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Tesla Coil Design 

This page will give you hints and tips for the design of your own tesla coils system. If some more experienced
coilers out there find any errors or ideas for improvements  please send me email.
 

Which steps are necessary? 


Selecting the transformer 


Designing the primary capacitor 


Designing the primary coil 


Designing the secondary coil 


Designing the main sparkgap 


Designing the filter unit 


Designing the toroid 


Formulas collection 


The Tesla Design Excel spreadsheet 

There are different steps to be done when designing a tesla coil. First of all, you will need to
decide, which type of coil you want to build. This page only deals with the "normal" type of coil,
at least for now. Other types are possible, like bipolar coil systems and magnifier systems.
See the theory page for more information on these different types of coils.
You will then need to decide how much power you want to use. This may also be restricted by the infrastructure
you have at home. Lowest power level should be about 500VA (my coil works at 400W). Large coils built by
hobby coilers may reach up to 10kVA (or even more?), but these are the really big ones. Professional coils even
reach much higher levels of power. Have a look at my links page. Once you have clear ideas
about that, you can start with selection of your components
It is generally important to design for minimum losses in the system, as these first reduce the effectiveness of your coil
and, maybe even more important, losses will be converted to heat, which may damage compontents, for example
your primary capacitor.
The transformer is usually a part in the system, that you do not build on your own. Usually, but actually some people even build
them, too! See my links page. Instead you will use transformers from commercial manufacturers.
So the design in this point is restricted more or less to the choice of transformer type and maybe to some repair actions.
At this point, you need to decide which type of transformer to use. There are several types of transformers available.
If you get used transformers filled with oil, make sure that the oil contains no PCB. PCBs are forbidden and disposal may be
difficult and expensive.
Neon sign transformers (NSTs)
Beginners like me generally decide to use neon sign transformers. These are suitable for power levels up to 2kVA. They have
many advantages. You even may get them for free if you ask at neon sign manufacturers. I did not pay anything for my transformer.
They are quite small, and you may put them in parallel to increase power. They have a built in current limiting by design.
You also may repair them. There are hints on the web for this. Their disadvantages are, that they are not the most robust
types and tesla coil application stresses them. That's why they need good protection circuits (filter unit and safety gap).
And (at least in Germany) the maximum voltage of neon transformers was restricted
to 8kV, so you could not obtain higher voltages. This has recently been changed to 10kV, but those transformers will not be available as used
ones in the near future. Some manufacturers just started production. Do not attempt to connect them in series to increase voltage.
They are centertapped with the tap connected to the core and this will cause breakdown of the isolation between the core and the windings.
The centertap must be connected to your RF ground.
Oil burner ignition transformers (OBITs)
Other alternatives are oil burner ignition transformers. These transformers also are current limited.
Microwave oven transformers (MOTs)
Other alternatives are microwave oven transformers. These transformers do not have any current limiting.
Power distribution transformers (pole pigs)
The largest ones (and most dangerous types) are power distribution transformers (pole pigs), which may be used for the highest
levels of power. For a 5kVA coil you will need transformers of this type. Pole pigs will need current limiting.
The choice of technical specs of transformers will generally also be determined by their availability (at least for cheap used units).
You should first get your transformer before building any other parts, as otherwise you may have problems to get a transformer
with the specs you want to have.
The voltage level of your transformer is of importance. You should not use transformers below 5kV (my transformer has 8kV, and I
still think, that it could be higher). This is because of problems getting the sparkgap working fine at low
voltages. Also higher voltages cause much higher energy stored in capacitor of same value. The energy stored in a capacitor is
proportional to the square of the voltage. Double voltage means four times the energy stored in the same capacitor. See the formulas
section.
On the other hand, higher voltages impose much more problems with isolation of your components and also increase
size and cost of your capacitor, but you do not need that high capacity for a certain power level with higher voltages.
Once you have found your transformer, the real design phase may begin.
What capacity is needed?
You will now calculate the capacity of the primary tank capacitor. This depends on several factors. The capacitor must store the energy
that will be transferred to the secondary. Therefore it should not be too small. The energy stored in a capacitor is proportional
to the square of the voltage. On the other hand, the transformer must be able to load the cap to the peak voltage within a quarter of a
mains frequency period. This means, that there is a maxiumum allowed value for the capacitor. This may be calculated with the following
formula:Cmax is in Farad, f is the mains frequency in Hz, and Z is the impedance of the
transformer in Ohm, which may be calculated by formula: U is the voltage in Volt, I
is the transformer current in Ampere.
The maximum capacitor value is the value, where the reactance of the capacitor and the transformer match for the given mains frequency.
For further base formulas see the theory page.
You calculate the maximum allowed capacity and normally choose a value lower than this. With the given capacity, you now may
calculate the energy stored in each bang using the formula:
E is the energy stored in
Joule, C is the capacity in Farad and U is the voltage in Volt. Of course, this depends also on your sparkgap. If your sparkgap does
not fire exactly at the peak value of your transformer voltage, you will have less energy stored.
You have to keep in mind different things when designing your capacitor:
The choice of dielectricumYou have to find a good dielectricum. The dielectricum must provide a high dielectric constant and
high dielectric strength to save material (size of the unit) and weight. And the material must have low losses at RF. As told above, avoiding
losses is essential. Losses are also dependent on the frequency. For many materials losses grow very fast with rising frequency.
As tesla coils use higher frequencies from about 100kHz to 500kHz, this must also be kept in mind. The following table gives a short
overview of some materials. The dissipation factor is the tangens delta value used to describe losses. This is defined as
the current ratio of Ires/Ireact. Ires is the resistive current, the one, that causes losses in form of heat. Ireact is the
pure reactive current. Delta is the phase angle between both currents.


