# Grounding, circuit protection and EMI

This is chapter 11 of the DRSSTC design guide: Grounding

This chapter will first cover the different hazards related to EMI, then go over some studies to understand the difference between grounding systems and at last present possible solutions to noise and grounding problems.

### Electromagnetic Interference (EMI)

Tesla coils are for the most operated in high energy pulse modes where a powerful but short lived electromagnetic field is generated to transfer a huge amount of energy in a very short time. Only with exceptions of SSTCs and VTTCs that in their nature have a lower peak current but higher RMS current flowing. A strong magnetic field around the coil is formed and it has its peaks just before a spark breaks out or if the grounding of the secondary coil is bad.

This powerful magnetic field can induce currents in all materials and equipment that is able to conduct a current. This can be lamps, shelving, computers and your measurement equipment. Most electronics have built in protection from static discharges and can to some extend withstand induced currents, but in the end this electromagnetic influence is not good for anything.

The fast rising edge of the pulse discharge also generates a huge amount of EMI and this is especially bad for cameras and microphones. To prevent this a breakout point inductor (read more about this further down) or local faraday cages around sensitive equipment can be used.

Interference is often seen in TV sets, radios or broadband DSL modems. These are all equipment and technologies that operate in- and around the same frequency spectrum as most Tesla coils operate in 30 kHz to 5 MHz. Table 1 below shows the most common frequency ranges of some different house hold items and technologies around us. I tried to give an idea of what kind of interference that could be expected from a unshielded Tesla coil of the given size.

Personal experiences only includes DSL modems being knocked off the line from a massive amount of noise in the upload spectrum.

### Fire hazards

Sparks from a Tesla coil can fly out in the open air and it can also seek towards or strike doors, walls or other building parts made from seemingly non-conductive materials like wood, plaster, cement and plastic. The sparks will however still look for the best way to ground and where it finds a metal part behind plaster or wood, a hot grounding spark can result in internal fires inside building parts. Avoid having sparks strike directly to building parts that are not properly grounded!

It is better to place some kind of sheet metal, aluminium foil, fencing or some other kind of conductive surface over building parts and surfaces than letting it strike directly on it.

### Static charges

The secondary form made of plastic material with a coil wound around combined with a low capacitance topload can easily get charged up to hold enough charge to give a good zap if you were to handle the secondary coil or topload after storage or running the coil.

Always use a grounded wire or a shorted wire to secondary ground to topload before handling the coil, this will discharge any static charge on the topload.

A static discharge is mostly harmless, but the shock from it could cause you to drop a expensive part of the Tesla coil or that you stumble and fall on the ground yourself.

### Legal issues

Most legal issues associated with Tesla coils are related to the operation of the first type of radio transmitters. These were similar coils to a Tesla coil and the modulation of the antenna for the radio signal was done with spark gap, which creates a massive amount of RF noise, as well as the transmitted signal have high energy peaks from where the spark gap fires.

This resulted in laws, later when technology was much more refined and better transmitter amplifiers/antennas was used, that banned the use of spark gap transmitters and due to combating pirate radios it is also illegal to modulate a transmitted signal.

These issues can be overcome with good enough grounding and completely enclosing the Tesla coil in operation in a so called Faraday cage which I will describe below.

### House mains and mains ground

House main ground is mostly connected to the water pipes of the house and a 1-2 meter ground rod that is knocked into the ground outside the house, these grounding methods are connected to all wall sockets and thus all electronic equipment in the house is also connected to this ground.

The following illustration of a apartment complex shows the earth wires as green/yellow and how they all connect back to a main ground bus bar and from here connects to the tap water piping and a ground rod.

House main ground should NOT be used for grounding Tesla coil circuits, where a normal house ground represents a zero potential and is used for measuring leak current faults and to lead potential insulation failures to ground instead of humans. The condition of the ground connection earth / tap water piping can also vary with age of the installation.

A ground used for a Tesla coil is often called a RF ground and that relates back to the days where a spark gap transmitter was used for radio broadcasting and thus the term RF refers to Radio Frequency.

A RF ground can be conducting several Ampere of high frequency current and if the mode of operation suddenly changes in the coil, it could be large and heavy ground strikes, the voltage profile can also suddenly change and the changed or higher voltage can result in flash overs between ground and phase/neutral in the house wiring.

