Secondary coil design and construction for Tesla coils

This is chapter 9 of the DRSSTC design guide: Secondary coil

Intro

Building the secondary coil be a very time consuming and tedious task, but it is of paramount importance that everything is done properly and that time is spent on making a high quality coil in order to avoid catastrophic failure while running it under high power conditions.

Due to switching losses in IGBTs, the most common resonant frequencies is somewhere between 35 kHz to 500 kHz, with most in the lower end around 100 kHz.

 

Spark loading

Spark loading is not yet fully understood as the load is never the same and many factors influences on it; complex in its branching structure, involves plasma physics with the calculation of arc resistance depending on how many thousand degrees hot the arc channel is, repetition rate, voltage profile that the secondary system is being charge with and the list goes on. This description on spark loading will only take the simple models into account.

Impedance matching should not be a foreign matter for most people that have worked with or designed electronics, it is simply a matter of ensuring that f.ex. your power supply can supply enough current to make a light bulb glow at its power rating. The secondary coil and the rest of the resonant system behind it is also a power supply that has to supply current to light up the spark and keep it fed with enough current for it to be able to grow.

As the spark gets longer and branches out to get bigger in a 3 dimensional array, the load grows in a way that can be represented by a resistance and a capacitance. This load will effectively change the resonant frequency of the secondary coil and at some point the load have pulled the system so much out of tune that it can no longer keep the spark channel fed with enough power and it collapses again. It is not just the frequency that can change so much that not enough energy is transferred, during heavy ground strikes the load can be so heavy that it pulls the voltage down completely on the secondary system and again the spark channel collapses.

Spark impedance is highly dependent on the amount of power that being fed into it and the impedance will drop with higher power levels. Typical spark impedance values are maybe around a few hundred kΩ. The relation to secondary impedance and coupling factor will be discussed further down.

Many people in the Tesla coil hobby have worked on simulating spark loading and comparing it to real experimental values. I would like to thank Terry Fritz, Steve Conner, Steve Ward, Udo Lenz, Bart Anderson and many others that I do not know by their full name.

 

Spark loading during ground strikes

Measurements and investigations into secondary charging currents, discharge currents and the voltages led out from this have shown that during ground strikes the spark impedance drops suddenly way below f.ex. secondary impedance of 50 kΩ and thus is clamps the topload voltage to less than 100 kV, bear in mind that these are rough estimates and not exact measurements.

A ground strike is a shorted circuit and consists of the following impedances: Secondary impedance Zsecondary, spark channel impedance Zspark and ground impedance Zground. Combined in series these impedances make up a new scenario compared to sparks just flying out in the air. As the spark impedance during a ground strike can suddenly drop to near zero and ground impedance can vary from near zero to some 10’s kΩ we have a system that is highly unpredictable.

The smaller ground impedance we have, the higher currents would suddenly rise in a low impedance ground strike, this rise in current have to be fed through the secondary impedance and is what pulls the voltage down. As the current propagates through the secondary coil the voltage distribution can get very uneven and there are many observations on secondary destruction from what seems to be reflected voltage rise from a good ground and has been called whiplash-effect.

More on grounding in Grounding and EMI chapter.

 

How to calculate the impedance and Q factor of the secondary coil system [1] [2]

Udo Lenz’ thoughts on optimal secondary impedance:
The power transfer to the secondary depends on the arc (resistive) load. For a given primary current it has a max at a specific arc resistance. If primary and secondary resonate at the same frequency this max is reached approximately, when Qsec = 1/k. Qsec is the ratio of arc resistance and secondary impedance.

Arc resistance depends very much on how much power you put into the arc and will decrease with more power. Typical values are maybe around a few hundred kohms, so the optimal secondary impedance would be k times a few hundred kohms, i.e. maybe 50k. I tend to believe, that a lower value might work somewhat better particularly for high power coils.

Since the arc detunes the secondary to a varying extent, the initial assumption, that primary and secondary resonate at the same frequency cannot really be upheld. Optimally this condition should be reached at the end of primary rampup.

Calculating the impedance for your secondary coil system makes you able to get a hint of what kind of performance you can expect from the coil and to determine how the coil should be driven or coupled. Q factor and its related calculations are shown and explained here, for those interested in more secondary coil parameters for the use of spark load modelling. I made a spreadsheet with all these and more example calculations.

