Friday, December 12, 2014

Front-to-Back is Overrated

After looking at Moxon and other directive antennas I realized it was time for a reset. That is, to ask just what it is one is trying to achieve with such an antenna, or indeed with any antenna? It is often far too easy to pick out a commercial product, install it and then declare to the the world how great it is, without ever really thinking through one's needs and desires.

My intention is not to disparage any products or designs, but rather to encourage some reflection. From my own years of observation it is a minority of hams that think through these matters and then can honestly state that their choice of antenna is the best one for their style of operating and personal circumstances. We all have constraints within which we must live.

I will start into this topic with the fundamental metrics of the typical directive (or gain) antenna to which most hams pay attention, and that manufacturers advertise:
  • Gain
  • Front-to-back (F/B)
  • Match
This is a pretty simple set of metrics to deal with. However in most cases there are trade-offs since it is a rare antenna that does comparatively well at all these metrics, or that does so in a way that is economical and not an installation and maintenance burden.

Let's look at each metric in turn to discuss why it might matter in the choice of an antenna. Although the title of this article is, in part, giving away the ending the process of getting there arguably matters more than any conclusion.


Gain is probably the most sought after feature in an antenna when an antenna of size or expense is considered. A forward gain of, for example, 3 db is equivalent to doubling transmitter power. Since gain is reciprocal it enhances reception by the same amount. There are few hams that don't want this. But why?

First, it increases competitiveness in getting through DX pile-ups faster. It that matters to you and you're running legal limit power, more gain is a reliable means of getting through.

Second, gain draws in more contest QSOs. A louder signal is a more attractive signal. If you doubt this you should reflect on your own behaviour on the bands. Hearing two signals of different strengths you are more likely to call the stronger one, or at least call it first. Since the size of stations relative to numbers is pyramid shaped, there are increasingly more stations of smaller capability. So the higher your gain the greater the score. To a limit since the ham population is finite.

Third, open propagation paths that are otherwise marginal or unusable. This is as true of EME as it is for HF DXing and contesting. For example, from my location the polar path to southeast Asia is relatively difficult. Most often when there is propagation it is marginal for those of us with modest antennas and power. Every decibel counts, even when there is no competition for a particular station.


Conservation of energy dictates that if you achieve gain in one direction there must be an equal decrease in other directions. This is inescapable. Depending on your objectives this can be a benefit or a problem. First we ought to list the types of signals that are adversely affected (attenuated) due to gain in the desired directions(s).
  • Stations other than those within the forward lobe
  • Local QRN
  • Atmospheric QRN
Why do you want to attenuate signals off the main forward lobe? The usual reason given is QRM that reduced readability of the desired station. I suspect that most hams have more of a QRM problem with stations in the same direction, those within the main lobe rather than other directions.

To make this more concrete think of an opening from my part of North America to Europe. Other NA stations will hear the same European station I am listening to and will, like the large majority of hams, avoid the frequency. That is, most hams are well behaved and avoid causing QRM. However within Europe other stations will often not hear the one you are listening to and may inadvertently cause QRM by transmitting on what to them is a clear frequency. The directivity of your antenna is no help.

In the case of a rare DXpedition it is more likely that the madding hordes will cause QRM, mostly accidental (over-enthusiasm) and some deliberate. Since most of these DX stations operate split the majority of QRM is avoided since they are not transmitting on the DX transmit frequency. F/B and rejection of other directions is only of significant benefit with a fraction of deliberate QRM. Since those stations are typically nearer to you it can take a lot of directivity to be beneficial.

During contests or other times when the band is open in two or more directions at once F/B can be more of an annoyance. Unless you have another antenna that favours directions that are rejected by the first you may have to turn the antenna (assuming a rotatable yagi) often. With a poor F/B you can often work other directions without turning the antenna. This is an advantage for contesters with small stations that need antenna diversity. I use the poor F/B of my yagi at some frequencies to improve contest results.

QRN requires a different approach. In the case of atmospheric QRN, unless there is an intense weather system in a specific direction you will benefit little from antenna directivity. While it may seem like a good idea to attenuate atmospheric QRN is most directions it does not really work that way. If the noise is truly omnidirectional the total noise power within your receiver bandwidth does not change with antenna direction. Again, we are dealing with conservation of energy. A directional antenna that rejects noise is most directions also amplifies noise from the main lobe due to forward gain. They balance exactly.

Local QRN due to switching power supplies for LED lighting systems, arcing power line insulators do have a particular direction allowing one QRN source to be nulled. Unfortunately that direction is often one where you can simultaneously beam toward the desired direction and sufficiently attenuate the noise. This is a problem more amenable to separate receive antennas such as a small loop or Beverage.


Operator convenience dictates that the antenna provide a simple match to the rig at all frequencies over which the antenna is stated to operate. Specifically this means a close to 50 Ω feed point impedance, allowing for efficient transmitter transfer of power without the need for an external or internal impedance matching unit. Yagis, for one, have a feed point impedance that can be far lower than 50 Ω at the frequency where gain is highest.

This is difficult to achieve over an appreciable bandwidth for an antenna, such as a yagi, that develops gain and F/B by cancellation of portions of the antenna's near field. This has made the internal ATU a common feature of modern transceivers, in order to improve the match over a wider bandwidth (preferably the entire amateur band) than the antenna alone can achieve. Arrays that achieve gain by additive techniques, such as the 4-square or multiple slopers, often require no external matching network.

The problem is exacerbated with multi-band antennas since traps and other loading elements further reduce bandwidth. Both subtractive gain and multi-banding increase antenna Q, where the feed point reactance (and sometimes the resistance) rapidly increases away from the resonant frequency (X = 0).

