Antennas for 136kHz

Antennas for 136kHz ON7YD
Antennas for 136kHz

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last updated on 18 September 2001

Index

Introduction
Short vertical antennas
Efficiency of antenna systems on LF (short vertical antennas)
Small loop antenna
Other transmitting antennas
Antennas for reception
Acknowledgements

1. Introduction

The main subject will be transmitting antennas for 136kHz as this often is the most important part of a longwave amateur radio station. The aim of the transmitting antenna is to radiate the power coming from the transmitter.
The power radiated by any antenna is determined by 3 factors :

The radiation resistance of the antenna
The antenna current
The gain (directivity) of the antenna

eg. : Assume we have an antenna with a radiation resistance of 10 Ohm, an antenna current of 2 A and a gain of 4 (6dB). This antenna will radiate a power of 10 x 2² x 4 = 160 Watt.

The gain of an antenna is always given relative to a reference antenna. Most common references are the 1/2 wave dipole and the isotropic radiator. This last is a virtual antenna that has no directivity at all, it radiates equally to all directions. In general the gain of any antenna relative to a 1/2 wave dipole is given as dB_d while the gain relative to an isotropic radiator is given as dB_i. Due to its directivity a 1/2 wave dipole has a gain 1.64 (2.15dB_i) relative to a isotropic radiator.

At first sight the radiation resistance of an antenna has no influence on the radiated power, as long as you match your transmitter to this resistance. But unfortunately the radiation resistance is not the only resistance that is consuming the transmitter power, there are also the loss resistances. These losses occur within the antenna (+ the antenna matching system) and in the environment of the antenna (ground, objects near the antenna). On HF these loss resistances are often negligible as they are rather small compared to the radiation resistance, but on longwave this is certainly not the case. For most longwave antennas used by amateurs the radiation resistance of the antenna is in the range of 10 to a few hundred milli-Ohm while loss resistances are in the range of 30 to 150 Ohm. This means that, dependent on the antenna and its environment, about 99% to 99.99% of the transmitter power is not radiated but absorbed in the loss resistances.

The two most common transmitting antennas on longwave are the short vertical monopole (Marconi antenna) and the small loop antenna. The short vertical monopole is an electric antenna, it creates an electric field 'on the spot' (near the antenna) while the magnetic field is created 'on the fly'. Opposite to this the small loop is a magnetic antenna, it creates a magnetic field 'on the spot' while the electric field is created 'on the fly'.
As a result of this the main source of losses for a short vertical monopole is in the environment (ground, trees, buildings etc.) while for a small loop the major losses are within the antenna. Therefore a small loop is less dependent on the environment for its functionality.
But for both types of antennas the goal is to get the ratio of radiation resistance versus loss resistances as large as possible. In practice most amateurs achieve better results with short vertical monopoles, only when environment losses are extemely high a small loop can be superior.

2. Short vertical antennas

2.1. Short vertical monopole

Assume we have a vertical monopole with a height H and fed against ground. If H is small compared to the wavelength then :

The antenna will act as a capacitance (C_V) in series with the radiation resistance (R_A) and the loss resistance (R_G)
The antenna current (I) will decrease linear from the feedingpoint to the top of the antenna, where it will reach 0
The voltage over the entire antenna will be the same

The current distribution, that is different from the sinusoidal distribution we are used to, can be explained as follows :
The antenna capitance is not located at one single point on the antenna, but is distributed equally over the antenna. As the antenna current flows into the antenna it gradually 'disappears' via the distributed antenna capacitance, resulting in a linear decrease.

Another - and maybe more correct - way to look at it is to compare a short vertical with a full size (quarter wave) vertical.
The full size vertical has a sinusoidal current and voltage distribution whith a 90 degrees phase shift between U and I. The short vertical can been seen as just the end of a fullsize vertical, where the voltage distribution is (almost) constant and the current distribution decreases (almost) linear.

The radiation resistance of vertical monopole with a height H and at a wavelength

is :

[1a]
or

[1b](in milli-Ohm, for 136kHz and H in meters)

The capacitance of a vertical wire of a height H and diameter d is :

[2a] (C_V in pF, H and d in meters)

In most cases the simplified formula C_V = 6pF/m [2b] is accurate enough.