The resonant frequency of the secondary coil system with topload can be calculated with a regular expression without taking care to the influence of the surroundings.

F_{resonant}=\frac{1}{2\cdot \pi \cdot \left ( L_{secondary} \cdot C_{topload} \right )}

The impedance of the secondary coil and topload is also calculated with a regular expression.

Z_{secondary}=\sqrt{\frac{L_{secondary}}{C_{topload}}}

Calculating the unloaded Q factor requires some more calculations as we need to know the DC and AC resistance, and to find those we first need to calculate the skin depth δ of the current flowing in the secondary coil. Coppers specific resistance at 20 oC is given as ρ 20.

\rho_{20} = 0.0179 \cdot 10^{-6}

\delta = \sqrt{\frac{\rho }{4 \cdot \pi ^{2} \cdot 10^{-7}}} \cdot \frac{1}{\sqrt{F_{resonant}}}

Next we calculate the DC resistance of the secondary coil. Coil diameter and wire diameter is given in meters and the result is in Ω.

R_{DC} = \frac{4 \cdot coil_{diameter} \cdot turns \cdot \rho}{wire_{ diameter}^{2}}

If the wire used is larger than what the skin depth is, we need to take this into consideration for the calculation of the AC resistance. We can calculate a factor that we multiply onto the DC resistance to account for this. It is simply the area of a ring and the factor of the area of the wire used divided by the area of the ring that the skin effect would represent.

\Xi_{factor} = \frac{\pi \cdot R^{2}} {\pi \left ( R^{2} \cdot \left ( R - \rho \right )^{2} \right )}

The proximity effect is the greatest contributor to the AC losses in a secondary coil, adjacent turns on a coil form simply induce losses in each other. The complex task of calculating the AC losses in a coil was simplified by Medhurst’ paper from 1947 where he based his work on Butterworth’s work. This table can predict the AC resistance within 3% if the frequency the coil is driven at is below the self resonant frequency of the coil, which it is when a topload is added to lower the frequency. The table also only holds true for coils with more than 30 windings, again not a problem with Tesla coils.

Table 1: Medhurst Φ factor values for AC losses in coils due to proximity [3]
spacing →

Ratio ↓

1.00 1.11 1.25 1.429 1.667 2.00 2.50
1 5.55 4.10 3.17 2.47 1.94 1.67 1.45
2 4.10 3.36 2.74 2.32 1.98 1.74 1.50
4 3.54 3.05 2.60 2.27 2.01 1.78 1.54
6 3.31 2.92 2.60 2.29 2.03 1.80 1.56

Spacing → is the ratio of distance between center point of turns divided by the wire diameter. So a closely wound coil using 0.25 mm wire would have approximately 10% wider diameter from varnish, that makes it 0.275 mm / 0.25 mm = 1.1 spacing ratio.

Ratio ↓ is the height/width ratio of the secondary coil. A coil that is 100 cm tall and 25 cm wide would have a ratio of 4.

If the above table is not precise enough or you need another H/W ratio, Mike derived the following formula to approximate proximity factor from plotting numbers calculated in Ed Sonderman’s excel spreadsheet VLOOKUP and getting a formula that is linearly for only ratios above 2.

\Phi_{factor} = 0.100976 \cdot \frac{height}{diameter} + 0.309630

Calculating the AC resistance is now as simple as to multiply the DC resistance with the skin effect factor and proximity factor.

R_{AC}=R_{DC}\cdot\Xi_{factor}\cdot\Phi_{factor}

Calculating the Q factor is done of an inductor is the ratio of its inductive reactance to its resistance at a given frequency, and is a measure of its efficiency.

Q=\frac{2\cdot\pi\cdot f\cdot L}{R_{AC}}

Steve Conner recommended the 50 kΩ impedance of the secondary coil system after working it out from Terry Fritz’s spark loading models and a assumption of a loaded secondary Q of 10. Steve Conner found that this “magic 50k”, as it has later been known as, agreed with  the better performing Tesla coils at that time, Tesla coils that mainly consisted of spark gap and off-line Tesla coils (the ancestor of DRSSTCs).

Udo Lenz describes the spark loaded secondary Q as it should remain equal for different sizes of coils. With spark load increasing with more power and bigger sparks, the impedance of the secondary should decrease slightly to compensate for the heavier load.

A higher impedance coil could however perform the same, just with longer on-time and more losses in the primary circuit as a result.

