design a tesla coil

As tesla coils first appeared around 1891 there is no so-called "rocket science"
involved with them. All the information presented here is for conventional
spark gap tesla coils, and not the solid state types,
and is based on Richie Burnett's Excellant SITE.

Firstly Some Basic Points to Consider:

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 knock-on effect.

Bart Anderson's JavaTC really does help A GREAT DEAL.
(It also includes an example you can load in to see how the program works ["Load Sample Coil" top right])

Remember these things are dangerous, and virtually all websites are by amateur enthusiasts like myself, so never take one single source of information 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: (concerns mainly bigger coils)
Consider where you're going to run the tesla coil before you build it, so you can then size it accordingly. My 8 inch coil is too big to run indoors, but running it in the garden is not the safest of places either, as you may have neighbours who might over-react to the noise they make.
As happened to one of my coils!

Transportation: (concerns mainly bigger coils)
It is a good idea to design it to breakdown and re-assemble fairly easily. Transportation and erecting it are the two main obstacles of any coil that is eight inches or larger.

The cost for virtually every component goes up significantly with the size of the coil. You can easily spend £700+ / $1000 (2013) just on capacitors on medium to big coils, so fully plan it out with software and then price everything up.
Lastly, things like variacs that are capable of handling big-coil power, can cost large amounts of money as well.

The HV power source, NSTOBITMOTPDT etc, and the secondary coil diameter size are totally inter-dependant on one another. If you wind a big secondary you will need 'big' everything else!
(Some HV components are hard to obtain in some countries, especially things like a PDT / Pig)

The AC equivalent of DC resistance is reactance. In an AC circuit, if the reactance of an inductor matches the reactance of a capacitor, the two cancel one another out, this state is called resonance.
With little resistance left in the circuit, it's possible for the voltage across the capacitor to get quite high.

The capacitor size chosen needs to be capable of being recharged within milli-seconds, so bigger capacitance values demand, higher wattage power supplies.
If you're using an NST some people say to avoid having a capacitance value that is in resonance [Note: 1] with the transformer's inductance or the mains frequency. This is because NSTs, unlike other power sources, can be rather fragile and may not handle a high resonant rise in voltage.
This is certainly true, but I feel that as long as you have a safety gap you should not have a problem, unless the transformer is exceptionally weak. The chance lays with you though.
Another point to consider is the peak current the caps will handle. The popular Cornell Dubilier 942C20P15K-F caps can handle a momentary peak current of 432 amps, so if you have two strings then the total safe momentary peak current is 864 amps.
Bigger MMC arrays can be kinder on their caps, as they tend to use more strings, and share the current out better. The peak current pulse on my 8 inch coil, although only lasting micro-seconds, (millionths) is 800+ amps in theory (source: JAVATC) so with 12 strings in the MMC each string is handling just 70 amps out of a possible 432 amps.

** [Note: 1]
Don't confuse resonance in this part of the circuit, with the resonance between the primary and secondary coils.

NSTs in the UK and Europe have a maximum output voltage of 10Kv, or a more useful 15Kv in the USA.

NSTs and OBITs etc, can be run in parallel to double the power, provided they are phased correctly. Multiple NSTs however cannot be run in series to simply double the voltage though. Just physically isolating them is not enough, as there are internal insulation issues with NSTs as well.

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 6 inches, over 3000 Watts and your looking at 8, 10, 12 inches or more! The largest I know of in the UK is 16 inches, and is currently under construction.

Aspect ratio:
This ratio is the actual height of the winding itself, divided by the secondary diameter. The aspect ratio for low power coils is best at a maximum of 5:1, for other sizes 4 to 4.5:1 seems to be popular. The actual former on which the coil is wound, needs at least 2 to 3 inches minimum left unused at each end, so allow for that amount to be added on afterwards before cutting the tube.
The aspect ratio is quite important, because tall skinny coils will lack sufficient inductance. This is because the secondary, unlike the primary, needs sufficient inductance to work efficiently, in fact veteran builder Richard Hull recommends in excess of 30mH for systems over 5kW, in his book, while short fat secondaries will suffer from continual primary strikes. (Proximity of toroid to primary)

