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Tesla Hairpin Circuit Stout Copper Bars Replication

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.

Version 1 of my Tesla Hairpin replication
Figure 1. Version 1 of my Tesla Hairpin replication

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).

30kV full-wave bridge rectifier (FWBR)
Figure 2. 30kV full-wave bridge rectifier (FWBR)

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!

Spark gap upgrade

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.

Half wave standing wave pattern on a 1/4 wave shorted transmission line
Figure 3. Half wave standing wave pattern on a 1/4 wave 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.

Super simple static spark gap
Figure 4. My super simple static spark gap

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.

Tesla air quenched spark gap replication
Figure 5. My air quenched spark gap

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.” 3

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.

Capacitor connection
Figure 6. Capacitor connection

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.” 2. 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! 

Hairpin circuit simplified into a resonant LC circuit, energized by the primary of the transformer
Figure 7. Hairpin circuit simplified into a resonant LC circuit, energized by the secondary of the transformer

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 4.

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:

resonant \thinspace frequency \thinspace in \thinspace hertz = 1/2\pi \sqrt{inductance \thinspace in \thinspace henries \times capacitance \thinspace in \thinspace farads}

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 calculations5.

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. ” 6

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 7. 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.” 8

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)
MMC capacitor bank, source: hvtesla.com
Figure 8. MMC capacitor bank

A MMC consists of several high voltage capacitors connected in series and parallel to achieve the desired capacitance and voltage rating, and is very popular under Tesla Coilers. TeslaMap has a nice tool to help you create one. However, it seemed like an awful lot of work to create these, and while MMC’s are known to be cheaper than purchasing a single big capacitor, two MMC’s with the capacitance and voltage rating I was looking for would cost me well over $200!

For these reasons I decided to settle for a cheaper and much simpler approach: purchasing two 40kV 10000pF capacitors. This yielded a series capacitance of 5000pF, which is a significant improvement over the 1000pF I was using at the time, and came close enough to the 6300pF we were aiming for to see if it had any positive effects on the results of the experiment. Not ideal, but at least this Less Than Resonant capacitance provided my caps and NST with some extra protection from damage due to voltage spikes caused by extreme resonant rise effects, while heeding Tesla’s advice to use a capacitor that is smaller rather than larger.

However, I did not get to perform many experiments with these brand new caps, because one caught fire after just 10 seconds of operation… Guess polystyrene film capacitors are just not up to the job.

Capacitor burned through after 4 seconds of operation
Figure 9. Blurry image of exploded capacitor

During that brief instant of operation, I noticed that the sparks in my gap were a lot “fatter” when using this larger capacitance (see video below), implying more current was being passed. I do not know, though, if this is preferable, since it appears that the goal is to maximize the time rate of change of voltage, and not necessarily of current. I could be wrong, and more testing is required to confirm this suspicion.

So while I am still unable to tell you what the perfect capacitor value is for a 15kV NST, my capacitor fund was empty after the explosion of my higher value ones, and so I was forced to switch back to using my original UHV-9A capacitors. Luckily, these capacitors perform very well, and easily achieve resonance in the circuit, although an ideal capacitor might offer more power throughput.

Replicating Tesla’s experiments

Now that almost every part of my Hairpin circuit was upgraded, I felt ready to attempt a replication of Tesla’s original experiments as described in his Philadelphia lecture.

Nikola Tesla hairpin circuit stout copper bars 1893 lecture
Figure 10. Tesla Hairpin experiment from his Philadelphia lecture

“The bars B and B1 were joined at the top by a low-voltage lamp l3 a little lower was placed by means of clamps C C, a 50-volt lamp l2; and still lower another 100-volt lamp l1; and finally, at a certain distance below the latter lamp, an exhausted tube T. By carefully determining the positions of these devices it was found practicable to maintain them all at their proper illuminating power. Yet they were all connected in multiple arc to the two stout copper bars and required widely different pressures. This experiment requires of course some time for adjustment but is quite easily performed.”2

So in this experiment, Tesla used four different incandescent light bulbs:

  1. “Low-voltage lamp” (l3)
  2. 50-volt lamp (l2)
  3. 100-volt lamp (l1)
  4. Exhausted tube (T)

It was not easy to procure these bulbs, since they have an unusual voltage rating, and because incandescent bulbs are no longer sold in Europe. However, the internet is an amazing place, and I was able to purchase the following bulbs to run this experiment with (same order as listed above):

  1. 12V, 10W car bulb
  2. 50-volt, 40W incandescent bulb
  3. 110-volt, 40W incandescent bulb
  4. 8W fluorescent tube

I connected the bulbs to the bar using a lamp fitting wired to two car battery charging clamps, which made them easy to move up and down the bar. When I fired up the circuit, the bulbs lit up, and after some careful adjustment I was able to make all four lights light up at full brightness! Success!!

Experimental results

Below you find a video with all the experiments I ran, including Tesla’s original experiments, as well as me touching the bars, lighting a bulb underwater, and single wire energy transmission.

Besides the experiments in the video, I have some other findings to share. For example, it is preferable to use high-wattage bulbs. So if you have the choice between a 110v 25w, or 110v 40w bulb, go for the 40w one, because it will work better in this circuit. Initially I (naively) thought: “40w requires more power than 25w, so it will be easier to light the 25w bulb.” However, a lower wattage only means that the resistance of the filament is higher, letting less current through, and thus resulting in a lower wattage for the same voltage rating. Higher wattage equals lower resistance, and this has worked better in my experiments.

For a successful result, it is also crucial that you adhere to the order Tesla uses for his lamps, so the lower voltage lamp at the top, and the highest voltage lamp at the bottom. If you change the order around, not all lamps will light up.

It is possible to light a fluorescent tube by simply holding it near the bars, or with a single thin wire connected near the capacitor end of the bar. If you move the tube over the bar from the bottom to the top, you notice that it lights up brightly near the capacitors, and turns off near the top. This is because, when the short bar is connected at the top, the Hairpin functions as a quarter wave shorted transmission line, resulting in a half wave standing wave pattern on the bar. This means voltage is maximum near the capacitors, and minimum near the top, while current is minimum near the capacitors, and maximum near the top, due to voltage and current being out of phase with each other.

In other words, we’re dealing with a single node. The “nodes on the bar” Tesla described in his lectures are possibly higher-order standing wave patterns. To achieve this higher-order resonance, I might need to use an even more powerful NST, since Tesla said:

“When a large induction coil is employed it is easy to obtain nodes on the bar.” 3

For this reason, I was very curious to know the frequency of the waves in my Hairpin. I used a simple frequency counter, which showed a frequency between 45 and 60 kHz.

Frequency counter result
Figure 11. Frequency counter result

I also measured the inductance of my copper bars with an LCR meter, which turned out to be 182.23uH. Since I used 1000pF total series capacitance, the self-resonant frequency equals:

    \[\frac{10^6}{2\pi\sqrt{182.23uH \times 1000pF}} = 372.8kHz\]

This is a lot higher than the frequency measured by my frequency counter. Of course, the larger you make the capacitance, the lower becomes the self-resonant frequency, possibly making it easier to push the bars into a harmonic resonance. For example, using 6300pF capacitance lowers the resonant frequency to just 148kHz. This is worth exploring further.

Besides the frequency, I was curious what the wave actually looked like. However, I was unable to find a good way to connect an oscilloscope to an 80kV circuit without frying it, which is why I simply placed a scope probe close to the bar and fired up the circuit, which resulted in the following image:

Hairpin oscilloscope result shows 50Hz input wave with superimposed high-frequency wave
Figure 12. Hairpin oscilloscope result shows 50Hz input wave with high-frequency wave superimposed upon it

You can clearly see the 50Hz input current, with a high frequency wave superimposed upon it. This is exactly what Tesla described when he discussed using spark gaps to achieve high frequency currents:

“Most generally there is an oscillation superimposed upon the fundamental vibration of the current.” 2

Those were some of the notable observations I was able to make while testing this circuit.

Parts list

In case you wish to replicate my setup, here are the parts I used, with links to where I purchased them:

Concluding remarks

For the past year I have been working towards publishing this article, so I am stoked to finally be able to make it public. I hope that this article, together with my previous foundational articles, will allow you to replicate Tesla’s Hairpin experiments and save you a lot of time, money, and frustration in the process. My research will now focus on the theory and application of the Tesla Coil, and ultimately of the Tesla Magnifying Transmitter. Exciting stuff ahead!

Impedance, the Skin Effect, and how they apply to Nikola Tesla

Impedance, the Skin Effect, and their Implications in High Frequency Circuits

Many of the famous experiments Nikola Tesla performed involved high frequency alternating- or impulse currents. At these high frequencies, something interesting happens: these rapidly vibrating currents pass with great difficulty through a seemingly low resistance conductor. This effect is caused by impedance, or the opposition of a conductor to the flow of alternating current. This article explains impedance in detail, since it plays a crucial role in understanding high frequency circuits, and because the subject has more layers of complexity to it that one might expect.

Let’s start by defining some key terms:

Resistance R: friction against DC

Reactance X: inertia against AC

Impedance Z: combination of resistance and reactance

Of course these short definitions don’t tell you too much, but it does show you that these three concepts are intertwined, and so we will structure the rest of our exploration of impedance around them, starting with the easiest one: resistance.

Resistance

Most people are familiar with resistance, which has the symbol R, is measured in ohm Ω, and is a way to state how difficult it is for a direct current to pass through a conductor. For example, copper has a very low resistance, so you don’t need a lot of pressure (voltage) to push a current through it, whereas lead, which is conductive, has about 12 times more resistance, and therefore requires 12 times more voltage to push the same amount of current through it.

This relation between resistance, voltage, and current is expressed in the formula for resistance:

resistance = \frac {voltage}{current}

Besides the type of material that is being used, the shape of the conductor also has a large influence on resistance. For example, a thin, long wire has a higher resistance than a thick, short wire, just like it is harder to push water through a thin, long straw compared to a short, thick pipe.

It is very important to reiterate that resistance applies to DC currents only, since the opposition against alternating currents is called reactance, which we will cover next.

Reactance

I just mentioned reactance is inertia against AC currents, but more precisely, it is the opposition of a circuit element to a change in voltage, and since AC changes its voltage constantly, reactance mainly applies to AC.

Changing currents, especially of high frequency, have a significant effect both on capacitors, as well as on inductors, so there are two parts to this puzzle:

  1. Capacitive reactance
  2. Inductive reactance

We will discuss both of these in detail, since each produces unique effects that are crucial in understanding some of Nikola Tesla’s experimental results.

