Played on my own DRSSTC2 Tesla Coil: http://kaizerpowerelectronics.dk/tesla-coils/kaizer-drsstc-ii/ Learn how to build your own DRSSTC to play music: http://kaizerpowerelectronics.dk/tesla-coils/drsstc-design-guide/ MIDI/Music interrupters you can build yourself: …
Played on my own DRSSTC2 Tesla Coil: http://kaizerpowerelectronics.dk/tesla-coils/kaizer-drsstc-ii/ Learn how to build your own DRSSTC to play music: http://kaizerpowerelectronics.dk/tesla-coils/drsstc-design-guide/ MIDI/Music interrupters you can build yourself: …
This content originally created by Steve Ward (stevehv.4hv.org) is re-posted with his permission.
Having built a few DRSSTC drivers using IGBT bricks, I realized what a pain it was to build the large gate driver circuit I had previously developed. In search of something simpler, I turned back to our old friend the Gate Drive Transformer (GDT). I used to believe that it was not possible to drive large CM IGBT modules with a GDT, but I proved myself wrong. There are a few important details that must be done properly to get good results from a GDT drive. They are:
- Low leakage inductance GDT. This requires a pretty large ferrite toroid.
- Low impedance gate drive circuit using high quality ceramic decoupling and DC blocking capacitors.
- Make all long wiring coaxial (or at least twisted pair), particularly on the primary side of the GDT where the impedance is 2 or 4 times more critical (depending on half-bridge or full-bridge).
This is the files for Universal Driver 1.1. Note, the original design (including PCB) have been modified. The files listed here reflect these changes. Please see further down this page for the newer design files.
- PDF schematic of driver/controller (error fixed 6/25/09)
- EAGLE board file (right click, “save as”)
- Top Component Placement (pdf)
- Bottom Component Placement (pdf)
This driver is very similar to my other ones, with a few important exceptions. The gate driver section is now very robust, using 16A P/N mosfet pairs. The input to the gate driver is set at 24VDC, so that a 1:1 GDT ratio can be used and still achieve 24V on the IGBT gate. I no longer believe its necessary to drive the gates to 30V unless you are absolutely pushing the IGBT to the extreme. Otherwise, the higher gate drive voltage just makes the possibility of gate oxide failure more likely. Even with 24V drive, TVS diodes should be placed right at the IGBT gate terminals to clamp the voltage to less than 30V.
In order to support the new gate drive setup, some additional logic was required, and was provided with a quad AND gate. I also switched over to the 74HC74 D-Flip Flop instead of the 74HC109 JK flip flop, because its 14 pins instead of 16. I also used some hacks to replace the 555 astable timer with just an RC on the input to an AND gate, in the overcurrent detection circuitry.
A picture of a completed driver and controller.
Another example of this driver in use can be seen in the DRSSTC-4. This coil uses a full-bridge of 40N60 mini-bricks from fairchild semi. The tank cap is a pair of special CDE caps, each rated 100nF at 8kVDC (estimated VAC rating of 2kV). The GDT was wound with cat-5e network wire, using the “white” conductors as the primaries (4 in parallel) and the other 4 wires as secondaries. A 5.1 ohm gate resistance is used, and is bypassed on the discharging edge with a 1N5819 diode. The primary is tuned low to 170kHz. This coil is a solid performer producing up to 38″ sparks with only an 11″ long secondary winding.
IMPORTANT: The over-current detection comparator has a limited operating voltage range for its inputs. When operating from 5V, as in this circuit, the trip level set by the potentiometer should NOT exceed 3.75V for reliable operation. Setting it above this voltage may completely disable the OCD functionality. Lower the burden resistance (on the ODC input) if this is a problem.