Dielectricum 
Dielectric Constant 
Dielectric Strength 
Dissipation factor
(x 10exp3) 
50Hz 
1MHz 
[kV/cm] 
50Hz 
1MHz 
LDPE 
2,29 
2,28 
370 
0,15 
0,08 
HDPE 
2,35 
2,34 
 
0,24 
0,20 
PP 
2,27 
2,25 
240 
0,40 
0,50 
PVCplasticized 
48 
45 
270 
80 
120 

Which type of capacitor to build?The type of capacitor is also to be chosen. This of course also depends on the dielectricum
you choose. A very cheap type of capacitor is the salt water cap. But this is a very lossy type and should only be used
for some experiments. I built one, but never used it with tesla coils.
Another type is the MMC (Multi Mini Cap) type of capacitor. This is built of an array of small MKP capacitors. Several capacitors
are connected in series to achieve sufficient voltage, and multiple of these strings are connected in parallel.
Apart from this you must decide whether to build a rolled capacitor or a plate stack capacitor.
The rolled cap is built of only 2 sheets of aluminium, which are very long and rolled with dielectricum.
 

This type has the disadvantage, that the current has to travel a long way at discharge, which is not optimum for pulse operation.
Also, longer sheets of aluminium have a higher inductance, which should be avoided. 

