDF and the gain.

The idea of increasing the phase angle on the front and rear elements in order to raise the null  is a well-known technique. It's the improvement mechanism which is happening in the 4-Square case, and even the end-fire K9AY and Flag arrays.

W8WWV Hex Array

This is a 6-element array that I have been working on for far too long. It is designed to be my solution for 80 and 40 meter transmit and receive, as well as 160 meter reception. The elements are arranged at the corners of a hexagon that has 40' spacing between elements and the center of the array. This distance was selected because it provided operation on 160, 80, and 40 meters, and fits within my available space. Each antenna element is a 50' tall 80/40 meter trap vertical. Each vertical has 60 ground-mounted radials. The total radial system consumes nearly two miles of wire. Sooner or later, I will get a description of this antenna on my web pages.

The antenna can be electrically switched in 6 different directions.

Some folks have asked me why I chose a 6-element array as opposed to something more common such as a 4-Square. My answer is not forward gain, but rather RDF, as well as multiband operation. Time will tell if this strategy made sense, but the modeled RDF is approximately 12.5 dB, which is approximately equal to a 1000' Beverage. It's also 2dB more RDF than a 4-Square.

Since I am using a MININEC ground, my gain value are no doubt high. Because this antenna is designed for 160 meter reception (not transmit), I do not use resonant elements. That implies a high SWR on the transmission lines, and additional loss. I suspect that this loss might be as high as 3 to 6 dB. With with that loss, however, the antenna still has much higher gain than the other receiving antennas.


In order to be useful as a metric, RDF must be balanced against take-off angle. Low dipoles and short Beverages have RDFs which are higher than Flags and K9AY's, but my own experience is that the Flag and K9AY perform better (for DX). The low dipole and short Beverage have very high take-off angles. Perhaps the better way to compute RDF is to subtract the average gain (which is always the average, no matter what direction is considered) from the gain at some desired take-off angle. If this were done to the low dipole (Inverted VEE in this case) and the short Beverage, their RDF numbers would drop. Perhaps this metric could be called the useful RDF, or DX RDF.

Unless you have the room for a very long Beverage, it is necessary to build multiple element arrays in order to obtain higher RDF values. Relatively simply broadside and 180 degree end-fire phasing can be used in many cases. If you are interested in multiple band operation, you will probably need to carefully consider your spacing and feed system so as to preserve multiple band operation.

Direction switching may be difficult unless the basic element is a simple vertical. Directional switching of more complex single antennas, such as the K9AY or Flag is complicated since each element has an inherent direction bias. The simple vertical has no direction bias (in the azimuth plane). Phased arrays of physically symmetric verticals can usually be electrically steered by networks of relays.

The numbers suggest that a good configuration would be a pair of K9AY arrays (4 total loops), with end-fire orientation in the preferred direction. In the eastern part of the United States, this would be toward the northeast/southwest. The northwest/southeast directions would be handled with broadside phasing. The RDF performance would be approximately that of a 700' Beverage, but with an actual length slightly more than 100'. This system would also provide 4 different directions, two with end-fire performance, and two with broadside performance. The take-off angle would drop by approximately half - from 40 degrees to 20 degrees. This system would work on multiple bands. Experimenting with the spacing  might improve the gain and RDF, but watch for problems on the higher bands (40 meters for example) as you separate the two antennas.

If you build a multiple element array, and you desired multiple band (or wide band) operation, carefully design your feed system.  The W8JI pages have a lot of good information on phasing systems which will work over a wide frequency range.

It is possible to further increase RDF by building arrays with more and more elements. One configuration that I have modeled has 4 Flags in a rectangular pattern using both broadside and end-fire elements. The RDF climbed to 14 dB. The system does start to take up some space, and you only have a single direction (two, if you build bi-directional Flags). Still, its performance is very good.


Many of the receiving antennas that amateurs use have an RDF between 7 and 12 dB. This is only a 5 dB range. Even the lowly vertical to an 1800' Beverage is only a 10 dB RDF difference. Very few people have an 1800' Beverage, and most everybody can put up (at least) a K9AY. Can a change of only a few dB in RDF cover the expanse of all of the typical receiving antennas used by amateurs? If this is true, then the implication is that optimization of RDF is a worthwhile pursuit, and each RDF dB is very significant.


While I am a big believer in the value of receiving antennas, always check your transmitting antenna. When noise is low, RDF will not matter as much, and no doubt your transmitting antenna will have substantially more gain. When noise is taken off of the table, gain again becomes dominant, at least on the low bands.

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Last update: Saturday, March 10, 2007 08:36:20 PM
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