A note on using fiber optic receiver OPF2412:
This one seems to come back and haunt me from time to time. Im using the OPTEK OPF2412 fiber optic receiver. These are noise sensitive devices, and not surprisingly, problems show up when I use them around tesla coils. Firstly, they really should be in a metal enclosure. Secondly (and quite surprisingly), the metal sheath that is at the end of the ST fiber cable should be bonded to the metal box. It may seem absurd that a small piece of metal just a few millimeters from the lens of the Rx would be able to effect the thing, but surely enough it does. The issue is either that this metal ring picks up some RF and couples it into the Rx, or its simply that the metal ring, when grounded, extends the electrostatic shielding of the Rx. Im gonna go with number 2. Anyway, the fix for me was to just put a small steel spring that presses against the box and the ST end when its plugged in. It may be wise to stick all of the low voltage electronics into a metal box too. One more odd problem discovered and solved!
UPDATE 11/23/2008 (some of this may not make sense as i have removed the original schematics):
There were a few quirks with this design that i wanted to correct. The RC circuit for the current limiter was fussy and hard to get working just how i wanted, also it turns out the difference between HCT and HC logic made a big difference in the circuit performance. So i present an updated schematic that is a much more robust design. Terry Blake gave me the inspiration for using the extra D flip flop to set the “disabled” state of the controller. Operation is simple, when the comparator senses a trip condition, its output drops low, causing the D flip flop to clear its output, which disables the interrupter pulse via the AND gate. The controller stays in the disabled state until a rising edge from the next interrupter pulse puts the D-FF back high. This also has the added benefit of keeping the indicator LED ON for the maximum permissible amount of time (rather than just 1mS or something). Below is a updated schematic that documents the surgery necessary for my PCB design.
Also, the BOM is probably a tad outdated. Most of the important parts are there (all the ICs and caps) but it may be lacking a resistor or 2 or something like that. I suggest you check over the new schematic before trusting the BOM solely.
Id also like to report that this driver is now used on my revised edition of the DRSSTC-0.5. It works great even at 300kHz! Truly a universal driver.
I have re-spun the PCB for this driver. The main reason was that I wanted to put the fiber optic receiver on the PCB, and also because i modified the over-current detection inhibit circuitry. Below are some helpful files for this new board. Another afterthought modification to this design deals with the current sensing circuitry. Having the burden resistance (R5) before the bridge rectifier (D8-11) and having yet more burden resistance (R4) after the bridge, made it less than straight forward to pre-determine the volts-to-amps scaling of the circuit. So now the burden resistance is moved to be only after the bridge rectifier, and to handle the larger currents, I suggest using 1n5819 schottky diodes instead of the 1n4148 signal diodes. Furthermore, the somewhat large .1uF filter cap on the sensing input to the LM311 comparator was causing other scaling errors (its a significantly low impedance at 100khz) so I’ve changed it to 1nF, or I find it can be left off altogether.
- Schematic 1.3b (error fixed 6/25/09)
- Board file 1.3 (.brd)
- Top Component Placement (pdf)
- Bottom Component Placement (pdf)
- A mostly complete Parts List (.xls) (updated 7/6/09)
Pictures of the new board:
While analyzing something with this driver, I realized the schematics were drawn incorrectly, the inputs to the UCC27423 dual gate driver were swapped. Updated schematics have been posted. This is a minor error that shouldn’t impact any design significantly.
All MIDI files played can be found in this thread: https://highvoltageforum.net/index.php?topic=118.0 DRSSTC1 information: http://kaizerpowerelectronics.dk/tesla-coils/kaizer-drsstc-i/ which I will soon update with the rebuilded bridge Popcorn Star Wars – Imperial …
Can you guess the song that was played? Silent death during a MIDI playback, once power is turned back on, the bridge short circuits and …
It only took me a mere 4 years from I first started this article about the MMC until it is now done for public released 🙂 …
Published on: 07. February 2019
This is chapter 7 of the DRSSTC design guide: MMC / resonant tank capacitor design for Tesla coils and inverters.
MMC is short for multi mini capacitor and is used to describe a resonant tank capacitor made from many smaller capacitors to achieve the needed ratings.
