W8WWV - Hex Array - Loss

Greg Ordy


I find myself spending way too much time considering the loss in a typical vertical phased array. Hopefully I can get it out of my brain on this page, and move on to something less esoteric. I find some of the material that discusses loss to be confusing, and in the worst case, in disagreement with other sources.

This topic keeps swirling around my head for two reasons.

The first is that I want to justify the huge amount of time and energy which is spent in designing and building an array. Broadly speaking, when we go from one element to two elements, we pick up around 3 dB of gain. Going from 2 elements to 4 elements, which is usually the maximum number of elements in amateur arrays, we add around 3 more dB. So, when to comes to gain, typical vertical phased arrays theoretically provide 3 to 6 dB of gain over a single similar element. I want to preserve and protect that gain since it's part of the reason why we go through all of the work. In between ground loss, transmission line loss getting to the phasing network, and loss in the phasing network, it is not too difficult to give back 2 to 3 dB which strikes me as a very large amount, since we are going through all of this work for 3 to 6 dB at best.

One way to get off of this gain kick is to realize that on the lower bands, gain is simply not everything. On reception, which is at least as important as transmission, if not more important, what matters is improving the signal to noise ratio, which an array will do because it has a more focused pattern. This gets into the subject of RDF and front to back as well as front to side ratio. Even if the gain of an array is a few dB under some theoretical maximum, the value of the array for reception will not be diminished (assuming the pattern is preserved).

This consideration of reception, however, brings me to the second reason. We do not need to build this sort of phased array if we want to improve reception. There are a number of other antennas and antenna arrays which can be used for reception. The Beverage antenna is an example. This is a single antenna with excellent reception performance. If you don't have the large space needed for a Beverage, there are many other alternatives, including the Flag, Pennant, K9AY, EWE, and arrays of those antennas, including Beverages and small verticals. These antennas are useful on reception because they have a higher RDF, which implies an improved signal to noise ratio in the direction that the antenna is pointing. If there is a negative side to these receive-only antennas, it is that they are all very lossy, and inefficient, and make little sense as a transmission antenna. But we have a great transmission alternate, a single excellent vertical.


As I evaluate my own station, I'm torn between two alternative approaches to low band antennas. This analysis is especially true on 80 and 160 meters. On 40 meters, there is a much larger range of high performance antennas.

The first alternative is to build an array, such as the Hex Array, which combines both transmission and reception. The second alternative is to build a single excellent vertical for transmission, and combine it with special receive-only arrays. As I look at these two alternatives, I believe they are both attractive, each with strengths and weaknesses. Here is a table listing some attributes of each antenna.

Attribute Combined Array Transmit Vertical/Receive Array
Transmit Gain   more less
Receive Gain   +dB -dB
RDF   good good
Physical Size   smaller larger
Cost   larger smaller
Bandwidth   smaller larger
Multiple Bands   no easier

Each of the following paragraphs discusses an attribute.

For the attributes of RDF, cost, bandwidth, and multiple bands, the single excellent vertical with receive antennas is the clear winner. The physical size issue can be important, but neither of these alternatives works on a city lot. If you can find 5 acres, perhaps you can find 10 (yeah, I know, easy for me to say).

That leaves transmit and receive gain. Although the receive gain difference is large, it often times does not matter.

So, here we are, where we started, back at the transmission gain.

If I had to build the single excellent vertical, it would be a full-size 1/4 wavelength 160 meter vertical. It's bandwidth should cover the entire band. I would use 120 ground radials, each 0.5 wavelengths long. It's hard not to call that an excellent vertical. On 80 meters, it would be an end-fed 1/2 wavelength vertical. With a few relays, and a tapped inductor and capacitor for matching the high impedance on 80 meters I would have another excellent vertical for 80 meter CW and SSB.

With that as a reference antenna, it would be very hard to build an array which was actually 3 to 6 dB stronger. It wouldn't be hard if the array was made from the same full-size elements and excellent ground radial system and the optimum spacing. How often do you think that happens? With most arrays, there is a strong tendency to cut some corners that end up reducing the gain, usually due to increased loss. It seems to me that if you give up too much gain, then there is no reason to stay with the combined array. If you have the space, you might as well go with the single excellent vertical, and then have a lot of fun experimenting with all of the interesting receive antenna alternatives.

I suspect that each station is confronted with this same choice. If you want the most honest evaluation of the trade-offs, then you need to evaluate the loss in the array to see if you can maintain the gain advantage. That information, coupled with all the particulars of the situation should hopefully suggest the right solution. Of course in the end, there is no single perfect antenna, optimum for all situations. If possible, erect a wide range of antennas with different characteristics.

Does a dB Matter?

I've already expressed my opinion that a dB matters on another page. Here are a few additional observations.