Capacitive reactance

When you apply a DC current to a capacitor, the capacitor will simply charge until it reaches the level of the supply voltage. In such a case there is no current at all flowing “through” the capacitor. The flow of current ends on one plate of the capacitor, never reaching the other side. However, when a high frequency current is applied, things change dramatically, as mentioned by Tesla:

“Another equally remarkable feature of high frequency impulses was found in the facility with which they are transmitted through condensers [capacitors], moderate electromotive forces and very small capacities being required to enable currents of considerable volume to pass.” 9

The reason high frequency currents pass through a capacitor with such ease, is because of something called capacitive reactance, which describes the opposition of a capacitor to a change in voltage. The amount of current passed through a capacitor is related to the capacitance and the rate of voltage change, according to the following formula:

current\thinspace through\thinspace capacitor = capacitance\thinspace in\thinspace farads \times \frac {change \thinspace in\thinspace voltage}{change\thinspace in\thinspace time}

Since voltage does not change for a steady DC current, apart from when the current is first switched on, the current through the capacitor equals zero. However, as frequency increases, the rate of change of voltage over time increases, letting more current pass the higher the rate of change.

Some feel it is incorrect to say that currents pass through a capacitor, since electrons do not actually move from plate to plate. However, when I read up on what it is then that causes a current to appear on the other side of the capacitor when high frequency currents are applied, wildly different explanations were offered.

The explanation that made the most intuitive sense to me, was that one could view the dielectric between the capacitor plates as a flexible membrane, that, when hit with a large pressure, can oscillate. This, then, would not actually let any current through, but it would apply pressure to the other side of the capacitor by pushing into it and then retreating again, setting up a wave. This would also explain why a DC current does not create a current on the other side of the capacitor, since a steady pressure does not make the membrane oscillate.

Oscillating membrane
Figure 1. Oscillating membrane

Not sure if this explanation is wholly accurate of what actually happens, but it gives us a decent mental model to understand the behavior of capacitive reactance.

The formula for capacitive reactance itself is:

capacitive \thinspace reactance \thinspace in \thinspace ohms = \frac {1}{2\pi \times frequency \thinspace in \thinspace hertz  \times capacitance \thinspace in \thinspace farads}

If you fill in 0Hz in the above formula, which describes a DC current, capacitive reactance approaches infinity, therefore blocking DC. However, if you fill in higher and higher frequencies, capacitive reactance starts to approach zero, therefore acting as a short circuit, letting the alternating current pass.

High pass filters

In audio engineering, a high-pass filter is a circuit which blocks low frequency signals from the waveform, and only lets high frequency signals through. As you might have guessed, high pass filters work by making use of the effects of capacitive reactance. Only above a certain frequency, called the cut-off frequency, the reactance of the capacitor in the circuit becomes low enough for a signal to pass.

This cut-off frequency can be calculated as follows:

cut-off \thinspace frequency \thinspace in \thinspace hz = \frac {1} { 2\pi \times resistance \thinspace in \thinspace ohms \times capacitance \thinspace in \thinspace farads}

In this sense, we could say that the capacitors in a Tesla Hairpin circuit act as high pass filters, blocking the 50 or 60Hz input signal coming from the transformer, allowing the capacitors to charge, but letting the high frequency pulses from the spark gap through with ease.

Frequency vs rate of change

So far I’ve used the terms “frequency” and “rate of change” interchangeably, but there is in fact a subtle distinction that should be made between the two, which becomes clear when Tesla describes his Hairpin circuit:

“These results, as I have pointed out previously, should not be considered to be due exactly to frequency but rather to the time rate of change which may be great, even with low frequencies.” 10

We already saw before that the “time rate of change” is calculated by:

\frac {change \thinspace in \thinspace voltage}{change \thinspace in \thinspace time}

For example, if we assume we have a 10kV, 50Hz power supply, then each cycle takes 0.02 seconds (1 second / 50Hz). The rate of change is then 500kV/s (10kV / 0.02). Now, this calculation assumes we’re working with a sine wave, but if we instead disruptively discharge a condenser 50 times per second, where each discharge only takes 0.01 seconds, so half the time of one sine wave oscillation, the rate of change increases from 500kV/s to 1000kV/s, while the frequency is still 50Hz!

We can also achieve a 1000kV/s rate of change with a sine wave, but then we either have to double the voltage at 50Hz, or double the frequency to 100Hz, using the original 10kV. These calculations clearly show that, yes, a higher frequency leads to a higher rate of change, but that by using rapid discharges we can achieve a “time rate of change which may be great, even with low frequencies.” With discharges, frequency is the time between pulses, while the rate of change is determined by the duration of a single pulse.

This also has implications for the capacitive reactance formula mentioned before, which contained frequency in Hz as one of its denominators. This formula works as long as we’re dealing with sine waves, but for disruptive discharges we have to replace 2\pi \times frequency with \frac {2\pi}{duration \thinspace of \thinspace discharge}, also known as angular velocity. This results in the following adjusted formula:

capacitive \thinspace reactance \thinspace in \thinspace ohms = \frac {1}{\frac {2\pi}{duration\thinspace of\thinspace discharge\thinspace in\thinspace secs} \times capacitance\thinspace in\thinspace farads}

We will see a similar theme when we describe the next component of reactance: inductive reactance.

As you can probably tell, I have a strong aversion to the traditional notation of mathematical formulas, especially variable names, since they trade off understandability for compactness, making them completely unreadable for the uninitiated. One is expected to know what a random Greek letter stands for, and also the unit used is often only implied (are we dealing with Hz or kHz, ohms or milliohms?), or, if one is lucky, the unit can be found in the text near the formula.

I develop software and so I work with variables all the time. HOWEVER, coding conventions state that one should “avoid ambiguous and small [variable] names which are hard to understand. Names should be descriptive such that it should tell what it is for” 11.  This is the reason why I use more verbose variables in my formulas. They are far from perfect as well, but at least it is clear what each variable stands for.

Inductive reactance

Where capacitors let more current through the higher the frequency, conductors and inductors behave in exactly the opposite way, providing more opposition to current flowing as frequency and/or inductance increase. The reduction of current flow in a conductor due to induction is called inductive reactance 12.

So why does a conductor oppose the flow of AC current at all? The reason can be found in Lenz’s law, which states that “an induced current has a direction such that its magnetic field opposes the change in magnetic field that induced the current.” 12 In other words, when a current is passed through a conductor, a magnetic field is created, which in turn induces a current in the same conductor (self-induction) in the exact opposite direction, a so-called “back emf”, thereby opposing the initial current that generated the magnetic field in the first place.

Since a changing magnetic field induces a voltage that is directly proportional to the rate of change of the current producing it, this means that when the rate of change is doubled, the self-induced back emf is doubled, reducing the flow of current through the conductor accordingly. This is captured in the following formula for inductive reactance:

inductive \thinspace reactance = 2\pi \times frequency \thinspace in \thinspace hertz \times inductance \thinspace in \thinspace henrys

As you can see from the formula, if frequency or inductance is increased, so is inductive reactance. Similar to the capacitive reactance formulas, the above formula can also be rewritten to apply better to pulse currents, like so:

inductive \thinspace reactance = \frac {2\pi}{duration \thinspace of \thinspace discharge \thinspace in \thinspace secs} \times inductance \thinspace in \thinspace henrys

So the shorter the discharge time, the stronger the effect of inductive reactance.

Tesla once mentioned:

“One of the prominent characteristics of high frequency or, to be more general, of rapidly varying currents, is that they pass with difficulty through stout conductors of high self-induction.” 9

We already learned that high frequency currents have a high rate of change, and therefore set up a strong back emf, causing the current to “pass with great difficulty” through a conductor.

Tesla also mentions that this effect is present in “stout conductors of high self-induction”, and on another occasion he said that “the thicker the copper bar… the better it is for the success of the [impedance] experiments” 13. Why? Because the thicker the bar, the larger the surface area, the greater the self-inductance 14, and the more powerful the effect of inductive reactance, or inertia to AC.

The skin effect

 

Skin effect visualization
Figure 2. Cross-section of a wire showing the Skin Effect, where the orange stands for the amount of current flow

We’ve seen how circuits behave differently to DC versus high frequency AC. One of the most curious effects is the so-called “skin effect”, which causes alternating currents to flow closer to the surface, rather than through the centre of a conductor, effectively increasing the resistance, since less volume is available for the current to flow through. In fact:

“For sufficiently high frequencies… the conductor might as well have a hollow core, as the central region of the conductor carries essentially none of the current.” 15

A 50kW radio transmitter, using hollow copper tubes coated with silver, to have great conductivity at the “skin”, where most of the current will be flowing.
Figure 3. A 50kW radio transmitter, using hollow copper tubes coated with silver, to have great conductivity at the “skin”, where most of the current will be flowing.

As the image above shows, the skin effect is a well known phenomena which has practical implications. This is also why stranded Litz wire is often used to transmit radio frequency AC, since it maximizes surface area of the conductor(s) and therefore minimizes losses due to the skin effect.

The first to mention of the skin effect, sometimes called the “thick wire effect”, was mathematical genius Oliver Heaviside around 1883. Heaviside also championed the idea of induction, and is the one who transformed Maxwell’s original quaternion equations into their vector form still used today by engineers around the world, so he was a real heaviweight (pun intended). To understand Heaviside’s explanation of the skin effect, we must, however, first understand how he, like John Henry Poynting, believed that all energy propagation along the direction of the wire takes place outside of the wire instead of through it:

“[Energy transfer] takes place in the vicinity of the wire, very nearly parallel to it, with a slight slope towards the wire… It causes the convergence of energy into the wire.” 15

What Heaviside is saying is that the energy is induced into the wire from the dielectric surrounding it. This leads him to the following explanations of the skin effect:

“Since on starting a current the energy reaches the wire from the medium without, it may be expected that the electric current in the wire is first set up in the outer part, and takes time to penetrate to the middle. This I have verified by investigating special cases. Increase the conductivity of a wire enormously, still keeping it finite, however. Let it, for instance, take minutes to set up current at the axis. Thus, ordinary rapid signalling ‘through the wire’ would be accomplished by a surface current only, penetrating but a small depth.” 15

And:

“Having been, so far as I know, the first to correctly describe the way the current rises in a wire, viz, by diffusion from its boundary, and the consequent approximation, under certain circumstances, to mere surface conduction.” 15

So if we accept that energy is induced into a conductor from without, then Heaviside’s explanation makes sense: the energy reaches the outer skin of the conductor first, and does not have the time to penetrate deeply into it when oscillating at high frequencies.