As with all the other aspects of designing a Tesla coil, many of the choices on component and design selection are interrelated in a non-logical way and it often makes it difficult to split up the design as I try to in this guide. That means some data and input used in selecting a MMC is based on prior choices regarding IGBT, topology or secondary circuit. For most people a MMC will first and foremost be designed from a money perspective, high power pulse rated capacitors are not cheap.
I will discuss the following three roads to take in the design of a MMC:
- Design by the DC voltage rating of the capacitor and operate as close to that as possible
- Design by peak / RMS current and temperature rise and let the DC voltage rating be satisfied as a a secondary parameter, often with more head room
- Design by peak voltage rating of the capacitor at the resonant frequency and determining the maximum allowed on-time.
1. Designing by DC voltage rating and peak current rating is a quick, dirty and easy method. The result is a working and cheap MMC, but failure at long run-times and shortened life time should be expected.
2. Designing by peak / RMS current rating and temperature rise results in a set of data where it has to be chosen what is acceptable, DC voltage rating is also a part of it and it is necessary to always adjust the design to have around 10-20 % voltage rating overhead by this method. Results in a robust and medium cost MMC.
3. Designing by peak voltage rating and maximum on-time for the current to flow in the LC circuit before the voltage rating of the MMC is hit. A conservative approach, especially if the AC voltage rating is used. Results in a indestructible but also very expensive MMC.
I use and recommend the peak current, RMS current and temperature rise method, which is also the method used in my MMC calculator. It is a more thorough result set, but I will demonstrate all three methods here.
What is the expected life span of the Tesla coil?
The first important decision to make is what the expected life time of the Tesla coil is.
- Is it just a weekend experiment?
- Is it something you want to show to family and friends?
- Is it something you want to perform with in a show?
- Is it something that will be used on a daily basis in a museum?
The further down you get on this list, the more important it is that the Tesla coil is reliable and here the MMC is often a part that fails due to inadequate design and abuse of a underrated part that is working under great stress.
For 1 and 2 it will be okay to design simple and cheap as it will be shown in the budget example, for 3 and 4 it is highly recommended that you use the advanced and more expensive design criteria that will be shown in advanced examples.
How to choose the value of the MMC capacitance?
This choice is also revolving around the money issue, high impedance primary circuits have lower capacitance, operate at longer on-times, lower peak currents and is generally cheaper to build. Low impedance primary circuits have higher capacitance, operate at short on-times, have very high peak currents and is generally more expensive to build due to more capacitors needed to get the capacitance and appropriate voltage rating for the higher peak currents. More details on low and high impedance is also covered in Secondary coil part of this guide.
The larger a system is, the larger should the MMC also be, in order to match the energy needed to push out longer and longer sparks, more pulse energy storage is also needed.
A general guide, using the same Tesla coil sizes as in the secondary coil design part, can be seen in Table 1. I will look at five different sizes of coil systems with a rough power input estimate:
- Micro, less than 0.5 kW
- Mini, less than 2 kW
- Medium, less than 10 kW
- Large, less than 20 kW
- Very large, more than 20 kW
|Coil diameter||Coil length||Capacitance range|
|0.1 – 0.2 uF|
|Mini||75 mm||300-375 mm||0.15 – 0.45 uF|
|0.3 – 0.6 uF|
|0.45 – 1 uF|
|Very large||315 mm
|0.6 – 2 uF|
1. How to design a MMC based on DC voltage rating and primary peak current
I find that the easiest way to design a DRSSTC primary circuit is so choose a maximum primary peak current that the IGBTs can handle and then design the MMC from this. So with a known value in the following example, I will demonstrate how to design a 0.45 uF MMC for use in a 70 kHz coil with 800 Ampere peak primary current, a medium size system that can produce somewhere around 1.5 to 2 meter sparks.
First we need to calculate the reactance of the MMC, F is frequency in Hertz and C is capacitance in Farad.
