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The mystery of radials

Erecting the antenna above ground (II)

The first effect of placing a 1/4l vertical at ground level is that the mirror-image of the "missing half" has consequences on the feed point impedance that displays about half the impedance of a dipole, or about 35 ohms plus ground loss resistance. At the risk to being repetitious, its lower end displays a low-voltage/high-current, conform to its large lobe firing all the output power at 0 and not higher above the horizon.

But other effects look more amazing... Some manufacturers state for example in their advertisings that they sold high performing antennas that do not request any radial or counterpoise (ground plane). Does it mean that if we raise our vertical a couple of meters above the ground, we can remove all our radials and keep its efficiency ? No, you can't. This is not really so simple, excepting if you are willing to loose all its efficiency... and your money.

Do you remember the 120 radials 1/2l long each lay on the ARRL's estate to make up all ground losses... ? Good news ! According Bencher one more time, "at heights between 2 and 8m about ground [...], four 1/4-waves radials for 40 meters do suffice to provide enough capacitive coupling to earth to work on 40, 75, 80 and even 160 m bands". And indeed, to avoid the detuning of wires running at ground level and reduce the ground currents you must raise the radials as low as 1 meter off the earth. Of course you will raise the antenna by the same occasion, and probably much higher as we will see in one moment.

In fact here also some amateurs confuse the height of radials above ground and the height of the antenna above ground. As both constitute the radiative part of a vertical antenna and that one without the other is ineffective, the melting is understandable. But try to see clearly in this new shallow fog. 

For example, if one states like Bencher that for the 40m band radials can be placed between 2 and 8 m high (1/20l to 1/5l high) to remove all ground effects, the antenna itself displays its best radiation pattern when placed at least... 3/4l above ground (see table below), so about 30 m high  ! Find the mistake... Both values seem incompatible, but they are not. In fact your radials will raise with your antenna and will be thus placed high enough above ground to be "out of reach" from the soil effects.

Height of antenna center (l)

Takeoff angle

1.5 0, 20, 43, 90
1 0, 30, 90
3/4 0, 43
1/2 0, 90 (large amplitude)
1/3 0, 90 (small amplitude)


0 or almost on the horizon

Ground plane antennas

We have not told yet, but although our vertical is now raised in height, it needs always its mirror-image to work properly. In this case, the earth is too far and our connection running to the ground will be detuned as we told before. So, instead of being grounded the vertical works against a simulated ground made of some 1/4l radials or stubs attached to the base of the antenna to create an artificial ground plane at a few meter high, hence its name. These radials are either open at 45 like a tripod or attached perpendicular to the antenna axis. For mobile operations the radials are removed at the benefit of loading coils in order to reduce their profile.

If we raise the antenna base at a height of 1/2l or so, as states Bencher usually four or six 1/4l radials only provide about the same efficiency as dozen or even an hundred 1/2l radials running underground. However, whatever state advertisings, when the height above ground decreases say below 1m, the number of radials required to get the same efficiency increases naturally. This is pure technical question, not of marketing... 

From 14 MHz and above (because it is impracticable on lower bands) the best radiation pattern for a vertical appears from 3/4l high above ground where an additional lobe appears at 43 of elevation. At 1.5l high the vertical antenna sees its main radiation lobes splitted in 4 parts, the main horizontal one splitting in 3 parts at 0, 20 and 43 of elevation and a fourth one appearing at 90 (vertical).

The "Bencher" configuration using some 1/4l radials placed in height is called a counterpoise. Used in HF and V/UHF bands, these Ground plane antennas are installed on small masts from 2 to 5m high usually erected above the common obstacles using as few as three radials or stubs. Rather efficient, these vertical antennas are largely used, not only by the ham community but also by other services using shortwaves, hence the presence of a large amount of V/UHF Ground plane antennas here and there at the HQ of many companies.

If you have a restricted place to install a vertical antenna or have possible issues with condominium (coproprietary) rules or with the neighborhood, erecting an antenna very high can be an impossible task.

As we saw in the table displayed above, for a vertical cut for the 20 m band, say 5 m high if we use its mirror-image in the ground, the best efficiency is reached erecting the antenna center up to 30 m high (100 ft) ! Waow, not easy for everybody.