Now let’s see what a modern textbook tells us about the skin effect:

“Skin effect: The tendency of alternating current (ac) to flow near the surface of a conductor, thereby (a) restricting the current to a small part of the total cross-sectional area and (b) increasing the resistance to the flow of current.” 16

A fair definition. Now what can the book tell us about the cause of the skin effect?

“Skin effect is caused by the inductance of the conductor, which causes an increase in the inductive reactance especially at high frequencies. The inner filaments of the conductor experience an inductive reactance with all the surrounding filaments, their reactance thus being higher than the outer filaments. Thus, the current tends toward the lower reactance filaments, i.e. the outside filaments. At high frequencies, the circumference is a better measure of resistance than the cross-sectional area. The depth of penetration of current at thigh frequencies can be very small compared to the diameter. Skin effect must be taken into account when designing antennas and metallic waveguides.” 16

So instead of Heaviside saying the current starts at the outside of the wire and does not have time to reach the centre, this explanation says that the skin effect is caused by a stronger inductive reactance at the centre of the conductor compared to the outside of the conductor, effectively pushing the current towards “the path of least reactance”, which is near the surface.

Disagreement on the cause of the Skin Effect
Figure 4. Disagreement on the cause of the Skin Effect

On Wikipedia I found yet another explanation, which highlighted eddy currents as the cause:

“The skin effect is due to opposing eddy currents induced by the changing magnetic field resulting from the alternating current.”

We know how to perform accurate calculations with electricity, but still don’t have a clue what electricity actually “is”. In the same vein, we can calculate the skin depth at any given frequency, but don’t seem to agree on what causes the phenomenon in the first place. This twilight zone seems to be the unfortunate fate of science in general, and physics in particular. While all explanations we just discussed of what causes the skin effect seem plausible, “the mere absence of nonsense may not be sufficient to make something true”, as Nassim Taleb once aptly said.

Thus, we are left with uncertainty about the exact cause of the skin effect, but at least everyone agrees that it increases resistance to current flow significantly at high frequencies. This is why I believe that the skin effect is a major cause for the unique Impedance Phenomena Nikola Tesla showcased in his Hairpin experiments.

Impedance

Well, that was quite the journey to finally arrive at the overarching phenomenon of impedance, another term coined by Oliver Heaviside 17. We already learned that when applying direct current (DC) to a circuit, there is no distinction between impedance and resistance. However, when an alternating current (AC) is applied, reactance leads to an increase in opposition to current flow. I tried to capture the relationships of these concepts in the image below.

Impedance infographic
Figure 5. Impedance infographic

The formula for impedance provides another way to show these relationships:

impedance = \sqrt{resistance \thinspace in \thinspace ohms^2 + (inductive \thinspace reactance \thinspace in \thinspace ohms - capacitive \thinspace reactance \thinspace in \thinspace ohms)^2}

It is important to mention that for a series resonant circuit, like the Tesla Hairpin circuit, impedance is at its minimum and current at its maximum at the resonant frequency. Conversely, for a parallel resonant circuit, impedance is at its maximum and current at its minimum at the resonant frequency:

“The resonance of a series RLC circuit occurs when the inductive and capacitive reactances are equal in magnitude but cancel each other because they are 180 degrees apart in phase.” 18

To wrap things up, I would like to share with you an old but must-see video demonstration, titled Similarities of Wave Behavior. In this video, the presenter uses a physical wave device to show, amongst other highly interesting things, the way (electric) waves reflect when they encounter a conductor with a different impedance:

Concluding words

We covered a lot of ground in this article, but I feel that a detailed understanding of impedance is a necessary prerequisite to understanding the behavior of high frequency circuits. It seems that we have now covered enough fundamental subject matter to take an informed shot at properly replicating Nikola Tesla’s Hairpin circuit and its curious effects. The next blog post will describe my own Hairpin replication, including a parts list, experimental results, and a detailed circuit analysis, so everyone will be able to follow along and duplicate the results. Feel free to leave some honest feedback in the comments below!

Nikola Tesla hairpin circuit stout copper bars 1893 lecture

A Brief History of the Tesla Hairpin Circuit / Stout Copper Bars

In his autobiography, Nikola Tesla called the Magnifying Transmitter (TMT) his “best invention” 19, but it is also one of his most complex and misunderstood inventions. I decided that the only way to truly understand the TMT, was to retrace all the steps that led up to this invention, and the Hairpin circuit, which is covered in detail in this post, seems to be at the root of it all. This seemingly simple circuit contained more surprises and subtle complexities than I anticipated, so let’s dive in and see what we can learn from the inventor himself!

A journey back in time

Before we discuss how to replicate this unique device, it is important to trace its origin. Tesla first described the Hairpin circuit during his 1891 lecture in New York:

Nikola Tesla hairpin stout copper bars circuit from his 1891 lecture
Figure 1. First mention of Hairpin circuit by Tesla during his 1891 lecture

“In operating devices on the above plan I have observed curious phenomena of impedance which are of interest. For instance if a thick copper bar be bent, as indicated in Fig. [1], and shunted by ordinary incandescent lamps, then, by passing the discharge between the knobs, the lamps may be brought to incandescence although they are short-circuited. 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, as shown roughly in Fig. [1]. The nodes are never clearly defined, but they are simply maxima and minima of potentials along the bar. This is probably due to the irregularity of the arc between the knobs.

In general when the above-described plan of conversion from high to low tension is used, the behavior of the disruptive discharge may be closely studied. The nodes may also be investigated by means of an ordinary Cardew voltmeter which should be well insulated. Geissler tubes may also be lighted across the points of the bent bar; in this case, of course, it is better to employ smaller capacities. I have found it practicable to light up in this manner a lamp, and even a Geissler tube, shunted by a short, heavy block of metal, and this result seems at first very curious. In fact, the thicker the copper bar in Fig. [1], the better it is for the success of the experiments, as they appear more striking. When lamps with long slender filaments are used it will be often noted that the filaments are from time to time violently vibrated, the vibration being smallest at the nodal points. This vibration seems to be due to an electrostatic action between the filament and the glass of the bulb.” 3

As you can see from figure 1 and Tesla’s description, this device mainly consists of thick copper bars, hooked up to a high voltage power source, which charges capacitors until they reach a high enough voltage to make them discharge disruptively through a spark gap. Looks like a rather simple circuit, right? Well, there is more to it than meets the eye, and the effects of “nodes on the bar”, hinting at electrical standing waves, and lighting lamps while they’re short circuited, are curious enough results to make this device worth investigating.

Nikola Tesla Chicago World Fair 1893 Hairpin Circuit
Figure 2. A picture taken at the Chicago World Fair of 1893, showing a Hairpin with bulbs connected to it on the right, and “six-pack” Leyden Jar capacitors on the table in the back

The next time Tesla mentioned this circuit was during a lecture two years later in Philadelphia, showing a slightly different setup:

Nikola Tesla hairpin circuit stout copper bars 1893 lecture
Figure 3. Tesla “stout copper bars” circuit from his 1893 lecture

“Referring to Fig. [3]a, B and B1 are very stout copper bars connected at their lower ends to plates C and C1, respectively, of a condenser, the opposite plates of the latter being connected to the terminals of the secondary S of a high-tension transformer, the primary P of which is supplied with alternating currents from an ordinary low-frequency dynamo G or distribution circuit. The condenser discharges through an adjustable gap d d as usual. By establishing a rapid vibration it was found quite easy to perform the following curious experiment. The bars B and B1 were joined at the top by a low-voltage lamp l3 a little lower was placed by means of clamps C C, a 50-volt lamp l2; and still lower another 100-volt lamp l1; and finally, at a certain distance below the latter lamp, an exhausted tube T. By carefully determining the positions of these devices it was found practicable to maintain them all at their proper illuminating power. Yet they were all connected in multiple arc to the two stout copper bars and required widely different pressures. This experiment requires of course some time for adjustment but is quite easily performed.

In Figs. [3]b and [3]c, two other experiments are illustrated which, unlike the previous experiment, do not require very careful adjustments. In Fig. [3]b, two lamps, l1 and l2, the former a 100-volt and the latter a 50-volt are placed in certain positions as indicated, the 100-volt lamp being below the 50-volt lamp. When the arc is playing at d d and the sudden discharges are passed through the bars B B1, the 50-volt lamp will, as a rule, burn brightly, or at least this result is easily secured, while the 100-volt lamp will burn very low or remain quite dark, Fig. [3]b. Now the bars B B1 may be joined at the top by a thick cross bar B2 and it is quite easy to maintain the 100-volt lamp at full candle-power while the 50-volt lamp remains dark, Fig. [3]c. These results, as I have pointed out previously, should not be considered to be due exactly to frequency but rather to the time rate of change which may be great, even with low frequencies. A great many other results of the same kind, equally interesting, especially to those who are only used to manipulate steady currents, may be obtained and they afford precious clues in investigating the nature of electric currents.

In the preceding experiments I have already had occasion to show some light phenomena and it would now be proper to study these in particular; but to make this investigation more complete I think it necessary to make first a few remarks on the subject of electrical resonance which has to be always observed in carrying out these experiments.” 2

You may notice that this time, the capacitors and spark gap have switched place in the circuit compared to the 1891 version. Also, the top shunt bar is now detachable, allowing for more types of experiments to be performed. Tesla also goes into much more detail here explaining his experiments with this device, achieving fascinating results, like lighting several lamps of different voltage ratings at full brightness… while they’re short circuited!

One thing to note is that Nikola Tesla himself never used the term “Hairpin circuit”. In fact, he never really seems to have given this device a name at all, but only refers to it as “stout copper bars”. Wherever the name Hairpin originated, it’s catchy, a lot of people use it already to describe this device, and it is easier to write, which is why I use the name Hairpin in this article.

There is one other time Tesla mentioned the Hairpin circuit, in an 1898 article on the electro-therapeutic benefits of high frequency currents, and it is possibly the most interesting article out of all the ones mentioned here.

“One of the early observed and remarkable features of the high frequency currents, and one which was chiefly of interest to the physician, was their apparent harmlessness which made it possible to pass relatively great amounts of electrical energy through the body of a person without causing pain or serious discomfort… these currents would lend themselves particularly to electro-therapeutic uses.” 9

So the high frequency currents generated from the capacitor discharges were so harmless that they were actually passed through the bodies of real patients, without pain! This explains how experimenters like Karl Palsness, whose Hairpin replication we will discuss at length later on, are able to hold the copper bars while the spark gap is firing, and even light a lamp while its submerged in water and then touching the water, without receiving as much as a shock.