In order to get a maximum radiated power we need a maximal current through the antenna. This can be done by compensating the capacitive component with an inductive component (loading coil), or otherwise said : bringing the antenna to resonance. Based on the formula for resonance (Thomson formula) we can calculate the inductance we need.

Example : Assume we have a 10m long vertical wire (3mm diameter) with and an enviromental loss of 60 Ohm.
Based on formula [1a] the radiation resistance is calculated as 8.2 milli-Ohm, the antenna capacitance, based on formula [2a] is 67pF. To bring the antenna to resonace on 136kHz we will need a loadingcoil of 20.2mH. The reactance of the coil is 17.4kOhm, so if we assume a Q of 300 then the coil-loss will be 58 Ohm. This brings the total lossresistance to 118 Ohm.
If we put a power of 100W into the antenna we will have an antena current of 0.92A, resulting in 7.5mW radiated power and a voltage of 16kV over the loadingcoil.

In the above example we calculated a radiated power of 7.5mW (0.92A into 8.2 mill-Ohm). To get the ERP (Effective Radiated Power) we have to take the gain of the antenna into account, for a short vertical monopole this is 2.6dB_d. So the calculated power in this case will be 13.7mW ERP.

2.2. Vertical antenna with capacitive toploading

The efficiency of a short vertical antenna can be improved by increasing the radiation resistance. This is done my improving the current distribution over the antenna, as the radiation resistance is proportional to the square of the average current through the vertical section. For a short vertical monopole, as described above, the average current is 50% of the current at the feeding point. One way to improve the current distribution is to add capacitive toploading to the vertical antenna.
The current distribution over the antenna has still a linear decrease, but due to the fact that the minimum now is at the end of the horizontal section the average current in the vertical part is higher.

The capacitance of a horizontal wire with a length L, a diameter d and at a height H is given by :

[3a] ( C_H in pF, H, L and d in meters)

In most cases the simplified formula C_H = 5pF/m [3b] is accurate enough.

The total antenna capacitance C_A = C_V + C_H. The antenna current at the top of the vertical section is determined by the ratio of C_H and C_V (assuming that the same amount of current 'disappears' via every pF) :

[4a]

And the radiation resistance is proportional to the square of the average current through the vertical section :

[5a]
or

[5b] (in milli-Ohm, for 136kHz)

This means that the radiation resistance can be quadrupled by adequate capacitive toploading.
An additional benefit of capacitive toploading is that the antenna capacitance can increase significantly.Therefore the inductance (loadingcoil) needed will decrease, resulting in lower losses in and lower voltages over the loadingcoil.

Example : Assume we still have the 10m long vertical wire (3mm diameter) and the enviromental loss of 60 Ohm of the previous example, but now we extend the antenna with a 20m long horizontal topload wire (at 10m height).
The capacitance of the vertical section will be 67pF (formula [2a]) while the capacitance of the topload will be 116pF (formula [4a]), resulting in a total antenna capacitance of 183pF. The radiation resistance will be 21.9 milli-Ohm (formula [5a]). The loadingcoil must be 7.4mH, at a Q of 300 the loss in the coil will be 21 Ohm and the total loss will be 81 Ohm.
If we put a power of 100W into the antenna we will have an antenna current of 1.11A, resulting in 27mW radiated power and a voltage of 7kV over the loadingcoil. Taking into account the gain of 2.6dB_d the ERP will be 49mW, this an overall 5.5dB improvement compared to the same antenna without capacitive topload.

The gain that can be achieved by having a better current distribution is 6dB, but due to the increased capacitance (and thus a smaller loadingcoil needed) some dB extra gain can be won, as you can see in this graph :

A vertical antenna with capacitive toploading can be constructed in various configurations, besides the 'inverted-L' configuration there are also the 'T' and 'umbrella' configurations that are frequently used. In general any shape of capcitive topload will work, the goal should be to get an many wire as possible as high in the air as possible. The topload wires can be sloping (umbrella antenna), but this will cause a decrease in the radiation resistance. As a rule of thumb can be said that sloping topload wires should never come lower than 50% of the antenna height.