One positive point is that it is usually possible to bring the frequency of best match within the frequency range where gain and F/B are best. The reason is that most impedance transformation networks that are part of the antenna (beta, gamma, delta, etc.) don't appreciably alter parasite behaviour. In my own past antenna articles I often emphasized that tuning a gain antenna during design and construction should focus first on gain and F/B optimization, and last on match.


Perhaps the greatest performance trade-off for a subtractive array such as a yagi is gain versus match. The reason is that gain is maximum when subtraction is greatest. This result in the lowest radiation resistance (highest antenna current, by Ohm's Law) and highest Q. Yagis can have a radiation resistance below 10 Ω, and commonly below 20 Ω. Both R and X values change quickly away from this frequency because of the high Q. A matching network with fixed component values can transform the impedance to 50 Ω, but with a narrow SWR bandwidth.

More typically a yagi is tuned for lower than maximum gain to reduce the above problems, and that of I²R loss in the elements which can be significant with wire elements.

F/B tends to be influenced more by adjusting boom length than gain. It is especially influenced by element coupling since high F/B requires close to equal element currents. This was discussed in my recent article on Moxon yagis.

Unfortunately that increased element coupling and current equalization does not favour optimum gain, even while it improves both F/B and match. Indeed the comparatively lower gain of a Moxon rectangle should be evident by its good match to 50 Ω coax since, as already mentioned, high gain is associated with low radiation resistance and high, not equal current.

The diamond vee wire yagi I built years ago for 40 meters had very good F/B, almost certainly due to the current equalization brought about by the element ends turned inward. Although I could not measure the gain (which is very difficult to measure in any case) nor compare it to a reference antenna I can still be certain that the gain was no better than my more recent EZNEC model shows. The gain would be comparable to a Moxon and worse than a wire yagi with parallel elements.

So we can't have it all. There are unavoidable trade-offs we much deal with in choosing or designing a gain antenna array.

Common factors

The are other factors that can substantially affect antenna performance in regard to the metrics introduced at the beginning of this article. Since these affect all antennas almost equally I call them common factors, and discuss some important one below. That is, they are not a basis of comparison among gain antennas.

All antennas do better with height. This even goes for vertically-polarized antennas, or at least those that do not have an extensive ground plane that prevents the antenna's near field from directly interacting with ground. However do keep in mind that increasing height requires longer transmission lines and therefore higher loss. If care isn't taken, especially if the match is poor at some frequencies, much of the low-angle gain increase due to height can be lost in the transmission line.

In the usual case of horizontally-polarized gain antennas like yagis height increases gain at low radiation angles and therefore DX effectiveness. Since height affects antennas in an almost identical fashion it does not distinguish one horizontal antenna from any other. The exception is high-gain antennas with a narrow main lobe in the vertical plane, which will put more power at lower angles than an antenna with a wider main lobe for an equal increase in height. Generally speaking it would take a gain difference of at least 3 db for this height affect to become significant. A good example is stacked yagis.

Low gain antennas can have their performance, in all respects, changed or worsened at low heights since a larger fraction of the antenna's near field will interact with ground. This negative effect is lessened at heights above about λ/2 (10 meters on the 20 meters band).


When antenna elements are bent from the parallel or otherwise loaded for shortening it is important to beware of comparisons that do not elaborate on the differences. Without knowing this it can be difficult to interpret the results. This also goes for height above real ground (and ground of different characteristics) since these also muddle the comparison. Don't implicitly trust the comparison by just reading the final numbers without knowing how those numbers were reached. In most cases the deception is unintentional, but are just as misleading.

One reason the Moxon has somewhat lower gain is that the elements are shorter than λ/2. Moxon himself notes this in his book. He believes this is a reasonable trade-off with respect to gain and match. I would only agree if shorter elements have a mechanical advantage, such as on 40 meters where a gain antenna can be quite large, and especially if it must be rotatable. In this latter case you would probably be better off with a W6NL design 2-element yagi, either built from scratch or as a modification to a conventionally-loaded yagi.

Once you get beyond a modest amount of F/B (or F/S, etc.) the increased cancellation of fields in various directions has little to no effect on gain. Look at the azimuth pattern comparison at right (Moxon in blue), taken from my earlier Moxon article. All of that additional field cancellation and yet the gain is lower. Where did the energy go if not forward gain?

The answer lies in two places: the shape of the forward lobe and the chart scale. The Moxon rectangle has a broader main lobe, which spreads the available power over a larger solid angle. The chart scale is logarithmic, not linear, so that deep F/B is not what it appears! To go from -10 db F/B to infinite F/B is only 10% additional power available for forward gain (obviously I'm generalizing since the pattern shapes are different). That's only another 0.5 db potentially available. As noted this is spread over a wider forward lobe.

From this it should be no surprise that in pretty much every yagi ever designed the frequency of greatest F/B differs from that for greatest gain. The greatest gain is rather where the current is maximum (sum of driven and parasites, assuming proper yagi design), which is also where radiation resistance is lowest.

Of course that low radiation resistance must be addressed if maximum gain is desired. The match is easy enough to achieve at one frequency but not always across the band because of the high Q associated with the maximum gain condition. This is particularly true with only 2 elements or on 40 meters and below.


To me high F/B is therefore of small value: it helps not at all with achieving greater gain, does little about noise, and limits directional diversity during contests. If match is a concern it is better to increase the array to 3 or more elements so that both gain and match can be had over a broader bandwidth.

Don't blindly follow an antenna's spec sheet or focus too much on F/B in any antenna design. Especially since the quoted high values typically are achieved over a narrow frequency range. Be very certain that the F/B you're really getting is a must-have feature for your operating objectives. Otherwise you'll pay a price, and that price may only be evident in unexpectedly poor results.

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