design a tesla coil




As these devices first appeared around 1891 there is no rocket science involved. I knew very little of them a while back and I only have both a basic electronics knowledge and academic background. If I can build one anyone can. So this page is just a collection of tips about designing coils that I have picked up from the web or other coilers, and I have found useful.
Also this information is for the 'old-fashioned' type of coil using conventional spark gaps, as I will leave the latest trend to solid state coils to others.


The basic points to consider:

Balance: Everything centres around getting a balance. Any one particular aspect of the design is either affected by something else, or it in turn will affect something else itself. So before you change anything, think of the consequences.

Software: Programs like JavaTC help enormously.

Research: Remember these things are dangerous, so never take one single website as your guide. Viewing various sources lets you see what advice is correct, what is wrong, and what is just plain dangerous. Hopefully the latter does not apply here.

Location: Consider where you're going to run the coil before you build it, so you can size it accordingly. Have I followed my own advice - No!
My 8 inch diameter coil is too big to run indoors, but running it in the garden is not the safest of places as you can see.

Transportation: It is a good idea to design it to breakdown and re-assemble easily.

Cost: The cost for virtually every component goes up significantly with the size of the coil that you are building. You can easily spend £500 just on capacitors alone on medium to big coils, so fully plan it out with software and then price everything up.

Components: The HV power source, NSTOBITMOTPIG etc, and the secondary coil diameter size are totally inter-dependant to one another. If you wind a big secondary you need 'big' everything else!

Capacitor: The capacitor size chosen needs to be capable of being recharged within milli-seconds, so bigger capacitance values demand higher wattage power supplies.
If your using an NST avoid having a capacitance value that is in resonance with the transformer's inductance. NST's, unlike other power sources, can be rather fragile and will not handle a high resonant rise in voltage. (Don't confuse resonance here with the resonance between the primary and secondary coils.) If though you are using a 'PIG' , resonance can be used to your advantage however.

Resonance:The AC equivalent of 'resistance' is reactance. With AC if the reactance of the inductor matches the reactance of the capacitor, the two cancel one another out, this is resonance. Then with little resistance left in the circuit, apart from the wires themselves and the internal resistance of the power supply, the voltage across the capacitor can soar.

NST: NST's in the UK and Europe have a maximum voltage of 10Kv, or 15Kv in the USA.

Power: NST's and OBIT's etc can be run in parallel to double the power. Multiple NST's however cannot be run in series to double the voltage though. Just isolating the cases is not enough, it is more complex than that.

Secondary Diameter: A good guide for low power coils below 500 Watts would be a 2 inch to 3 inch diameter. While 500 to 1000 Watts would be 3 to 4 inches, 1000 to 3000 Watts is 5 or maybe 6 inches, over 3000 Watts and your looking at 8, 10, 12 inches or more!

Aspect ratio: The secondary diameter versus the actual height of the winding itself. The aspect ratio for low to medium power is around 5:1, for other sizes 4 to 4.5:1 seems to be popular. The actual former on which the coil is wound needs around 2 inches unused at each end, so add that measurment on afterwards.

Secondary Turns: Nowadays people aim for around 1200 / 1400 turns or even up to 1600 turns for smaller power coils. The 'golden' figure used to be 900 to 1000 turns, and even today there is debate over this matter.
It's important to remember that these are not like conventional transformers where the number of turns affects the output voltage.

Coupling Coefficient: The physical proximity or coupling coefficient (k) between the two windings affects the number of cycles needed to exchange all the energy between the primary and secondary. A too high a coupling will give the problem of racing sparks, while too low a coupling means more cycles, and may result in more losses in the spark gap.
I used to over-couple my coils but after advice from more experienced coilers I found that sometimes under-coupling can actually produce bigger sparks. Under-coupling can't damage the coil, but over-coupling certainly can!

Normally the bottom of the ACTUAL secondary winding (not the coil former) would be within an inch or so higher of the horizontal plane of the primary.



design method


The best component to get first is probably the HV power source (NSTOBITMOTPIG) so you will then know the power that you have available. The HV power figure is very important because it not only dictates the diameter of the coil that you can build, but also affects the amount of capacitance.