“Now, why is it that in a space in which such violent turmoil is going on living tissue remains uninjured?”, Tesla asks the reader. He continues:

“One might say the currents cannot pass because of the great self-induction offered by the large conducting mass. But this it cannot be, because a mass of metal offers a still higher self-induction and is heated just the same. One might argue the tissues offer too great a resistance. But this again cannot be the reason, for all evidence shows that the tissues conduct well enough, and besides, bodies of approximately the same resistance are raised to a high temperature. One might attribute the apparent harmlessness of the oscillations to the high specific heat of the tissue, but even a rough quantitative estimate from experiments with other bodies shows that this view is untenable. The only plausible explanation I have so far found is that the tissues are condensers. This only can account for the absence of injurious action.” 9

So while Tesla does not seem to have a conclusive explanation for the apparent harmlessness of his high frequency currents, it does help to hear his reasoning and insight on the matter, since I’ve heard many people say in forum posts that “it’s just RF”, suggesting that it is simply a characteristic of radio frequency currents to not injure the human body. However, do not try this at home, because there is also something called Electrosurgery, which is “the application of a high-frequency (radio frequency) alternating polarity, electrical current to biological tissue as a means to cut, coagulate, desiccate, or fulgurate tissue.” Not sure what those last three things are, but they sound awful! Be careful.

Also crucial to note is how Tesla never attributes his peculiar results to an exotic type of energy. There is no mention of scalar waves, longitudinal energy, cold electricity, or any of that stuff people love to throw around. He is simply talking about high voltage, high frequency currents.

So what does his electro-therapy device look like? Tesla actually shows us several different setups in the article, as shown in figure 4 below.

Tesla high frequency oscillators for electro-therapy hairpin circuit
Figure 4. Eight “modes of connection” for Tesla’s electro-therapeutic device

The circuits in figure 4 might be a bit much to take in at one time, so I would like to point your attention now to figure 4.3 specifically, which is in fact a circuit identical to the Hairpin! Let’s see what Tesla had to say about that particular setup..

“One of the prominent characteristics of high frequency or, to be more general, of rapidly varying currents, is that they pass with difficulty through stout conductors of high self-induction. So great is the obstruction which self-induction offers to their passage that it was found practicable, as shown in the early experiments to which reference has been made [The Hairpin from his lectures?], to maintain differences of potential of many thousands of volts between two points — not more than a few inches apart — of a thick copper bar of inappreciable resistance. This observation naturally suggested the disposition illustrated in Fig. [4.3]. The source of high frequency impulses is in this instance a familiar type of transformer which may be supplied from a generator G of ordinary direct or alternating currents. The transformer comprises a primary P, a secondary S, two condensers C C which are joined in series, a loop or coil of very thick wire L and a circuit interrupting device at break b. The currents are derived from the loop L by two contacts c c’, one or both of which are capable of displacement along the wire L. By varying the distance between these contacts, any difference of potential, from a few volts to many thousands, is readily obtained on the terminals or handles T T. This mode of using the currents is entirely safe and particularly convenient, but it requires a very uniform working of the break b employed for charging and discharging the condenser.” 9

So two movable contacts were connected to the conductors, the terminals of which which were then applied to the patient’s skin in an “entirely safe” way! Tesla does mention that the spark gap has to operate very consistently for this to work, or else the waves created on the conductors, and therefore the voltage applied to the patient’s skin, will start to vary. The fact that Tesla required a very uniform working of the spark gap to achieve his results, is what made me research Tesla’s spark gaps in detail, and led me to create a modern version of his air quenched spark gap.

Tesla also mentions another revolutionary effect he could achieve with this device: single wire energy transmission!

“Among the various noteworthy features of these currents there is one which lends itself especially to many valuable uses. It is the facility which they afford for conveying large amounts of electrical energy to a body entirely insulated in space. The practicability of this method of energy transmission, which is already receiving useful applications and promises to become of great importance in the near future, has helped to dispel the old notion assuming the necessity of a return circuit for the conveyance of electrical energy in any considerable amount.” 9

Wow… Tesla already called the need for a return wire an “old notion” in 1898, and still all our electronics require a return wire more than a hundred years later!!

This 1898 article is full of revelations and gives us valuable insight into completely new uses of the Hairpin circuit, but possibly the most interesting part of it is how Tesla shows several different setups of what he seems to view as the same device: some with just one loop of wire, like in figure 4.3, but many come with both a primary and a secondary, like figure 4.2 and 4.4. Yet, the most telling schematic of the bunch is shown in figure 4.5, about which Tesla had the following to say:

“The circuit connections as usually made are illustrated schematically in Fig. [4.5], which, with reference to the diagrams before shown, is self-explanatory. The condensers C C, connected in series, are preferably charged by a step-up transformer… The primary p, through which the high frequency discharges of the condensers are passed, consists of very few turns of cable of as low resistance as possible, and the secondary s, preferably at some distance from the primary to facilitate free oscillation, has one of its ends–that is the one which is nearer to the primary–connected to the ground, while the other end leads to an insulated terminal T, with which the body of the patient is connected. It is of importance in this case to establish synchronism between the oscillations in the primary and secondary circuits p and s respectively.” 9

This sounds an awful lot like a Tesla Coil, complete with a resonantly coupled primary and secondary, where the secondary has one end connected to ground and the other to an insulated terminal. And the most astonishing thing is that Tesla mentions this device in one breath with the Hairpin circuit from figure 4.3! The reason this is of such importance, is because it is like finding a transitional fossil, which describes how the Hairpin eventually evolved into the Tesla Coil.

This might be the reason why some people claim the Hairpin circuit is “just a single turn primary of a Tesla Coil”. Though this might seem like a valid point at first, the Hairpin was clearly used to experiment with electrical standing waves, hence the “nodes on the bar” 3, while standing waves are not required in a Tesla Coil primary, as well as impedance phenomena, which is also not the purpose of a Tesla Coil. So yes, the Hairpin definitely has things in common with a single turn Tesla Coil primary, but they have completely different use cases.

Lecher Lines

When reading forum posts and watching YouTube videos on the Hairpin circuit, there is always someone screaming in ALL CAPS that Tesla is a fraud, because he did not invent this circuit, Ernst Lecher did in 1888 when he invented the Lecher Line. Even though Tesla never actually claims to have invented this circuit, I decided to dig into Lecher’s original paper to see if these assertions had any merit, but when I found out the title was Eine Studie über elektrische Resonanzerscheinungen, I knew I would first have to brush up my German! I even looked into hiring a native speaker to perform the translation, but at 21 pages, that would have cost me a small fortune. Luckily I am Dutch, so German comes fairly naturally to me, and I have several German friends who could help me out with the tricky parts.

It took me a tremendous amount of time, but I finally managed to translate the entire paper (click here for the full translation), which contains a wealth of useful information, and really helps to get a better understanding of the Hairpin circuit. Let’s see how Lecher describes his setup “in its simplest form”:

Orignal Lecher Lines schematic
Figure 5. Lecher Lines schematic taken from the original 1890 article by Ernst Lecher

“A and A’ are square sheet metal plates with 40cm sides; they are connected by means of a 100 cm long wire segment, which is cut in the middle and at F two brass balls of 3 cm in diameter are added (in Fig. 1, only the cross-section of the square plates is drawn). The two brass balls are at a distance of 0,75 cm from each other and are connected using thin wires to the poles of a very strong inductor, whose coil has a length of 35 cm and a diameter of 18 cm; the inductor is fed by four powerful accumulators [batteries], and in some cases by a dynamo. A Foucault mercury interrupter serves as electric break. Across from the plates A and A’ are two plates B and B’ of identical size at a distance of around 4 cm. From these plates B, B’ run two wires against s and s’ and from there parallel until t and t’. The distance between the parallel wires (s to s’) is 10-50 cm; the length st (s’ t’) on the other hand should be at least 400 cm. The diameter of these parallel wires is here and for all experiments in this publication 1 mm. For this first experiment we assume the length [of the wire] to be about 600 cm (drawn too short in the figure ), and the distance of the parallel wires from each other 30 cm. At the end of the parallel wires (t and t’) a cord is connected to each, which extends the length of the wires by about 100 cm and allows for a gentle and comfortable tensioning thereof… Over the wire ends t and t’ I now lay an exhausted glas tube without electrodes g g’, ideally filled with nitrogen and a trace of turpentine vapor; this glass tube starts to light up due to the electrical vibrations in the wires.” 20

It is great that Lecher described his setup in such detail. The “Foucault mercury interrupter” mentioned by Lecher is not to be confused for the spark gap; its function was merely “to rapidly connect and disconnect a direct electric current to create the changing magnetic field needed for induction coils.” 21 In other words, it took the direct current from the batteries and turned it into a pulse current, which then powered the “very strong inductor”.

The metal plates A A’ and B B’ function as the two capacitors we also find in the Hairpin circuit, and because Lecher mentions their specific dimensions and distance from each other, we are even able to calculate their capacitance. Two plates of 40×40 cm, placed at a distance of 4 cm from each other, have a capacitance of 35.4 pF. Since they are placed in series in this circuit, given the short x x’ is present, the total series capacitance in Lecher’s circuit was around 17.7 pF. Lecher also mentions his spark gap was 0,75 cm wide, and since the dielectric strength of air at 25ºC and ordinary atmospheric pressure is 31.300V per cm 22, we can assume that Lecher discharged around 0,75 * 31.300 ≈ 23.500V through his spark gap. Fun facts.

Difference between Lecher Lines and Hairpin circuit

By comparing Lecher’s paper with the writings of Nikola Tesla, we learn that while the circuit diagrams of the Hairpin circuit and the Lecher Lines look similar, and Lecher also lit up lights with it, there are some significant differences. For starters, Lecher did not use “stout copper bars” like Tesla did, but instead used 1 mm wires. Lecher also mentions his wire was more than two times 600 cm, or more than 12 meters, long. Later in the paper he even uses 2 x 20 meter long wires! If we compare this to the Hairpin image in figure 2 at the beginning of this article, we see that Tesla’s bars were a lot shorter than that (looks like the bar is approximately 14 light bulb lengths long, which most definitely is shorter than 12 meter).

Besides, Tesla mentioned that “electromotive forces of many thousand volts are maintained between two points of a conducting bar or loop only a few inches long9, suggesting that his conductors did not need to be that long, possibly because Tesla was able to achieve higher frequencies, and therefore shorter wavelengths, by perfecting the condenser discharge process through the invention of advanced spark gap designs, whereas Lecher used a simple static gap with two brass balls as electrodes.

