## History of the Tesla Coil and its Geometries

The first time I ever heard about a Tesla Coil, was actually while playing the video game Red Alert during my teenage years. In the game, the coil was a powerful weapon which shot massive bolts of lightning at the enemy. Shooting big sparks is actually the main association people have with the Tesla Coil, since that is what modern “coilers” use it for.

However, Nikola Tesla, it’s original inventor, had many practical uses for these high voltage, high frequency coils besides shooting sparks, and it actually came in many shapes and forms, all with their own characteristics and use cases. This article shows how the Tesla Coil evolved over time, and what it was used for.

## Where it all began

In 1887, Heinrich Hertz created the first experimental proof of the electromagnetic waves predicted by Maxwell’s theory. This created a lot of buzz around high frequency currents and sparked Tesla’s curiosity as well, who had up till then mainly been working on his AC motors and transmission system, as is evident from his patent history.

Today we are used to hearing “gigahertz” being thrown around, which is equal to 1 BILLION oscillations per second, while in Tesla’s time 20 to 30 THOUSAND oscillations was considered a very high frequency. The reason is that we have transistors now, which switch on an atomic scale, while bulky mechanical oscillators were used in the late 1800’s, and there was just no good way to make them run much faster.

However, Tesla wanted to push beyond the 30 kHz limitation, and in 1891 he patented his Method and Apparatus for Electrical Conversion and Distribution, in which Tesla described how he created rapidly oscillating currents without a mechanical oscillator:

“I have thus succeeded in producing a system or method of conversion radically different from what has been done heretofore—first, with respect to the number of impulses, alternations, or oscillations of current per unit of time, and, second, with respect to the manner in which the impulses are obtained. To express this result, I define the working current as one of an excessively small period or of an excessively large number of impulses or alternation or oscillations per unit of time, by which I mean not a thousand or even twenty or thirty thousand per second, but many times that number, and one which is made intermittent, alternating, or oscillating of itself without the employment of mechanical devices.” 1

So how did Tesla achieve this impressive feat?

“I employ a generator, preferably, of very high tension and capable of yielding either direct or alternating currents. This generator I connect up with a condenser or conductor of some capacity and discharge the accumulated electrical energy disruptively through an air-space or otherwise into a working circuit containing translating devices.” 2

In other words, Tesla found practical use for Lord Kelvin’s condenser discharge – who he regularly credited 3 – and patented it. Tesla now had a way to create high frequency currents.

The first application of this high frequency setup is found in another patent granted to Tesla in 1891, titled System of Electric Lighting 4. In this key patent, we see the first ever diagram and description of a complete Tesla Coil circuit, and the text contains a revealing passage about the reason why this device was invented:

“For a better understanding of the invention it may be stated, first, that heretofore I have produced and employed currents for very high frequency for operating translating devices, such as electric lamps, and, second, that currents of high potential have also been produced and employed for obtaining luminous effects, and this, in a broad sense, may be regarded for purposes of this case as the prior state of the art; but I have discovered that results of the most useful character may be secured under entirely practicable conditions by means of electric currents in which both the above-described conditions of high frequency and great difference of potential are present. In other words, I have made the discovery that an electrical current of an excessively small period and very high potential may be utilized economically and practicably to great advantage for the production of light.” 5

So the very first Tesla Coil ever was used to produce light using not just high frequency currents, not just high voltage currents, but both high frequency and high voltage at the same time! The Tesla Coil essentially expands the high frequency circuit mentioned earlier with a high voltage step up transformer to achieve “enormous frequency and excessively high potential”.

Another telling passage from the patent text mentions how Tesla noticed that a single wire could be used to light a bulb:

“I have discovered that if I connect to either of the terminals of the secondary coil or source of current of high potential the leading-in wires of such a device, for example, as an ordinary incandescent lamp, the carbon may be brought to and maintained at incandescence, or, in general, that any body capable of conducting the high-tension current described and properly enclosed in a rarefied or exhausted receiver may be rendered luminous or incandescent, either when connected directly with one terminal of the secondary source of energy or placed in the vicinity of such terminals so as to be acted upon inductively.” 6

The diagram in the patent shows two bulbs connected by a single wire (the other end of the coil connected to a conducting wall), and Tesla even shows two custom single wire bulbs which he used in these lighting experiments. All very interesting stuff, and no mention of large sparks yet! So what did this first coil look like? And did it have other uses besides lighting?

## Bipolar coil (1891)

The first drawing of a Tesla Coil are found in Tesla’s 1891 lecture before the American Institute of Electrical Engineers, in which various experiments are shown utilizing the coil, including an extensive study of “discharge phenomena”, or sparks.