Once you know the power you decide on the secondary diameter and aspect ratio. Next having decided on the number of turns needed you reach for your trusty calculator.
By trying different gauges of wire, try to find a combination that gives you all the requirements your looking for (number of turns, within the height and diameter constraints that the aspect ratio allows).
You will normally find that the inductance value of your secondary design will work out satisfactory and you need not concern yourself with it at this stage.

Once you know your secondary specifications you decide on the 'top load' or Toroid size. Its minor diameter will normally be similar to the secondary diameter, while the toroid's major diameter will be similar to the height of the secondary winding.
A very good guide can be found at the Deep Fried Neon website. Also using free software like JAVATC is undoubtedly the best way of seeing how one component affects another.

As already mentioned, knowing the HV power source specifications (voltages and current) allows you to choose a suitable primary capacitance value. Small coils will use 10 to 20 nano farad (nF) up to very large 10-15KW coils needing up to 150nF. A bigger cap means more energy discharged into the secondary, but you MUST have sufficient power from your transformer source to fully recharge the cap in the short (milli secs) time period available.

The next stage is to work out the number of primary turns you require. It is best to try to aim for around 12 to 14 turns to be available (allows for adjustment) on the primary and aim to have your tap at around 10 turns if your using a static gap.
With a rotary you can use less primary turns if you wish. The reason is that lower turns will mean more current flowing and a static gap with several spark interfaces would loose more power. A rotary uses a much smaller gap and also has less interfaces so it's not so much of a problem.

An 'interface' occurs where the spark leaves a solid and enters air and vice versa. So a single air gap will have two interfaces and two places for losses to occur.

Getting the primary coil's geometry correct so you will tap it in the correct place is best done using the JavaTC program. The inner diameter coil of the primary wants at least an inch clearance around the secondary coil's diameter for small secondaries. While a 6 inch secondary coil may have 1.5 inches or so. My 8 inch has a 2 inch gap. This spacing also affects the 'k' coupling value.
Most people use small diameter copper tubing for the coil. The spacing between each turn being at least 1.25 times the diameter of the tube you're using to avoid 'flashover' between turns and leave room for a clamp onto the tube.
Fortunately if you follow those guidelines you should find the primary ends up with a reasonable inductance value all of its own accord.

If you don't balance things correctly the coil will still run, but the performance will be below that possible from a well designed coil, and it may damage some of your components.

The Very Basic Tesla Circuit Diagram

Circuit diagram of a normal Tesla Coil

Tesla coils nowadays have very little real use in main stream science so any building and research is nearly all done by amateurs. The result is that some issues are ongoing and yet to be resolved. A good example was the size of the capacitor needed. At one time it was always considered desirable to use a value that was resonant with the HV supply. This is now recognised to be bad practice with NST's for the reason mentioned above.



choosing the capacitor value


mmc graph


Static Gap Capacitor

This is a simulation (PSpice) of my pig and the 61.3mH primary ballast it is using in conjunction with my 64.1nF capacitor on a static blown gap. The 61.3mH value on the primary multiplied by the turns ratio squared = 130.8H which is the inductance value on the secondary side that the capacitor 'sees', and resonates with.

This value of ballast and capacitance gave me a resonant frequency of 55Hz, which is uncomfortably close to the UK mains frequency of 50Hz. If the two resonant values had not been so close, the capacitor might expect to reach 36Kv approx'. However now my capacitor will see a possible voltage (this is a simulation - not the real world!) of 94Kv.

Static gaps are not too fussy about capacitance size (provided there is enough charging power available), but SRSg's require specific values of capacitance and ballast to complement one another if you wish to get the max amount of power throughput.
This was all new to me until visiting Richie Burnett's site, so his page here is well worth a visit.
In fact if you wish to fully optimise your system, his is the website to visit.


200 bps SRSG Capacitor

With my 200bps SRSG the original capacitance value I was using was 72nF, so I carried out some Spice simulations to find the best ballast value with that capacitor value and a 200bps SRSG.
A smaller value ballast will cause more current to flow, but when used with a SRSG that does not necessarily mean more power will flow, because of a thing called the Power factor (External Link Wikipedia), and it is this issue which Richie's page on Resonant Charging deals with.

Below are the results using a range of differing ballast values.


tesla ballast graph



You can clearly see that with a 200bps SRSG, 60H to 62H of ballast gives the best power throughput when used with a 72nF capacitor. This ballast figure would change if either the bps rate or the capacitance value change.

