## How to build a Tesla coil. Design, theory and compromises!

A live broadcast that I did on Sunday, February 4, 2018 with focus on designing Tesla coils with special focus on the DRSSTC topology. Questions …

## How I came to build a 4 meter spark generating Tesla coil, a technical story from 2008 to 2016.

Here is the recording of the live stream I did on 2018 January 31, Wednesday at 2000 CET, I performed a live stream on youtube …

WARNING!: Working with electricity is dangerous, all information found on my site is for educational purpose and I accept no responsibility for others actions using the information found on this site.

## Introduction

DO NOT REPLICATE THIS PROJECT!

If you do anyway, be aware of large switching transients that may damage nearby electronics, read this entire article before proceeding.

The idea to this coil came with Steve Ward showing off his first QCW DRSSTC that used a buck regulated DC supply to ramp up the supply voltage along with a long on-time to grow straight and very long sparks compared to the secondary coil length.

I thought it could be done simpler, yet with less control, by using the rising edge of 50 Hz mains supply voltage. From start of the sine wave to the top it corresponds to a on-time of 5000 uS and to be able to use large IGBT bricks the frequency would have to be kept down. Sword like behaviour of sparks is however mostly seen at above 300-400 kHz, where as lower than that results in more branched sparks.

## Considerations

A high impedance primary circuit is needed to keep peak current at a level that the IGBTs can handle to switch for very long pulses, for a DRSSTC, up to 5000 uS. In order to get enough primary windings, I went for a upside-down U shape primary as a regular helical coil with high enough coupling would quickly get as tall as the secondary coil itself.

To use 3 IGBT bricks in parallel it is important to ensure as even current sharing as possible, this is done by mounting them close to each other on the same heat sink, drive them from the same gate drive transformer with individual gate resistors matched as close as possible.

Steve Wards universal driver 2.1b only has a robust enough 24 VDC section to run up to about 300 uS on-time with large gate capacitance, when trying to run with longer on-times than that, the 24 VDC 1.5 A regulator is now longer enough to supply the needed current. A external 26 VDC 8 A power supply is used instead and output stage will have to be reinforced to conduct higher currents and dissipate more heat.

## Specifications

 Bridge 3x  SKM145GB123D IGBT bricks in a parallel half bridge configuration Bridge supply 0 – 260VAC through a variac Primary coil 21 turns of 8 mm copper tubing in a up-side-down U shape MMC 10 strings in parallel of 10 in series Kemet R474N247000A1K capacitors for 0.047 uF at 9000 VDC, 280 A peak and 40 A rms rating. Secondary coil 160 mm diameter, 330 mm long, 1500 windings, 0.2 mm enamelled copper wire. Resonant frequency Around 100 kHz. Topload 100 x 330 mm spun aluminium toroid. Input power 10BPS, 500 cycles, 50A limiter: 750W at 260VAC at 3A. Spark length Up to 500 mm long sparks.

## Schematic

Bridge section

Driver section

Same as Steve Wards universal driver version 2.1b. Just made on single sided PCB without SMD components and the 24VDC part has traces reinforced, MOSFETs heat sinked and uses a external power supply. A external 26VDC / 8 Ampere power supply is used to ensure that under voltage will not be a problem, at least not before something starts to smoke.

## Construction

31st October 2011
I put the bridge together on a heat sink with 3 phase rectifier used with all inputs in parallel for 1 phase supply and connected all 3 half bridge IGBT bricks in parallel with 3 straight bus bars. All recycled components from a DC link inverter.

Designed staccato PCB as the old layout used in my VTTC I was on a vero board. A optical output was added to use the interrupter with a standard DRSSTC driver.

Started construction of the secondary coil.

2nd November 2011

Etched PCB board for staccato controller.

Finished winding the secondary coil. It was made with a total of 1500 turns of 0.2 mm wire and dimensions 160 x 330 mm. Varnished the secondary coil with polyurethane varnish.

3rd November 2011
The secondary coil was given a second thick layer of varnish, not the most pretty job as I tried to pour as much varnish on as possible and let it rotate and settle it around the coil by itself. As the secondary coil was not completely in level it result in a little running, but overall a fair result of adding a lot of thin varnish.

Finished assembly of the staccato controller and bench tested it.

The project got shelved due to starting on a new job, after a long rest of over 3 years the box with parts was once again brought out in the light and construction could continue.

7th March 2015

Etched driver PCB and started populating the board with all passive components.

6th October 2015

Construction of a very cheap MMC from capacitors that was bought from a 10\$ ebay auction for 100x Kemet R474N247000A1K, rated for 900VDC 28 A peak and 4 A rms. A easy and uniform construction, with current sharing in mind, is to construct it around a round piece of wood or plastic tube.