If you are living in a apartment building and decide to use the mains ground, there is very little chance that any of the RF current will even reach the earth connection that is most likely found near the basement with the tap water installations. Instead it will be the wires in walls, floor and ceiling that contribute as the return ground for the capacitively coupled displacement current between the sparks and the secondary base ground connection to the mains ground.

A noise filter should be used between the mains and input to the Tesla coil, to try to filter and prevent as much noise as possible to run backwards into the mains supply. The most important part of the line filter in regard to Tesla coils is the Y capacitors as they couple the line and neutral to the ground, around 10 nF is suitable if you are building it yourself.

You can also use a line filter that is easy to salvage from old electronics or industrial equipment for filters with higher current ratings.

### Earth impedance factors [1]

To understand why a normal house ground system is not a good idea to use for Tesla coils and which parameters are the most important in making a good grounding system for Tesla coils, let us take a look at the following earth impedance formula.

$\mbox{Earth impedance Z}=\frac{\sqrt{R+j\omega L}}{\sqrt{G+j\omega C}}$

R is the resistance in Ohm of the material used in the grounding system. Flat conductors are better than round (at same cross sectional area) when skin effect at high frequencies is taken into consideration.

G is the earth conductance, related to earth resistivity and contact resistance between the ground system electrodes and the soil. This can be increased by use of additives to increase contact resistance between the ground system electrodes and the soil.

L is the inductance of the earthing system. This can be reduced by use of shorter multiple conductors instead of single one of equivalent total length.

C is the capacitance between earth and earth system electrodes. Capacitance can be increased by larger earth contact area by using plates and flat conductors which has a higher conductor to earth capacitance than round conductors.

Much like in designing a inverter bridge, we are interested in the lowest possible inductance to avoid high voltage transients induced by a high frequency current passing through a inductance, here a larger capacitance can help reduce the impedance.

### Equivalent electrical network of horizontal grounding electrode [2]

To visualise the above earth impedance equation we can show a grounding rod as a equivalent electrical network of a infinite number of elements.

The lightning current entering the conductor in the left side of the schematic is moving along the conductor through its resistance (R) and inductance (L), while energy on the way is dissipated through ground resistance (G) and capacitance (C) to ground.

### Earthing system ground impedance at higher frequencies [1]

This part is included to give the reader a understanding of how the ground systems made for 50/60 Hz mains failure and optional lightning protection systems to the same interact. Just because a ground system is good for its intended purpose does not mean that we can uncritically use it as a RF ground.

A French group of researchers (A. Rousseau and Pierre Gruet) made a case study where the impedance of different earthing systems on different industrial buildings and constructions was tested with a injected 10 kA impulse and measured with a  computer controlled micro-ohmmeter (AES 100x series).

Measurements is done in a range of frequencies from 10 Hz to 1 MHz. It applies a sinusoidal voltage at a varying frequency between the earthing system and a current injection rod, and allow the measurement of the current received by an auxiliary rod. The resistance, the reactance and impedance are measured and recorded.

Case studies

• A: Building with a large grounding system
• B: Extension of a existing factory
• C: Metal silos
• D: Metallic framed large shed
• E: Group of chimneys
• F: Metallic tanks

Case A – Building with a large grounding system

Top layer soil is a low resistance mix of earth and dirt, it is however only around 1 meter in thickness at most. Underneath is a rough and rocky base soil that has a high resistance.

The building was considered to have a good earthing system, with many copper tape conductors embedded around the different buildings and interconnected. The highest building is protected by a lightning rod connected to the earthing system by one conductor going to ground while the other buildings are protected by a mesh system.

The low frequency resistance was only 4 Ohm. But at 1 MHz the impedance was around 70 Ohm. The induced RF voltage spike can now reach around 700 kV and cause flash overs in the grounding system instead of being led directly to ground.

Case B – Extension of a existing factory

In preparation to a future expansion of the factory, a secondary grounding system was laid out and it was tested before construction of the new buildings.

There is only a very thin layer of low resistance soil on top of a very rocky soil underneath, the earthing system uses a 3 legged crow foot system that has a very high low frequency resistance of 150 Ohm. But there will not be the same dramatic increase in impedance as the frequency goes up as this system has a good capacitively coupling to ground, but it is still a very bad result with a impedance of 93 Ohm at 1 MHz.

Case C – Metal silos

A silo where all surfaces are made of metal, but being tall and only having a diameter of 3 meters leaves it with a small foot print where very little of it is in contact with the soil, due to the concrete foundation.