Something that stands out immediately is that this coil is placed horizontally, not vertically like “modern” Tesla Coils. Also, there is no “terminal capacitance” on one end, and a ground connection on the other, like you usually see in a Tesla Coil. This setup is what is now known as a “Bipolar” Tesla Coil.

Another interesting fact is that the primary coil is actually placed inside the secondary coil, as can be seen in the image below. Tesla instructed to “introduce it from one side of the tube, until the streams begin to appear.” 7

Modern Tesla Coils have an air core, but these early models had their primary wound on top of an iron core:

“In many of these experiments, when powerful effects are wanted for a short time, it is advantageous to use iron cores with the primaries.” 8

Iron cores increase magnetic fields, resulting in more powerful induction effects. However, these iron cores had a major drawback:

“In these experiments if an iron core is used it should be carefully watched, as it is apt to get excessively hot in an incredibly short time.” 9

And at the end of the lecture Tesla already predicted that using iron cores would become a thing of the past:

“In the present systems of electrical distribution, the employment of the iron with its wonderful magnetic properties allows us to reduce considerably the size of the apparatus; but, in spite of this, it is still very cumbersome.  The more we progress in the study of electric and magnetic phenomena, the more we become convinced that the present methods will be short-lived.” 10

In the lecture, Tesla describes how he used his coil to study, amongst other things:

1. Discharge phenomena
2. Single wire & wireless light
3. HF / HV electrical insulation
4. Impedance phenomena

It is interesting to read that Tesla did not have any math at hand to calculate the ideal primary length and capacitance, he simply said that “the length of the primary should be determined by experiment.”11 Also, no mention of resonance between the primary and secondary is mentioned in the lecture, so it seems like Tesla’s 1891 coil was still a tightly coupled, “normal” induction coil.

Now, was this bipolar coil used often, or only during the 1891 lecture? Well, years later, in an article in the Electrical Experimenter of July 1919, Tesla shared a whole range of bipolar coils and the things he used them for.

It is clear from the picture above that Tesla used this type of coil extensively, and came up with all sorts of ingenious improvement. Further, it is funny to note that Tesla sometimes calls this device a “Tesla Coil”, and other times a “Tesla Transformer” or even a “Tesla Oscillator”.

Some of the uses of these coils mentioned in the article:

• Gas engine ignition
• Wireless
• Ozone production
• Creation of undamped waves

A very versatile device!

After reading all this info, I wondered how big these coils actually were, since size is hard to gauge from the pictures and drawings above. Luckily I found an image of an original coil displayed in the Tesla museum in Belgrade, powering an original Tesla light tube, and which has someone standing next to it, providing a good estimate of the size.

## Conical coil (1894)

After the 1891 lecture, Tesla gave several other lectures on high frequency, high voltage devices, and in 1893 Tesla got involved in developing the world’s first hydroelectric power plant at Niagara Falls, together with George Westinghouse. We see that during that period Tesla filed for several generator, motor, and power transmission patents. However, on the side he kept developing his coil, resulting in the massive conical Tesla Coil shown below.

“This coil, which I have subsequently shown in my patents Nos. 645,576 and 649,621, in the form of a spiral, was, as you see, [earlier] in the form of a cone.” 12

The cone shape was chosen to minimize the potential difference between the turns near the top of the coil, so there was less risk of damaging the insulation of the wires. In his comment, Tesla references two of his most famous wireless energy transmission patents, saying that he first used a conical geometry, and later a spiral one, but that in essence they were one and the same device.

Inspired to “develop electric forces of the order of those in nature”, this conical coil was Tesla’s first to reach 1 million volts:

“The first gratifying result was obtained in the spring of the succeeding year when I reached tensions of about 1,000,000 volts with my conical coil. That was not much in the light of the present art, but it was then considered a feat.” 13

This cone shaped coil was a very significant step in the development of the Tesla Coil, since we now for the first time see an upright coil with one end connected to ground. This is what Tesla had to say about this coil:

“This [Figure 6] shows the first single step I made toward the evolution of an apparatus which, given primary oscillations, will transform them into oscillations capable of penetrating the medium. That experiment, which was marvelous at the time it was performed, was shown for the first time in 1894.” 14

So Tesla was figuring out a way to create waves that could penetrate the surrounding medium, and his setup was as follows:

“The idea was to put the coil, with reference to the primary, in an inductive connection which was not close—we call it now a loose coupling—but free to permit a great resonant rise. That was the first single step, as I say, toward the evolution of an invention which I have called my “magnifying transmitter.” That means, a circuit connected to ground and to the antenna, of a tremendous electromagnetic momentum and small damping factor, with all the conditions so determined that an immense accumulation of electrical energy can take place. It was along this line that I finally arrived at the results described in my article in the Century Magazine of June 1900.” 15

According to Tesla’s words, this coil was the first of his coils to implement a loose coupling between the primary and the secondary, and the reason for this was to allow the secondary to vibrate more freely without being weighed down by the primary, thus allowing for much greater voltages at the top of the coil, resulting in beautiful discharges.