Now we can calculate the impedance of the MMC, ESR is the combined ESR of the series and parallel connected capacitors in the MMC. For the 0.45 uF MMC I chose to use 6 parallel strings of 2 CDE 942C20P15K-F capacitors in series. Each capacitor has a DC voltage rating of 2000 V and a ESR rating of 5 mΩ, which results in 4000 V series rating and a 1.66 mΩ rating for the chosen MMC.
As it can be seen, with low ESR polypropylene pulse capacitors, the ESR is almost negligible when calculating the impedance.
Last we can calculate the peak voltage across the MMC and see if it is higher or lower than the combined series VDC rating of the capacitors. Zc is the MMC impedance from above and primary peak current in Ampere.
The multiplied DC rating of the capacitors in series is just on spot of what is needed to run the system at 800 Ampere peak. You can now just adjust the primary peak current in this last formula to find out when you will be below or above the voltage rating of your MMC.
2. Designing a MMC based on peak current, RMS current and temperature rise
This will be a fairly long part, as the calculations and explanations will go hand in hand with my MMC calculator, as that is the tool I made after this design method but also to give a more in-depth introduction to those that use the MMC calculator.
This method is based on designing a MMC from a certain maximum peak current, as the IGBTs often is a set-in-stone parameter and they are the limiting factor in the design.
Then there is seven important capacitor specifications in order to get the most precise results. It is Capacitance, Voltage rating, Peak current rating, RMS current rating, dV/dt rating, ESR rating and specific dissipation factor. These values also have to be calculated / extrapolated for the chosen resonant frequency. Help on getting these values can found bottom of the good MMC capacitors list.
Input parameters for the Tesla coils primary circuit is also important to be able to calculate the ratings of the MMC. When all these numbers have been plotted in, it is just as simple as using the +/- buttons to adjust number of capacitors, on-time, BPS or primary peak current to see that the results are equal to or better than the requirements.
To use the same example I will once again use the 0.45 uF MMC where I choose to use six parallel strings of two CDE 942C20P15K-F capacitors in series. Each capacitor has a DC voltage rating of 2000 V in a 4000 V series rating. A MMC to be used in a 70 kHz coil with 800 Ampere peak primary current.
We can reuse the calculations and results from the example above, so we can continue from where the calculated MMC impedance is 5.05 Ω and peak voltage across the MMC is 4040 V.
Steve McConner proposed the following equation to calculate the RMS current across the MMC based on a square waveform, BPS and on-time
The 6 parallel strings of CDE 942C20P15K-F capacitors, which has a 13.5 A RMS current rating each, gives us a 81 A rating, so the actual load is just shy of hitting the rating, so we should think seriously about limiting on-time, BPS, peak current or overall run times lengths. The peak current rating of these capacitors are 432 A each, so multiplied by 6 strings in parallel that gives us a total peak current rating of 2592 A which is with plenty of headroom in respect to the 800 A peak current we planned to run this coil at.
We also need to check that the rate of voltage change across the MMC does not exceed that rating of the MMC. First we calculate the actual dV/dt imposed on the MMC. V is peak DC voltage over MMC and F is frequency in Hertz. This will give a result in V/uS.
The actual dV/dt rating of the MMC is a simple equation and this number have to be higher than the above calculated imposed dV/dt. Primary peak current in A and MMC capacitance in F.
In this case there is plenty of headroom for the dV/dt.
The last step to ensure that we have a sturdy MMC that can be operated for extended periods of time is to calculate the temperature rise of the single capacitor according to its dissipated power.
First we need to calculate the dissipated energy in a single capacitor for a 1 second time period. So this means we divide the combined Irms result of 80A from earlier with the six strings in parallel and that gives us 13.33A.
Temperature rise for a single capacitor can now be calculated, this now the last simple task of multiplying the dissipation with the dissipation factor. For this example I have it given in the datasheet as 11ºC/W, which means that this capacitor will rise 11ºC for each 1 Watt of power dissipation. If you can only find a rating given in W/K, look at the bottom of this page on how to convert that value.
While almost 10ºC does not sound like much, we have to remember that this is for a single second of operation. It is important that we let the capacitor be able to cool down enough between pulses that the temperature does not just keep adding up until disaster happens.