Static Gaps:
With an NST, these are best set by connecting the gap straight across the bare transformer, as you would a Jacob's Ladder. Then in stages, with the power OFF, gradually open the gap up, before switching on again. Continue with this procedure until it won't fire with the NST on.
For any other power source, do the same procedure, but with a suitable ballast in place.
* (Newbie Note: A Ballast is something that restricts the current flow, usually in the form of an inductor)

Secondary Turns:
Nowadays people aim for around 1200 / 1400 turns or even up to 1500 turns for low power table-top coils. The golden figure often quoted used to be 900 to 1000 turns, and even today there is still some debate over this matter, so 1200 should prove a safe average.
It's important to remember that these are not like conventional transformers where the number of turns affects the output voltage.

Coupling Coefficient (k):
This is a result of the physical proximity between the primary & secondary windings, and will affect the number of cycles needed to exchange all the energy between the primary and secondary. Too high a coupling, will cause the problem of racing sparks, [Note: 2] while too low a coupling could mean too many cycles are needed for the energy exchange, and may result in excessive losses in the spark gap.

** [Note: 2]
Normally a secondary will have a rising voltage gradient from bottom (ground) up to the top (HV), but if the coupling becomes too much the normal single secondary resonant frequency can become two separate frequencies quite close together. This results in an uneven voltage gradient from bottom to top. The effect of this is racing-sparks where sparking appears to jump up and down the secondary form.
This in some instances can ruin the secondary winding.

I used to couple my coils to the point that is called 'critical coupling', which is just short of the onset of racing sparks. But after advice I found that sometimes under-coupling can produce better streamers.
Experimenting is the only way here, as can be seen in this test video I did of my 8 inch coil.
Remember: under-coupling can't damage the coil, but over-coupling certainly can!
Both the actual and suggested values of 'k' for any coil, are given with other useful parameters, in the JavaTC program, and usually lay in the range of 0.1 to 0.2
Normally, provided the primary and secondary are spaced suitably, the bottom of the ACTUAL secondary winding (not the coil former) would be within ½ inch of the horizontal plane of the primary, to achieve the right amount of coupling.

design method

The best component to get first of all has to be the HV power source (NSTOBITMOTPDT), so you will know from the outset the power that you have available. The HV power figure is very important because it not only determines the overall physical size, and therefore the diameter of the tesla coil, but also the amount of capacitance the coil can efficiently charge.

Once you know the power level, you can decide on the secondary diameter and aspect ratio. Next, having decided on the approximate number of turns you will be using, you reach for your trusty calculator.
By trying different gauges of wire, you will need to find a combination that gives you all the requirements you're looking for. That is the number of turns, within the height and diameter constraints that the chosen aspect ratio of the secondary allows.

AWG 24 wire is 20.1 thou diameter, with the varnish insulation this may amount to 23 thou, and you will probably end up with a 5 thou gap between adjacent turns, no matter how close you try and wind it, so say 28 thou overall.
Therefore a 1200 turn coil will need 1200 x 0.028 inches height. This equals 33.6 inches, and allowing 3 bare inches of pipe each end, you would need a tube that is 39.6 inches long minimum. The 33.6 inch winding would probably be happy using a 6 inch diameter tube, giving an aspect ratio of 5.51, or a 7 inch tube giving an aspect ratio of 4.8

American Wire Gauge
Cross Sectional
0000 0.46 11.68 107.16
000 0.4096 10.40 84.97
00 0.3648 9.27 67.40
0 0.3249 8.25 53.46
1 0.2893 7.35 42.39
2 0.2576 6.54 33.61
3 0.2294 5.83 26.65
4 0.2043 5.19 21.14
5 0.1819 4.62 16.76
6 0.162 4.11 13.29
7 0.1443 3.67 10.55
8 0.1285 3.26 8.36
9 0.1144 2.91 6.63
10 0.1019 2.59 5.26
11 0.0907 2.30 4.17
12 0.0808 2.05 3.31
13 0.072 1.83 2.63
14 0.0641 1.63 2.08
15 0.0571 1.45 1.65
16 0.0508 1.29 1.31
17 0.0453 1.15 1.04
18 0.0403 1.02 0.82
19 0.0359 0.91 0.65
20 0.032 0.81 0.52
21 0.0285 0.72 0.41
22 0.0254 0.65 0.33
23 0.0226 0.57 0.26
24 0.0201 0.51 0.20
25 0.0179 0.45 0.16
26 0.0159 0.40 0.13

You will normally find that provided you stick to the guidelines above, regarding number of turns and aspect ratio, then the inductance value of your secondary will work out satisfactory of its own accord.