“The discharge there was 5 or 6 feet, comparatively small to what I subsequently obtained.” 16

We encounter this conical coil once more in an 1897 “Electrical Transformer” patent.

Tesla mentions how different shapes can be used for the same purpose:

“Instead of winding the coils in the form of a flat spiral the secondary may be wound on a support in the shape of a frustum of a cone and the primary wound around its base, as shown in Fig. [7].” 17

In another drawing from the same patent, it becomes clear how Tesla intended to use these coils to transmit energy at extremely high voltages over a single wire, stepping it up at the transmission end, and stepping it down at the receiver end to power loads.

In this drawing we also see that a magnetic core is still part of the design.

## Flat spiral coil (1897)

In the same patent discussed above, Tesla mentions that around 1897 he usually worked with flat spiral coils:

“The type of coil in which the last-named features are present is the flat spiral, and this form I generally employ, winding the primary on the outside of the secondary and taking off the current from the latter at the center or inner end of the spiral. I may depart from or vary this form, however.” 18

So Tesla generally used a flat spiral coil, but said other geometries worked as well.

The main reason Tesla started using flat spiral coils was because they better suppressed the sparks, which were essentially losses in the circuit, allowing him to achieve higher voltages:

“In carrying on tests with a secondary in the form of a flat spiral, as illustrated in my patents, the absence of streamers surprised me, and it was not long before I discovered that this was due to the position of the turns and their mutual action.” 19

Another major benefit of using flat coils is that they are relatively safe, since the highest potential terminal is at the center, out of reach:

“Those portions of the wire or apparatus which are highly charged will be out of reach, while those parts of the same which are liable to be approached, touched, or handled will be at or nearly the same potential as the adjacent portions of the ground, this insuring, both in the transmitting and receiving apparatus and regardless of the magnitude of the electrical pressure used, perfect personal safety, which is best evidenced by the fact that although such extreme pressures of many millions of volts have been for a number of years continuously experimented with no injury has been sustained neither by myself or any of my assistants.” 20

The “transmitting and receiving apparatus” referred to in the quote above are from two patents filed in 1897 for a revolutionary “wireless” energy transmission system, which planned to use the earth as a conductor.

From the patent drawing it is clear that iron cores were not longer being used at this point. We also see a new part being introduced: an “elevated terminal… preferably of large surface”. This terminal acted as a capacitance, and Tesla tweaked his circuit so that the point of highest potential would coincide with these elevated terminals:

“It will be readily understood that when the above-prescribed relations exist the best conditions for resonance between the transmitting and receiving circuits are attained, and owing to the fact that the points of highest potential in the coils or conductors A A are coincident with the elevated terminals the maximum flow of current will take place in the two coils, and this, further, necessarily implies that the capacity and inductance in each of the circuits have such values as to secure the most perfect condition of synchronism with the impressed oscillations.” 21

Here we see clearly that the Tesla Coil has officially evolved from a traditional, magnetically coupled transformer, into a resonant transformer, based on resonant inductive coupling. This is a crucial point in which Tesla Coils differ from regular transformers. It’s all about tuning the primary circuit to the secondary, and the receiver to the transmitter.

Bifilar spiral coil

As early as 1893, Tesla already patented a very unique flat spiral coil design, now commonly known as the “bifilar pancake coil”. This coil was wound using two parallel wires, and then connecting the end of one to the beginning of the other wire. This setup resulted in a larger difference in potential between the turns, and therefore a much larger self-capacitance in the coil, with the goal to do away with expensive capacitors altogether, and let the coil itself contain all the capacitance it needs to oscillate at a certain frequency:

“My present invention has for its object to avoid the employment of condensers which are expensive, cumbersome and difficult to maintain in perfect condition, and to so construct the coils themselves as to accomplish the same ultimate object.” 22

However, Tesla kept using capacitors, mainly Leyden jars, in many of his later experiments. So even though the idea behind the bifilar coil is brilliant, it seems like Tesla did not find it useful enough in practise.

## Helical coil (1899)

It’s interesting that we’ve already discussed 3 different coil geometries, none of which resembles the “modern” helical Tesla Coil. So did Tesla himself even use this shape at all? Yes, he sure did, as you can see from the beautifully preserved original below, as displayed in the Tesla museum in Belgrade.

In the picture above we see the familiar thin helical coil shape with a toroid as terminal capacitance, as well as three 10-turn primaries, which could most likely be connected in series to vary the operating frequency of the coil.