If some amateur installations exceed largely this height, for most of us this is neither feasible or economical. So for the lower bands of 40 to 160 m, amateurs have found some hybrid solutions, like using together a vertical from 9 to 15 m high associated to a radial system made of only 4 wires as long buried in the ground.

The antenna being less than 1/4l high, the input reactance without loading is capacitive. In this case a simple series loading coil placed at the base of the antenna will ensure the matchting to the feed line and the transceiver.

QST magazine and the other publications edited by ARRL about antennas have provided several models of such designs (including several models using wire antennas tight in inverted-V or forming a loop).

Radiation and SWR : the antenna efficiency

Another question arises when speaking of efficiency : what becomes the power put in the antenna and how losses affect the SWR ? First let's do a bit of theory.

The antenna efficiency (er, also named antenna radiation efficiency) is the radio of the radiated power Pout to the input power Pin of the antenna :

er = Pout / Pin

While it is a number without dimension between 0 and 1 (or expressed as a percentage), it can also be quoted in decibels. Knowing that the power ratio in dB = 10 log Pout/Pin, an efficiency of 0.1 or 10% is 10 log 0.1, so er = -10 dB, and an efficiency of 0.5 is -3 dB.

The antenna efficiency (er) is different from the antenna "total efficiency" (eT). This later considers the antenna system as whole. The total efficiency of an antenna is the radiation efficiency multiplied by the impedance mismatch loss of the antenna, when connected to a transmission line or "receiver", a radio receiver or a transceiver. This can be summarized by the next relation :

eT = ML * er

where eT is the antenna total efficiency, ML is the antenna loss due to impedance mismatch, and er is the antenna radiation efficiency.

Note that many consumer products show a low antenna efficiency, typically ranging from 0.3 to 0.7 or -5 to -15 dB.

Calculating the efficiency, the 3R equation

Calculating the antenna efficiency using the above relations can not be easily performed manually. This calculation requires to measure the above factors by means of tools that we rarely find in ham shacks like an antenna analyzer or better, its graphical version, the vector network analyzer (see end of page).

However, it is not enough to own such an analyzer to use it properly. Many novices consider the SWR readout as equivalent to the resonant point of the antenna. Not necessary. It is only true when the input impedance display a 50 W resistivity (R=50, X=Fj). For other non reactive values, both the transmission line (coax) and the analyzer will alter this result by an amount depending of the mismach amplitude. So the first to do to prevent errors, is to perform this measurement not ta a few meters away on the coax line but almost at the contact of the antenna (within a few centimetres).

Three main factors can modify the antenna efficiency :

- Ground losses, Rg

- Radiation resistance, Rr

- Coil losses, Rc

The total loss (RT) is practically, we will see why, the sum of all these "3R" :

RT = Rg + Rr + Rc

Now, the antenna total efficiency (eT) is the ratio between the radiation resistance (Rr) and the total loss (RT) :

eT = Rr / RT

As above, you can express this result in dB using the relation 10 log (Rr / RT).

Note that if in laboratory we can get a very high efficiency almost on any band with a short antenna, according to tests performed by ARRL staff using a 3.15 m (10.5') whip, in the field figures are much lower : 0.1% on 160 m, 7% on 80 m, 31% on 40 m, 69% on 30 m and 88% on 20 m.

Let's review now each loss type affecting the antenna efficiency.

Ground losses dominate the other losses and thus must be kept as low as possible. Ground losses depend on many factors like the antenna mounting, how the antenna is wired and bonded, where the ground plane (mass of metal) begins, how much metal is used beneath the antenna in order it radiates properly at low elevation (<15), how coax is terminated and whether it is in good state, how chocke and coils are designed, etc.

Radiation resistance is another word for input impedance or resistive losses. It is a concept, a mathematical function, rather than a parameter that we can measure as it. It defines the effective electrical length (not the physical length) and how the current flows in this circuit. The longer the antenna electrical length, the higher is the radiation resistance.

Its value change as a square law function (x2) : from a whip 2-m high to 3-m high, the radiation resistance is roughly multiplied by 2. Changing a 2-m whip for a 4-m high antenna, the radiation resistance will be 4 times higher. With a value of 0.2 W for an antenna cut for the 80-meter band, the radiation resistance can reach 36 W on the 10-meter band.