The resulting MMC has a capacitance of 0.047 uF at 9000 VDC, 280 A peak and 40 A rms rating. Which is spot on for this coil to be running with design goal primary inductance of around 100 uH, 300 A peak, 5000 uS on-time and maximum 10 BPS.

11th October 2015

Construction of acrylic primary supports, that has 21 slots and is formed for a up-side down U shape primary coil. A way of getting a large primary inductance and still maintain a certain distance to the topload as the secondary coil is very short.

The supports are made by hand using a saw, file and drill press.

16th October 2015

Getting the coil winded from the inside and out was no easy task, the whole large roll of copper tubing is heavy, easily bends too sharp and is like a spring. It will lock itself in the wrong slots and it can be a very frustrating piece of work. The complete result is however worth the effort, it looks smooth and even.

As the slots was not made to snap the copper tube in, from shear fear of cracking the acrylic, I made a small hole behind each slot that made it possible to tie each turn at each primary support, with a little piece of copper wire it is secured from deforming the coil.

As water cooling of the primary coil is going to be a must with the long on-times, simple clamps was made from copper sheet and two screws the fastens the 4 braided copper flexible wires to the tubing. The same 4 braided copper wires was soldered to the MMC terminals, as even as possible distributed around the circular copper wire terminal.

Having made the MMC on a wooden stick makes it easy to mount with two wooden blocks with holes in for the extra length of the round rod.

29th December 2015

Driver board populated with all active components. 24 VDC regulator is left out as this will be supplied externally from a 26 VDC, 8 A power supply. All traces related to the 24 VDC is reinforced by soldering a 0.5 mm2 copper wire along them. Four 2200 uF 35 VDC capacitors was added to the underside of the board, one at each N- and P-channel MOSFET. All output stage MOSFETs have heat sinks mounted.

All these precautions are hopefully enough to ensure no under voltage or over heating situation is possible when running at 5000 uS on-time.

25th July 2016

The coil have been put together with power supply, bridge, driver, platforms, secondary and topload. Two fuse holders for large bussman fuses was used at the end of the flexible copper braids for primary tap.

7th October 2016

First test of the coil after all the components have been put together, there are still a few things not in place, but it is good enough for initial testing.

The first test is without power on the DC bus. This is solely to test if the driver and power supply is good enough to drive the 3 IGBT bricks’ gates in parallel with a satisfying gate waveform. The following oscilloscope shots show the coil being driven at 5 ms on-time at 100 BPS, corresponding to every rising edge of the half wave rectified 50 Hz mains supply.

The following months, where I had only little time to do more testing, I could not get the coil to run properly with power on the DC bus. I could measure oscillation at the resonant frequency, but nowhere near enough for the coil to actually produce a output ever so slightly or just so small as to light up a close by fluorescent tube.

I tried running the coil with added 6000 uF capacitance, with normal interrupter, with and without DC bus snubber capacitor, with much fewer primary windings etc. I did a lot of changes to it, so it would be more like a regular DRSSTC, than a QCW, little did it help and I did not get much further before putting it away for Christmas holidays.

26th March 2017

After some online discussions as to what the problem could be, and showing off the coil for the first time, it was suggested that the regular 1:1000 cascaded current transformer for feedback was simply not delivering a strong enough signal as a high impedance coil naturally works with a much lower peak current. From the thread on the forum here https://highvoltageforum.net/index.php?topic=24.0 it is decided that I will try to make a new 1:50 turns ratio current transformer to see if increased feedback will help the coil oscillate.

The only capacitance on the DC bus was a 0.68 uF snubber capacitor, this was also increased to a 10 uF capacitor bank of MKP film capacitors. A small amount of energy storage is needed to make the phase correction driver able to run stable.

First light was achieved with some 20 cm long sparks, remember that the coil is far from tuned for maximum performance and the input voltage was only 200 VAC.

1st April 2017

I made a wide range of secondary and primary circuit measurements to find the resonant frequencies, as the U-shaped primary makes it difficult to simulate with tools like JavaTC.

The measurements was done with secondary in place inside the primary. But secondary ground was unconnected and primary circuit was left open loop by removing the tapping point. I am not sure if this is the correct method, as resonant frequencies are much different when measured with secondary ground or primary loop closed, this is because energy is then transferred between the two resonant systems. The results could however vary with 10-20 kHz compared to the open loop measurements…

Secondary circuit test results
Setup with a 80 cm long wire with 3 bend wires hanging over and pointing down to be “branches”. Signal from signal generator connected to ground terminal on the secondary coil, ground left floating. Signal into oscilloscope captured from open loop probe hanging next to secondary coil.