Finally, the main difference between the Lecher Lines and the Hairpin circuit — and this took me a long time to figure out — is in their purpose: Lecher studied resonance phenomena with his Lecher Lines, while Tesla studied impedance phenomena with his Hairpin circuit. Therefore, Lecher used an electrodeless exhausted tube, which did not have an electrical connection to his conductors, assuring the standing waves were not disturbed, but lit up due to the vibrations in the wires. Tesla, on the other hand, used several incandescent lamps of various voltage ratings, and did connect them electrically to his conductors, since he was showing how high-frequency currents “pass with difficulty through stout conductors”9, causing the current to prefer the resistive path of an incandescent lamp filament over the normally inappreciable resistance of the copper bars.

So did Lecher feel like he invented this circuit? Not really..

“This part of my arrangement is similar to that stated in the beautiful work of Hertz, and was also used in the experiments of Sarasin and De la Rive.”20

Lecher actually credits Hertz, Sarasin and De la Rive for a similar circuit, so the internet crusaders who are fighting to protect Lecher’s primacy and honor at every mention of the Hairpin circuit can hopefully calm down now.

Concluding remarks

In this article we learned that Tesla used his Hairpin circuit to display curious impedance phenomena, single wire energy transmission, apply apparently harmless currents to patients for medical purposes, and, finally, to “create pulsations through metal bars, or pipes, and test for harmonic frequencies and standing waves.”23, as one biographer put it.

We also learned that Tesla does not ascribe these effects to any exotic form of energy. He simply talks about high voltage, high frequency currents. It also became clear that the Hairpin eventually evolved into the Tesla Coil, but that the Hairpin cannot simply be seen as a single turn primary, since the use cases are totally different. The same goes for Lecher Lines, which look similar to the Hairpin in many respects, but differs in several crucial ways, mainly again in its use case.

The information in this article gives us a solid foundation in the journey to understand and eventually replicate the Hairpin circuit, according to Nikola Tesla’s own specifications. There is still one thing we have to cover in more detail before we start the replication and experimentation, one thing which plays a crucial role in understanding why the Hairpin works the way it does, and that is impedance, specifically the so-called “skin effect”. This innocuous sounding term has far reaching consequences for high frequency systems, and also has a surprisingly bumpy past. Click here to read all about impedance and the skin effect.

Orignal Lecher Lines schematic

Lecher Lines: A Translation of the Original Paper by Ernst Lecher

While reading up on Nikola Tesla‘s Hairpin circuit, I constantly came across people saying that Tesla’s circuit was identical to Lecher Lines, invented by the Austrian physicist Ernst Lecher around 1890, which was an apparatus used to measure the wavelength of high frequency electric waves by creating standing waves on two parallel wires, and then measuring the distance between the antinodes. However, apart from a Wikipedia article and some obscure blog posts, there was not a lot of information available on Lecher Lines, how to use them, and the values of the circuit components. That’s why I decided to look up the original Lecher Lines paper, written by its inventor, Ernst Lecher, titled  Eine Studie über electrische Resonanzerscheinungen 24.Read more…

Tesla air quenched spark gap replication

Tesla Air Quenched Spark Gap Replication

In a previous post I performed a detailed literature review on the various types of spark gaps Tesla employed in his experiments. My motivation for that research was that I am trying to replicate Tesla’s stout copper bars, or  ‘hairpin’, circuit, and I wanted to figure out which type of spark gap he was most likely using for that particular experiment. My conclusion, based on the research I performed, was that he most likely used an air quenched spark gap. In this article I show you my replication of Tesla’s air quenched spark gap design from his 1893 lecture with a modern twist, including a parts list and my laser cutter ready files.Read more…

Nikola Tesla Spark Gaps

Tesla’s Spark Gaps: A Literature Review

Spark gaps play a central role in many of Nikola Tesla’s devices, most prominently in the circuits powering his famous Tesla Coils. In its simplest form, a spark gap is nothing more than two electrodes with some space in between through which an electric spark passes when the voltage in a circuit reaches a high enough level. However, Tesla took the spark gap, which hte often referred to as a “break”, to a whole new level and devised several ingenious ways to make them more effective. In this post I present a literature review of the various types of spark gaps Tesla employed over the years, how they work, and what the pros and cons of each of them are… in Tesla’s own words!

Yes, you will find a lot of direct quotes from Nikola Tesla in this text. I do this to stay as close as possible to Tesla’s original design specifications, since I have seen a lot of “replications” by experimenters who only follow half of his instructions, and then say the device does not work as advertised. This is what Tesla himself had to say about this:

“Some experimenters who have gone after me have found a difficulty. They said: “No, we cannot produce a constant train of oscillations.” Well, it is not my fault. I never have had the slightest difficulty. I produced constant oscillations and I have described how I produced them. Anyone who has no more than my own skill can do it.” 1

The reason the spark gap deserves such detailed analysis is because it plays a key role in the authentic replication of Tesla’s high frequency experiments, but is one of the hardest parts to procure; it is easy to purchase a high voltage transformer, and it is also easy to buy high voltage capacitors and copper wire, but a properly functioning spark gap built according to Tesla’s design specifications is something that you cannot really buy and will most likely have to construct yourself. Therefore it is crucial to understand the nitty-gritty.

Now that it’s clear why it pays off to study spark gaps, let’s start by looking at the often underestimated subject of how a spark gap actually works, and the main role it plays in many of Tesla’s circuits.

Why use a spark gap?

“The effects which are produced by currents which rise instantly to high values, as in a disruptive discharge, are entirely different from those produced by dynamo currents which rise and fall harmonically.” 25

As you can see from this quote, Tesla referred to the firing of the spark gap as a “disruptive discharge”. So what exactly was “discharging” through his spark gaps?

“The general plan is to charge condensers [capacitors], from a direct or alternate-current source, preferably of high-tension [high voltage], and to discharge them disruptively while observing well-known conditions necessary to maintain the oscillations of the current [resonance].” 25

So Tesla used a high voltage power source, like a generator or a transformer, to charge capacitors. When these capacitors reached a certain voltage, the air (or other discharge medium) between the electrodes of the spark gap gave way, and a disruptive discharge took place. But why would you want to discharge a condenser through a spark gap in the first place? Tesla explains:

With these 44,000 volts I charged my condensers. Then by discharging the condensers, either through a stationary gap or through a gap with a mechanical interrupter, I obtained any frequency I desired, and perfectly undamped waves.” 1

And when Tesla spoke about the problems he had creating a high frequency alternator:

“It appeared desirable to invent a simpler device for the production of electric oscillations. In 1856 Lord Kelvin had exposed the theory of the condenser discharge… I saw the possibilities and undertook the development of induction apparatus on this principle.” 26

This statement is in line with what he mentioned back in his 1891 New York lecture:

“The discharge of a condenser affords us a means of obtaining frequencies far higher than are obtainable mechanically.” 27

So Tesla used condenser discharges as a way to generate the high frequency oscillating currents he used in many of his famous experiments and lectures, as well as undamped or continuous waves, which played an important role in radio transmission. On top of that, these disruptive discharges also enabled extreme power magnification:

“I charged the condenser with 40,000 volts. When it was charged full, I discharged it suddenly, through a short circuit which gave me a very rapid rate of oscillation. Let us suppose that I had stored in the condenser 10 watts. Then, for such a wave there is a flux of energy of (4 x 104)2, and this is multiplied by the frequency of 100,000. You see, it may go into thousands or millions of horsepower.” 1

It is not entirely clear to me where the (4 x 104)2 comes from, but the underlying idea makes sense: you “slowly” fill up a bucket of water [capacitor], and then release all of the water nearly instantaneously [disruptive discharge], creating a massive water pressure [voltage] much greater than the pressure of the water pump [power source].

And according to Tesla, the effects of these discharge currents “are entirely different” than those produced by regular AC. In Tesla’s words:

“The differences of potential at the various points of the circuit, the impedance and other phenomena, dependent upon the rate of change, will bear no similarity in the two cases.” 25

And this brings us to an important and often overlooked point: the rate of change. Many people who try to replicate Tesla’s experiments, including myself at first, believe that the spark gap has to fire at a certain frequency to create the curious effects Tesla describes in his lectures, however…

“When working with currents discharging disruptively, the element chiefly to be considered is not the frequency, as a student might be apt to believe, but the rate of change per unit of time… with low frequency currents it is impossible to obtain such rates of change per unit of time as with high frequencies, hence the effects produced by the latter are much more prominent… Frequency alone in reality does not mean anything, except when an undisturbed harmonic oscillation is considered.” 25

And when a lawyer asked him during an interview in 1916 if the effects “depend upon the suddenness of the discharge”, he replied:

“Yes. It is merely the electrical analogue of a pile driver or a hammer. You accumulate energy through a long distance and then you deliver it with a tremendous suddenness. The distance through which the mass moves is small—the pressure immense.” 1

So maximizing the rate of change of voltage per unit of time, by making your capacitors release their energy as fast as possible, is way more important than making your spark gap fire at the highest frequency possible. In fact…

“It is not, as a rule, of advantage to produce a number of interruptions of the current per second greater than the natural frequency of vibration of the dynamo supply circuit, which is ordinarily small.” 25

So if your high voltage power supply is 50Hz, then a 50Hz firing of your spark gap is fine according to Tesla, as long as the rate of change is high. You can look at the firing of a spark gap as the “ringing” of a bell, which in this case is a conductor. The spark “hits” the bell, which makes it vibrate a certain number of times, until the vibration dies down. So one spark creates several waves. This is how a low spark gap frequency can still generate a high wave frequency in the conductor.

Damped wave
Figure 1. A so-called “damped wave” which occurs when a bell is struck

Since a spark through a gap is essentially an ON/OFF event, it is comparable to a square wave. The rate of change in this case can be thought of as the slew rate and the duration of the pulse as the duty cycle. Looking at it in these terms, you want your slew rate to be as high as possible, by making your duty cycle as short as possible.