The low frequency resistance is measured to 15 Ohm and the impedance at 1 MHz is around 41 Ohm,.

Case D – Metallic framed large shed

A large metallic shed used for storage was measured to 4 Ohm at low frequency and the impedance at 1 MHz was 38 Ohm, the increase in impedance is also less steep than the previous examples, mainly due to the sheds large capacitance to ground.

Case E – Group of Chimneys

A seemingly good earthing system where each stainless steel chimney is grounded and all chimneys are interconnected by copper tape. This give 5 Ohm low frequency resistance to ground, but as the tape is not used for better connection to ground, but only between the chimneys, the impedance at 1 MHz is 116 Ohm. This makes for a very bad grounding system.

Case F – Metallic tanks

A large metallic tank with a diameter of 6 meters standing on a concrete base immersed in a sand/water mixture as the structure is located next to the sea.

There is no dedicated grounding system and yet the low frequency resistance to ground is only 1 Ohm. This tank has the least steep climbing impedance and it is only at higher frequencies that it really starts to increase. The very low resistance and surface to ground area is large is the contributing factors to the low impedance.

Test results for Case A to Case F

A 10 kA 1/20 wave was injected in the earthing system represented by coupled (R, X) function of the frequency as given by the measuring device. The crest value of U given by a simulation using the earthing model is then divided by 10 kA in order to calculate the equivalent lightning resistance (RHF). Assuming that 1 m of conductor is represented by a 1 uH inductance, the equivalent length of the earthing system is given in meters.

 kHz Case A Case B Case C Case D Case E Case F 63 19 178 14 4 7 5 80 22 212 16 5 7 6 100 26 204 21 7 10 7 125 35 214 26 10 14 9 156 42 237 34 14 18 9 199 49 227 48 22 24 11 250 53 230 53 28 33 14 316 55 208 52 33 47 14 398 57 180 66 35 52 16 500 57 152 59 33 75 25 633 59 142 54 38 84 36 797 61 114 44 30 104 35 1000 69 93 41 38 116 43 RHF(Ω) 47 203 35 22 47 16 Avg.Z(Ω) 47 184 41 23 46 18 Eq.length(m) 24 102 18 11 24 8

If RHF is high, this means that equal potentiality in the system needs to be very good to avoid flash overs due to expected high over-voltages. In the same way, if the equivalent length is long, this means that the earthing system behaves as a single long conductor having a high inductance and thus a high impedance potentially generating high over-voltages.

Study conclusion

It has been show that a low DC resistance grounding system is not a guarantee of a good system to lead lightning strikes to ground. It is useful to measure the earthing system impedance in order to evaluate the installation and do improvements from there.

Long or deep earthing systems are not good lightning earths, more specific shapes or plates as ground conductors are need in order to decrease the impedance.

These measurements can not take into account other extreme conditions during a lightning strike, such as soil ionisation and sparking/branching off from high voltage potential causing flash overs.

### Issues when doing live shows for audiences in non-laboratory environments

Doing a show with a Tesla coil as part of a live performance, TV recordings in a studio or some other setup will most likely end up with the Tesla coil causing trouble with all other electronics on stage.

A simple solution to the noise problem from a fast rising edge of the discharge current, is to slow that discharge current from the topload down. ArcAttack utilized a breakout point inductor to do this, read further down for details.

### Issues with using a Tesla coil outside in free air

Operating a Tesla coil outside is not a problem in itself, there is usually lots of space and possibly no metallic constructions near by. There is however issues around sun set and as Tesla coils are mostly used in darkness there is a problem with dew. As the dew point changes at the end of the day, dew settles on ground, grass and plants and that creates a huge blanket of conductive moisture that can conduct high frequency noise.

The solution is to keep everything elevated from ground and use professional power connectors that are moisture and water proof.

If there is water or dew on the secondary coil itself, this can result in flash overs and racing sparks.

### Primary circuit protection against spark strikes

High voltage and high frequency sparks from the topload of a Tesla coil is not just a high voltage discharge, but also a high energy discharge where each spark contains from a few joules of energy to much more, several hundred times a second. This energy is enough to destroy the power electronics of the Tesla coil itself if the primary circuit or control circuit is hit.