The situation where a dB doesn't matter is the one where you are talking on a relatively uncrowded band, with signals that are 10, 20, or more dB above the noise level. In this case, there is an abundance of signal strength.

While this situation is common, I often think about the pile-up, whether with DX, or in a contest. There, a number of stations can be calling a single station, all at the same time. How does the receiving station decide who to work? The usual answer is the loudest station.

The decibel (dB) has a particular mathematical definition. Due to the history of the definition, it's also true that one decibel is very close to the change in signal level which is first noticed as being different. This is the just noticeable difference. A bel (B), or 10 decibels, represents a factor of 10 difference in power, which is interpreted by our brains as being twice as loud. So, 10 dB or 1 B more signal power is perceived as being twice as loud, and 1 dB is the smallest incremental change which is detectable. These are not absolutes, but how they usually sound to typical ears and brains.

My interpretation of this definition is that an increase of one dB in a given signal will tend to pull it out of set of signals with identical signal levels. So, if there are 100 stations calling a single DX station, and they all happen to have identical signal levels, then if one transmitting station adds one dB of strength, they might well be the next station worked. The other stations will eventually work the DX, but by the time their turn comes, the propagation may have shifted, or the DX signed off to go and eat dinner. In the contest situation, your score will suffer if you have to make repeated calls to work the other station. In this case, I believe that a dB matters.

There are other techniques which attempt to make a station stand out in a pile-up. Using a narrower transmit bandwidth can concentrate the power into a narrower band of frequencies. Using speech compression can also increase the signal punch. These are SSB techniques, not applicable to CW. The technique which can be used for all modes is to attempt to call the DX when other stations are not. This creates an advantage since there are fewer stations to compete with. One example of this practice is called tail-ending, where the caller attempts to guess the end of the previous contact, and throw out their callsign before anybody else. The problem is that often times the previous contact is really not complete, and this practice becomes nothing more than rude. Another common practice  is to keep calling and calling, hoping that the other callers will stop to listen, and you will be the last station standing, oh, I mean heard, the last station heard. This is just plain inefficient, as way too much time passes before a contact can be made. The best solution to this situation is to use split-frequency operation, where the DX can be heard returning to a station even if others want to call on and on. A good DX station can also manage the tail-ending problem if they use a consistent style that clearly indicates when new calls are appropriate. I would like to encourage all operators to refrain from being rude, and encourage all DX stations to develop a professional style that controls the mayhem to the greatest degree possible.

The value of a dB increases as the total dB range decreases. An S meter on a radio typically covers a range of approximately 100 dB. That's a large range. When we are talking about an array of phased verticals, the typical gain is between 3 and 6 dB.  In that case, a single dB is simply a larger percentage of the whole range. Another metric, measure in dB, and applicable to low band operation is the RDF. RDF ranges between 5 dB for a poor receiving antenna to 12 dB for a very good antenna. In this narrow range, a single dB represents a significant change.

There are times when a dB matters more, and others when it matters less. Perhaps the real skill is to know which is which, and spend the time and effort where it pays off the most.

Attributes of Common Vertical Arrays

To provide some data to consider in future sections, here is a table with attributes of some of the vertical arrays presented in the ON4UN book, third edition.

Array Gain Element Z Coax Length Coax Loss
 90, 1/4 λ Spacing Cardioid  3.1 dB  1  51 + j 20  1/4 λ 0.134 dB
 2  21 - j 20  1/4 λ 0. 343 dB
 135, 1/8 λ Spacing Cardioid  3.7 dB  1  13 - j 21  1/4 λ 0.522 dB
 2  18 + j 23  1/4 λ 0.168 dB
 Two Elements in Phase with 1/2 λ Spacing  3.8 dB 1, 2  31 - j 14  3/4 λ 0.602 dB
 Three Elements in Phase, 1/2 λ Spacing, Binomial Current Distribution  5.2 dB  1, 3  25 - j 19.4  3/4 λ 0.723 dB
 2  30.7 - j 13.7  3/4 λ (25 Ohms) 0.645 dB
 Two Element Bidirectional End-Fire Array, 1/2 λ Spacing, 180 Out of Phase  2.4 dB  1, 2  45.5 + j 14  3/4 λ 0.476 dB
 Three Element 1/4 λ Spaced Quadrature Fed End-Fire Array  4.1 dB  1  76.1 + j 51  3/4 λ 0.608 dB
 2  26.3 - j 0.4  3/4 λ 0.577 dB
 3  15 - j 22.6  5/4 λ 1.634 dB
 1/4 λ Spaced 4 Square  5.5 dB  1  61.7 + j 59.4  1/4 λ 0.157 dB
 2, 3  41 - j 19.3  1/4 λ 0.224 dB
 4  -0.4 - j 15.4  1/4 λ ---
 Two 1/4 λ Spaced Cardioid Arrays, side by side, spaced 1/2 λ  6.8 dB  1, 2  54.6 -j 5.1  3/4 λ 0.496 dB
 3, 4  5.5 - j 21.2  3/4 λ 2.314 dB
 Two 1/8 λ Spaced Cardioid Arrays, side by side, spaced 1/2 λ  7.0 dB  1, 2  24.9 + j 12.5  3/4 λ 0.574 dB
 3, 4  3.1 - j 19.2  3/4 λ 3.408 dB

The data in the book was computed with a ground loss of 2 Ohms, at 3.8 MHz. The transmission lines are RG-213.