While this analogy of a square wave is useful, it is important to keep in mind that a square wave generated by a spark gap differs greatly from a square wave generated with a function generator. While you can easily create a short duty cycle square wave of any frequency using a function generator, this shorter duty cycle does not actually increase the rate of change, it will simply push less energy through the circuit. Making the duty cycle, or discharge time, of a capacitor shorter on the other hand greatly magnifies the rate of change.

disruptive-discharge-vs-function-generator-square-wave
Figure 2. Disruptive discharge vs function generator square wave

For example, say we have a capacitor that is charged to 40.000 Volts. If we discharge this through a spark gap in 10 milliseconds, the slew rate is 4.000 Volts per millisecond. However, if we discharge this same capacitor in 1 millisecond, the slew rate is 40.000 Volts per millisecond. In the latter case the rate of change is ten times greater, while the frequency remains unchanged! And since Tesla mentioned that maximizing the rate of change is one of the main goals of a good spark gap, it seems that one of the main goals of the person designing the spark gap should be to allow as much energy as possible to pass through in the least amount of time possible, and preferably in a consistent way.

It seems Tesla’s main way of achieving this was by “quenching” his sparks…

Quenching

“Quenching” is the art of extinguishing an already established arc. According to Tesla, quenching lets “the fundamental discharges occur in quicker succession.” 28

So proper quenching results in better spark gap performance. The best explanation of quenching I found was by Richard Quick:

“A cold, non-firing, spark gap is “clean”. It contains no plasma, or hot ions. On applying voltage to the gap, a tension is established, and electromagnetic lines of force form… Once the voltage punctures the air (or other dielectric gas) the gap resistance drops. The breakdown ionizes the gas between electrodes, and the arc begins to ablate and ionize the metal electrodes themselves. This mixture of ions forms a highly conductive plasma between the gap electrodes. Without this highly conductive channel through the gap, efficient tank circuit oscillation would be impossible. But the plasma also shorts the gap out. A gap choked with hot ions does not want to open and allow the capacitors to recharge for the next pulse. The gap is gets “dirty” with hot ionized gases, and must be quenched.” 29

In short, the sooner we can extinguish an established arc, the sooner the capacitors can recharge for the next discharge. However, it is easier to start a spark gap than to stop it. Luckily Tesla managed to devise a wide variety of spark gap designs which all dealt with this problem in their own way, let’s have a look!

Static gap

Super simple static spark gap
Figure 3. Super simple static spark gap

As mentioned before, the simplest type of spark gap is two, often movable, electrodes with some air in between through which a spark can pass when the voltage is high enough. These gaps offer no form of active quenching (hence “static”), but because of their simplicity this type of spark gap is the first spark gap I created, and is also the type that many experimenters seem to use.

However, Tesla hardly mentions the use of these simplest of “breaks” and, as we will soon see, resorted mostly to using more complex devices, although he does admit that more complex does not always equal better performance:

“…they [complex spark gaps] may be sometimes a source of trouble, as they produce intermittences and other irregularities in the vibration which it would be very desirable to overcome.” 25

So what do these more advanced spark gaps look like?

Magnetically quenched spark gap

tesla-magnetically-quenched-spark-gap
Figure 4. Magnetically quenched spark gap

The first type we will discuss is the magnetically quenched spark gap, which quenches the spark by the use of a strong magnetic field close to the arc.

“The intense magnetic field… serves to blow out the arc between the knobs as soon as it is formed, and the fundamental discharges occur in quicker succession.” 28

The current in an arc creates a field. The strong magnets, placed at right angles to the arc, pull on the arc and disrupt it, allowing the next charging cycle of the capacitors to begin.

“The rapidity of the interruptions of the current with a magnet depends on the intensity of the magnetic field and on the potential difference at the end of the arc. The interruptions are generally in such quick succession as to produce a musical sound.” 25

So the intensity of the magnetic field, to a large extent, determines the effectiveness of this type of quenching. Therefore Tesla shaped the magnets into points and placed them as close to the arc as possible, as shown in figure 4 above.

When to use it

In which situations should you use magnetic quenching? And does it work equally well for DC and AC sparks? Tesla had several things to say about this:

“The employment of an intense magnetic field is of advantage principally when the induction coil or transformer which charges the condenser is operated by currents of very low frequency.” 28

And…

“The magnet is employed with special advantage in the conversion of direct currents, as it is then very effective. If the primary source is an alternate current generator, it is desirable, as I have stated on another occasion, that the frequency should be low, and that the current forming the arc be large, in order to render the magnet more effective.” 25

So what Tesla makes very clear here is that magnetic quenching works best when you are working with:

  1. DC
  2. Low-frequency AC
  3. Large currents

To increase the amount of current in the arc, which improves magnetic quenching, Tesla recommends connecting the spark gap in a specific way:

Ideal circuit for using magnetically quenched spark gap
Figure 5. Ideal circuit for using magnetically quenched spark gap

“When a magnet is employed to break the arc, it is better to choose the connection indicated diagrammatically in Fig 5, as in this case the currents forming the arc are much more powerful, and the magnetic field exercises a greater influence.” 28

Construction

The pole pieces of the magnet are movable and properly formed so as to protrude between the brass knobs [A B], in order to make the field as intense as possible; but to prevent the discharge from jumping to the magnet the pole pieces are protected by a layer of mica, M M, of sufficient thickness.” 28

It is clear from Tesla’s drawings and description, that the magnets he used were formed into pointy shapes to maximize the magnetic field near the arc and to be able to place the tips of the magnets as close as possible to the arc, with a layer of dielectric material (mica) in between to prevent the spark from flying from the electrodes to the magnets. He even thinned down the ends of the electrodes so the magnets could be placed even closer to the arc!

Magnetically quenched spark gap from 1893 lecture
Figure 6. Magnetically quenched spark gap from 1893 lecture

“The discharge rods d d1, thinned down on the ends in order to allow a closer approach of the magnetic pole pieces” 25

However, in many replications of the magnetically quenched spark gap, round neodymium magnets are used instead of pointy magnets (this), and sometimes there is not even a layer of dielectric in between the arc and the magnets, forcing the experimenter to place the magnets farther away (this). This is not according to Tesla’s specifications, and so it is hard to draw any reliable conclusions from the results of these experiments.

We discussed before that magnetic quenching works well with large currents, but these can also easily damage the electrodes. Tesla has a suggestion:

“When the current through the gap is comparatively large, it is of advantage to slip on the points of the discharge rods pieces of very hard carbon and let the arc play between the carbon pieces. This preserves the rods, and besides has the advantage of keeping the air space hotter, as the heat is not conducted away as quickly through the carbons, and the result is that a smaller E. M. F. in the arc gap is required to maintain a succession of discharges.” 25

So pieces of “very hard carbon” can preserve the electrodes of your spark gap. Do notice however that Tesla does not recommend to use electrodes made entirely out of carbon, like the often used carbon welding rods (like in Karl Palsness’ Hairpin replication here). In figure 4 at the beginning of this post, Tesla actually used brass knobs as electrodes, which can withstand higher temperatures than aluminium, but are about three times more conductive than carbon steel 30.

We learned that magnetically quenched spark gaps work best with large DC currents, however, DC spark gaps don’t always start automatically and need some help, so Tesla came up with a solution:

“When it is desired to start the arc, one of the large rubber handles h h1 is tapped quickly with the hand, whereby the points of the rods are brought in contact but are instantly separated by the springs r r1.” 25

So Tesla could bring the electrodes close together for an instant to start the initial spark, and then a spring would immediately push it back into place. A nice example of such a system can be found in this spark gap.

In an alternative arrangement, Tesla did not place the magnets at right angles, but used them as the electrodes:

“In another arrangement with the magnet I take the discharge between the rounded pole pieces themselves, which in such case are insulated and preferably provided with polished brass caps.” 28

And again in another lecture:

“In another form of discharger, combining the features before mentioned, the discharge was made to pass between two adjustable magnetic pole pieces, the space between them being kept at an elevated temperature.” 25

It is interesting to note here that, like when Tesla mentioned using carbon pieces, he apparently believed it was beneficial to warm up the space between the electrodes, which lowers the breakdown voltage of the gap.

Finally, and this is something not many of us will be able to replicate I’m afraid, Tesla mentioned that he used hydrogen in some of his magnetically quenched spark gaps:

“In this form of break [figure 6], I changed the atmosphere in which the arc was operating. The atmosphere was mostly hydrogen, and with this device I performed my experiments before the Franklin Institute in Philadelphia and the National Electric Light Association in St. Louis.” 1 *

* In the online version of the text an image of an air quenched spark gap is shown near this quote. This is incorrect, since the airflow through the air quenched spark gap would make it impossible to contain the hydrogen. Besides, later Tesla makes reference to the similarity between his design and the Poulsen arc, which also uses hydrogen and is magnetically quenched.

He mentions that this magnetically quenched, hydrogen filled spark gap is the one he used in two of his famous lectures. Tesla continuous in a bitter tone that this design was later attributed to Valdemar Poulsen, whose spark gaps powered radio transmission for years 31.

“This has been used by Poulsen and it is now called the “Poulsen arc” and “Poulsen system.” But, of course, there is no invention in it. I am on record with prior publications, and besides, the hydrogen does not have any other effect except that it lowers the tension under which the device can operate. It has the disadvantage of producing asymmetrical or distorted waves, and the impulses obtained are not best suited for tuning.” 1

So while using hydrogen has advantages, it clearly also has disadvantages. From Tesla’s comment it does not seem like hydrogen is a key component.

Air quenched spark gap

Air quenched spark gap
Figure 7. Air quenched spark gap

Another spark gap Tesla successfully used is the air quenched spark gap, which quenches the arc through a “draught” of warm air which removes hot ions from between the electrodes and physically disrupts the arc, allowing the capacitors to recharge for the next pulse.