The amount of topload capacitance is often limited by the space available. To get maximal topload capacitance on a limited space parallel wires can be used. Practical results proved that capacitances upto 15pF/m can be achieved, while a single wire is about 5pF/m :

Capacitance of multiple topload wires
Station	number of wires	Spacing	Height above ground	Capacitance
EI0CF	4	1m4m1m 1)	10m	15pF/m
G3XDV	3	all 0.5m - 1m (2)	14m
G3AQC	3	all 0. 45m	13.5m	12pF/m
ON7YD	4	all 0.8m	12.5m	13pF/m

(1) : spacing between outer wires is 1m, between inner wires is 4m (total 6m)
(2) : spacing is 0.5m at one end and 1m at the other end

2.3. Umbrella antenna

For practical reasons many toploaded verticals have sloping topload wires. These kind of antennas are called umbrella antennas. A sloping topload wire has 2 contradictory effects on the radiation resistance (R_A) of the antenna. One the one hand it increases the top capacitance, thus increasing R_A. But on the other hand it will introduce a 'downward current' that cancels a part of the (upward) current through the vertical, thus decreasing R_A.
The influence of both effects depends of the number of topload wires, their length and their sloping angle. John Sexton (G4CNN) did develop a mathematical model for umbrella antennas with the goal to optimize the parameters (number of wires, length and sloping angle) for a maximum radiation resistance.
Detailed calculations how to optimize the slope and length of the topload wires can be found here.
Assume an umbrella antenna with a unity height (1) and n topload wires of a length L, sloping under an angle �. The topload wires will 'shield' the vertical part over a length X = L*cos(�) (L and X relative to the unity height '1').
The gain (in dB, relative to a vertical without toploading) will be :

[6]

The graphs below give the relative gain of an umbrella antenna for sloping angles of 30, 45 and 60 degrees - depending on the 'shielding length' (X) and the number of tophat wires :

As expected higher sloping angles give the better results, but also note that for a certain sloping angle many short tophat wires are more effective than a few long.
The above formula and graphs assume that the tophat wires do not affect each other. In practice this will not be true in the case of many short tophat wires, the effective gain will be less than the calculated one.

2.4. Vertical antenna with inductive toploading

Another way to improve the current distribution over the antenna is to place to loadingcoil at an elevated point (H_L) of the antenna.
As the voltage is built up over the loadingcoil, only the part of the antenna above the coil wil be at high voltage. The voltage at the lower part of the antenna is negligible so the antenna current will not 'disappear' via the capacitance C₁, only via C₂. The antenna current below the loadingcoil will remain at maximum value and the result is an improved average current :

[7]

The radiation resistance of a vertical antenna with elevated loadingcoil is :

[8a]
or

[8b] (in milli-Ohm, for 136kHz)

Example : Assume we have a 10m high vertical wire (3mm diameter) and 60 Ohm enviromental loss. If we place an elevated loadingcoil at 5 m height the radiation resistance will increase from 8.2 milli-Ohm to 18.5 milli-Ohm (resulting in a theoretical gain of 3.5dB). But at 5m height we will need a loadingcoil of 40.4mH, at a Q = 300 the coil-loss will be 116 Ohm. This brings the total loss to 176 Ohm.
If we put a power of 100W into the antenna we will have an antenna current of 0.75A, resulting in 10.5mW radiated power and a voltage of 26kV over the loadingcoil. Taking into account the gain of 2.6dB_d the ERP will be 19.1mW, this only a 1.4dB improvement compared to the same antenna without elevated loadingcoil.

As shown in the example, inductive toploading has also a big disadvantage :
The loadingcoil has to be resonant to the antenna capacitance of the upper part (C₂) what means that the inductance has to be larger as the coil is placed higher. A larger coil means also a larger coil-loss and from a certain height the additional loss induced by the larger coil cannot be compensated by the improved current distribution, as you can see in the graph below. Apart from that the voltage over the loadingcoil increases and stable mounting of an elevated loadingcoil creates also mechanical problems.

2.5. Vertical antenna with capacitive and inductive toploading
The radiation resistance of a short vertical monopole with limited capacitive toploading can be improved significantly by adding inductive toploading (elevated loadingcoil).
But based on the improvement of the currentdistribution, adding inductive toploading to an antenna with sufficient capacitive toploading is not very efficient. In most cases the theoretical gain is no more than 0.1 or 0.2dB. Practical experiments by a number of amateurs however have shown that in some cases combined capacitive / inductive toploading can lead to a significant gain (of up to 5dB).
More detailed information about combined capacitive / inductive toploading can be found here.