 

How to choose coupling coefficient between primary and secondary coils

The coupling coefficient, or just talked about as coupling, is denominated “k” and represents the ratio of the electromagnetic field between the primary coil and secondary coil. Generally k is in the low end somewhere between 0.12 to 0.2, compared to normal transformers that are often considered to be 1.

Low coupling coefficients are needed to avoid too high voltage stress from the fast energy transfer, with higher coupling comes faster energy transfer. We do however still want to get the coupling as high as possible as this is one of the limiting factors in how much energy we can transfer from the primary coil to the secondary coil and thus how long sparks we can produce.

With a optimal coupling and depending on the secondary coil being driven at the lower or upper resonant frequency, the secondary coil would have a either convex or concave voltage gradient. With a convex voltage profile the potential is high at the bottom of the secondary near the primary coil and at the top, whereas the middle of the coil is the valley of the convex curve. With a concave voltage profile the potential is close to ground at the grounded bottom to a high voltage at the middle with is the top of the concave curve and again a lower voltage at the top terminal. If the coupling is too high then the voltage gradient is no longer within these two defined distributions and there can be several places along the secondary coil with a high voltage present, this can cause flash over sparks going up and down the secondary coil, this phenomena is known as racing spark and could ruin the secondary coil if the sparks can punch through the insulation of the varnish and wire.

Poor tuning or high power runs can also cause racing sparks, but more on these issues in the chapter on tuning and testing.

Table 2: Pros and cons for low and high coupling
Low coupling coefficient Longer energy transfer time

More primary cycles needed

Tuning point is less critical

High power Tesla coils with low tank impedance

High coupling coefficient Faster energy transfer time

High voltage stress

Risk of racing sparks

Tuning point is more critical

Higher secondary peak currents

Possible longer sparks

Fewer primary cycles needed

High power Tesla coils with high tank impedance

As table 2 gives a overview of some of the fall pits and advantages, it does however also fail to give any finite answer to the coupling. A thumb of rule have been developed by Bart Anderson to start with 0.117 for a 1 inch diameter secondary and as diameter increases, so does the “recommended first try” coupling coefficient k.

There is absolutely no fixed result to the coupling coefficient value and experimentation is encouraged, but the above can give a good starting point.

 

How to find the right secondary coil size and ratio

As a well designed DRSSTC is easily capable of producing sparks that are 2-3 times the length of the secondary coil, I will advice on using a width:height aspect ratio of 1:4 to 1:6, personally I prefer 1:5.

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
Table 3: Selection of ratio with coil length span and recommended start coupling
  Coil dia. Coil length Ratio Coupling
Micro 40 mm

50 mm

160-200 mm

200-250 mm

1:4 – 1:5 0.120

0.125

Mini 75 mm 300-375 mm 1:4 – 1:5 0.128
Medium 110 mm

160 mm

440-550 mm

640-800 mm

1:4 – 1:5 0.130

0.135

Large 200 mm

250 mm

800-1000 mm

1000-1250 mm

1:5 – 1:6 0.140

0.146

Very large 315 mm

400 mm

1250-1575 mm

1600-2000 mm

1:5 – 1:6 0.154

0.165

 

How to find the right secondary coil wire size and number of turns

The number of turns on the secondary coil is not directly comparable to the primary:secondary ratio known from normal power transformers. It is not important with fewer or more turns, but more to create a secondary circuit between coil and topload that has a impedance that matches the load presented by the sparks that we want to create.

I will use the five different coil system sizes for a table on wire size and turns to achieve a circuit impedance as described above. This table assumes using a toroid that follow the rule of thump found in the topload part of the DRSSTC design guide. Major diameter as secondary coil winding length and minor as secondary coil diameter.

I will start the table at 0.1 mm wire, as it is my own experience that anything thinner than this is practically impossible to wind a coil from, even with 0.1 mm the risk of wire snapping or breaking is very high.

This table represents a optimal range of values for designing a classic low impedance Dual Resonant Solid State Tesla Coil. Secondary coil systems with a higher impedance can achieve the same results by longer on-time with lower peak currents, but however with more losses in the system.

The color coding of the secondary system impedance should be understood as a guide line towards the magic 50k which was explained further up. I made a spreadsheet with all these and more example calculations. The magic 50k is thought to be too high for large or very large coils that will experience serious spark loading, here it properly is more suitable with 40k or even as low as 30k. Experimentation is needed to confirm these assumptions.