To give a better idea of how much is tolerable, here is a rule of thumb list for temperature rise per second.
- 0 – 5 ºC = Very good
- 5 – 10 ºC = Good
- 10 – 15 ºC = Not good
- 15+ ºC = Bad
3. Designing a MMC based on peak voltage rating and maximum on-time
This path of design is from Matt “Sigurthr” Giordano and he starts his design by asking two questions, “how long a burst length can I use?” and “which voltage rating do I need on the tank capacitor?”.
This is not so much designing a MMC, but more a method to check how hard you can drive a existing MMC without damaging the capacitors.
Maximum on-time in uS and the voltage rating needed for the MMC are inter-related, but the link is not straight forward as it has to do with some inductive load inverter theory.
Each half cycle the inverter switches polarity it adds more voltage, and thus more current is flowing into the tank circuit. The longer your burst length, the more the voltage and current can ring up. So, how do we know when voltage or current is too high?
We would like to know the maximum primary peak current that we can adjust our OCD circuit to. This is dependent on the voltage we will allow according to the voltage de-rating that we choose for the MMC capacitors. Here we can either use the AC voltage rating or use the DC voltage rating with a head room between 20 to 50%.
So to avoid damage to the MMC, we can limit the voltage across it by calculating a OCD maximum peak current value and determine what the maximum on-time is before the voltage is so high that the interrelated current is too high aswell.
These calculations disregard the fact that primary current is, in normal operation, limited by the secondary arc load. A well tuned and built coil should never have its OCD trip as all the energy should be transferred into making sparks.
To use the same example I will once again use the 0.45 uF MMC where I choose to use six parallel strings of two CDE 942C20P15K-F capacitors in series. Each capacitor has a DC voltage rating of 2000 V in a 4000 V series rating, but for protection I will de-rate that 20% so the calculations are done with a maximum allowed 3200 V across the MMC.
Peak voltage V_peak is given in Volt, Primary inductance L_primary is given in Henry and frequency F_resonant is given in Hertz.
The result shows with good precision why I ran my DRSSTC1 at 500 Ampere OCD settings, as this corresponds to the low voltage rating of the MMC, but not lower than it was a good match with the IGBTs used.
The maximum on-time to stay below 3200 V across the MMC, and thus also stay below 472 A peak primary current can be calculated, but it is dependent of the inverter type.
The maximum on-time for a half-bridge
10 half-cycles at 70 kHz on a half-bridge, according to table 2 is around 72 uS before we have either 3200 V across the MMC or 472 A flowing in the primary circuit.
The maximum on-time for a full-bridge
5 half-cycles at 70 kHz on a full-bridge, according to table 2 is around 35 uS before we have either 3200 V across the MMC or 472 A flowing in the primary circuit.
The table below can be used as reference for these calculations, as a general lookup table instead of calculating the time half a period lasts at a given frequency or just for sanity check of your own calculations.
RMS current and MMC heating damage
RMS current rating is often overlooked as people focus on the voltage and peak current rating. Too high RMS current will slowly heat up the capacitors to a point where failure is imminent. Pay close attention to the achieved RMS current rating and be sure to honor this as well.
Capacitors with a larger physical size will often have a advantage over many smaller capacitors due to their large thermal mass, but they are also slower to cool down again.
Path resistance to each capacitor should be equal to assure equal current sharing, as it was described in Chapter 1: Rectifiers. The rectifier closest to the supply would conduct the most current, it is the capacitor closest to the load that will conduct the most current. The 40% current derating rule can also be used for capacitors in parallel to correct for uneven current sharing.
While ripple current divides among the capacitors in proportion to capacitance values for low-frequency ripple, high frequency ripple current divides in inverse proportion to ESR values and path resistance. 
This means that parallel capacitors in applications with low frequency load will share the current according to the capacitance of each capacitor in parallel. Whereas a load operating at a high frequency, like a DRSSTC does, the current sharing is up to ESR values and resistance of the busbar and wires in the circuit.