2.6. Vertical antenna with tuned counterpoise

Pat Hawker describes in an article in ELECTRONICS WORLD + WIRELESS WORLD (February 1990) a kind of umbrella antenna with a tuned counterpoise. Both the antenna and the counterpoise are isolated from the ground.
The antenna is tuned by the loadingcoil (L₁), an elevated loadingcoil can be used to improve the current distribution. By adjusting L₂ the counterpoise is tuned to minimize ground loss. In practice L2 has to be tuned for maximal signalstrength in the far field.
This type of antenna has been used successfully on mediumwave with a gain upto 5dB measured by adding the tuned counterpoise. To my knowledge this antenna has not been tested by amateurs on 136kHz, but it might be worth a try.
No references to calculate the value of L₂ are given, but the article refers to US Patent no 3,742,511 and to IEEE Trans. on Broadcasting, June 1989, pages 237-240 (download it as zipped GIF file) .

2.7. Meander antenna

The performance of meander antennas for shortwave is described by Warnagiris and Minardo in IEEE Trans. on Antennas and Propagation, December 1998, pages 1797-1801. They show that the radiation resistance of short electrical antennas, such as a short vertical monopole, can be significantly increased by using u number of folded elements. Experimental investigations on a 44cm high meander antenna with 21 elements resulted in a resonance on 20.1MHz and an impedance of 21.9 Ohm. For a simple vertical monopole of the same length a radiation resistance of 0.34 Ohm can be expected. When scaled to 136kHz this 0.029 wavelength antenna becomes 64m high and for the 21 elements over 1.3km (!) of wire would be needed. But, assuming 60 Ohm groundloss, this antenna would perform almost 18dB better than a vertical monopole of the same height.
A meander antenna can be built rather compact arround a grounded tower.
The line-spacing has to be at least 20 times the wire diameter for optimal performance. Further experiments have shown following Size Reduction Factor (SRF) versus the number of lines (N) :

Size Reduction Factor
SRF	N	antenna height	wirelength
0.6	3	329m	987m
0.3	9	164m	1481m
0.15	27	82m	2221m
0.075	81	41m	3332m
0.0375	243	20.5m	4998m
0.01875	729	10.3m	7497m

red = extrapolated from experimental data (black)

For acceptable antenna heights (20m and less) the number of elements and the wirelength needed are not very realistic. Using 3mm Cu-wire (loss = 1 Ohm per 100m at 136kHz) the 20m version would have a 50 Ohm wire-loss, the 10m version even 75 Ohm. The weight of the wire would be resp. 330kg and almost 500kg.
But a meander antenna with a limited number of elements and tuned to resonance by a loadingcoil could be an acceptable alternative antenna for 136kHz. But remind that a meander antenna has many resonances at higher frequencies, so an adequate filtering of the transmitter signal (harmonics !) will be necessary.
To my knowledge meander antennas have not been used by amateurs on longwave so far.

2.8. Antenna with multiple vertical elements

The radiation resistance of a short vertical monopole can be significantly improved by the use of multiple vertical elements. These elements are connected through the capacitive topload wires and the antenna is fed through one of the elements, while the others are connected to ground. The radiation resistance will increase with the square of the number of elements, x4 for 2 elements, x9 for 3 elements etc...
If each of the elements has its own ground-network this can reduce the total loss-resistance.
But this system has also a disadvantage : as all the elements share the same capacitive topload the capacitance of each individual element will decrease and larger loadingcoils will be needed, resulting in additional coil-losses and a higher antenna voltage.

2.9. Using a non isolated antenna tower as LF-antenna

A short vertical monopole normally has to be isolated from ground at its base. But most antenna-towers are not isolated, for mechanical and electrical safety reasons. Here are 2 possibilities shown how to use a non isolated tower as vertical antenna for longwave :

The antenna can be fed via an isolating transformer (T) at the top of the tower.

If you prefer to have the loadingcoil at groundlevel there is an alternative solution. Currents I₁ and I₂ are equal and in opposite direction so they will cancel each other. As a result of this the antenna current I_A will not be affected by the proximity of the tower. This feeding system in combination with multiple vertical elements is described in US patent no 3,984,839.