Table 4: A range of secondary design parameters that should result in a good performing system
  Wire dia.
(mm)
Secondary_ (turns) Frequency
(kHz)
Impedance
(kΩ)
Q
unloaded
Micro

40 mm

1:4 – 1:5

0.09

0.1

0.127

1600-2000

1460-1830

1150-1430

401-322

439-353

558-451

57-59

52-53

41-42

34-27

41-34

67-55

Micro

50 mm

1:4 – 1:5

0.127

0.143

0.16

1440-1800

1280-1600

1150-1430

356-287

401-323

446-361

51-52

45-46

40-42

53-44

67-55

84-69

Mini

75 mm

1:4 – 1:5

0.16

0.2

0.25

1700-2150

1370-1700

1080-1370

201-160

250-202

317-251

61-62

49-50

39-40

57-46

88-73

139-113

Medium

110 mm

1:4 – 1:5

 

 0.25

0.3

0.35

0.4

 1600-2000

1330-1650

1150-1420

1000-1250

146-117

175-142

203-165

233-188

57-58

47-49

41-42

36-37

94-77

136-112

180-152

219-188

Medium

160 mm

1:4 – 1:5

 

0.35

0.4

0.45

0.5

1650-2080

1450-1800

1300-1600

1150-1450

97-78

111-90

123-101

139-111

59-61

52-53

46-47

41-42

128-104

166-137

204-173

242-205

  Wire dia.
(mm)
Secondary_ (turns) Frequency
(kHz)
Impedance
(kΩ)
Q
unloaded
Large

200 mm

1:4 – 1:6

 

 0.45

0.5

0.6

0.7

1600-2420

1450-2170

1200-1820

1050-1550

80-54

88-60

107-72

122-84

57-61

52-55

43-45

37-39

169-118

206-147

272-204

321-255

Large

250 mm

1:4 – 1:6

 

0.6

0.7

0.75

0.8

1530-2280

1300-1950

1220-1820

1130-1700

67-46

79-54

84-57

91-62

54-57

46-49

43-45

41-43

233-168

293-222

317-245

344-268

V. large

315 mm

1:4 – 1:6

 

0.75

0.8

0.9

1.0

1520-2300

1430-2150

1280-1900

1150-1720

54-36

57-39

64-44

71-48

54-57

51-54

45-48

41-42

283-207

308-232

354-277

397-315

V. large

400 mm

1:4 – 1:6

 

0.9

1.0

1.2

1.4

1600-2420

1450-2180

1200-1820

1050-1550

40-27

44-30

53-36

61-42

57-61

52-55

43-46

37-39

317-235

362-277

443-350

505-412

 

How to find the right wire for the secondary coil

Most magnet wire is advertised and listed with its temperature classes as that is a major design impact for relay, motor or transformer winders. Breakdown voltages are less important here as it is standardized with a minimum set of requirements to all different wire diameters. Breakdown voltage depends on the thickness of the insulation, which can be of 3 types: Grade 1, Grade 2 and Grade 3. Higher grades have thicker insulation and thus higher breakdown voltages.

Table 5: Minimum breakdown voltage of magnet wire according to IEC-60317 [4]
≤ 0,100 mm measured using cylinder method, diameters > 0,100 mm measured using twist method
 Wire size Grade 1 Grade 2 Grade 3
0.090 mm 500 V 900 V 1300 V
0.100 mm 500 V 950 V 1400 V
0.127 mm 1500 V 2800 V 4100 V
0.143 mm 1600 V 3000 V 4200 V
0.160 mm 1700 V 3300 V 4700 V
0.200 mm 1800 V 3500 V 5100 V
0.250 mm 2100 V 3900 V 5500 V
0.300 mm 2200 V 4050 V 5950 V
0.350 mm 2300 V 4300 V 6400 V
0.400 mm 2300 V 4400 V 6600 V
0.450 mm 2300 V 4400 V 6800 V
0.500 mm 2400 V 4600 V 7000 V
0.600 mm 2600 V 4800 V
0.700 mm 2700 V 4800 V
0.750 mm 2700 V 4800 V
0.800 mm 2700 V 4900 V
0.900 mm 2700 V 4900 V
1.000 mm 2700 V 5000 V
1.200 mm 2700 V 5000 V
1.400 mm 2700 V 5000 V

Although most insulated copper wire is described as “enameled”, it is not enameled wire, which would be coated with either a layer of enamel paint or with vitreous enamel made of fused glass powder.