Toroid Size:

Once you know your secondary specifications you decide on the top-load or toroid size. For a safe starting option, make the minor diameter similar to the secondary coil's diameter, while the toroid's major diameter will be similar, or a bit larger, than the height of the secondary winding.
(Minor diameter determines how high the voltage will need to be before breakout occurs - make it too big, and no breakout will occur, and a small breakout point will be needed. While the major diameter, apart from determining the amount of capacitance, also provides shielding to the secondary.) Some powerful, experimental coils in America, have been built with toroids as large as three times the secondary winding length apparently.
A measure of voltage gain is given by: gain = sqrt (Cp / Cs ), so the smaller the total secondary capacitance, the more the voltage gain - in theroy. A smaller minor diameter toroid, although keeping the overall capacitance value down, will not allow a high charge to build up though, so in practice a bigger toroid is more favourable.

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 that size of capacitor in the short, (milli-secs), time period available.

Primary Turns:

The next stage is to work out the number of primary turns you require. This will mainly depend on the size of the capacitor and the secondary characteristics, but your decision will also need to account for the type of spark gap being used as well.
Most of the losses always occur in the spark gap, so if the type of spark gap chosen has high losses associated with it, it's best to restrict the current by having more primary turns.
This because you will loose even more power as the current increases: power lost equals R Ohms x I² ('R' being the reactance of the primary inductance).
Now although the primary inductance may be a small value, typically 20μH to 40 μH [micro Henries] the current value can be very high, especially when its value has been squared, so the losses can soon mount up!

With an RQ gap (named after Richard Quick, and consisting of multiple bits of pipe side by side) it is best to try and aim for around 12 to 14 turns (allows for adjustment). This type of gap is quiet lossy, so more primary turns will keep the current (and losses) down. So use JAVATC to get both the cap value and the number of primary turns that will balance both the needs.

With a rotary gap that has far less losses, you can generally use less primary turns. Less primary turns will mean less inductive losses and therefore more current can end up in the streamers, making them appear whiter in colour, instead of purple.
(The purple colour is actually caused by the breakdown of Nitrogen in the air, and can be seen easier if less current is present.)

The reason for rotary gaps incurring less loss, is because they use a much smaller gap spacing and also have far less interfaces. [Note: 3]
So more turns will keep the primary current down with RQ gaps that are known to have high losses, but with improved rotary gaps, you can have less turns allowing more current, and so benefit from brighter streamers.
But remember, by allowing more current with a rotary it will mean it will start to get more losses, so once again, it's all about achieving a balance through 'trial and error' testing: like so many other things on a tesla coil.

** [Note: 3]
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.

The same advice above generally applies for a sucker gap as well, although they tend to have less interfaces than a RQ type.
Apart from RQ gaps needing more than 10 primary turns, there may be times when even though you are using a rotary gap, you just can't avoid having to use more than 10 turns, simply to get the tuning right.
Although this is generally caused by bad planning at the outset, it's not the end of the world, and the remedy is to either proceed with using more turns, or add more capacitance to allow you to use less turns.

The actual number of primary turns needed to tap it in the correct place, and the overall primary dimensions, are best determined by using the JavaTC program. The inner turn of the primary wants a minimum of an inch or so clearance all around the secondary coil's diameter, for small secondaries. While a 6 inch secondary coil may need 1.5 inches or so. My 8 inch has a 2 inch gap.
This spacing greatly affects the 'k' coupling value, as also does raising or lowering the primary in relation to the bottom of the secondary winding. Remember once the primary is built, you can then only alter the coupling by raising or lowering either the primary or secondary, in relation to one another. I solved it on my coil like this

Most people use small diameter copper heating tubing for the primary coils, making sure the spacing between each turn is at least 1.25 / 1.5 times the diameter of the tube you're using, so as to avoid any flashover between turns. Also it is important to make sure you leave enough room for a clamp to grip onto the tube, without it touching adjacent turns, or the clamp itself will cause a flashover.