One of the most important primary strike inhibitors is the electromagnetic field shaping done by the round and smooth surface of the topload. A even, smooth and round surface all around the toroid shaped topload generates a field that provokes the sparks to seek outwards from the secondary coil. The topload also has to follow the general design specifications, described in secondary coil design and topload design chapters, to bring the breakout point as far away from the coil as possible.

To control the direction of the sparks a breakout point is used. This is something as simple as a wire or rod with a smooth surface that is securely mounted to the topload with a good electrical connection and the sharpened end pointing away from the coil. The breakout point can be used to elevate the point at which sparks come from and also gain more distance to the primary coil. The longer the breakout point is, the more corona losses.

The most common safe guard against this is the strike rail, a piece of copper tubing all around the outer turn of the primary winding and risen somewhat above the primary coil. It is important that the strike rail is not! a closed loop, a closed loop will look like a 1 turn winding to the primary coil and excessive heating of the strike rail or failure of the inverter can be a result of this. The strike rail is grounded and thus it should provide a current path to ground that is preferred over going through the primary circuit. This method works 99% of the time.

Scroll further down and see a schematic of the recommended grounding scheme with decoupling capacitors to handle primary strikes and protects the IGBTs and control circuitry.

### Recommended grounding plan for Tesla coils

This ground scheme also implements decoupling capacitors to take care of sparks hitting the primary circuit, they will leave a path for accidental RF current going through the primary circuit and IGBTs to ground rather than destroying the IGBTs and control circuitry.

### Counterpoise ground and artificial ground planes [3]

Counterpoise grounding is known from old radio transmitters and it is a network of radial outreaching wires from the centre of the antenna. The length of these wires should at least be half the wavelength to be effective. This does however pose a significant problem with Tesla coils in the range of 30 to 300 kHz as this corresponds to a half wave length of 5000 to 500 meter.

We would have to use a rule of thumb in regard to capacitive voltage sharing between the topload and the grounding system. To avoid spark formation at the bottom of the secondary coil, we need to have 10 times the capacitance in our grounding system than the topload has.

Very low impedance grounding systems will also result in very high peak current strikes and the risk of whiplashes (described further down) becomes another issue. Combining practise and theory I think that the best system resembles those used for wind turbines, where a counterpoise ground is buried only 0.8 meters below ground and a ring formation is used as this has the best potential distribution as show in these simulations.

The result of a numerical method analytical formula comparing the different grounding system voltage distribution resulted in these non-unit ratio numbers where lowest is best.

The lower number, the less chance there is of flash-over from grounding system to other parts, before the energy is lead down to ground.

 Right-angle turn 8.41 Three-point star 6.45 Four-point star 5.5 Six-point star 4.61 Eight-point star 4.19 Ring of wire 3.49

A practically approach would be to use a regular ground rod but then add radial rods in a star formation from this center rod.

A artificial ground plane is also a possibility if the Tesla coil is being operated in a indoor area where it is not possible to establish a local grounding system.

First let us look at some estimated numbers on rods and plates capacitances to make a table of required grounding system sizes to obtain the needed 10 times higher than topload capacitance.

[4] For a thin rod: amateurs often use the rule of thumb “10 pF per meter of length”. That is only an approximation. The precise value also depends on the ratio between length and thickness of the rod, but 10 pF is around 1/100 in diameter/length ratio. For example, for a one meter long rod, with a diameter between 1.5 and 14 mm, the rule of thumb is accurate to within 20%.

For a plate: a square of 1 by 1 meter has a capacitance of 40.8 pF; if the square is bigger or smaller, this changes directly proportional to the length of the sides of the square (which is not directly proportional to its area). A square of 1 by 1 meter has, as noted above, a capacitance of 40.8 pF, and a circumference of 4 m, so that 40.8/4=10.2 pF/m. For other rectangles we see that the capacitance per meter of circumference is lower. As an example with say a 35 by 80 mm plate: its length/width ratio is 2.3, and that means 9.7 pF/m; the circumference is 0.23 m, so the capacitance is 2.2 pF. An easy rule of thumb is 10 pF per meter of circumference; in the above example, this gives an error of just 3%.