Modern magnet wire typically uses one to four layers of different polymer film insulation, most likely a combination of two different compositions, to ensure mechanical strength and a high electrical insulating layer. Magnet wire insulating films are made from the following, in order of increasing temperature class: polyvinyl formal, polyurethane, polyamide, polyester, polyester-polyimide, polyamide-polyimide and polyimide. These insulation polymer films are rated from 90 up to 250 °C.

Most varnishes used for magnet wire has a Volt per micron insulation rating of about 200 V/µm.

Table 6: minimum enamel thickness in mm added to bare wire of magnet wire diameter according to IEC-60317 [4]
 Wire size Grade 1 Grade 2 Grade 3
0.090 mm 0.008-0.017 mm 0.016-0.023 mm 0.024-0.030 mm
0.100 mm 0.008-0.017 mm 0.018-0.025 mm 0.026-0.032 mm
0.127 mm 0.010-0.019 mm 0.020-0.029 mm 0.030-0.038 mm
0.143 mm 0.011-0.020 mm 0.021-0.031 mm 0.032-0.041 mm
0.160 mm 0.012-0.022 mm 0.023-0.034 mm 0.035-0.045 mm
0.200 mm 0.014-0.026 mm 0.027-0.039 mm 0.040-0.052 mm
0.250 mm 0.017-0.032 mm 0.033-0.048 mm 0.049-0.063 mm
0.300 mm 0.019-0.034 mm 0.035-0.052 mm 0.053-0.069 mm
0.350 mm 0.020-0.037 mm 0.038-0.056 mm 0.057-0.073 mm
0.400 mm 0.021-0.039 mm 0.040-0.059 mm 0.060-0.078 mm
0.450 mm 0.022-0.041 mm 0.042-0.063 mm 0.064-0.083 mm
0.500 mm 0.024-0.044 mm 0.045-0.066 mm 0.067-0.087 mm
0.600 mm 0.027-0.049 mm 0.050-0.074 mm
0.700 mm 0.028-0.052 mm 0.053-0.079 mm
0.750 mm 0.030-0.055 mm 0.056-0.084 mm
0.800 mm 0.030-0.055 mm 0.056-0.084 mm
0.900 mm 0.032-0.059 mm 0.060-0.089 mm
1.000 mm 0.034-0.062 mm 0.063-0.094 mm
1.200 mm 0.035-0.066 mm 0.067-0.099 mm
1.400 mm 0.036-0.068 mm 0.069-0.102 mm

It is important to use magnet wire that is in a good shape without damage to the varnish or have had kinks, this could results in cracked insulation which means the insulation voltage is down to zero.

Turn to turn voltage can not exceed the voltage rating of magnet wire. But even a relatively short coil with 1000 turns, stressed to 500 kV would only have 500 V between turns.

 

How to find the right secondary coil form material

Plastic materials all react differently in a high frequency electromagnetic field and thus some plastics are more suitable to use for a secondary form than others. Let us first take a look at the different dissipation factors of the following plastic types.

Table 7: Electrical properties of plastic materials
Name Loss tangent / dissipation factor Maximum temperature
Polyacrylonitrilebutadiene-styrene (ABS), molded 0.005 – 0.019 @ 1 MHz – 0 + 105
Polyethylene (LDPE/HDPE) 0.0001 – 0.001 @ 1 MHz – 70 + 80
Polycarbonate (PC / Lexan) 0.00066 – 0.01 – 0 + 135
Polyethylene terephthalate (PET, PETP) 0.002 @ 1 kHz  – 0 + 120
Polymethylmethacrylate (PMMA / Acrylic) 0.014 @ 1 MHz  – 70 + 65
Polyvinylchloride soft (PVC-P) 0.12 @ 1 MHz – 50 + 105
Polyvinylchloride hard (PVC-U) 0.015 @ 1 MHz – 50 + 105
Polyvinylidenfluorid (PVDF) 0.17 @ 1 MHz  
Polypropylene (PP) 0.0003 – 0.0005 @ 1 MHz – 10 + 90
Polystyrene (PS) 0.0002 @ 1 kHz

0.0001 @ 100 MHz

– 0 + 65
Teflon (PTFE) 0.00028 @ 3 GHz – 0 + 250

High frequency heating: tan δ > 0,1 easily, tan δ > 0,01 possible and tan δ < 0,001 impossible.