The reason is that the charging circuit (ballast and primary capacitor), is at resonance and the Power Factor (PF) is therefore at its highest. A 200bps charging circuit will resonate at around 75Hz and my 72nF & 62H ballast resonate together at 76Hz. The charging circuit will resonate at differing frequencies dependant on the rotary BPS rate that is used. So for resonant-charging to occur you need to match your charging components (ballast and the capacitor) to this desired frequency.
This is discussed in depth by Richie Burnett on his webpage here, which also gives you the different resonant frequencies that differing BPS rates demand.
Richie bases his method on using a PF of 0.85 rather than the optimum value of 0.9+ which my graph above shows. He explains the reasoning behind this on his site.

The first graph on his webpage shows that his chosen 0.85 PF can be achieved by either a resonant frequency of 60Hz or 85Hz. Richie uses the lower 60Hz figure as this will need a larger capacitor size than 85Hz. As I wanted 6.5Kw of true power I was using a 40H ballast and chose the higher of the two resonant frequencies of Richie's range. This meant I could use a slightly smaller and more attainable value for my MMC.
I consider it better to have the advantage of resonant charging, albeit with a slightly smaller MMC and a lower PF in my case, than to be without it entirely and have a poor PF.
Richie's graph shows that a resonant charging frequency of between 55Hz to 95Hz should give a PF of 0.8+ For that reason I aimed for a frequency in the 90Hz range that should give a PF of 0.83+.

Once you know the resonant frequency required you then decide on a value for Cp that combined with the ballast value needed for your respective power level, will give the required resonant-charging frequency.
Richie's webpage is unfortunately incomplete and awaiting completion after this stage but he does give the full procedure in an earlier TCML posting of 16 Jun 2001 entitled "Resonant Charging Design" This posting can be found here.
In it he refers to two diagrams but both the links he gives have been moved to the following locations.
The first diagram is here. While the second can be found here.

This second diagram deals with his 'adjustment factor' that is needed for the ballast and is for 50 Hz (UK) systems only by the way!
Once you have adjusted the ballast value it is then a simple matter to find the relevant value for Cp using standard formula.

To increase the power of the coil in the future by reducing its ballast value you would then only need to adjust the MMC to maintain the same charging frequency.
Using the circuit below, I got 95Hz instead of the expected 92Hz, but the frequency generator / meter and scope are not calibrated to any reliable degree however (bad workman blames his tools etc). But it is a figure I can use for comparison later on if I wish to alter the existing ballast value.

mmc graph


The circuit I used to measure the frequency of my own charge system

Designing my 8 inch coil

Secondary Voltage equals (Pri Volts * sqrt(L sec/L pri)) or Sec Voltage= Pri Volts * sqrt ( C pri/C sec)

I therefore decided that with my latest coil I wanted a high secondary inductance (but the secondary capacitance shouldn't be too high) and a low primary inductance combined with a large primary capacitance. Unfortunately the low primary inductance causes more current in the primary circuit and more spark gap losses, and a lot of coils are designed to avoid this.  Taking some advice though I decided to take a chance and because I was using a SRSG with less losses than a static, it seems to have paid off.

The JavaTC output file of my 8 inch:

J A V A T C version 12.2 - CONSOLIDATED OUTPUT
01 June 2010 11:10:13

Units = Inches
Ambient Temp = 68F

----------------------------------------------------
Surrounding Inputs:
----------------------------------------------------
50 = Ground Plane Radius
50 = Wall Radius
110 = Ceiling Height

----------------------------------------------------
Secondary Coil Inputs:
----------------------------------------------------
Current Profile = G.PROFILE_LOADED
3.9365 = Radius 1
3.9365 = Radius 2
30.258 = Height 1
64.588 = Height 2
1395 = Turns
0.0220471 = Wire Diameter

----------------------------------------------------
Primary Coil Inputs:
----------------------------------------------------
5.2165 = Radius 1
10.468 = Radius 2
29.133 = Height 1
29.133 = Height 2
8.7613 = Turns
0.32 = Wire Diameter
0.1 = Primary Cap (uF)
24 = Total Lead Length
0.2 = Lead Diameter

----------------------------------------------------
Top Load Inputs:
----------------------------------------------------
Toroid #1: minor=8.25, major=32, height=71, topload