While this is the shape that first comes to mind for most people when they think of a Tesla Coil, Tesla did not actually write much or anything about this geometry in particular. However, we do see this coil shape return on multiple occasions in pictures taken around 1899 inside Tesla’s Houston Street and Colorado Springs laboratories. These helical coils are sometimes wide and short instead of thin and tall.

From the pictures above, and especially the Colorado Springs pictures, it seems like Tesla used a wide selection of helical receiver coils for experimentation purposes. Many of them even come without a primary and terminal capacitance, which suggests that this was not the “final form”, but merely a simple-to-put-together version of a coil used for testing purposes. We also see that the Houston Street coils were wide and short, while the Colorado Springs coils were of the thin and tall variety.

## Magnifying Transmitter (> 1899)

We have now arrived at the final and most advanced Tesla Coil ever created: the Tesla Magnifying Transmitter (TMT). This coil, developed in Colorado Springs and patented in 1902, was intended to transmit ultra high voltage electrical energy around the globe, by using the earth as a conductor. In his autobiography, Tesla explained the TMT in the following way:

“It is a resonant transformer with a secondary in which the parts, charged to a high potential, are of considerable area and arranged in space along ideal enveloping surfaces of very large radii of curvature, and at proper distances from one another thereby insuring a small electric surface density everywhere so that no leak can occur even if the conductor is bare.

… this wireless transmitter is one in which the Hertz-wave radiation is an entirely negligible quantity as compared with the whole energy, under which condition the damping factor is extremely small and an enormous charge is stored in the elevated capacity. Such a circuit may then be excited with impulses of any kind, even of low frequency and it will yield sinusoidal and continuous oscillations like those of an alternator.

… Taken in the narrowest significance of the term, however, it is a resonant transformer which, besides possessing these qualities, is accurately proportioned to fit the globe and its electrical constants and properties, by virtue of which design it becomes highly efficient and effective in the wireless transmission of energy. Distance is then absolutely eliminated, there being no diminution in the intensity of the transmitted impulses. It is even possible to make the actions increase with the distance from the plant according to an exact mathematical law.” 23

As you can read in the above excerpt, the TMT was created to reach as high of a voltage as possible by spacing the conductors appropriately and in large circles, an insight he gleaned from working with his flat spiral coils 24, whereas on a modern Tesla Coil secondary the conductors are always wound close together. Also, Tesla’s intention was to minimize “Hertz-wave radiation” (electromagnetic radio waves), because he wanted to focus all the energy of the coil into the earth for his “wireless” energy transmission scheme. This massive coil’s dimensions were such that it would oscillate with the earth’s natural electric charge to enable this energy transmission, as Tesla explains in more detail in a short 1908 article:

“When the earth is struck mechanically, as is the case in some powerful terrestrial upheaval, it vibrates like a bell, its period being measured in hours. When it is struck electrically, the charge oscillates, approximately, twelve times a second. By impressing upon it current waves of certain lengths, definitely related to its diameter, the globe is thrown into resonant vibration like a wire, forming stationary waves.” 25

### Extra coil

But was the only difference between a “regular” Tesla Coil and a Magnifying Transmitter the fact that the conductors were properly spaced? Not exactly. The biggest difference in fact is the addition of another coil into the circuit. Whereas a Tesla Coil has a primary and a secondary coil, the Magnifying Transmitter has a third, freely oscillating coil, which Tesla simply called the “extra coil” (in the patent drawing above).

Tesla explains the purpose of the extra coil as follows in his Colorado Spring Notes:

“It is a notable observation that these “extra coils” with one of the terminals free, enable the obtainment of practically any e.m.f. the limits being so far remote, that I would not hesitate in undertaking to produce sparks of thousands of feet in length in this manner.

Owing to this feature I expect that this method of raising the e.m.f. with an open coil will be recognized later as a material and beautiful advance in the art.” 26

So the extra coil is what allowed the TMT to reach such immense voltages, but how? The primary coil and secondary coil oscillate at an identical frequency and are therefore resonantly coupled. While this coupling is key to induce current from the primary into the secondary, it also weighs the oscillations down. It adds a certain damping factor, since the secondary coil is not 100% free to oscillate as it pleases. Tesla’s brilliant insight here was that he would have a resonantly coupled primary and secondary, but then add an extra coil which is not tuned to the same exact frequency and can therefore oscillate more freely, allowing the voltage to rise to even greater heights.