Element Loading Loss

If your elements (verticals) are not full-size, you will need to bring them to resonance with some form of loading. There are many alternatives. All introduce some amount of loss. In addition to the loss of the loading mechanism, the shortened element will have a reduced radiation resistance. That radiation resistance is combined with the loading loss and the ground loss to arrive at the self impedance. The efficiency of a single element is the radiation resistance divided by the self impedance, which includes the loss.

The ON4UN book goes into great detail on loading schemes, their loss, and the resulting radiation resistance.

Ground Loss

Ground loss is the loss usually associated with vertical antennas. A number of sources treat the subject in detail.

The ON4UN book, Low-Band DXing, has an extensive chapter on verticals, radials, and ground loss. The ARRL Antenna Book has less specific information about vertical radial systems, but a lot of general information on the influence of ground around antennas. One question that usually comes up is how to trade off radial length versus radial number. A recent QST article tackles this topic, and presents formulas derived from the historic Brown data. The article is entitled Optimum Radial Ground Systems, by Robert Sommer, N4UU. It appeared in the August, 2003, issue of QST.

What is less highlighted is the possible negative impact on efficiency (loss) due to mutual coupling.

On my web page that describes the vertical antennas in my array, I arrived at impedance and loss measurements. On 40 meters, the self-impedance is 39 Ohms, of which 34.3 Ohms is radiation resistance, and 4.7 Ohms is loss. The efficiency is 88%. On 80 meters, the self-impedance is 33 Ohms, of which 25 Ohms is radiation resistance, and 8 Ohms is loss. The efficiency is 76%, which is a loss of slightly more than 1 dB as compared to a 100% efficient vertical.

These numbers are for a single vertical over the entire radial system of all six verticals.

Depending upon the currents in the array, and the physical spacing between elements, it's not uncommon for the drive impedance to be lower than the self-impedance. The reduction in resistance causes more current to flow, and that's a good thing, since current flow in elements is the source of radio waves. The problem is that the loss resistance does not change. This apparently causes a further reduction in efficiency - happy days, another source of loss has been found.

Here is a direct quote from the ARRL Antenna Book, 20th edition, page 3-10.

When antennas are combined into arrays, either parasitic or all-driven types, mutual impedances lower the radiation resistance of the elements. This drastically increases the effects of ground loss because I0 will be higher for the same power level. For instance, an antenna with a 50 Ω feed-point impedance, of which 10 Ω is ground-loss resistance, will have an efficiency of approximately 83%. An array of two similar antennas in a driven array with similar ground losses may have an efficiency of 70% or less.

That step down, from 83% efficient to 70% efficient is almost 1 dB.

Now I personally believe that the actual impact on the array can be difficult to determine.  This is because several elements are involved, and there will most certainly be asymmetric addition of loss.  This next table is a direct copy from my Band by Band Design page. It contains the computed drive impedance values for my array on 40 meters.

Element Design Current EZNEC or Measured Drive Impedance Current Voltage Power
Front 1 A @ -120 EZNEC 81.00 + j 34.27 Ohms 2.083 A @ -120 183.20 V @ -97.07 351.3 Watts
Front 1 A @ -120 Measured 93.31 + j 34.27 Ohms 1.870 A @ -120 186.07 V @ -99.83 326.9 Watts
Middle 2 A @ 0 EZNEC 18.82 - j 6.48 Ohms 4.165 A @ 0 82.91 V @ -19.02 326.5 Watts
Middle 2 A @ 0 Measured 26.06 + j 13.48 Ohms 3.740 A @ 0 109.85 V @ 27.35 365.3 Watts
Rear 1 A @ +120 EZNEC 16.65 - j 19.05 Ohms 2.083 A @ +120 52.70 V @ 71.15 72.22 Watts
Rear 1 A @ +120 Measured 16.49 - j 5.55 Ohms 1.870 A @ +120 32.57 V @ 101.38 57.80 Watts

The initial data to consider is the Drive Impedance column, and the Measured rows. I believe that these values are close to what my array presents on 40 meters. The reference self-impedance of a single vertical is 39 Ohms.

The middle and rear elements do indeed show a drop in the resistance of the drive impedance, down to 26 and 16.5 Ohms respectively. But, the front element has an increase in resistance to 93 Ohms. If I understand the quote from the ARRL Antenna Book, we need to remember that there are 4.7 Ohms of loss present in each of those values. The efficiency is now related to the drive resistance of 93, 26, and 16.5 Ohms, not the single element radiation resistance of 34.3 Ohms.