 Topload Topload capacitance Rods Plate size 50 x 200 mm 9 pF 9 x 1 m 2.25 x 2.25 m 100 x 300 mm 13 pF 13 x 1 m 3.25 x 3.25 m 150 x 600mm 26 pF 26 x 1 m 6.5 x 6.5 m 200 x 1000mm 42 pF 42 x 1 m 10 x 10 m 250 x 1200 mm 51 pF 51 x 1 m 12.5 x 12.5 m 300 x 1500 mm 63 pF 63 x 1 m 16 x 16 m

It quickly becomes clear that these solutions are far from practical possible, the required number of rods or size of a plate is simply too overwhelming and time consuming to set up.

Compromises have to be made and a possible solution could be a ring ground with radial ground rods connected to it.

A faraday cage can be used to effectively and relatively cheap, shield off any electro magnetic interference from both coming outside of the cage but also from outside source entering inside the cage. Here is a few examples of practical industrial uses of faraday cages, a old shielded radio transmitter, a shielded microscope in a laboratory and a complete room around a CT scanner in a hospital.

The following pictures shows that the larger holes a shielding has, the deeper the electromagnetic field can penetrate the shielding. It can however be countered, even with holes large enough for hands / arms to pass through, if a tubular opening is made, as illustrated here.

Table 5 shows the effectiveness of square masked wire mesh where the size in the left column is the grid square sides and the row is the frequency.

So regular honeycomb fence used for chickens is roughly around 25 mm in diameter, and would damp a 100 kHz signal around 90 db.

 100 kHz 1000 kHz 10000 kHz 1 mm 125 dB 105 dB 85 dB 10 mm 105 dB 85 dB 65 dB 100 mm 85 dB 65 dB 45 dB 1000 mm 65 dB 45 dB 25 dB 10000 mm 45 dB 25 dB 5 dB

It is not just a faraday cage around a Tesla coil that can used to prevent noise issues in electronics, you can instead also use local small faraday cages for the sensitive equipment. For better sound reproduction it is highly recommended to use a faraday cage around cameras and microphones.

### Breakout point inductor to limit EMI

A clever and simple construction used by ArcAttack to limit the EMI is to slow down the discharge current pulse. This method is also used in electric fences and defibrillators (also known as heart stoppers you can find in many public places), the trick is the same, to slow down the discharge current, but still deliver the same amount of energy.

A defibrillator does this to avoid damaging skin tissue from a rapidly pulse charge that would just be a electrical explosion. The slowed down pulse delivers that same high amount of energy, but over a longer period of time.

When using a breakout point inductor there will be a different kind of performance. There are some losses in the inductor, but nothing too serious and it is reported to never become too warm to worry about it, but most noticeably will be less bright arcs as the current discharge rate is slowed down.

The construction of the breakout point inductor is very demanding as its sitting where the potential is highest, so it is important to provide high insulation resistance and control the field to avoid corona. It is just a mini secondary coil with topload mounted on the large topload.

For a large DRSSTC there was used AWG32 / 0.2 mm copper wire wound around a 25 mm diameter acrylic tube, placed into a 40 mm diameter acrylic tube, filled up with epoxy for insulation. The coil is 300 mm long. The breakout point is mounted on a small toroid corona suppressor that will prevent breakout from the end windings of the inductor.

This series LC filter could be viewed as a low pass filter, but for this purpose it is only the inductance to slow down the discharge current pulse that is interesting, we ignore the effect of the capacitance added by the mini toroid as it is only used for field shaping.

Here is a illustration of the breakout point inductor, it is not drawn in right scale to the above given measures. For smaller Tesla coils the breakout point inductor should be down-sized accordingly.

### Secondary coil protection and the whiplash effect

The secondary coil has to be solidly built as described in the secondary coil design chapter of the guide, with all possible material choices made for the best performance and durability it would be a shame to see it burn up from a poor or too good grounding scheme.

A relatively unknown and yet not fully discovered problem is be called the “whiplash effect”.

When a large DRSSTC produces a heavy ground strike, those that are bright, loud and shows a clearly peak on the current meter feeding the power in, those strikes are so violent because the low impedance path makes it possible to discharge the topload potential in a very short time, much faster than the electrons can start moving in the secondary coil wire. The proposed failure mode, called the “whiplash effect”, is when the wave front of the electrical discharge is so fast that it backlashes a amount of energy from the topload, from the “vacuum” left behind from the fast discharge, and that happens to show as a extreme over voltage condition in the bottom 20% of the secondary coil and the results are arcing between turns, shorted turns and almost explosion like behaviour have been seen, where several turns have gone missing at the impacted area.