Here is a example from Amaury Poulain where the MMC failed from asymmetrical current sharing and the result is heating damage of the strings that carry the most current, those with the shortest current path between MMC conection terminals.
Another example of a unblanced MMC that failed due to uneven current sharing. A capacitor was melted completely apart from excessive heat dissipation.
Best practices for MMC construction
Even current sharing can easily be obtained from ensuring even length current paths between the strings in regard to the MMC connection terminals.
Amaury Poulain’s failed MMC from above was remade with better cooling and even current paths in mind.
Here is a another example of a PCB designed by Franzoli Electronics after the same principles.
Here Jeroen Van Dijk made a very compact MMC, could have better air cooling distance between the capacitors, but the even current sharing is ensured.
Here are some of my own MMC constructions and it is always important that terminals are connected in a way so that current paths are an even length.
Which capacitor types can be used in a MMC for a DRSSTC
Film and Mica capacitors are generally the best for Tesla coil tank circuit use, Mica capacitors can however be hard or expensive to find at the capacitance needed for a DRSSTC.
Lets first have a look at a comparison between some film capacitors that have ratings in the range of what we could use for a MMC.
|Dielectric str. (V/µm)||580||500||470||650|
|Max DC (V)||1000||250||100||2000|
|Max temp. °C||+125||+150||+150||+105|
|Dissipation factor (•10−4)|
If we solely look at the voltage rating and capacitance of a film capacitor when building a MMC, there could be problems with heat dissipation at DRSSTC frequencies. As it can be seen, polypropylene capacitors have a very low dissipation factor even at high frequencies, which makes them our preferred choice.
The FKP type of polypropylene capacitors are made from layers of film and foil, the FKP type does not have self-healing capabilities and will fail short circuit. The MKP type is made from metallized film that is self healing, if a local punch through of the film happens, the small internal explosion will burn away the metallized layer around the punch through hole and thus isolates it from the rest of the layer. This way a punch through in a MKP type will fail open circuit, which makes them our preferred choice.
Some more details on polypropylene film capacitors
The temperature and frequency dependencies of electrical parameters for polypropylene film capacitors are very low. Polypropylene film capacitors have a linear, negative temperature coefficient of capacitance of ±2,5 % within their temperature range.
The dissipation factor of polypropylene film capacitors is smaller than that of other film capacitors. Due to the low and very stable dissipation factor over a wide temperature and frequency range, even at very high frequencies, and their high dielectric strength of 650 V/µm, polypropylene film capacitors can be used in metallized and in film/foil versions as capacitors for pulse applications, such as CRT-scan deflection circuits, or as so-called “snubber” capacitors, or in IGBT applications. In addition, polypropylene film capacitors are used in AC power applications, such as motor run capacitors or PFC capacitors.
Most power capacitors, the largest capacitors made, generally use polypropylene film as the dielectric. Polypropylene film capacitors are used for high-frequency high-power applications such as induction heating, for pulsed power energy discharge applications, and as AC capacitors for electrical distribution. 
A word on physical dimensions of capacitors for either DC link or MMC
As demonstrated by El-Husseini, Venet, Rojat and Joubert in their article “Thermal Simulation for Geometric Optimization of Metallized Polypropylene Film Capacitors”, the physical geometry of a capacitor can have an impact on capacitor temperature, power loss and life. They demonstrated that for the same electrical stress, taller capacitors experienced higher temperature and losses than shorter capacitors.
As stated in their article, in taller capacitors, the current must travel a longer distance through the very thin metal films, thus the total I²R is higher compared to a short capacitor. The authors demonstrated that the total power loss in the capacitor is
proportional to Equivalent Series Resistance (ESR) and to the square of the true RMS current. ESR represents the eddy current and dielectric losses, which are affected by both frequency and current. If capacitor current is elevated, power loss increases. Likewise, power loss in a metallized film capacitor increases if the frequency of the current increases. Thus, harmonic current flowing in a metallized film capacitor, the power loss will be higher than if pure sinusoidal current were to flow. 