A good secondary coil form material needs to have a low high frequency dissipation factor, have a wide temperature range to avoid thermal expansion / contraction ruining the copper winding and be mechanically stiff enough to be handled and support the weight of the topload assembly.

ABS, PMMA(Acrylic), PC(Lexan), PP and orange hard PVC pipes easily fulfill these requirements whereas PTFE is too soft and slippery, despite its superior high frequency properties.

HDPE, PET and PS only comes on soft and flexible pipes and tubes that are impractical to use.

From a cost perspective I have compared prices as of 2016 from different retailers and using hard PVC as 100% starting point the relative costs of other materials are listed for the same size pipe.

3 meters of 160 mm diameter pipe would cost:

  • 100% PVC
  • 166% PP
  • 175% PMMA
  • 285% ABS and PC.

PVC is by far the most cost effective material and PMMA(Acrylic) is still a good option if you want to pay extra for the looks.

PVC sewer piping usually comes in grey and orange. The grey being a little softer than the more rigid orange. Grey is used for indoor piping and orange is used for outdoor installation in gravel and thus their differences in rigidness.

Typical composition of orange PVC-U piping: 70-90% polyvinylchloride, 3-16% calcium carbonate filler, 3-16% modifiers (chlorinated PE, & 0 ‐ 5% acrylics). 1-6% stabilizer & lubricants and 1-4% titanium dioxide.

Calcium carbonate is used for higher mechanical strength and stiffness of the pipe, also higher electrical resistance. Titanium dioxide is used for UV resistance.

Used PVC pipes found on construction sites have a tendency so have absorbed some water when it has been lying unprotected in all kinds of weather. Avoid the use of old PVC pipes.

As pipe diameter goes up, so does the wall thickness for giving the wider pipe mechanical strength to be dug into the ground, thicker walls does however means more material affected by the electromagnetic field and thus there  are greater RF losses in thicker materials, so choose as thin walled pipes as possible.

 

How to wind the secondary coil

Before winding the secondary coil it is important to prepare and clean the secondary form. A good and easy way is to sand it down to get a as even as possible surface free of dirt, scratches and possible metal fillings that are stuck in the plastic.

Some people who can not source a PVC pipe or other plastic form have been forced into using card board tubes, here it is important to dry it in a oven at 100 oC for many hours to drive out any moisture that is trapped inside the card board. When it is baked it needs to be varnished to prevent it from absorbing new moisture from the air.

In the illustration below I have three different kind of secondary winding methods.

Method A is the most common, magnet wire is wound on the secondary form and the orange color shows how the varnish is lying on top of the windings, but there is still air underneath and between the windings.

The following pictures show how we used a variable frequency drive to control a small motor with a gear on, to turn the secondary coil. The magnet wire was being kept at a good tension just by the weight of the reel alone, which was 10 kg. The VFD was controlled by a foot switch, ramp up time set to 15 seconds and at maximum speed it would turn 30 turns a minute.

The following pictures show how I used a broom handle and just turned the secondary form by hand while keeping the magnet wire in tension with the other hand. A tiresome work but it will get you a perfectly fine secondary coil without having to build a rig. As shown further down, I was however forced to make a rotating rig to varnish the coil.

Method B is similar to method A, a single layer coil is made with turn against turn, but here the secondary form is varnished and the coil is wound upon the wet and not yet dried varnish in order for it to fill out the gaps and get coil to better stick to the secondary form.

Method C can be done in two different ways, the main concept is that there is much more distance between turns than just the layer of varnish on the magnet wire. It can be done by winding nylon fishing line unto the secondary form along with the magnet wire, side by side, so that the nylon wire can afterwards be removed and left is a space wound coil. It can also be done by carving a small slit into the secondary form, but this will require building a lathe type of rig to do this cutting.

The turns does not need to be aligned and close together 100%, a coil with gaps and uneven winding will still work fine, but overlapping turns is a absolutely guarantee of failure,  the overlapping wire will represent a higher point on the coil and will become subject to corona discharge and possible sparks breaking out from it. Turn to turn voltage would also be higher with overlapping and that will result in insulation break down and a short circuited secondary coil.