The radiation resistance also increases in using cap hats on vertical antennas. Properly designed, they increase the effective electrical length and increase the current node. This accessory is the most efficient on the lower bands where correctly installed the radiation resistance can be multiplied by 4.

 For short, better using a long antenna, specially in portable or mobile operations, than a short one.

You will find more information about effects of current in the article describing degree-amperes and field strenght written by Edmund A. Laport.

Coil losses are by definition losses in all antenna systems using loading coils. There are mainly installed on small portable and mobile antennas without to forget shortened beams that often included coils on all elements (reflector, driven and directors) to compensate losses.

Indeed, coils are used in all "small" antennas shorter than l/4 on the working frequency, and thus displaying a capacitive reactance (know a -j). A coil is then added showing an opposite value, thus a positive reactance (+j). Of course, logically, the smaller the antenna is cut, the larger the coil reactance will be. Consequently, all else being equal, will note an increase in coil losses.

As we explained in Basics of antennas about the Q-factor and the interest of installing a capacitance hat (cap hat), one can easily increase coil losses in trying to improve the performances of a small vertical. Indeed, if the cap hat is place just on top of the coil, the antenna system will display an excess capacitance and coil losses will increase.

In the same way, although using large coils vs small ones can increase the Q-factor on specific frequencies or on the low bands, they also become very lossy at the same low bands.

At last, we stated above that the total loss is "practically" the sum of the 3Rs because there are always additional very small losses in all metallic accessories connected to the antenna : in the mast, the whip, the material in which the antenna is made of (stainless steel affect more for the lower bands), the possible trailer hitch mounting, and even depending on the diameter of the antenna tubing. Some will add serial losses, others capacitives losses, serial or in parallel with the input impedance.

Results in the field

Now that we installed our antenna system and know what factors can affect its performances and how to correct them, let's see what really happens in the field, and specially what values do we measure and calculate.

The radiation resistance or RF energy radiated by your antenna has to be consider as a "good lost" compared to the lost induced by the ground and conductor resistance that are consider as a total loss. Thus, knowing that some "conductors" (including traps, loading coil, etc) loose more energy than others, we can use the concept of form factor, the famous Q-factor.

But due to ground losses, than can easily exceeded the losses in conductors, traps and coils, a well tuned vertical cut at 1/4l can display a high SWR in the middle of a band (over 2:1) what means that some dozen of ohms vanished in pure ground loss resistance. Here are some tests made in situ. The first shows the efficicency before (first row) and after (second row) installing 6 radials of 2m long at ground level around the base of a 1/4l vertical :



Line Impedance (ohms)


Resistance (ohms)

Total Losses (ohms)


1/4l vertical






1/4l vertical






SWR is measured at the antenna feed point in place of the RTX end to avoid transmission losses and increase the accuracy. Total losses are due to radiation lost in coax, traps, loading coils, and ground loss resistances. The efficiency is expressed as the ratio of power radiated to the total power fed to it (or the ratio between the radiation resistance to total losses).

Below is the efficiency before and after installing 6 radials at the base of the previous vertical but resonating at half-frequency (e.g. on 80m in place of 40m), the third case using 120 radials to reach a zero ground resistance :



Line Impedance (ohms)


Resistance (ohms)

Total Losses (ohms)


1/8l vertical






1/8l vertical






1/8l vertical






For comparison purposes, here is the efficicency of a dipole :



Line Impedance (ohms)


Resistance (ohms)

Total Losses (ohms)


1/2l dipole






From these figures we can conclude that several parameters are very important to get the highest efficiency of a vertical :

1. The radiation resistance must be kept as high as possible, but it depends on total losses thus,

2. The radiation resistance depends on the height of the vertical, but as height over 1l are not always practicable, we can reduce the ground loss resistance using as many radials as possible in using high-Q loading inductors of large diameter. Therefore the slim loading coils and traps made of thin wire encasted in metal usually found in ham stores are NOT at all adapted to this usage.

3. A low value of SWR does not mean that your antenna system is operating efficiently. Even the fence installed in the end of your backyard or an electric heater could be fine-tuned with an ATU to display a SWR 1:1 but it will not radiate the least watt of power as explained on this page dealing with SWR.