“It is found best to make [the] extra coil 3/4 wave length and the secondary 1/4 for obvious reasons.” 27

Since we’re talking about geometries in this article, it is also crucial to note that the extra coil had a 1:1 length to diameter ratio. The reason is that a coil’s self-capacitance is at its lowest at a 1:1 ratio, as was later determined through research by Medhurst 28

Anyone who has ever experimented with Tesla Coils know how sensitive the circuit is. For example, if you put your hand close to the coil, the frequency immediately drops due to the extra capacitance your body adds to the circuit, without even touching it! So the lower the self-capacitance, the less the circuit is weighed down, and the higher the voltage rise that is attainable.

### Wardenclyffe

Once Tesla finished up his research in Colorado Spring, he started working on his first full-scale transmitting tower in Shoreham, New York, called the Wardenclyffe Tower. Construction was never completed, and only scattered notebook drawings remain, so we have no idea if Tesla’s groundbreaking wireless transmission system would have worked in practise.

Many “conspiracies” have popped up over time that big industry and banking powers did not want Tesla to transmit “free” energy all over the globe and therefore shut the project down. You often read that J.P. Morgan, who financed the initial construction of the Wardenclyffe tower, said something along the lines of “you can’t put a meter on that”, and therefore cut the funding. In fact, reading this very statement fueled my quest into the world of Nikola Tesla. However, Tesla himself felt that Morgan lived up to all his promises and was not to blame:

“I would further add, in view of various rumors which have reached me, that Mr. J. Pierpont Morgan did not interest himself with me in a business way but in the same large spirit in which he has assisted many other pioneers. He carried out his generous promise to the letter and it would have been most unreasonable to expect from him anything more. He had the highest regard for my attainments and gave me every evidence of his complete faith in my ability to ultimately achieve what I had set out to do. I am unwilling to accord to some small-minded and jealous individuals the satisfaction of having thwarted my efforts. These men are to me nothing more than microbes of a nasty disease. My project was retarded by laws of nature. The world was not prepared for it. It was too far ahead of time. But the same laws will prevail in the end and make it a triumphal success.” 29

However, when one reads the letters between Tesla and J.P. Morgan from that time, it does appear that J.P. Morgan might not have been as helpful as he could have been, and that in the above statement Tesla simply did not wish to speak ill of him in public.

Despite that, Tesla’s energy was not “free”, as some claim. Tesla had to put in thousands of horsepower to kick his transmitter into motion, and even fried the power station near his Colorado lab once because he was using so much energy. However, his system being an open system, like a windmill or solar panel, rather than a traditional closed circuit, it is not impossible to conceive that energy already present in the earth or the ambient medium, which oscillated at the same frequency, could be resonantly coupled in to reinforce his input.

Also, once an oscillating current was established in the earth, a lot less energy would be required to keep it going, just like how you need a lot of power to push someone on a swing, but once they are going you only have to give a tiny push to keep them swinging about.

Magnifying Transmitter Design Sheet
The TMT is a complex device and therefore harder to replicate than a Tesla Coil, which is why I was ecstatic to find a Colorado Spring Magnifying Transmitter Design Sheet, created by Simon from Tesla Scientific. There are designs for several operating frequencies, and you can even request a custom frequency design. Click here to check it out.

## Modern coils

After discussing the Magnifying Transmitter and its bold purpose to transmit power across the globe, it feels like a gigantic step backward to now talk about how modern “Coilers” apply some of Tesla’s ideas, simply to create big sparks and light fluorescent tubes in their hands. However, this is the current state of the Tesla Coil, and the reason why many people are unaware of the original grand purpose of these coils.

On a positive note, thanks to the active coiling community, modern Tesla Coil calculators like TeslaMap have emerged, which make coil calculations a whole lot easier. These coils are almost exclusively helical coils with one terminal grounded and a toroidal terminal capacitance on the top end.

Another very interesting development is that today’s Tesla Coils are not always powered by spark gaps anymore, like in Tesla’s time, but often by electronics. Such coils are called Solid State Tesla Coils (SSTC), or Dual Resonant Solid State Tesla Coils (DRSSTC), and their circuit diagrams are mental, but work very well.

The only thing I find funny is that the community’s general solution to creating larger sparks is to add more turns on the secondary and push more power through the circuit, while a much smaller coil, designed according to the Magnifying Transmitter specifications, would result in way larger discharges.

## Closing thoughts

The goal of this article was  to clear up some of the confusion surrounding the use cases for these high frequency, high voltage coils, as well as to show the various stages of development they went through and the different shapes they came in, as each of the geometries had their own pros and cons. Tesla himself called his Magnifying Transmitter his best invention, and solely based on that fact it is worth researching in more detail, which I plan to do in the future.

I hope you enjoyed this little journey through time! In my next article I dive deeper into the various electrical transmission systems Tesla devised over his lifetime.