----------------------------------------------------
Secondary Outputs:
----------------------------------------------------
80.74 kHz = Secondary Resonant Frequency
90 deg = Angle of Secondary
34.33 inch = Length of Winding
40.6 inch = Turns Per Unit
0.00256 inch = Space Between Turns (edge to edge)
2875.3 ft = Length of Wire
4.36:1 = H/D Aspect Ratio
60.8463 Ohms = DC Resistance
40275 Ohms = Reactance at Resonance
4.23 lbs = Weight of Wire
79.39 mH = Les-Effective Series Inductance
82.457 mH = Lee-Equivalent Energy Inductance
80.687 mH = Ldc-Low Frequency Inductance
48.944 pF = Ces-Effective Shunt Capacitance
47.123 pF = Cee-Equivalent Energy Capacitance
68.851 pF = Cdc-Low Frequency Capacitance
10.28 mils = Skin Depth
40.464 pF = Topload Effective Capacitance
130.8943 Ohms = Effective AC Resistance
308 = Q

----------------------------------------------------
Primary Outputs:
----------------------------------------------------
80.74 kHz = Primary Resonant Frequency
0 % = Percent Detuned
0 deg = Angle of Primary
35.98 ft = Length of Wire
3.64 mOhms = DC Resistance
0.279 inch = Average spacing between turns (edge to edge)
1.533 inch = Proximity between coils
1.22 inch = Recommended minimum proximity between coils
38.351 uH = Ldc-Low Frequency Inductance
0.09906 uF = Cap size needed with Primary L (reference)
0.662 uH = Lead Length Inductance
221.261 uH = Lm-Mutual Inductance
0.126 k = Coupling Coefficient
0.141 k = Recommended Coupling Coefficient
7.94 = Number of half cycles for energy transfer at K
48.66 us = Time for total energy transfer (ideal quench time)

----------------------------------------------------
Transformer Inputs:
----------------------------------------------------
250 [volts] = Transformer Rated Input Voltage
11550 [volts] = Transformer Rated Output Voltage
525 [mA] = Transformer Rated Output Current
50 [Hz] = Mains Frequency
260 [volts] = Transformer Applied Voltage
30 [amps] = Transformer Ballast Current
0 [ohms] = Measured Primary Resistance
403 [ohms] = Measured Secondary Resistance

----------------------------------------------------
Transformer Outputs:
----------------------------------------------------
6064 [volt*amps] = Rated Transformer VA
22000 [ohms] = Transformer Impedence
12012 [rms volts] = Effective Output Voltage
30 [rms amps] = Effective Transformer Primary Current
0.6494 [rms amps] = Effective Transformer Secondary Current
7800 [volt*amps] = Effective Input VA
0.1447 [uF] = Resonant Cap Size
0.217 [uF] = Static gap LTR Cap Size
0.3773 [uF] = SRSG LTR Cap Size
309 [uF] = Power Factor Cap Size
16988 [peak volts] = Voltage Across Cap
42469 [peak volts] = Recommended Cap Voltage Rating
14.43 [joules] = Primary Cap Energy
865 [peak amps] = Primary Instantaneous Current
127.6 [inch] = Spark Length (JF equation using Resonance Research Corp. factors)
146.1 [peak amps] = Sec Base Current

----------------------------------------------------
Rotary Spark Gap Inputs:
----------------------------------------------------
1 = Number of Stationary Gaps
4 = Number of Rotating Electrodes
3000 [rpm] = Disc RPM
0.25 = Rotating Electrode Diameter
0.25 = Stationary Electrode Diameter
9 = Rotating Path Diameter

----------------------------------------------------
Rotary Spark Gap Outputs:
----------------------------------------------------
4 = Presentations Per Revolution
200 [BPS] = Breaks Per Second
80.3 [mph] = Rotational Speed
5 [ms] = RSG Firing Rate
9.249 [ms] = Time for Capacitor to Fully Charge
2.7 = Time Constant at Gap Conduction
353.68 [us] = Electrode Mechanical Dwell Time
93.3 [%] = Percent Cp Charged When Gap Fires
15850 [peak volts] = Effective Cap Voltage
12.56 [joules] = Effective Cap Energy
730135 [peak volts] = Terminal Voltage
2512 [power] = Energy Across Gap
130.6 [inch] = RSG Spark Length (using energy equation)







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