The most negative  interpretation of the ARRL Antenna Book paragraph is that of the 16.5 Ohms resistance in the rear elements, 4.7 Ohms is loss, same as always. The efficiency is then reduced to 78% from the initial 88%. But, if we apply that same analysis to the front element, the efficiency rises from 88% to  95%. Even more important is the power needed by the elements. The front element consumes 327 watts out of 750 watts on that side of the array, whereas the rear element only consumes 58 watts. Lower efficiency in an element that does not accept much power would seem to reduce the size of the problem from a total system perspective. Even if the power argument is incorrect, the worst that it becomes is a current argument, and the rear element has 1 amp of current, versus 2 in the middle, and 1 on the front.


If nothing else, these changes in efficiency make it increasingly difficult to design a phasing network without measurements and final current verification. This is because there are all of these factors floating around out there which influence the relationships between the elements.

Transmission Line Loss

It seems as if many sources do not spend a lot of time discussing the loss on the feed lines between the vertical elements and the phasing box. With single element antennas such as a dipole or single vertical, it's common practice to match the impedance of the antenna to the transmission line right at the antenna. The transmission line will then operate with the minimum SWR, which gives the lowest loss. On an array, it's nearly impossible to impedance match at each element, since the impedance of the element will change as the array direction is changed. This would imply that you would need a matching network for each possible drive impedance in the array. You would switch the networks as the direction changed. While I suspect that somebody has built an array with this sort of design, it is the exception, not the rule. In order to simplify the system, we accept the drive impedance of each element, and connect it as the load to the transmission lines going to the phasing network.

The driving impedance resistance values are usually well under 50 Ohms, and there may be substantial reactance.

The current forcing network design approach uses transmission lines which are odd multiples of 1/4 wavelength. In many cases 3/4 wavelength lines must be used so that they can all physically reach a common point. While current forcing is a powerful concept, it can cause transmission lines to be longer than needed. If there is a high mismatch in the line, the loss can quickly accumulate.

In the above table, the right-most Loss column was computed by the TLDetails program. There are many programs which can be used to determine the loss and impedance transformation on a transmission line. In addition to TLDetails, there is TLA, TLW, and software within the ON4UN package.

In most cases, the loss is relatively low, under 0.5 dB. There are several cases, however, where the loss exceeds 1, 2, or even 3 dB.

When evaluating the impact of transmission line loss, you need to be sure to factor in the percentage of the overall power which is being directed to the elements. Fortunately, it is often the case that the transmission line with the most loss also carriy a small percentage of the total power. This means that the impact of the loss is reduced.

The most important part of computing transmission line loss is to make sure that the phasing network design computations are made with the impact of the loss taken into account. The transmission lines transform the drive impedance, and add loss.

Because the transmission lines will always have loss, I favor feed system approaches that keep the transmission lines as short as possible. That means that the lines will probably not be an odd multiple of 1/4 wavelength. This tends to bias me towards the Gehrke approach, as opposed to the current forcing approach.

Phasing Network Loss

Once we get our transmission lines to the control location, they will be combined in the phasing network. This is usually done through a set of relays, so that the array can be rotated electrically. The phasing network typically consists of inductors and capacitors. Each component will have a Q, or quality factor. As the Q drops, the loss in the network rises.  Some typical Q measurements are shown on another page. It is impossible to estimate the loss in a phasing network without doing an analysis of the specific circuit. In many cases, the loss will be at least 1 dB in the phasing network. There are many programs which can be used to compute the phasing network loss. A free program is XLZIZL. An alternative is WinSmith.


In between the various forms of loss, it is very easy to lose 1 to 3 dB unless great care is taken. Given that the array is only providing a theoretical maximum of 3 to 6 dB of gain, this can be a large part of the potential gain.

Higher loss will be encouraged by using shortened elements, and relatively closer spacing. The shortened elements reduce radiation resistance, and add loss in the loading devices. The closer spacing tends to lower drive impedance values, creating additional loss on the transmission lines, and additional loss in the ground radial system. A smaller radial system usually goes along with closer element spacing, adding even more loss.

Even if you lose several dB in the implementation of the array, that does not mean that you should not build it. Performance on transmission will probably still exceed a single vertical, and on reception, the loss in gain is unimportant. Don't deceive yourself, however, that you are achieving the theoretical gain, unless you have worked very hard to preserve it. My own opinion is that the alternative to consider is a single excellent vertical, and companion receive-only antennas. That alternative may be less expensive to build, and operate over a greater bandwidth and even multiple bands. The downside may be that even more physical space is required.

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Last update: Friday, January 02, 2004 10:30:57 PM
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