Unloaded result: 101 kHz, 80 cm wire result: 91 kHz and 80 cm wire with branches result: 88 kHz.

Primary circuit test results
Setup with signal generator and oscilloscope connected across the primary LC circuit and with a jumper across the IGBTs to have a closed loop. Signal generator is connected through a 10K resistor.

Primary resonance with secondary ungrounded – 7th turn from bottom 102kHz, 6th turn from bottom 96kHz, 5th turn from bottom 90kHz and 4th turn from bottom 86kHz.

Rest of the measurement results did not have individually saved oscilloscope shots, so here is a overview of the primary tapping frequencies.

I recorded video from oscilloscope and spark formation (dark dark video, blerg, sorry). There are 4 tests where primary is tapped at 96 kHz, 90 kHz, 86 kHz and last at 65 kHz, where it for reasons I still do not fully understand, performed the best! This is a huge detuning compared to the loaded 88 kHz secondary measurements. I also tried all the taps between 86 kHz and 65 kHz, with only increasing performance until I could detune it no further.

The staccato interrupter is not particular stable and does not really give a good clean 5ms on-time, it starts conducting before the zero crossing, possibly due to non-adjusted phase correction on the driver, this will get looked into next time its running. Waveforms are highly distorted, peak currents are low in the magnitude of 50 A peak. (Blue 100V/div inverter output – Yellow 100A/div current – 5-6 ms on-time)

and also some close up pictures of the beautiful sparks, still much shorter than what I expected, but maybe the very high impedance primary circuit just limits the current way too much, future experiments would be with a step up transformer for a higher primary peak voltage.

4th April 2017

From last nights experiments, I think that this idea might work on a small scale, the peak currents drawn by this large coil simply creates too large switching transients.

I tried tuning the coil at 120 kHz and 130 kHz, way above the estimated loaded secondary resonant frequency of 88 kHz. It performed better than ever before at 120 kHz tap, which properly makes a little sense compared to the better performance at 65 kHz, it certainly does seem to be a harmonics pattern here. But I do not think I can tap it any further down on the inner side of the primary coil right now.

There was however also much higher current draw, loud clunks from the variac and lights dimming! The voltage spikes on the mains supply are at levels where my voltmeter was damaged in my variac. This is also why I call quit on the project as it is, its future will be rebuilding it to a conventional, properly PWM controlled, QCW.

I had sparks fly out to about 50 cm as it can be seen in the video

## Conclusion

So far the prototype has worked and shown that the concept works. The spark formation is more straight than first anticipated, as most QCW coils operate above 300-400 kHz to get long sword like sparks. It is however clear that the sparks produced by this coil, resonating below 100 kHz, is swirling a lot.

Tuning is very different from a regular DRSSTC where the sweet spot that produces the longest sparks at the lowest current can be within a few centimetre on the primary coil. Here I could get the same performance over a wide span of 60 kHz, tapping the primary anywhere would give me around 30 cm sparks, but it was easy to recognize when a true sweet spot was found, as the very abrupt current draw could be heard clearly from the variac clunking loudly and lights dimming slightly.

The switchings transients are however a great danger to nearby electronics and is of a magnitude where filtering is properly not enough, certainly it is not a solution to add more passive components to counter a problem that can be completely eliminated by using a different topology and have a control scheme that can control a ramped voltage from a capacitor energy storage, like the class D amplifier, phase shifted or PWM controlled QCW coils demonstrated by other Tesla coil builder.

I wanted to try this method, to see if simplicity could do the same job, it could not.

## Demonstration

There is not a overall demonstration video yet, but the 3 videos from research development above.

# Secondary coil design and construction for Tesla coils

Published on: Jun 3, 2015. Last updated: Feb 14, 2019.

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 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.

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. In the following equations inductance L is given in Henry, capacitance C in Farad and frequency F in Hertz.

$F_{resonant}=\frac{1}{2\cdot \pi \cdot \sqrt{ L_{secondary} \cdot C_{topload} }}$

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. r is diameter.

$\Xi_{factor} = \frac{\pi \cdot r^{2}} {\pi \left ( r^{2} \cdot \left ( r - \delta \right )^{2} \right )}$

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.

 spacing →  Ratio ↓ 1 1.11 1.25 1.429 1.667 2 2.5 1 5.55 4.1 3.17 2.47 1.94 1.67 1.45 2 4.1 3.36 2.74 2.32 1.98 1.74 1.5 4 3.54 3.05 2.6 2.27 2.01 1.78 1.54 6 3.31 2.92 2.6 2.29 2.03 1.8 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.