This description is somewhat hypothetical as it has not yet been proven by measurements, but the destructive forces have been witnessed many times with high power Tesla coils producing heavy ground sparks into a low impedance ground circuit.

The following picture is from Terry Blake where four frames from a video captures two heavy ground strikes and the subsequent flash-over at the secondary bottom.

The following picture is from Kizmo / Tuomas Koivurova where a frame from a video captures the event during a heavy ground strike.

Eric Goodchild posted the following story online:

Now this is even more interesting, this run was first with both counterpoise ground (1x2m metal mesh on ground) and ground rods. It may or may not have something to do with this..

To my point, ever sense we have started using a counterpoise ground I have noticed that the coil is more prone to flashing over and burning up secondaries. I thought this was just a coincidence but your guy’s comments have made me think otherwise.

The counterpoise ground helps to reduce radiated interference (lower impedance path to ground) however could it be a problem when dealing with ground strikes?

Maybe a poor, high impedance ground absorbs the “whiplash” instead of reflecting it.

Maybe it’s time for someone to measure ground impedance too! (at TC frequencies obviously). If it turns out to be anywhere near the secondary impedance then the increased-secondary-destruction-with-counterpoise phenomenon would make a lot of sense, as a terminated transmission line wouldn’t have a big reflected wave causing high voltage at the bottom of the secondary.

### Conclusion

There is no clear answer as to what is a perfect solution, as that is yet to be concluded and should be based on measurements that are hard to do and require expensive equipment. So educated guesses will have to be made on each location as what is possible.

• A low impedance ground will help prevent excessive EMI
• Counterpoise ground will help prevent excessive EMI
• A noise filter on the mains supply will suppress injected EMI
• A break out point inductor will help prevent excessive EMI
• Avoid humid and places where dew occur, lift all equipment from ground to avoid EMI
• Isolate your own RF ground from other metallic installations or mains ground to avoid EMI

on the other hand

• A piece of busbar with a large gauge cable to a single grounding rod have shown to be good and reliable in many cases, but excessive EMI could be a problem.
• A normal to high impedance ground will help protect secondary coil from flash-over and whiplash accidents.
• A break out point inductor will reduce spark output brightness and have some losses

The most important part of the line filter in regard to Tesla coils is the Y capacitors as they couple the line and neutral to the ground, around 10 nF is suitable if you are building the filter yourself.

Practical solutions to a mobile Tesla coil earthing system, where a reasonable impedance / capacitance to ground can be achieved is either as many rods as it feels practical to do, a ring ground or rolls of aluminium food grade foil or metal fence for animals.

The behaviour of a earthing system is different from 50/60 Hz fault currents to lightning impact, the low frequency response is dominated by the resistance, but the high frequency response is dominated by the impedance. R ≠ Z !

Microsecond rise time of lightning current pulses contains high frequency components which leads to over-voltage and can cause flash-over problems.

Earthing system resistance reduced by:

• Increasing length of electrodes can reduce resistance-to-earth

Earthing system impedance reduced by:

• Lowering resistance of electrodes and associated conductors (typically negligible)
• Lowering inductance of electrodes and associated conductors
• Lowering resistance-to-earth
• Increasing capacitance of earth-electrode interface
• Flat conductors and plates increase capacitance and reduce impedance
• Multiple paths better for high frequency response

### References

[1] A. Rousseau, Pierre Gruet. “Practical high frequency measurement of a lightning  earthing system”, HAL Id: ineris-00976157, https://hal-ineris.ccsd.cnrs.fr/ineris-00976157. Submitted on 9 Apr 2014.

[2] Sotirios A. SUFLIS, Ioannis F. GONOS, Frangiskos V. TOPALIS, Ioannis A. STATHOPULOS. “Transient behaviour of a horinzontal grounding rod under impulse current”. National Technical University of Athens, Department of Electrical and Computer Engineering, Electric Power Division.

[3] Rodolfo Araneo, Salvatore Celozzi. “Transient behavior of wind towers grounding systemsunder lightning strikes”. https://www.researchgate.net/publication/286543153_Transient_behavior_of_wind_towers_grounding_systems_under_lightning_strikes Accepted: 6 November 2015.

[4] Pieter-Tjerk de Boer, PA3FWM pa3fwm@amsat.org. “Capacitance of antenna elements”. http://www.pa3fwm.nl/technotes/tn08b.html