While winding the coil you will quickly find that you want to take some breaks, either from arms, hands or fingers going fatigue or you are starting to getting cross-eyed from looking at the wire. Electrical tape is perfect for holding the wire in place and I just leave the pieces on as I go, should I get unlucky and loose the grip of the wire, much less of the coil would unwind itself and get loose.

Space wound coils are especially useful in high power coils where the losses in the secondary wire is governed by the proximity losses of the nearby turns.

Space wound coils are also believed to solve the whiplash problem as the greater distance between turns provide enough additional insulation so that the reflected voltage can not break down the turn to turn insulation.

If you want to seal the ends of the secondary coil with large caps or disks, it is important that you still have a small hole or other way of venting out fumes from varnish or glue that is used to put them in place, if there is flammable fumes or gasses trapped inside a secondary coil that fails, it might fail exploding instead of just smoking!

 

How to insulate the secondary coil with varnish

Corona glow can happen at spots with imperfections in the varnish on the secondary coil, it could be air bubbles, hairs from the brush or insects. UV light from the sparks can even help to make this become a fatal breakdown of the air and the corona spot will turn into a burning spot that quickly can damage the secondary for good. It is therefore important to put a great deal of work into insulating the secondary coil.

Three commonly used varnishes, resins or what other names it has among people is listed here with their respective break down voltages and loss tangent.

Table 8: Electric break down voltage and loss tangent of varnish and resins [5] [6] 
  Break down voltage (rms) Loss tangent 1 kHz
Polyurethane  13 – 25 kV/mm 0.01 – 0.06
Polyester (unfilled) 20 kV/mm 0.006 – 0.04
Epoxy (unfilled)
bisphenol type
16 – 22 kV/mm 0.002 – 0.02
Epoxy (unfilled)
cycloaliphatic type
20 – 21 kV/mm 0.035 – 0.039

If you already have a winding rig you also have a varnishing rig. You will get the best and most even surface by having the secondary coil rotate while you apply the varnish and while it dries up.

Spray on varnish from cans leaves a very thin layer and it will literally take hundreds of layers before it reaches a good enough thickness.

Brushed on varnish is easier to control and you can even apply large amounts at a time, as the rotating movement will even it out.

Poured on epoxy is preferred by those that can buy it, with epoxy it is possible to achieve a layer as thick as 40 layers of polyurethane varnish, but it can done in one setting.

Between layers it is a good idea to wait for it to harden and using very fine sand paper, remove any air bubbles that might have been trapped in the varnish. Some people also use a hot air gun to quickly pop the air bubbles without overheating the varnish.

In the following pictures I am using a polyurethane varnish and apply it in plenty amounts, the brush is used to even out the varnish, burst air bubbles and almost shovel more varnish on. A large amount can be applied at one time when using a rotating rig to help it even out and not run or drip while drying

In the following pictures I also used a polyurethane varnish and that was more in the league of smearing it on, I applied as much as possible and when the rotation could no longer keep it from dripping I stopped. To keep things as simple as possible, I used my accu drill to turn the secondary coil around.

 

Termination of the wire ends of secondary coils

There are a few, but important, rules to keep in mind when terminating the ends of the wire on the secondary coil. It is less important with small systems, here you can get away with breaking the rules, but in high power systems it will result in damaged secondary coils.

  • Never drill holes in the side wall of the secondary coil form, even the slightest gap is enough for high voltage to pass through.
  • Never have any conductor inside of the secondary coil form, the risk of internal sparks are just greater.
  • Never use metal to pass through a hole in the side wall of the secondary coil form.

The following examples are all from secondary coils that I have made myself and I have not yet experienced a secondary flash over, despite that some of the coils does not obey the above rules, but this is due to them being relatively “low” voltage systems. Some of these coils would not work in a DRSSTC, but I am showing all these examples for inspiration on terminations.

The first example is from my second DRSSTC, here I have the wire going through a hole inside the top of the secondary coil form and at the bottom there is a brass screw through for the earth connection. I broke all three rules but got away with it because it is a small system.

The second example is from the first Tesla coil I built, a dual 811A VTTC. At the top there is again a hole in the side and the wire goes through and at the bottom there is a solid brass connector glued to the side wall. I broke two rules but still got away with it because a VTTC has a much lower RMS current and voltage than a high power DRSSTC have.

The third example is from my second SSTC, here I have the wire going through a hole inside the top of the secondary coil form and at the bottom there is solid brass connector. I broke two rules but have had no problems despite this coil have pushed 2 kW through and in peaks up to 4 kW.