## Tesla Hairpin Circuit Replication & Experimental Results

After more than a year of research and development, I am excited to finally share my Tesla Hairpin replication and experimental results! I share things that worked, and things that didn’t work, as well as why. This article also contains a detailed parts list, so you can easily replicate my setup and experiments.

This article will be pretty hands on, and assumes you have read my foundational articles, A Brief History of the Tesla Hairpin Circuit and Impedance, the Skin Effect, and their Implications in High Frequency Circuits. If you haven’t, I highly recommend you check them out first, as we will build upon that knowledge here.

## Why the Hairpin circuit?

You might rightly ask yourself why I spent so much time researching this seemingly simple circuit. Isn’t it obvious what it does? It clearly isn’t, judging from the lack of proper replications out there and the unsubstantiated claims around this device. But isn’t the Hairpin overshadowed by the much more impressive feats of the Tesla Coil and Magnifying Transmitter? Sure, but these devices have different purposes, and their working cannot be understood properly without first understanding the Hairpin, out of which these more advanced devices evolved. Thoroughly understanding the Magnifying Transmitter, Tesla’s “best invention”, is what made me start this journey, and the Hairpin is the first step of the way.

## My journey so far

My journey started when I watched a 10-part series of YouTube videos where Karl Palsness presented his Hairpin replication. He showed single wire energy transmission over a very thin wire, a bulb lit while submerged in water, and Karl touching the copper bars without getting hurt, even though thousands of volts pulsed through the circuit, a result he attributed to “scalar waves”. I was very impressed!

I did my best to find out more about his particular setup, and found an article on Transformacomm in which many practical details were shared. The article mentions the following parts:

Nothing fancy there! This gave me the confidence to create my own replication, even though all I had seen or read about this circuit was contained in the Transformacomm article and the previously mentioned video series. I purchased the same capacitors Karl used, the first affordable 10kV power supply I could find, copper bars of similar dimensions, and attached a basic spark gap consisting of two bolts facing each other. The end result can be seen in the picture below.

Unfortunately, the circuit did not work. In fact, the spark gap even refused to fire! I asked for help on the Energetic Forum and simultaneously started to perform more research, since I felt my knowledge, even of basic electrical concepts, was severely lacking.

Based on what I learned, I continually tweaked and improved my Hairpin, until I was able to perform a true replication of Tesla’s experimental results, at which point I had upgraded every single part of my initial circuit…

## The right power supply for the job

As mentioned previously, Karl Palsness used a 10kV oven transformer, and I naively thought that all transformers are the same, which is why I ended up buying the first affordable 10kV transformer I could find: a Seletti 10kV neon sign transformer (NST).

I was impressed when I connected the transformer to my super simple spark gap and saw sparks flying across, but was sorely disappointed when I added the rest of my Hairpin circuit to the mix, and all sparking ceased. Why did this happen? The main difference between the transformer Karl used versus mine, is that his ran at 60Hz and mine at no less than 34kHz!! This turned out to make all the difference in the world.

Soon after my post on the Energetic Forum about this issue, I came across the concept of capacitive reactance (explained in detail here), which makes capacitors let more current “through” the higher the frequency of that current. This is the same effect high-pass filters use in audio applications.

In other words, the 34kHz current coming from my NST was not charging the capacitors and then discharging these capacitors through the spark gap, but instead, due to capacitive reactance, the high frequency input current directly passed through the capacitors, creating a short circuit, and preventing the gap from firing at all.

My first idea was to try to reduce the 34kHz current to a lower frequency. One of the solutions I came across was to use a full-wave bridge rectifier (FWBR) setup to convert the alternating current to a direct current, and so I purchased some high voltage, high frequency rectifier diodes, which were capable of withstanding 100mA at 30kV. I created my bridge setup, as shown in the image below, and I was excited that my spark gap finally fired, albeit with a deafening noise (DC sparks are apparently louder than AC sparks).

Before my excitement had fully settled in, sparks already started to fly from one side of a diode to the other side, causing it to catch on fire… This wasn’t going to work: the only way forward was a lower frequency power supply.

On AliExpress I found a proper 10kV neon sign transformer which ran at the European power line frequency of 50Hz. This one also specifically mentions “no GFI”, which stands for Ground Fault Interrupter. A GFI shuts off an electric power circuit when it detects that current is flowing along an unintended path. So a GFI makes an NST safer, but in the case of a Tesla circuit, it can also prevent your device from functioning properly, which is why a “no GFI” NST is recommended. This does mean you have to be extra careful of course.