2.10. Antennas with a long horizontal section
Based on the calculated current distribution and coil-losses very little gain can be won by having a horizontal section that exceeds the length of the vertical section by more than a factor 5. But in practice several hams achieved very good results using antennas with a very long horizontal section. OH1TN uses an antenna with a horizontal section of about 500m, bringing the antenna to resonance on 136kHz without inductive loading.
Despite the fact that the antenna is mainly horizontal, its polarization is mainly vertical as long as the height of the antenna (compared to the wavelength) is low and it is a monopole antenna (with ground as counterweight). An example of a large horizontal antenna with vertical polarization is the DDRR antenna.

2.11. Helical antenna

In the helical antenna the loadingcoil (or a part of it) is incorporated in the vertical section of the antenna. So with this antenna both capacitance and inductance are distributed over the entire antenna. As the antenna voltage builts up over the loadingcoil, the antenna voltage increases with the height. This voltage increase results in an improved current distribution, as in the lower part of the antenna (where the voltage is low) less current will 'disappear'. Without capacitive toploading the radiation resistance of a helical antenna will be 1.54 times larger as for a 'straight' vertical of the same height, this is a gain of 1.9dB.
When capacitive toploading is added the advantage of a helical antenna will be less, for 2 reasons :

As the antenna has more capacitive toploading the importance (and thus the gain) of the distributed inductance decreases.
As the capacitance of the vertical part of a helical antenna is rather large compared to a 'straight' vertical (because of the larger diameter of the vertical part) the effect (and thus the gain) of the capacitive toploading decreases.

An additional problem is that it is not so easy to built a mechanical stable helical antenna . The only amateur who (to my knowledge) used a helical antenna with succes was HB9ASB, until the antenna was destroyed in a storm (december 1999).

3. Efficiency of antenna systems on LF (short vertical antennas)

3.1. Antenna system
Under the term antenna system I mean more than just the antenna itself. It includes all surrounding parts that affect the radiation of the transmitter power : the transmission lines, matching devices and even enviroment.

3.2. Efficiency
If an antenna is fed with a certain power it will radiate a part of that power. The remaining part is dissipated 'useless', in most cases converted to heat in or arround the antenna. Simplified one can say that the transmitter feeds its power into 2 resistors, the radiation resistance (R_A) and the loss resistance (R_L).
The efficiency (n) of an antenna is :

[9]

On HF the efficiency of most antenna systems is very high, 90% or more. The most important sources of loss are skin effect in the antenna wires and dissipation in the transmission line (coax cable). On VHF and higher frequencies these last can become very important.
On LF the situation is completely different, efficiencies of most antennas used by hams are in the range of 0.01 to 1%. The source of these high losses is dependent on the type of antenna. For electrical antennas the major losses will be mainly in the enviroment and the loadingcoil. For transmitting the efficiency of the antenna system will directly affect the amount of radiated power and thus is very important. But for receiving on LF it is mainly the ratio between wanted signal and unwanted signals (noise, QRM) that determines the quality of the antenna system. Therfore the efficiency is rather unimportant in a receiving antenna system.

3.3. Antenna system efficiency, antenna directivity, ERP and EIRP
There is often a confusion between the terms efficiency and directivity or gain. While the efficiency is determined by the ratio of the transmitter power that is radiated, the directivity (often also called gain) is determined by the shape of radiation pattern. Even the term directivity is often only associated with directional antennas as Yagi's, Quads etc... But in practice any antenna has a certain gain, unless it radiates equally in all directions and under all angles. This 'gainless' antenna (that does not exist) is called a isotropic radiator and is taken as reference for the gain of other antennas (then the gain is given in dB_i). A 1/2 wave dipole has a gain of 2.15dB_i and is often also taken as reference (then the gain is given in dB_d). Despite the fact that a short vertical antenna has a omnidirectional radiation pattern in the horizontal plane, it has a gain of 4.77dB_i or 2.62dB_d due to its directivity in the vertical plane. This gain is almost independent of the antenna height, as long as it it short compared to the wavelength. For 136kHz this means that any vertical antenna with a height of less than 100m will have the same gain of 4.77dB_i.
Apart from the unchangable propagation parameters the signalstrength of a certain station on a certain frequency depends on the transmitter output power, the directivity of the antenna and the efficiency of the antenna system. These 3 parameters combined determine the ERP (Effective Radiated Power) of the station. This is the power that has to be sent into a perfect (lossless) 1/2 wave dipole to create the same signalstrength.
Example : Assume we feed a short vertical antenna with a radiation resistance of 0.04 Ohm and a loss resistance of 60 Ohm with a power of 200W. The efficiency of the antenna system is 0.067% or -31.8dB (0.04/60). This means that from the 200W transmitter power there will be 133mW radiated. As the gain of a short vertical is 2.62dB_d (x 1.83) the ERP is 244mW. This means that the antenna system and transmitter as described here will produce the same signal strength as a power of 244mW sent into a perfect 1/2 wave dipole.
With EIRP (Effective Isotrope Radiated Power) the reference antenna is not a 1/2 wave dipole, as for ERP, but an isotropic antenna. Therefore the EIRP is always 2.15dB higher than the ERP.