The fourth example is of my third  SSTC and is a design with broken rules, but measures are taken to make up for it. The wire at the top is inside of the secondary form through a hole, but the top have been filled out with epoxy casting. The bottom has a hole through, despite I used a nylon screw there is still a hole making it easier for flash over to find a way. This is however not a big problem with a low power SSTC.

The fifth example is of my first DRSSTC and here I did a proper job on the terminations to ensure the best possible insulation, mechanical strength and for it to be practical. The top wire is led through a slit in the secondary form to the top across a end cap of acrylic plastic. It is soldered to a rounded brass connector that has a banana male connector that fits into a female connector on the topload. The wire at the bottom is soldered to a piece of copper strip with brass connector soldered on to. This is a optimal design with end cap, no broken rules, rounded surfaces and good mechanical strength and considerations to make it easier to assemble and disassemble.

The sixth example is of my third DRSSTC which is a large and high power coil. The top wire is guided to the top in a deep and very rounded curve slit in the secondary coil form and end cap material, it ends up screwed into the large aluminium topload holder. At the bottom there is a copper strip with a large brass connector soldered to it. Only thing missing here is a closed end cap at the top, but we did not have any material large enough to close the hole.

 

Failure modes of secondary coils

This example is from Michael, a user on 4hv called crashstudio, and he describes the what lead up to this failure, but the main culprit here could just aswell be a damaged secondary form or a spark that stroke through the secondary varnish layer, which seems to be thin.

There were 2 factors that contributed to the failure.
1- I ran the secondary winding leads through the inside of the coil form, so the connections to toroid and ground were both inside.
2- I literally forgot to complete the insulation of the 2 connections.
So with the added power of the industrial capacitors, the spark length was far greater than the 23 inches it needed to arc inside the coil form.

 

Life cycle of secondary coils

A secondary coil feels like a living organism as the plastic form changes shape and stiffness by temperature and so does the varnished windings. When lifting a heavy secondary coil it can be felt that the wire is not sticking to the secondary form or you can hear it expand and contract if moved between places of different temperature.

Transportation is a major culprit in secondary failures as here you get bumps and scratches in the varnish and these weak points could be the start of the end.

Some people have hundreds of run hours on their secondaries, but eventually they will fail and mostly around the bottom or near the ground connection.

 

References

[1] Coil calc with Medhurst & G3YNH, 04.11.2017, http://g3ynh.info/zdocs/magnetics/appendix/hb9dfz/Mathcad_Coil_calc_w_Medhurst_et_G3YNH_131014.pdf

[2] “An introduction to the art of Solenoid Inductance and Impedance Calculation”, “Part II Solenoid Impedance and Q”, David W Knight, Jan 4th 2016. http://g3ynh.info/zdocs/magnetics/SolenoidZ.pdf

[3] “H. F. Resistance and Self-Capacitance of Single-Layer Solenoids”, R G Medhurst (GEC Research Labs.). Wireless Engineer, Feb. 1947, p35-43; Mar. 1947, p80-92. + corresp.; June 1947, p185; Sept. 1947, p281.

[4] IEC 60317-0-1:2013, “Specifications for particular types of winding wires – Part 0-1: General requirements – Enamelled round copper wire”

[5] Global Polymer Industries Inc. Technical information: http://globalpolymer.com/technical.htm and document: http://globalpolymer.com/documents/uhmw_specs.pdf

[6] Electrical Engineer’s Reference Book, Sep 27, 2002, by M. A. Laughton and D.F. Warne. Table 7.13.

4 Responses to Secondary coil design and construction for Tesla coils

  1. Max says:

    Hello !
    Can I use a resin of inclusion (polyester GTS) for the secondary varnish?

  2. Mads Barnkob says:

    Hi Max

    It is detailed and described in this article under the head line “How to insulate the secondary coil with varnish”

    Kind regards
    Mads

  3. Max says:

    Yes I’ve already read ^^
    I just want to know if this resin especially Could work ? ( resin of inclusion gts polyester)

  4. Mads Barnkob says:

    Hi Max

    It will properly work just fine, but bear in mind that it is only rated for temperatures up to 55 °C. So be sure to check for secondary coil heating and inspect the coil for damages if you have heavy arcing to/from it.

    Kind regards
    Mads

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