When I received my NST a few weeks later, it turned out they shipped me a 15kV version instead of the 10kV one I ordered. First I was annoyed, because I thought I might now not be able to achieve the same results as Karl Palsness, but then I read the following words by Nikola Tesla:

“A large capacity and small self-inductance is the poorest kind of circuit which can be constructed; it gives a very small resonant effect.”1

And:

“The higher the tension of the generator, the smaller need be the capacity of the condensers, and for this reason, principally, it is of advantage to employ a generator of very high tension.” 2

In other words, a small capacity and large inductance is preferable, and the higher the voltage of an NST, the higher the inductance, since more turns of wire are used. So in the end, a 15kV transformer should actually achieve even better results than a 10kV one. And indeed, it worked like a charm!

While my new 15kV NST produced beautiful sparks through my simple spark gap, I was not getting the same results Tesla described:

“When a large induction coil is employed it is easy to obtain nodes on the bar, which are rendered evident by the different degree of brilliancy of the lamps.” 3

My Hairpin did not show any nodes; it simply showed a maximum voltage, minimum current near the bottom, and maximum current, minimum voltage near the top of the bars, which is to be expected if you compare the Hairpin to a shorted transmission line.

However, I figured that if the spark hit the other side of the gap with enough force, it would shock the circuit into a higher order resonance, creating the enigmatic “nodes on the bar”. I took one good look at my current spark gap, consisting of two opposing bolts glued to the wooden base, and I knew that this was not a setup worthy to be called a true replication of Tesla’s work.

I knew Tesla had experimented with some advanced spark gap designs, and so I decided to perform a detailed literature analysis to figure out which type of spark gap Tesla used in his original Hairpin demonstrations. After much research, I came to the conclusion that it was most likely an air quenched spark gap, of which I then created a modern replication.

This spark gap functions really well, as long as you keep the tips of the aluminum electrodes clean. I was able to push the spark gap distance to over 25mm, which significantly increased the rate of change of voltage in the circuit, and therefore led to more impressive impedance effects. However, still no nodes on the bar, and so I looked at the next possible culprit: the bars themselves!

## Thicker bars

Thanks to my new NST and improved spark gap, my Hairpin was functioning quite well, but the “nodes on the bar” Tesla mentioned were still not showing up. By now I had a hunch that the skin effect, also referred to as the “thick wire effect”, might have something to do with the nodes, and so I looked into ways to maximize this phenomenon. It turns out that the ticker you make the bar, the larger its surface area becomes, and the more pronounced the skin effect will be. I then read the following words by Tesla:

“The thicker the copper bar… the better it is for the success of the experiments, as they appear more striking.” 4

I decided that it was time to make a trip to the hardware store for a thicker bar! My original bar was a 12mm copper pipe, which I upgraded to a 22mm copper pipe of about 220cm in total.

## Shorter connections

While upgrading my Hairpin’s copper bar, I also decided to upgrade some of the wired connections in the circuit, since I was afraid that part of the wave generated by the spark gap was reflected back due to an impedance mismatch. To learn more about impedance mismatches, I strongly recommend you watch the following highly informative video:

I initially used the excess high voltage wires from 10kV Seletti NST to connect each component. However, these wires were not rated for the 80kV surging through my circuit, and so I considered using multiple wires instead of a single wire for some of the connections. While using more wires lowers impedance, it is even more effective to do away with the wires completely, and so I connected my capacitors directly to the base of the bar, similar to the Karl Palsness setup.

## Achieving resonance

While describing the Hairpin experiment during his 1893 lecture, Tesla mentioned that “electrical resonance… has to be always observed in carrying out these experiments.” 5. However, I did not really know what electrical resonance meant and how to achieve it in this circuit, so I sort of skipped over it. Then I started watching some YouTube videos of other experimenters who replicated the Hairpin circuit, and came across the highly informative circuit analysis below by Fred B.

In this video, Fred shows us that the Hairpin circuit can be simplified into an LC circuit, which is a very common type of circuit capable of generating oscillating currents when in resonance!

Resonance occurs at a specific wave frequency, where the inductive reactance of an inductor becomes equal in value to the capacitive reactance of a capacitor, resulting in nearly zero impedance 6.

Pfew!! That’s a lot of terminology being thrown around… just remember that when a circuit is resonating, the current oscillates between the inductor and the capacitor, as explained in the video below.

So to establish resonance in a circuit, there are three essential components to take into account:

1. Inductance (L)
2. Capacitance (C)
3. Frequency (F)

This is captured in the formula for the resonant frequency:

Now, since we are using an off-the-shelf neon sign transformer which runs off of mains power, both the frequency and the inductance of our circuit are unchangeable. Therefore, we will have to find the correct capacitor value that will resonate with the inductance of our coil, at the mains frequency of 50 or 60Hz, depending on where on this beautiful planet you live. This proved to be much harder than I had envisioned…

### Finding the ideal capacitor value

Unfortunately, Tesla himself did not specify the specific capacitance values he used in his Hairpin circuit, but in figure 2 we can spot two “six-pack” Leyden Jar capacitors, and from the always trusty Wikipedia we learn that “a typical Leyden jar of one pint size has a capacitance of about 1 nF”, which is equal to 1000pF, while Tesla himself uses 0.003mfd, or 3000pF, as mentioned in his Colorado Springs Notes calculations7.