Antenna Gain and Directivity

The antenna gain (G) is related to the antenna efficiency (er) and the antenna directivity (D) as next : 

G = er D

The gain is quoted in decibel (dB). The antenna radiation pattern can be expressed as a function in spherical coordinates (polar angle q and azimut f).

In a diagram in cartesian coordinates showing the elevation plane, the radiation pattern is only a function of the polar angle q :

F(q,f) = (sin q)

F(q,f) = (sin q)5

In using of one of these equations, and plotting the values for each angle in a cartesian graph (polar angle vs decibel), you can easily plot the radiation pattern of an antenna in elevation and display its lobes as below right. At left, the similar plotting in polar coordinates (sometimes faulty named "3D radiation pattern") showing the azimuth plane pattern.

Document Cisco.

Software and antenna analyzer

Of course, all measures and calculations executed manually can be performed automatically either using electronic devices or software.

There are free solutions like Smith Charts from AC6LE or the VOACAP propagation prediction program (see also this review) that includes a EZNEC module from W7EL, but you must know the specifications of your antenna.

These programs do not calculate the total efficiency and are limited to the SWR and lobe pattern calculations. EZNEC+ is also able to display Smith charts, return loss, and reflection coefficient magnitude while EZNEC Pro also includes the loss in wire insulation among many other features.

More complete but more expensive, you can purchase an antenna analyzer like MFJ-259C (or the previous model MFJ-259B) from MFJ Enterprises. Its price of 299.95$ and much lower on the second hand market makes it available to amateurs.

At last, with a lot money, you can also purchase a professional vector network analyzer like Keysight E5061B ENA. But even if you are lucky and found an used model on the second hand market (there are very scarce), it will cost more the 17000$ knowing that a brand new model costs more than 27000$. So, it is not really in reach of the "poor ham radio operator", but who knows.

To read : Catalog of Vector network analyzers, UCL University

From left to right, the MFJ-259C antenna analyzer from MFJ Enterprises, the Keysigh (ex-Agilent) E5061B ENA vector network analyzer, and a plotting from EZNEC module included in VOACAP propagation prediction program (see also this review).

By way of conclusion

I think that this time we emerged safe and sound from our fog so much dreaded. We discovered that a ground plane radial system is recommended as it provides low-loss "return" paths to currents that can be "recycled" in the antenna, that might otherwise flow on the lossy earth. If these return of current come back to the shack they can be stopped using a current choke, a variant of balun 1:1.

Even if a "no-radial" system displays a low SWR, by itself it tell us nothing about the antenna efficicency, and mainly how the ground interacts with the system. For short, a simple vertical 8m long using radials and a commercial "no-radial" vertical will display the same performances, but the SWR of the second antenna at the feed point can reach 20:1 or more without losing any energy but without neither emitting the least watt !

When an antenna is placed near ground level, the earth losses are the major factor limiting the antenna performances, and no antenna tuner or matching device can do anything about that physical law, excepting maybe some bad advisers.

Thus if you have to remember only one think, that will be the next one :  radials reduce the ground losses and increase the antenna efficiency. A side effect, too few or too short radials affects the SWR.

With all this information, it looks no more as an idle fancy or diligence from a manufacturer if he tells us that radials are useful ! Now you know why.

For more information

Basics of antennas (on this site)

All about transmission lines (on this site)

From dB to S-point : Learn to play with power units (on this site)

How Many Radials Does My Vertical really Need?, Rudy Severns, N6LF? QEX, May/June 2008 (PDF, 700 KB)

RADIAL_3.EXE,  Reg Edwards, G4FGQ, calculates the efficiency of any system of radials

ARRL Antenna Book, ARRL, specially chapter 16 about the efficiency, also available on CD-ROM

Vertical Antenna Classics, ARRL

Degree-amperes and field strenght, by Edmund A. Laport (about antenna currents).

Another Look At Reflections, by Walter Maxwell, W2DU (sk), QST magazine, 1973-1976 (PDF on K6MHE website)

In QST magazine, September 2006 issue (pp56-57), VE2CV explains how to use an antenna analyzer and EZNEC.

About the coil theory, Alan Payne, G3RBJ, wrote an interesting article in QEX magazine, May/June 2011, page 39.

Technical notes about antennas are also available in PDF format on the website of major manufacturers and portals :

Butternut, Cushcraft, eHam.

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