3.4. Optimizing the antenna system efficiency
In order to improve the ERP of a LF station one can either increase the transmitter power or improve the antenna system efficiency. Although some dB's can be won by brute power the practical limit of increasing the transmitter power is often reached at 1-2kW. Any further improvement has to be done by optimizing the effeciency of the antenna system. This means increasing the radiation resistance of the antenna and/or decreasing the loss resistance.
The radiation resistance can be increased by making the antenna higher and adding capacitive and/or inductive toploading. A more complicated option is to implement multiple vertical elements.
The two most important components of the loss resistance are the losses in the loading coil and the ground/enviromental loss. The coil loss can be reduced by improving the coil's Q but indirectly also the capacitive topload will affect the coil loss, as for a larger antenna capacitance a smaller loading coil is needed. Depending on the value and Q of the loading coil, in most cases its loss resistance will be in the range of 5 to 20 Ohm.
The major component of the loss resistance is almost always the enviromental loss. It of often just called ground loss, although this last is only a part of the enviromental loss. The enviromantal loss is dependent of many factors such as soil type, objects near the antenna and even the shape and size of the antenna. In most cases it will be in the range of 30 to 150 Ohm.

3.5. Enviromental losses

A short vertical antenna is capacitive coupled to its surrounding (the ground, trees, buildings, etc...). All of these surrounding objects also have a certain resistance that contributes to the enviromental loss of the antenna system. The RF current that is fed into the antenna seeks its way back via these capactive coupled objects and power is disipated in the resistances that these objects have.
The picture shows a simplified model : a T-antenna with a nearby tree. The antenna has capacitive coupling to the tree (C_T) and to the ground (C_G). Each of this 2 capacitances will form a return-path for the antenna current.
Example : Assume that C_T is 300pF and C_G is 150pF. Further assume that the loss resistance of the tree (R_T) is 200 Ohm and the loss resistance of the ground (R_G) is 50 Ohm.Finaly we assume that the antenna voltage is 5kV. The electrical model of this antenna system is shown right off the picture. Each return-path is represented by a capacitor in series with a resistor and we can calculate the impedance of each return-path : for a frequency of 136kHz the path via the tree is 3.9 kOhm and the path via the ground is 7.8 kOhm. With an antenna voltage of 5kV this means that there is a current of 1.28A via the tree and a current of 0.64A via the ground.
Based on the values of C_T, C_G, R_T and R_G the total capacitance (C_X) and enviromental loss resistance (R_X) can be calculated : 450pF and 94 Ohm. At first glance it might look strange that R_X is larger than R_G. But this is due to the fact that in this example the capacitive coupling between the antenna and the tree (C_T) is much larger than the capacitive coupling between antenna and ground (C_G) and therefore R_T contributes much more to R_X than R_G does. Notice that about 2/3 of the total antenna current is flowing back via C_T and R_T.
The presence of objects as trees and buildings near the antenna will have several effects :

The enviromental loss resistance will increase. In the above example the loss resistance increases from 50 Ohm (if the ground would be the only return path) to 94 Ohm.
The capacitance of the antenna system will increase. In the above example the capacitance increases from 150pF (if there would be no tree or other object near the antenna) to 450pF.
If a part of the antennacurrent returns via nearby objects (via a shorter and often not vertical path) the radiation resistance will decrease.

The increase of the enviromental loss resistance and decrease of the radiation resistance has a negative effect on the efficiency of the antenna system. The increased antenna capacitance has a positive effect, as you will need a smaller loading coil, but by no means it will compensate the negative effects.