Tesla coil scales analogy

always think of a tesla coil to be like a set of scales. On the one side you have the product of the primary inductance & the MMC capacitance, that determine the primary frequency.
This should then be balanced on the other side by the secondary frequency resulting from the product of the secondary inductance & the toroid's capacitance.
If you alter one value, you need to alter something else on the other side to maintain that balance.
[Note: 4]
If you don't balance things correctly, meaning it's not correctly tuned, the coil may still run, (if not too much out of tune), but the performance will be below that possible, and it may even damage some of your components.

** [Note: 4]
In the real world you tune the primary slightly lower than the secondary, (Streamer Loading) explained on the Tuning Page

The Very Basic Tesla Circuit Diagram
(Shown using a centre tap NST)
Some people swop the position of the spark gap and the capacitor, so the capacitor is placed across the transformer. While this will work, it has no advantages, and in fact is more likely to result in damage to the secondary of the transformer.
This is because the preferred method shown below, has the spark gap shorting the transformer's secondary winding when it fires, and this protects the winding from the RF that is flowing in the tank circuit at that time.

Circuit diagram of a normal Tesla Coil

choosing the capacitor value

Static Gap Capacitor

Static gaps are not too fussy about capacitance size (provided there is enough charging power available), but SRSGs prefer specific combinations of capacitance and ballast to complement one another, if you wish to get the maximum amount of power out.
A good explanation of this is on Richie Burnett's site, so his page here is well worth a visit.

200 bps SRSG Capacitor

With my 200bps SRSG the original capacitance value I was using was 72nF, so I carried out some PSpice simulations to find the best ballast value with that particular capacitor value, while using a 200bps rate SRSG.

Although using a smaller value ballast will allow more current to flow when used with an SRSG, that does not necessarily mean it will result in more useable power. This is because the Power factor (Wikipedia), comes into play, and it is this issue which Richie's page on Resonant Charging deals with.

Below: Results of using a 72nF cap with a range of different 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 changed of course.

This phenomena is "Resonant Charging", and as my coil's
success is down to Richie Burnett's work
it is worth explaining in its own section.

Resonant Charging

Any rotary gap which is synchronous (SRSG) will fire at fixed pre-determined rates (bps) and in fixed positions, relative to the AC mains voltage cycle. Because of this regular arrangement or frequency of events, the capacitor can charge quicker if the frequency is compatible with the charging ballast. This means differing bps rates will need different charging frequencies, if they are to achieve a decent power factor. A decent power factor will mean we have more power to use!
So Richie Burnett undertook endless PSpice simulations to find the relevant frequencies for differing bps rates.
The result was that he found that a 200bps charging circuit achieves its best power factor when the charging components, (the MMC's capacitance & ballast's inductance), resonate at 75Hz (for a SRSG 200 bps only) (see Richie's chart here).
In my own 200bps graph above, my 72nF & 62H ballast are resonating together at 76Hz.

So the charging circuit's preferred resonate frequency, with a synchronous rotary, is always dependant on the rotary BPS rate that is being used. So for resonant-charging to occur you need to match your charging components (ballast and capacitor) values, so that their resonant frequency is suited to the bps rate that you have chosen to use.

Representation of the two different charging circuits:

resonant charging path

Note: Do not get this confused with the coil's primary resonant frequency, shown in Red. That comes into play when the spark gap fires and puts a short-circuit across the transformer.

The resonant charging circuit's frequency, shown in Blue, is determined by the ballast (via the transformer coupling) the capacitor and primary coil in series.

(In the blue circuit the small inductance value of the primary is insignificant in comparison to the ballast's large value inductance, but it still forms part of the circuit.
In the red circuit however, this small primary inductance value is no longer insignificant, as now it determines the primary's resonant frequency in conjunction with the main capacitor's value (in nano-farads).

This method is an excellent way to get the most out of a coil running a SRSG, and is discussed in depth by Richie Burnett on his webpage here. On it he gives what he considers to be the different resonant frequencies, that differing BPS rates will need to be tuned to.