I will let Tesla describe the construction and working of his air quenched gap:

Another form of discharger, which may be employed with advantage in some cases, is illustrated in Fig. 3/167.  In this form the discharge rods d d1 pass through perforations in a wooden box B, which is thickly coated with mica on the inside, as indicated by the heavy lines.  The perforations are provided with mica tubes m m1 of some thickness, which are preferably not in contact with the rods d d1. The box has a cover c which is a little larger and descends on the outside of the box. The spark gap is warmed by a small lamp l contained in the box. A plate p above the lamp allows the draught to pass only through the chimney a of the lamp, the air entering through holes o o in or near the bottom of the box and following the path indicated by the arrows. When the discharger is in operation, the door of the box is closed so that the light of the arc is not visible outside. It is desirable to exclude the light as perfectly as possible, as it interferes with some experiments.” 25

So Tesla used a lamp at the bottom of the spark gap to warm the air inside the gap, which is drawn in from the holes that are visible near the bottom of the drawing, but says other methods are acceptable too:

“Instead of using the lamp, it answers the purpose to provide for a draught of warm air in other ways.” 25

Tesla further describes the reason why warming the air in the gap is important, especially in an air quenched spark gap:

“This form of discharger is simple and very effective when properly manipulated. The air being warmed to a certain temperature, has its insulating power impaired; it becomes dielectrically weak, as it were, and the consequence is that the arc can be established at much greater distance. The arc should, of course, be sufficiently insulating to allow the discharge to pass through the gap disruptively. The arc formed under such conditions, when long, may be made extremely sensitive, and the weal draught through the lamp chimney is quite sufficient to produce rapid interruptions. The adjustment is made by regulating the temperature and velocity of the draught.” 25

So the warm air ultimately allows longer arcs to form, and the longer the arc, the easier it is to extinguish it with a draught of warm air. It is important to note that Tesla mentions using warm air several times, and that a “draught” of air should do the trick if the correct conditions are established, so a 12V computer fan blasting away at full speed next to a spark gap is not really following Tesla’s instructions…

To further assist in making the arc “long and unsteady”, Tesla recommended connecting the spark gap in a different manner than the magnetically quenched gap we discussed previously:

Air quenched spark gap circuit
Figure 8. Ideal circuit for air quenched gap

“Instead of the magnet, a draught or blast of air may be employed with some advantage. In this case the arc is preferably established between the knobs A B, in Fig. [8] (the knobs a b being generally joined, or entirely done away with), as in this disposition the arc is long and unsteady, and is easily affected by the draught.” 28

So this setup, which bears some resemblance to the “original” Hairpin circuit, results in smaller currents through the spark gap, and for smaller currents Tesla recommends using aluminium electrodes:

“With small currents through the gap it is best to employ aluminum, but not when the currents are large.” 25

So use the air quenched gap when working with small currents and long, feeble sparks. Also make sure you use aluminium electrodes and warm air. Ideally you should be able to control the temperature and the air velocity inside your air quenched spark gap to find the perfect conditions for your sparks to fly. Tesla did not mention whether these gaps are better used with AC or DC currents.

Series static gap

Series static gap
Figure 9. Series static gap

“This device is now known in the art as the “quenched spark gap.”” 1

In this next type of spark gap, the arc is spread out over multiple conductors, and was called, as you can see from the quote above, a “quenched spark gap” in Tesla’s time. Personally I believe this name is a bit misleading, because in fact this gap is not actively quenched. Richard Quick has a more accurate name for it:

“Gaps of this type are known as “series static gaps”. “Static” in this use refers to the fact that the gap is not actively quenched. The plasma is formed in several locations, and the voltage at each gap is lowered as more electrodes are placed in series. Heat, hot ions, and voltage are distributed.” 29

Distributing the arc over several gaps in series has several benefits according to Tesla:

“In the use of this kind of discharger I have found three principal advantages over the ordinary form. First, the dielectric strength of a given total width of air space is greater when a great many small air gaps are used instead of one, which permits of working with a smaller length of air gap, and that means smaller loss and less deterioration of the metal; secondly by reason of splitting the arc up into smaller arcs, the polished surfaces are made to last much longer; and, thirdly, the apparatus affords some gauge in the experiments. I usually set the pieces by putting between them sheets of uniform thickness at a certain very small distance which is known from the experiments of Sir William Thomson [Lord Kelvin] to require a certain electromotive force to be bridged by the spark.” 28

So the “three principal advantages” of this type of spark gap are:

  1. Less energy lost in the arcs
  2. Electrodes last longer
  3. Offers a way to measure voltage through the gap

Another not mentioned benefit is that smaller arcs are of course a lot less noisy than larger arcs.

It seems like only the first point is of real interest to the experimenter trying to replicate Tesla’s effects, since less energy lost means a bigger rate of change. Having to change electrodes less frequently, measuring voltage, and reducing noise are often not necessarily critical.

Of course Tesla managed to push this spark gap to its limits again, and was able to achieve a remarkable feat:

“With this kind of discharger I have been able to maintain an oscillating motion without any spark being visible with the naked eye between the knobs, and they would not show a very appreciable rise in temperature.” 28

And several years later:

“This device incorporated many spark gaps in series. It had a peculiar feature; namely, through the great number of gaps, I was able, as I have pointed out in my writings, to produce oscillations without even a spark being visible between the knobs.” 1

Tesla also mentioned that it worked best in the “Hairpin” setup indicated in Figure 8:

“I have used it preferably in a disposition similar to that indicated in Fig. [8], when the currents forming the arcs are small.” 28

As to the construction of his series static gap:

It consists of a number of brass pieces c c (Fig. 6), each of which comprises a spherical middle portion m with an extension e below which is merely used to fasten the piece in a lathe when polishing up the discharging surface and a column above, which consists of a knurled flange f surmounted by a threaded stem I carrying a nut n, by means of which a wire is fastened to the column. The flange f conveniently serves for holding the brass piece when fastening the wire, and also for turning it in any position when it becomes necessary to present a fresh discharging surface. Two stout strips of hard rubber R R, with planed grooves g g (Fig. 7) to fit the middle portion of the pieces c c, serve to clamp the latter and hold them firmly in position by means of two bolts C C (of which only one is shown) passing through the ends of the strips.” 28

As you can read in the above passage, Tesla used brass electrodes in this type of gap, and these electrodes were easy to turn in order to twist a fresh piece of brass surface into place, which was one of the main benefits mentioned earlier on.

Richard Quick, who we quoted before in this article, developed a variation of the series static gap which is popular among Tesla Coil builders who are trying to produce large sparks (I will discuss at length in upcoming posts why large sparks are not what Tesla’s main purpose was with his coils). This gap is knows as the RQ gap (link), and is essentially several copper tubes placed inside a cylinder, and a fan blowing some air through it to improve quenching. While this type of gap seems to work well for some experimenters, this design does not really fits Tesla’s idea of having movable and rotatable electrodes.

He did make an observation worth mentioning through:

“The lesson learned was too many gaps in series kills the Q of a spark gap. By adding gaps in parallel, and reducing the number of gaps in series, some Q was regained while power levels increased. This is a valuable hint in spark gap designs.” 29

So there is a limit to the amount of electrodes you can put in series before performance starts to drop significantly.

Rotary spark gap or Mechanical break

Rotary spark gap
Figure 10. Rotary spark gap

Another interesting form of spark gap employed by Tesla was the rotary spark gap, or “mechanical break”. I give the floor to Richard Quick once more:

“The rotary gap is a mechanical spark gap usually consisting of revolving disk with electrodes mounted on the rim. The rotor is spun and the electrodes move in relation to a set of stationary electrodes nearby. As a moving electrode comes near a stationary electrode, the gap fires. As is moves away the arc is stretched and broken. The rotary gap offers the sophisticated coiler the opportunity to control the pulse in the tank circuit. A properly designed rotary gap can control the break rate (bps) and the dwell time.” 29

While Tesla used rotary gaps extensively and even used them in several patents (514,168 & 568,180), he did not seem too enthusiastic about them in 1892:

“I may here mention that I have also used dischargers with single or multiple air gaps, in which the discharge surfaces were rotated with great speed. No particular advantage was, however, gained by this method, except in cases where the currents from the condenser were large and the keeping cool of the surfaces was necessary, and in cases when, the discharge not being oscillating of itself, the arc as soon as established was broken by the air current, thus starting the vibration at intervals in rapid succession. I have also used mechanical interrupters in many ways. To avoid the difficulties with frictional contacts, the preferred plan adopted was to establish the arc and rotate through it at great speed a rim of mica provided with many holes and fastened to a steel plate.” 28

So the benefits were mainly cooling and quenching, which are in fact fair benefits. However, the gaps described in the passage above do not seem to rotate the conductors around, like in a classic rotary gap, but instead the surfaces were rotated or a rim of dielectric material was rotated through the arc.

Tesla also mentioned he had a rotary spark gap in some of his labs during that time:

Rotary spark gap in Tesla's lab
Figure 11. Rotary spark gap in Tesla’s lab

“This is the apparatus I had at 35 South Fifth Avenue and also Houston Street.  It shows the whole arrangement as I had it for the demonstration of effects which I investigated.” 1

However, this too wasn’t exactly his favourite setup:

“That is the way I had it for the production of current effects which were rather of damped character because, at that period, I used circuits of great activity which radiated rapidly… It was a transmission by electromagnetic waves. The solution lay in a different direction. I am showing you this simply as a typical form of apparatus of that period.” 1

It is not 100% clear if he meant the spark gap was the problem, or that the problem lay in the fact that his circuits radiated too much energy as high frequency Hertzian waves. Tesla described another form of rotating gap he used at his Houston Street lab:

Rotary spark gap at Tesla's Houston Street lab
Figure 12. Rotary spark gap at Tesla’s Houston Street lab

“Here I show an apparatus that was installed in the Houston Street laboratory prior to the other break because I wanted to get as high a number of impulses as possible. The drawing dates from the spring of 1896.  It is a break with which I could reach from 15,000 to 18,000 interruptions per second. I used it very much until later I found it was not necessary [to create so many interruptions per second]. That is the innocent device which Marconi thought a great invention.

…It consists of two discs of aluminum, with teeth of aluminum on the side. They were rotated by two motors in opposite directions, and as they rotated they alternately closed and opened the circuit. In some instances I used an uneven number of teeth on one and and even number on the other so that I could produce as many breaks as I desired. I will show you later an apparatus more perfect than this one, and of a different kind, in which I have 24 stationary contacts, and 25 rotating elements that established the contact and broke it, so that by one revolution I obtained 24 times 25, or 600 interruptions [per revolution].” 1

Tesla mention that this rotating gap, which again consists of aluminium electrodes, allowed him to reach a very high firing frequency, up to “18,000 interruptions per second”, but that a high firing frequency turned out to be something that wasn’t necessarily desirable. Nevertheless, it is interesting to hear Tesla mention that the wave frequencies he could obtain with this setup were “from a few thousand up to a million per second.” 1. When asked what the actual frequencies were that he used, he mentioned a spark frequency of “5,000, 6,000—sometimes higher still” 1 and a wave frequency “from 30,000 to 80,000” 1.

Tesla also found out another powerful feature of the rotary spark gap; it allowed him to let the arcs occur at the exact peak of the alternating input, which maximized the amount of voltage through the primary at each spark. This powerful method was patented in 1896.