3.6. Ground loss
On 'its way back' to the feeding point the antenna current flows (partly) through the ground. Since the soil is a rather poor conductor a loss resistance will be created.
The value of this loss resistance depends on :

The type (composition) of the soil
The frequency
The shape and dimensions of the antenna
Presence and size of a radial system

3.6.1. Type (composition) of the soil
The ground loss is very dependent on the composition of the soil and is inverse related to the conductivity of the soil (the higher the conductivity the lesser the loss). Soil conductivity can be measured, but the results of these measurements should be taken with some caution for several reasons :

- soil conductivity can be frequency dependent
- soil composition can change in the depth, you might have thin layer of 'good soil' over 'poor soil' or vice versa
- soil conductivity can be weather (season) dependent

Typical soil conductivity :

Soil type	Conductivity (mS/m)
salt water	1000
fresh water	1
wet sand	1 - 10
dry sand	0.01 - 0.1
loam	0.008 - 0.02
marsh	0.03 - 0.06
clay	0.5

Soil conductivity can be improved by salting the soil, but due to the ecological impact this is not recommened (in many countries it is unlawfull). Also most fertilizers will improve the conductivity of the soil. Often (but not always) wet soil has a higher conductivity than dry soil. On LF the use of salt or excessive amounts of fertilizers will have little or no effect as this will only improve the conductivity in the upper layer of the soil while the LF signal penetrates deep into the ground. But longer periods of rain will wet the soil deep enough to affect the ground loss.
The signal radiated by the antenna penetrates in the ground. The deeper the signal penetrates the larger the ground loss will be. This penetration depth is inverse proportional to the square root of the of the soil conductivity. If the soil conductivity (S in mS/m) is known the calculation depth can be calculated (for 136kHz only) :

[10]

3.6.2. Frequency
The penetration depth of the signal in the ground is not only dependent of the soil conductivity but also of the frequency. In the LF and lower HF region (30kHz - 3MHz) the penetration depth is proportional to the square root of the wavelength (or otherwise said : inverse proportional to the square root of the frequency).
Based on the frequency (F in Hz) and soil conductivity (S in S/m) the penetration depth can be calculated :

[11]

In most cases (and on 136kHz) the penetration depth will be between 40 and 150 meter, depending on the soil type. On salt water it will be only 1.5m.

3.6.3. Shape and dimensions of the antenna
Increasing height of a vertical antenna will increase the radiation resistance and thus the efficiency. But also increasing the topload will improve the efficiency. Apart from the fact that a larger topload creates a better current distribution several hams have also noticed that the loss resistance can significantly decrease when the topload covers a larger area.

Laurie Mayhead (G3AQC) has significantly improved his station by experimenting with different configurations of the topload, read his comments :
I started out with a 3 wire Marconi "T" antenna. This had a 30m top and a 15m vertical section, spacing between the top wires was 0.5m. I increased the spacing to 0.7m with no measurable difference in antenna current. The ground system was quite modest so I buried several hundred metres of wire with 10 earth rods at the ends of these radial wires. There was still very little increase in current, so I ran a 100m wire into the salt water and another 100m wire out to my 4 square array which has about 100 radials and a further 20 ground rods. Still no better. I was getting about 1.8A antenna current at the start and less than 2A at the finish. I measured 120 ohms total loss resistance. Then I decided to change the top loading, although analysis with Eznec indicated no improvement. So the 3 top wires became a single wire not quite 3 times as long. There was no great change in capacitance (no change in the loading coil), but the current was now over 2.2A and the measured resistance 80 ohms. Next I extended the top wires to 150m in a zig zag configuration because I didn't have the room to go in a straight line. I then got 3A and about 40 ohms loss.Small improvements to my loading coil result in about 3.2A now.
I think that there may have been a slight improvement because the aditional wire is further from the trees but I believe that the majority of the improvement is due to change in "current density" in the ground under the antenna. I call this my "Footprint theory". Basically its as if the antenna was a shower head and the ground a big bath with lots of outlets. Take the case of a basic vertical with no top load. The longer the vertical the higher the shower head and thus more outlets covered by the spray of water from the shower.Since each outlet can only get rid of a certain amount of water the more that are covered the more water gets away, the analogy is the lower the resistance! With an inverted-L or T ant the top wires are like several shower heads spaced out along the wire. So the longer the wire the more outlets recieving water.So its possible to bend the wire back on itself so long as the parts dont get too close. Alan Melia (G3NYK) commented that he visualised the fringing fields of a stripline over a conducting plane,he surmised that the effective width of the spray might be of the order of half the height of the wire. This would indicate that for maximum efficiency the normal parrallel top wires would need to be spaced by a distance equal to the height of the wires. I don't think that this is too far wrong.
In a recent mail to the reflector about the RUGBY 16kHz antenna it was mentioned that the original installation consisted of several multi wire cages,but that these were later replaced by a network of wires covering all the available ground area. This tends to support my Footprint theory and I would really like to find a reference to this work in the literature.