Cooling of capacitors by forced air can be a solution to get a longer life time.
Approximately 2/3 generated heat rise moves out axial and 1/3 radial.
So it is most important to cool a capacitor at its terminals as it does not radiate the heat evenly from all over its surface.
The thermal resistance (Rth) from case to ambient is given for still air in most datasheets, so if forced air cooling is used the thermal resistance can be de-rated. Some manufacturers supply equations to calculate a exact thermal resistance in regard to capacitor surface and forced air speed velocity.
How to read capacitor datasheets and calculate missing values
Capacitive reactance Xc, where f is frequency given in Hertz and C is capacitance given in Farad
ESR can be calculated from the tangent of loss angle given as TANδ in the data sheets. ESR is frequency dependent. C is capacitance given in Farad, f is frequency given in Hertz.
Thermal resistance (Rth) when given in data sheets are either Watt needed to raise the temperature by one Kelvin or degree Celsius the temperature raises by one Watt dissipation. Conversion from W/K to °C/W is to divide one by W/K dissipation factor.
Ipeak or Ipulse is calculated from the dV/dt rating times the capacitance of the capacitor. Capacitance given in micro Farad times pulse rise time given in micro seconds will give a result in Ampere.
As a rule of thumb ESL is about 1.6 nH per millimeter of lead distance between the capacitor itself and the rest of the circuit. This also includes the leads of the capacitor itself. This only applies to well designed capacitors.
 M.H. El-Husseini, Pacal Venet, Gerard Rojat and Charles Joubert, “Thermal Simulation for Geometric Optimization of Metallized Polypropylene Film Capacitors”, IEEE Trans. Industry Appl, vol. 38, pp713-718, May/June 2002.
 CDM Cornell Dubilier, “Aluminum Electrolytic Capacitor Application Guide”, http://www.cde.com/resources/catalogs/AEappGUIDE.pdf
A live broadcast that I did on Sunday, February 4, 2018 with focus on designing Tesla coils with special focus on the DRSSTC topology. Questions …
Here is the recording of the live stream I did on 2018 January 31, Wednesday at 2000 CET, I performed a live stream on youtube …
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.
|Frequency range||House hold item||Tesla coil size|
|15 – 50 kHz||TV sweep scanning (CRT)||Large DRSSTC|
|20 – 190 kHz||Maritime mobile||Large DRSSTC
|25.875 – 138 kHz||ADSL upload range||Large DRSSTC
|50 – 1000 kHz||Switch mode power supplies||Medium DRSSTC
|59 – 61 kHz||Stanford Time Signal||Large DRSSTC|
|70 – 130 kHz||Radio location||Large DRSSTC
|138 – 1104 kHz||ADSL download range||Medium DRSSTC
|190 – 535 kHz||Aeronautical mobile||Small DRSSTC
|535 – 1605 kHz||AM radio||Tiny DRSSTC
|1.800 – 1.900 MHz||Amateur radio||Class E SSTC|
|1.900 – 2.000 MHz||Radiolocation||Class E SSTC|
|2.000 – 2.194 MHz||Maritime mobile||Class E SSTC|
|2.194 – 2.495 MHz||Mobile||Class E SSTC|
|2.495 – 2.505 MHz||Stanford Time Signal||Class E SSTC|
|2.505 – 2.805 MHz||Mobile||Class E SSTC|
|2.805 – 3.500 MHz||Aeronautical mobile||Class E SSTC|
|3.500 – 4.000 MHz||Amateur radio||Class E SSTC|
|4.995 – 5.005 MHz||Stanford Time Signal||Class E SSTC|
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.
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.
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 
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.
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 
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 
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.
- 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|
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.
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 
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.
|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.
 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.
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
 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.
 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.
 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.
 Pieter-Tjerk de Boer, PA3FWM email@example.com. “Capacitance of antenna elements”. http://www.pa3fwm.nl/technotes/tn08b.html