The plate stack type capacitor uses multiple plates of aluminium sheet. The advantage of this type is, that it has better performance
for high current pulses, as opposed to the rolled type, where only 2 large plates exist, in a stack many plates are in parallel and the current
has much shorter ways to travel. Also, inductance of this type is lower.
In my design I decided to use a plate stack cap with LDPE dielectricum. The construction of a plate
stack capacitor is explained in the construction page and you find photos and data about the capacitors
used in my first coil in the My Coil page
Parallel or series?There exist many ways to build the capacitor. One way is to build one single large unit.
The other option is to build multiple units and connect them together in series and/or parallel. This has the obvious advantage,
that you may combine your caps to different values without the need to build new units each time.
Apart from this, splitting down the capacitor has other advantages, too.
Series connection will distribute the overall voltage over all capacitors, resulting in a lower voltage per unit. This means, that the
thickness of the dielectricum in each unit does not need to be that high. The series connection reduces the overall capacity of the unit,
but because of the thinner dielectricum the single units have higher capacity. By this, the overall capacity may remain the same. Or it
may even be higher, as for thin dielectricum, the breakthrough voltage per mil is higher than for a thick layer of the same material.
You may use this effect to increase the capacity of the single units. I will try to do some measuements of this effect with PE at a later
time.
Another advantage is, that corona effects will be reduced, as the voltage over a single unit is reduced. For very high voltages
this may be of importance, because even in oil, some corona effects may happen at those levels.
Parallel connection may be exploited to increase overall capacity to the desired size. When connecting multiple series connected
arrays in parallel, the overall capacity is jsut the sum of the single arrays.
The MMC Capacitor Type (Multi Mini Cap)This type of capacitor is built from a large amount of small commercial capacitors
which are assembled in a parallel circuit of several caps in series. Each string can withstand high voltage because it consists of
let's say 20 capacitors in series. The parallel strings increase capacity.  
The primary coil is designed for very high currents. Therefore, the wire must be very thick. As the currents are of high frequency
you do not need to have massive wire because of the skin effect. Also, sharp edges should be avoided because of possible corona
effects. Therefore, copper tubing is a very good choice.
There exist mainly 3 types of primary coils. They form different shapes of the magnetic field. The helical primary is not a very good
choice, because spacing between primary and secondary as well as distance to the top toroid may be quite low. Helical primaries
may be used in magnifier systems. For small to medium coils, a inverse conical (saucer) coil is a good choice, using an angle of
about 20 to 30 degrees. The flat spiral primary will be best for higher power levels. With this type of coil, distance to the toroid
is maximum and minimizes the chance, that sparks hit the primary. Of course, you should provide a strike protection ring.
The graphics show a cross section view of the 3 types of primary discussed.
Flat primary coil
The flat primary is wound in a single plane. The inductivity may be calculated with following formula:
The inductivity L is in microhenry, N is the number of turns, W is the winding width and R is the average radius of the coil.
Values of W and R are in inches. See the javascript calculator for conversion of units.
Helical primary coil
 

The helical coil is wound as a cylinder. The inductivity is calculated with the formula (Wheeler equation):


The inductivity L is in microhenry, N is the number of turns, R is the radius of the coil and H is the height.
Values of H and R are in inches.
Inverse conical primary coil
The inverse conical coil is wound in a shape of a saucer. The inductivity may be calculated with a formula, that bases on the assumption, that
this type of coil can be interpreted as a mixture of the above types. Both parts are calculated together using the angle
of gradient. The inductivities L, L1 and L2 are in microhenry, N is the number of turns,
W is the winding width, R is the average radius and H is the height of the coil. Values of W, H and R are in inches.
L1 represents the value of the helical component while L2 represents the flat coil component. L1 and L2 are calculated separately
with the formulas for the flat and helical coils shown above and then are combined using the geometric sum.
 