 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
 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.

 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.

 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.

 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.

 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.

 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.

Here is some other secondary coil failures where the high voltage have punched through the secondary coil form or arced on the inside.

A faint flash-over on the inside.

A huge and brutal flash-over on the inside.

A huge and brutal flash-over from a internal ground connection has left carbon tracks all over the inside of the secondary form.

All of the above, small as large carbon tracks through the secondary coil form is just as bad, it is ruined and needs extensive repairs or just has to be discarded.

### 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.

# Spiral coil calculator

Here you can calculate the inductance for a given size of a spiral coil wound in one layer. It is optional to add the capacitance for f.ex. a primary tank capacitor or topload capacitance to find the resonant frequency of the LC circuit.

The formulas used to derive the inductance is simplified and correct to within 1%. Source “Harold A. Wheeler, “Simple Inductance Formulas for Radio Coils,” Proceedings of the I.R.E., October 1928, pp. 1398-1400.”

Switch between the input fields to automatically calculate the values.

 Number of turns Turns Inner diameter mm Wire diameter mm Turn spacing mm Outer diameter mm Wire length m Inductance uH Optional extra f.ex. tank capacitance size Capacitance nF Resonant frequency kHz

Formulas used

Outer diameter = inner diameter + ( 2 * number of turns * ( wire diameter + wire spacing))

Wire length = ((Pi * number of turns * (outer diameter + inner diameter)) / 2) / 1000

Inductance
Width w = ((wire diameter / 25.4) + (wire spacing / 25.4)) * number of turns
Radius r = ((inner diameter / 25.4) + w) / 2
Inductance = (radius^2 * number of turns^2) / (8 * radius + 11 * width)

Resonant frequency = (1 / (2 * pi * sqrt((inductance / 1000000) * (capacitance / 1000000000)))) / 1000

# Helical coil calculator

Here you can calculate the inductance for a given size of helical coil wound in one layer. It is optional to add the capacitance for f.ex. a primary tank capacitor or topload capacitance to find the resonant frequency of the LC circuit.

The formulas used to derive the inductance is simplified and correct to within 1%. Source “Harold A. Wheeler, “Simple Inductance Formulas for Radio Coils,” Proceedings of the I.R.E., October 1928, pp. 1398-1400.”

Switch between the input fields to automatically calculate the values.

 Coil diameter mm Number of turns Turns Wire diameter mm Turn spacing mm Wire length meters Coil height mm Inductance uH Optional extra f.ex. tank/topload capacitance size Capacitance nF Resonant frequency kHz

Formulas used

Wire length in meters = ((coil diameter * pi) * number of turns) / 1000

Coil length in mm = number of turns * (wire diameter + turn spacing)

Coil inductance in uH = (number of turns * (((coil diameter / 25.4) / 2)*((coil diameter / 25.4) / 2))) / ((9 * ((coil diameter / 25.4) / 2)) + (10 * (coil length / 25.4)))

Resonant frequency in kHz = (1 / (2 * pi * sqrt((inductance / 1000000) * (capacitance / 1000000000)))) / 1000

# Coil winding machine

## Introduction

A coil winder is essential when it comes to making a beautiful coil on large forms.

It takes considerable less time to wind large coils and varnishing the coils while they are rotating gives a much better finish.

## Considerations

Control of speed and acceleration is key issues when building a coil winder.

The best choice is to get a Variable Frequency Drive meant for 3 phased asynchronous induction motors, especially if the motor have a gear.

With a VFD it is possible to control the speed with a potentiometer, control start and stop with a single push and hold button and control ramp up and down times.

Having both hands free to guide the wire onto the form is important

## Construction

27th March 2010

With materials at hand the motor was secured to a horse with a custom drive wheel with a rubber band to get contact to the form. A gear is attached to the motor with the ratio of 1:14, this makes it possible to run the motor at higher speeds with the VFD. Running at speeds close to its native speed makes cooling more efficient as its self cooled from the rear fan.

The form is pressed against the roller wheels which keeps the form in place.

Controlling the winders motor is done with a Siemens Micromaster Vector 0.37kW VFD, a potentiometer is used to adjust the speed and a foot pedal is used for start / stop.

## Conclusion

The machine was built without buying any new materials and is quickly put aside as the rollers are hold to the horses with welding clamps.

Further improvements could be a turn counter and automatic wire guide, but with the relatively low number of large coils I make there is other fields I like to focus on.

## Demonstration

A time lapse movie of me winding 0.25 mm wire on a 160 mm diameter form.