Patent to break AC at peak of the wave using a rotary spark gap
Figure 13. Patent to break AC at peak of the wave using a rotary spark gap

“This is a form of break which I developed in working with alternators. I recognized that it was of tremendous advantage to break at the peak of the wave. If I used just an ordinary break, it would make and break the current at low as well as high points of the wave. Of this apparatus I had two forms; one in which I drove the break right from the shaft of the dynamo and the other in which I drove it with an isochronous motor. Then, by a movement of these knobs (K K), I would make the adjustments so that the makes would occur exactly at the top of the wave. That is a form of break which is embodied in hundreds of patents and used now extensively.” 1

And later:

“I used this machine [a Westinghouse alternator], as I said, either to produce alternating currents and then interrupt them with a mechanical break at the high peaks of the wave; or, I used alternating currents and interrupted them with an independent rotating break having a great number of teeth.” 1

This last passage hints at two modes of operation: a synchronous mode where the arcs occur only at the peak of the input wave, while in the other mode the arcs are asynchronous and occur whenever the electrodes pass each other. The latter version requires less fine tuning and is therefore easier to construct and control, but will result in more irregular voltage levels per discharge.

One major danger in using a rotary spark gap is that if your tuning is off, or the rotation is disturbed, the electrodes will take too long to pass each other, allowing a voltage to build up in the capacitors that is too high and which can then damage your capacitors and/or your transformer. To prevent this from happening, a simple static safety gap can be put in parallel to the rotary gap. When the voltages reach a point that is dangerously high, the static gap allows a path to safely discharge this pressure, protecting the rest of your circuit.

Liquid dischargers

Tesla also worked on a sub-class of rotary spark gaps which were immersed in a liquid.

“The ideal medium for a discharge gap should only crack, and the ideal electrode should be of some material which cannot be disintegrated… A liquid, especially under great pressure, behaves practically like a solid, while it possesses the property of closing the crack. Hence it was thought that a liquid insulator might be more suitable as a dielectric than air.” 25

So Tesla believed that air was not the ideal medium for discharges, since air does not “crack”, but it actually “breaks” and then creates a conducting path of hot ions, which reduces the performance of the gap. Therefore he started experimenting with different discharge mediums.

Liquid discharger
Figure 14. Liquid discharger

* This image was missing from the online text, but is present in the book

“The discharge gap was filled with a medium which behaved practically like a solid, which possessed the duality of closing instantly upon the occurrence of the break, and which moreover was circulating through the gap at a rapid rate. Very powerful effects were produced by discharges of this kind with liquid interrupters, of which a number of different forms were made. It was found that, as expected, a longer spark for a given length of wire was obtainable in this way than by using air as an interrupting device. Generally the speed, and therefore also the fluid pressure, was limited by reason of the fluid friction, in the form of discharger described, but the practically obtainable speed was more than sufficient to produce a number of breaks suitable for the circuits ordinarily used. In such instances the metal pulley P was provided with a few projections inwardly, and a definite number of breaks was then produced which could be computed from the speed of rotation of the pulley. Experiments were also carried on with liquids of different insulating power with the view of reducing the loss in the arc. When an insulating liquid is moderately warmed, the loss in the arc is diminished.” 25

Tesla observed that his “liquid interrupters” possessed nearly instant quenching capabilities, resulting in very powerful effects and longer sparks. He again mentions the importance of warming the discharge medium to improve performance, in this case by reducing energy losses. Another major benefit of a rotary spark gap, whether discharging through air or a liquid, is that it creates “a definite number of breaks” which can be “computed from the speed of rotation”.

However, despite these benefits, this type of gap was not without downsides:

“A point of some importance was noted in experiments with various discharges of this kind. It was found, for instance, that whereas the conditions maintained in these forms were favorable for the production of a great spark length, the current so obtained was not best suited to the production of light effects. Experience undoubtedly has shown, that for such purposes a harmonic rise and fall of the potential is preferable.” 25

This passage implies that the currents from this spark gap were not harmonic in nature, but quite possibly powerful and extremely abrupt, due to the fast quenching times.

So far Tesla mentioned that he experimented with several liquids, but what liquid did he prefer to use? He mentions this while discussing one of his patents which includes a liquid rotary gap.

CIrcuit Tesla used at the Chicago World Fair
Figure 15. CIrcuit Tesla used at the Chicago World Fair

“This [Figure 15] is the apparatus used in the Chicago Exposition of 1893, at which time I explained for the first time to Professor Helmholtz my plan for transmitting energy… The break was automatically effected by means of a turbine. The oil was circulated by a pump, and the current of oil drove the turbine which effected the make and break. Owing to the fact that the oil used was a very good insulator, rapidly flowing and of great dielectric strength, these make-and-break points were very close together, and the arcs extremely short. The effects were accordingly more intense. Here [T in Fig. 1 of figure 15] is a cooler through which the oil was circulated. The oil was forced through the gaps at great speed, and as it flowed out it was supplied again to the tank and the current driving the turbine…. It had vanes like those of a propeller and constituted a rotary break in the circuit… The rotary gap is shown in detail [Fig. 2 in figure 15]” 1

There we have it: the liquid Tesla used in this type of rotary gap was oil. He also reiterates that arcs created with this type of gap can be made extremely short, resulting in a large rate of change.

Vacuum tubes & gas filled tubes

Figure 16. Vacuum tube spark gap

The final type of spark gap we will discuss is the vacuum tube, in which two electrodes are enclosed in a vacuum. The idea is that a spark in a vacuum is better able to create a single frequency and more undamped waves, where “regular” spark gaps generate fairly broad-band signals and more damped waves, even though Tesla insisted he was able to create undamped waves without a vacuum.

Damped waves in air vs vacuum
Figure 17. Damped waves in air vs vacuum

Tesla did experiment with vacuum tubes, although he initially experienced some difficulties using them.

“The use of the magnet permits, however, of the arc being replaced by a vacuum tube, but I have encountered great difficulties in working with an exhausted tube.” 28

We learned before that warming up the air between the electrodes can lower the breakdown voltage, and a vacuum can have a similar effect.

“The air may be rendered dielectrically weak also by rarefaction. Dischargers of this kind have likewise been used by me in connection with a magnet. A large tube is for this purpose provided with heavy electrodes of carbon or metal, between which the discharge is made to pass, the tube being placed in a powerful magnetic field The exhaustion of the tube is carried to a point at which the discharge breaks through easily, but the pressure should be more than 75 millimetres, at which the ordinary thread discharge occurs.” 25

The lower breakdown voltage due to the vacuum has a similar benefit to the series static gap discussed before: lower voltages create smaller sparks, which in turn make less noise and give the electrodes a longer life span. It is also good to note that Tesla combined his vacuum discharges with a strong magnetic field for better quenching.

However, Tesla believed that a pressurized gas is even more effective than a vacuum.

“Air or other gas under great pressure is of course a much more suitable medium for the discharge gap [relative to a vacuum]. I have carried on long-continued experiments in this direction, unfortunately less practicable on account of the difficulties and expense in getting air under great pressure.” 25

The high-pressure gas was apparently just a lot more difficult to work with. Even though Tesla experimented with vacuum tubes early on -devices which would soon replace nearly all spark gaps- it seems from our investigation that he preferred the rotary spark gap over the vacuum tube in the end.

What happened to spark gaps?

We just discussed an exotic array of spark gaps, all with their own unique characteristics. However, these days it is hard to find spark gaps still in active duty, apart from people building Tesla Coils. Why is that? Here is a brief history of the end of the spark gap era.

“Although the spark gap transmitter was developed and improved to a very large degree, it could never compete with transmitters using valves [vacuum tubes] that were able to create a proper single frequency signal. Spark gap transmitters were inherently wide band and although improvements in the design meant they occupied considerably less spectrum, they could never be as flexible and effective as those using valve based equipment.

As a result of this their use declined in the late 1910s and early 1920s. Although spark transmitters were retained for many years as a last ditch form of emergency communications on distress frequencies, they were ultimately rendered obsolete and their use banned as they caused interference to others.” 32

It is sad to note that in the Spark gap transmitter timeline on the page quoted above, no mention of Tesla is made, even though he invented, perfected, and patented multiple types of ingenious spark gaps and would eventually build the largest spark gap transmitter ever produced on Long Island. The main problem seems to be that Tesla invented and experimented a lot, but didn’t always turn his devices into actual products people could readily buy and use.

So the problem with spark gaps was, as mentioned before, that they generally create a wide range of frequencies as well as damped waves, while radio communication requires a single frequency of undamped or continuous waves of constant amplitude. Again, Tesla said he was able to achieve this with his spark gaps as well:

“I can obtain oscillations of any frequency I desire. I can make them damped or undamped. I can make them of one direction or alternating in direction as I choose.” 1

But he said others had trouble achieving similar results, as we read in a quote I mentioned earlier in this text:

“Some experimenters who have gone after me have found a difficulty. They said: “No, we cannot produce a constant train of oscillations.” Well, it is not my fault. I never have had the slightest difficulty. I produced constant oscillations and I have described how I produced them. Anyone who has no more than my own skill can do it.” 1

In the end, the desired results were easier to achieve using vacuum tubes, and so they replaced spark gaps. These days, vacuum tubes are mostly replaced by solid state devices, like transistors, so sparks have officially left the scene.

Closing thoughts

Wow, this article turned out to be a lot longer than I anticipated! What started off as some research into what spark gap Tesla preferred to use, ended up in a comprehensive literature analysis. So what was Tesla’s preferred spark gap?

Well, as we learned, certain spark gaps work better in certain situations. However, most of the spark gaps discussed here were described in Tesla’s 1892 and 1893 lectures, while Tesla used a liquid rotary gap at the 1893 Chicago World Fair, and has patents containing rotary gaps from 1894 and 1896, so it seems like the rotary gap was the main device Tesla was using in later years.

This makes sense, since the rotary gap, while tricky to construct, allows accurate control over the spark frequency, creates a consistent train of oscillations, has great quenching capabilities, and delivers the highest possible voltage per spark, since it can break the input wave at its peak.

However, if you’re looking at replicating Tesla’s “stout copper bars” circuit, which is what started my journey into spark gap land, it seems more likely that Tesla was using an air quenched spark gap for that particular experiment based on the circuit described in figure 8, so it depends on what your goal is.

Whatever spark gap you decide to use, one thing seems to be a good idea across the board, and that is to warm the medium through which you are discharging. Just don’t perform any transmission experiments using spark gaps, or you risk jamming existing radio transmissions, which could get you (and them) in trouble.

It is worth appreciating the fact that we can now simply purchase a $50 function generator from AliExpress and generate undamped waves of any desired frequency with ease, while this was an incredibly difficult feat to achieve in Tesla’s time when the only method available was a spark gap! I hope reading this information was as useful to you as it was for me putting it together.