The secondary coil does not need to be designed for that high currents, but it must also withstand very high stress. As there
will be a standing wave across the coil, at the base of the coil, where the RFground is connected, currents will be
in the range of several ampere while at the top currents will be low but voltage will be extremely high.
The high voltage requires a good insulation. Do not use too thin wire because the high base currents, which could cause too high losses.
Typically, the ratio between height and diameter of the secondary is in a range of 3:1 to 5:1. This has to do with the coupling
between primary and secondary circuit. For high power coils, 3:1 is mostly used. Smaller coils go up to 5:1.
There exist several factors influencing your coil dimension:
 Inductance must match resonance frequency together with self capacitance and toroid capacitance.
 Self capacitance should be at maximum half of toroid capacitance.
 The wire length should be one quarter of the wavelength at resonance frequency.
 Number of turns should be in range of about 1000 windings.
The inductance of the secondary coil can be calculated with the Wheeler formula:
L is the inductance in microhenry, R is the radius of the coil in inches, N is the number of turns and H is the height of the coil in inches.
See also the theory page for calculations of inductivities.
As mentioned above, I try to use wire length of a quarter wavelength of the wanted resonance frequency. I do this, because there will
be a standing wave on the secondary, i.e. current will not be same everywhere. Instead, at the base, current will be high and voltage will
be low, while at the top, current will be low, but voltage will be high. Are there any thoughts about that? Using quarter wavelength strongly
reduces the variability for coil forms.
You will need to play around with your parameters until you get a close match for all conditions. You can use the
Excel spreadsheet for that, which can be downloaded from my site.
The material used for your coil form should be of very low loss for RF frequencies. PVC tubes are easy to get, but as PVC is very lossy,
you should dry it and then seal it with polyurethane varnish before winding. After winding, I used PU varnish to seal the coil. For my new
coil, I use epoxy resin for sealing.
The design of the main sparkgap is very important for the performance of your system. There exist 2 basic types of sparkgaps:
the static and the rotary types. Static gaps are typically used in small systems, while with higher power, rotary gaps or
even combinations of both are used. The rotary gaps are further divided into synchronous and asynchronous gaps.
This chapter will deal with the design of the sparkgap and necessary calculations in general. Construction descriptions are
found in the construction page and photos and data about the sparkgap used in my first
coil are found in the My Coil page.
See the theory page for details about sparkgaps and their important parameters.
Static sparkgapsFor small coils, you will construct a static sparkgap. The simplest type of sparkgap consists of
two electrodes at a specific distance to each other. The form of the electrodes is important because it determines the
shape of the field and thus the breakdown voltage. Breakdown voltage is also influenced by many other different factors
like humidity, temperature and pressure of the medium (air) between the electrodes. A very large influence results from
ions already present in the gap. It is not possible to design the gap for constant and reproducible breakdown voltage.
It is a good practice to split the sparkgap into a series of single gaps.
Be sure to provide an air flow through your gap. This will remove ions from the gap and also has some cooling effect.
Rotary sparkgapsFor coils with higher power levels, you will need to use a rotary sparkgap. While a static gap will
be able to close the circuit very fast (microseconds range), the switch off process is much slower because of ions still left
in the gap. See also the theory chapter about quenching. This can be handled by airflow. For larger coils, a rotary sparkgap
will be used. This has the advantage, that switch off time also is low. The distance of the gap may be reduced to an absolute
minimum, which in turn lowers the losses.
For a rotary gap, you will need to select your materials carefully. The material for the rotating disk must withstand the high Gforces,
which are produced by the electrodes placed at the outer diameter of the disk. At about 3000rpm a failure could have very serious
consequences, having screws behaving like bullets. Materials to use are composites of epoxyglass fiber. These are described
in NEMA G10 norm. In Germany, the DIN equivalent is HGW 2372.
The electrodes will be made of tungsten or of tungstencopper mix. This material is very robust.
To protect your transformer and power supply from RF high voltage
strikes which return back from the primary, you should include a filter unit into your system. This filter is designed to
block high frequency high voltage peaks from being fed back from the primary circuit to the power supply. This filter is
built as a simple LRC low pass filter.
The chokes for the filter should be wound on a ferrite core and range from 2 to 10mH. You also can wind your chokes on a
pipe, but the air core choke has low losses. This can result in resonances within the filter unit itself. To avoid this effect,
use high power resistors in series to reduce the Q value of the chokes.
You should take measurements of the characteristics of your filter with all components connected and feeding the system with
a variable frequency from a signal generator. This way, you can make sure, that critical frequencies are really filtered.
The toroid should not be too small.
In general, the higher the power level, the larger the toroid should be. Large toroids
will allow for higher voltage to build up before breakout. I asked myself, how the
ratio of outer diameter of the toroid and the thickness of the toroid itself would
influence the capacity value, i.e. is there an optimum ratio for highest capacity.
I did some math and found, that for a given outer diameter, the thickness of the toroid
must be 29 percent of the outer diameter. Other values of thickness will decrease
capacity. Download a zipped MS Word document of the math here:
Maybe this is not of really great importance, but it was just interesting and it was
it was an opportunity to find out, how much of even the learned simple math has been lost over the years not using it any more ;). Please let me know about your opinion.
The tesla transformer exists of the primary and secondary
coil. The primary transfers energy to the secondary. For this transfer, the coupling factor is of importance.
This coupling factor is determined by the form of the primary and the position of the secondary. If a secondary coil is very
high, the flux produced by the primary will not be able to uniformly enclose the secondary. This will result in low coupling.
Coupling can also be reduced by raising the secondary. Poor coupling will result in bad energy transfer.
If coupling is too close, additional harmonic frequencies may be produced. These will result in additional spark breakouts
along the secondary. Richard Quick describes this as "splitting". In this case, the coil is overdriven. Overdriven coils
may also show visible field flux due to excessive corona. Reducing the coupling by raising the secondary may help.
The following table provides a collection of the formulas used for calculating the different components of
a coil system.
Inductivity of a flat spiral coil
L=inductance in microhenry, R=average Radius in inches,
N=number of turns, W=width of coil in inches 