This suggests that one six-pack of parallel connected Leyden Jars could yield a capacitance of up to 18,000pF. Two of these arrays connected in series, like in the Hairpin circuit, would result in a total series capacitance of 9000pF, which is a lot more than the 17.7pF Lecher used in his circuit, and also way more than the 1000pF my initial UHV-9A caps yielded. The same article also mentions the energy stored in a Leyden Jar “may be as high as 35,000 volts.” If we again place two of these arrays in series, the combined voltage rating of the capacitors could be an impressive 70kV, again, much more than the 24kV Lecher discharged. This makes sense, because while Lecher merely studied resonance effects and therefore did not need as much power, Tesla tried to achieve the highest rate of change possible in his circuit to maximize impedance effects.

Since I had not much to go on, I simply used the same capacitors Karl Palsness used in the first version of my Hairpin replication, which were two UHV-9A caps rated at 40kV 2000pF, without having any clue as to why he used these particular values. Since these two capacitors are placed in series in the Hairpin circuit, the effective total capacitance is 1000pF. So is this the capacitance required to resonate with my 15kV 50Hz NST?

According to the Fred B video discussed earlier, a 15kV 60Hz NST requires ~1.8nF, or 1800pF, to achieve resonance. This was almost twice the amount of capacitance my two caps were providing! However it is not completely clear from the video how he arrived at this figure, and my NST runs at 50Hz instead of 60Hz, which is why I decided to measure the inductance of my NST, so I could calculate the ideal capacitor value myself.

I tried three different ways to measure the inductance of the NST’s secondary coil, but despite numerous attempts, I got such wildly different results that I could not rely on their accuracy. I then bought an LCR meter, but the inductance of my NST appeared to fall outside of the range of the meter, resulting in overload errors on the display.

Finally I thought, why not use one of the available Tesla Coil design calculators out there, since they also include calculations for ideal capacitor size. Below you find the calculators I used and the results:

Very interesting results, and all way higher than the 1000pF Karl Palsness used and the 1800pF Fred B suggested in his video, even when we take into account that they run their circuits at 60Hz instead of the 50Hz NST I used in these calculations. But why does TeslaMap give us a value that is so much higher than the other two calculators?

This is because the value TeslaMap returns is a so called Larger Than Resonant (LTR) capacitance, which is explained as follows by Kevin Wilson from TeslaCoilDesign.com:

“A resonant sized cap can cause a condition known as resonant rise which causes voltages in the primary circuit to increase far above normal levels. These high voltages can easily damage a NST, so NSTs should only be used with Larger Than Resonant (LTR) primary capacitors. To minimize the risk of a resonant condition in the primary circuit I use a MMC at 1.618 times the resonate size. The ratio of 1:1.618 is known as pi or the golden ratio. Any two numbers in this ratio will have the fewest common multiples which will result in virtually no chance of resonance. ” 8

Wow, “virtually no chance of resonance” is not what we are aiming for here! Of course he has a point, because resonant rise is definitely a real thing, and can result in hundreds of kilovolts running through your circuit, even though your input is “only” 15kV 9. However, the spark gap essentially acts as a current limiting device in the Hairpin circuit, protecting your capacitors from overvoltage, as long as you don’t make the spark gap too wide.

Still, at these enormous pressures, there is always a risk of damaging your NST and capacitors. But if you’re aiming to replicate Tesla’s original experiments, and Tesla says that “electrical resonance… has to be always observed”, it doesn’t make any sense to me to pick a capacitor size “which will result in virtually no chance of resonance”! And I will mention here again what Tesla said about using a large capacitance:

“A large capacity and small self-inductance is the poorest kind of circuit which can be constructed; it gives a very small resonant effect.” 10

Since the LTR size is 1.618 times the actual capacitance required for resonance, this means TeslaMap calculated 10300pF / 1.618 = 6388pF to be the ideal size, which is exactly in between the results of the other two calculators, and so I assumed that this was a good value to aim for.

### Finding the ideal capacitor

Now that I knew what value to look for, the next challenge was to find and procure two capacitors with (approximately) this value when placed in series, which could also withstand the extreme voltages present in the circuit. You essentially have three options:

1. Purchase two big and expensive capacitors
2. Assemble a Multi-Mini Capacitor (MMC)
3. Build your own capacitors from scratch (e.g. Leyden Jars or variable capacitors)