The first graph on his webpage shows that a 0.9 PF or better can, for 200 bps, be achieved by a resonant frequency in the range of 65Hz to 80Hz. In reality I chose the higher end of this frequency range as this allowed me a better capacitor size (not too large). Richie though favours a 0.85 PF for the reasons he states, but on lower bps systems, as in my case at 200bps, this can result in a rather large capacitor value being needed.

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 (The blue circuit above).
Richie's webpage is unfortunately unfinished after this stage, but he does give the full procedure needed in an earlier TCML posting of 16 Jun 2001 entitled "Resonant Charging Design" That post though has the two important graphs missing.

I have though made a copy of this post that you can find here

This is the original TCML post with the complete method
and also with the missing graphs added.

His original TCML posting (dead graph links) can be found here

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. As mentioned above, the low primary inductance causes more current in the primary circuit and more spark gap losses, but because I was using a SRSG with less losses than a static, it has paid off.

The current JavaTC output file of my 8 inch:

14 June 2013 18:26:01

Units = Inches
Ambient Temp = 68F

Surrounding Inputs:
84 = Ground Plane Radius
0 = Wall Radius
0 = Ceiling Height

Secondary Coil Inputs:
Current Profile = G.PROFILE_LOADED
3.963 = Radius 1
3.963 = Radius 2
29.375 = Height 1
63.587 = Height 2
1395 = Turns
0.0220471 = Wire Diameter
Primary Coil Inputs:
5.196 = Radius 1
10.288 = Radius 2
28.75 = Height 1
28.75 = Height 2
8.5912 = Turns
0.312 = Wire Diameter
0.125 = Primary Cap (uF)
12 = Total Lead Length
0.2 = Lead Diameter

Top Load Inputs:
Toroid #1: minor=8.34, major=34.64, height=74.019, topload

Secondary Outputs:
84.39 kHz = Secondary Resonant Frequency     (** 81kHz in reality)
90 deg = Angle of Secondary
34.21 inch = Length of Winding
40.8 inch = Turns Per Unit
0.00248 inch = Space Between Turns (edge to edge)
2894.7 ft = Length of Wire
4.32:1 = H/D Aspect Ratio
61.2559 Ohms = DC Resistance
43105 Ohms = Reactance at Resonance
4.26 lbs = Weight of Wire
81.294 mH = Les-Effective Series Inductance
84.045 mH = Lee-Equivalent Energy Inductance
81.97 mH = Ldc-Low Frequency Inductance
43.752 pF = Ces-Effective Shunt Capacitance
42.32 pF = Cee-Equivalent Energy Capacitance
64.024 pF = Cdc-Low Frequency Capacitance
10.03 mils = Skin Depth
35.283 pF = Topload Effective Capacitance
135.9531 Ohms = Effective AC Resistance
317 = Q

Primary Outputs:
74 kHz = Primary Resonant Frequency
12.31 % high = Percent Detuned     (10% in reality see note** above)
0 deg = Angle of Primary
34.83 ft = Length of Wire
3.71 mOhms = DC Resistance
0.281 inch = Average spacing between turns (edge to edge)
1.215 inch = Proximity between coils
1.22 inch = Recommended minimum proximity between coils
36.716 uH = Ldc-Low Frequency Inductance
0.09612 uF = Cap size needed with Primary L (reference)
0.289 uH = Lead Length Inductance
240.668 uH = Lm-Mutual Inductance
0.139 k = Coupling Coefficient
0.141 k = Recommended Coupling Coefficient
7.19 = Number of half cycles for energy transfer at K
48.02 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 Impedance
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
18.04 [joules] = Primary Cap Energy
991.2 [peak amps] = Primary Instantaneous Current
127.6 [inch] = Spark Length (JF equation using Resonance Research Corp. factors)
18.5 [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
11.562 [ms] = Time for Capacitor to Fully Charge
2.16 = Time Constant at Gap Conduction
353.68 [us] = Electrode Mechanical Dwell Time
88.49 [%] = Percent Cp Charged When Gap Fires
15033 [peak volts] = Effective Cap Voltage
14.13 [joules] = Effective Cap Energy
817035 [peak volts] = Terminal Voltage
2825 [power] = Energy Across Gap
133.1 [inch] = RSG Spark Length (using energy equation)

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