Inductivity of a helical coil
L=inductance in microhenry, R=radius in inches,
N=number of turns, H=height of coil in inches 

Inductivity of an inverse conical coil
L=inductance in microhenry, R=average radius in inches,
H=height in inches, W=width in inches, N=number of turns,
L1=helix inductance, L2=flat spiral coil inductance,
alpha=angle of rise in degrees 

Maximum primary capacity
Cmax=Capacity in F, Z=transformer impedance in ohm
f=mains frequency[Hz] 

Toroid capacity
C=Capacity in pF, d1=toroid diameter, d2=inner diameter 

LC circuit resonance frequency
f=frequency in Hz, L=inductance in H, C=capacity in F 

Capacity of a PE plate stack capacitor
C=Capacity in pF, A=area in square cm,
n=number of alu sheets, d=dielectricum thickness in mm 

General capacity of a plate stack cap
C=Capacity in F, A=area in square m,
n=number of alu sheets, d=dielectricum thickness in m,
er=diectric const, e0=fixed value. 

Parallel circuit of capacitors
C=resulting capacity, C1,C2,C3=single elements


Serial circuit of capacitors
C=resulting capacity
C1,C2,C3=single elements 

Parallel circuit of inductivities
L=resulting inductivity
L1,L2,L3=single elements 

Serial circuit of inductivities
L=resulting inductivity, L1,L2,L3=single elements 

Take care of the units of measure. Some formulas use inches others use meters and centimeters. I have
included a Javascript calculator for this.
To simplify the design phase I have developped a spreadsheet for MS Excel. It will help you play around with your
variables to find good matching parameters. The spreadsheet helps you calculating coil parameters
and shows you, when parameters like secondary height to diameter ratio are out of reasonable range.
Download the zipped Excel spreadsheet here:
Some remarks to the spreadsheet:
The spreadsheet is still a draft version and by far not a complete calculator.
But it is useful for just playing around with parameters and for doing a
quick design. The values you find in the downloaded table are values for
a small micro coil I'd like to build.
All dimensions are in metric system, mm, cm, meters...
All grey fields are input, the rest is calculated output. The output fields
are not protected yet. So be careful not to overwrite formulas.
There are some conditional fields, that change color, if results do not match.
For example h/d ratio of secondary or resonant frequencies.
The spreadsheed was started at a time, when I believed in the quarter wavelength
theory. That means, the wirelength conditional field will also show a warning
 just ignore it.
The plate stack cap section is not finished, I don't think it will be that
useful in the MMC era.
Feel free to play around with it, modify it, delete it if you don't like it.
If you have questions, please send me an email. And if you make improvements, I would appreciate, if you send me your updated version.



© 1999 by Herbert Mehlhose 