3.6.4. Radial system and ground rods
As mentioned before the antenna current 'returns' via the soil to the feeding point of the antenna. By adding a radial system and/or ground rod(s) the ground loss can be reduced.
The radial system contains a number of wires on or in the soil. As a general rule buried radials of blank wire are superior to radials on the ground or buried isolated radials. Burried radials should be at least 15cm (6 inch) deep in the soil. Although blank copper radials can be used, galvanized iron radials are cheaper and will be less affected by corrosion. The additional loss of iron radials (difference in conductivity between iron and copper) is almost always insignificant compared to the other losses.
Regarding the number of radials and their length the rule is simple : the more and the longer, the better. But there are some practical limits, once you have put a certain length of radials in the soils further extension of the radial system will only result in a marginal reduction of the ground loss.
In general the efficiency of a radial system is based on :

The total length of the radial system : Within reasonable limits a smaller number of long radials will give the same result as a larger number of short radials (eg. 10 radials of 30m each will be more or less equal to 20 radials of 15m each).
The frequency : The lower the frequency the less efficient the radial system will be.
The soil conductivity : The higher the soil conductivity the less efficient the radial system will be.
Other environemental losses : The higher eventual other environemental losses are the less efficient the radial system will be.

Beste result are achieved when the radials are equally distributed over the area below the antenna (see left picture). Placing 2 radials too close is not very effective and will hardly bring any improvement over a single radial. Depending on the soil conductivity, radials need to be spaced at least 2m to 10m for optimal effect. When using many radials an optimized layout can reduce the ammount of wire needed (and the work to burry the radials) without loosing efficiency (see right picture).
In addition to radials, ground rods can reduce the ground loss. These rods can be located at the feeding point of the antenna or at the end of the radials, eventually also somewhere 'half way' the radials. Due to their relative small length it is essential that ground rods are blank metal. The longer (deeper) the ground rods are, the better. Getting the rods into the ground can be hard labour if you do it using a sledge hammer and brute force. If you don't have too much rock in the soil there is an easier way :

Use 1 inch galvanized iron tubing used for plumbing and often sold in practical 3m lengths. Connect your garden hose to one end of the tube and let the water flow trough the tubing. Hold the tube vertical on the soil, the water will wash the soil away and the tube will gently sink into the soil. Be aware that the tube can keep sinking into the soil even if you shut the water off, so it might be nessecary to secure the tube for some days to avoid a 'China syndrome'.

As so many things will influence the efficiency of a radial system (with or without ground rods) it is very difficult to predict how many radials and/or ground rods will give an optimal result in a particular case. The best way is to start with a limited number of radials / ground rods and gradually increase the ground system while measuring the loss resistance. That way you will find the point where further extension gives little or no improvement.
If you have problems to get long ground rods into the soil : one long rod can be replaced by some shorter rods, keeping the total length the same. In order to have maximum efficiency all rods should be separated by a distance that is at least their length (if possible twice their length).
I have found some result of research on the effect of the radials on the antenna efficiency in the long wave range. But this was in regard of commercial stations, where an efficiency of 80% was aimed. For a soil conductivity of 2mS, a wavelength of 2000m (150kHz) and an antenna length of less than 50m (170ft) the optimal length of a radial was found as 150m (500ft) and the optimal number of radials is 120. But I am afraid that only very few hams will have the possibilty to install such a radial system.

3. Small loop antenna

under

construction

4. Other transmitting antennas

under

construction

5. Antennas for reception

Alan Melia (G3NYK) for checking spelling and grammar
Laurie Mayhead (G3AQC) for his contribution in 'Shape and dimensions of the antenna'
John Sexton (G4CNN) for the calculations on umbrella antennas

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since 21 feb. 2000