Stefan's Tesla-Pages

Technological background, part#2
(or 'how to produce your own indoor lightning')

Elements of a TC: Control board, variac High voltage transformer Filter board Bypass Caps Safety gap Damping resistors Chokes (not recommended any longer) Tank circuit Main system spark gap Cap with safety gap (+ resistors) Primary with strike protection ring Secondary (circuit) Secondary coil RF-ground Top capacitance
How to calculate a TC "from bottom up"

Units:

1" = 1 inch = 25.4 mm
1 mil = 1/1000 inch
1 foot = 12 inch
1 mm = 1/10 cm = 1/1000 m
1 CM = 1 Circular Mil = (1"/1000 * 0.5)² * Pi = 0.5067 * 10^-3mm² = area of a circle with 1 mil diameter

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Elements of a TC:

Control board

The first thing to build for a Tesla coil is a control board for providing save operation of the device. A typical (read 'mine') control board contains the following elements:

line filters (* see text in table below!), varistors, snubbers fuse main switch (panic button) key switch (prevents unauthorized operation) pushbutton (still-alive button) analog meters for U and I sockets for variac (for a soft start of the coil) socket for a timing device (bypassing the pushbutton) socket for the HV-xfmr(s) Click to see the full size of the image.

Provide proper fusing and power switches. Provide a power-on indicator so you KNOW when power is applied. A key switch will also keep someone from accidently turning on the power while your are making adjustments. Make it a habit of keeping the key WITH YOU. Do not make any kind of adjustments with the power on. It's easy to forget sometimes.
For slowly bringing up the voltage to the HV-xfmr, a variac is necessary. A variac is an autotransformer with a hand wheel for rotating the tap on the winding. The variac is one of the most expensive parts of the Tesla coil system, because not everyone has the chance to acquire a used one. New ones can cost several hundreds of dollars. Here you can have a look on my 20A-variac (I opened the case for a better view, you can clearly see cooling fins on the wiper). Make it a habit of switching the power OFF. Just turning down the variac to zero is not good enough. Some (most?) variacs will put out 1-2 volts at their zero setting. Two volts into a 15kv neon transformer would result in 300 volts. Enough for a nasty shock, even lethal. Never assume anything is OFF. Check for yourself. And use at least two switches in series (if one will fail...) or better a big contactor. One problem I had with my variac: nearly every time I turned the main switch on the control board into the ON-position and let the line voltage to the variac, the main breaker tripped. This happened due to the high current flowing during the switch-on procedure. To overcome this situation, I buildt a small timer circuit with a relay which shorts out some power resistors in series to the variac after the first second I turn the thing on. This is a kind of a 2-phase soft start and limits the current to 4A for the first half second. (This is only a problem with breakers, I never had a fuse fail this way.)

* concerning the line filters (and grounding in general):

http://www.pupman.com/listarchives/2000/December/msg00810.html

Subject: Re: EMI filter hookup
Date: Mon, 18 Dec 2000 07:58:39 -0700
Original poster: "Marco Denicolai by way of Terry Fritz <twftesla@uswest.net>" <Marco.Denicolai@tellabs.fi>

<SNIP>

I don't know about pro and cons of "backward" connection, but I can say something about grounding. With my old TC and Thor's DC switching power supply I had this configuration:

room with concrete floor and a solid, thick copper sheet embedded in the concrete (for all the floor surface). Copper was well grounded, of course. We'll assume this is a perfect ground.
Tank (case) grounded to this perfect ground by a 5" wide copper sheet, about 5' long.
TC grounded to the tank (case) ground (a solid copper bar) by a 5" wide copper sheet, 10' long.
Table covered with aluminium sheet, grounded to the floor by the same copper sheet, again about 5' long.
Tank sitting on the table, having two wood logs between the two of them.

Running the coil I had 1/2" CONTINUOUS sparking between table and tank rack, even if both of them were grounded to the SAME POINT by 5' length of copper sheet!

So there is no doubt: you have such transients on the TC ground, that even a very low inductance connection will result in generating a (relative high) potential on the TC ground path and even on the grounding point.

With the EMI filter you want to protect the mains phase and neutral from potentials too high in respect to the plug (3rd wire) ground. That ground is definitevely NOT your TC RF ground. If you connect the EMI filter GND to the RF ground (I.M.H.O. :) ) you'll possibly achieve nothing or just a damage. The RF GND is practically floating to a potential driven by transients and its own (even if low) impedance.

To limit the potential on plug phase and neutral, I believe you must connect the EMI filter GND to your plug (3rd wire), that is:
plug GND: variac, EMI filter, anything you can touch (control panel, etc.) RF GND: NST filter (on the HV side), NST case, secondary base, strike rail, RSG motor case, etc.

Some more remarks on line filters and grounding:
The line filter should be wired in the standard direction (NOT in reverse as an old myth says) and the filter gnd should not be connected to RF-gnd but to household gnd instead! Else you will fry the caps in the filter which go from neutral and hot to the gnd. The filter should be located directly at the line connector far away from the coil else the cable will pick up RF AFTER the filter (making it useless)

Remark: The xfmr-core should be grounded to the plug-gnd IMHO!

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High voltage transformer:

If one wants a powerful Tesla coil, the first thing to find is a powerful high voltage transformer. The maximum power which can ideally be delivered to the Tesla coil is determined by the equation

P=¹/₂^.C_prim^.Û^2.bps

In this equation, C_prim is the capacitance of the main capacitor in the tank circuit. Û is the peak voltage applied to the high voltage capacitor (determined by the gap setting of the main system spark gap or the safety gap). And bps is the number of "breaks per second" and says how often the main spark gap shorts and delivers the power to the primary coil. Of course, the high voltage xfmr must be able to charge the cap to the peak voltage bps times per second. This means, it has to have a minimum amperage. The voltage should be in the range of 6kV-20kV, preferable 6kV-12kV for beginners coils. Big coils usually run on higher voltages (up to 20kV). This higher voltage has two major advantages: you need a lower capacitance value and the performance of the spark gap is better. The disadvantages are that the costs for the cap explode with higher voltages, the need for a better insulation requires more thougts on wiring.
Go to my neon page for more info about the most common xfmrs.

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Filter board

The purpose of a high voltage filter board is to protect the high voltage xfmr from any overvoltage condition. It usually consists of bypass caps, a safety gap and damping resistors. The filter acts like a shock absorber and protects the HV windings of the high voltage transformer from the RF generated in the coupled primary and secondary circuits. This RF can easily cook the insulation of the transformer which results in breakdown. The bypass cap with the safety gap across it is in parallel to the HV windings of the high voltage xfmr. The damping resistors are located in each high voltage line to the tank circuit and back to the HV xfmr.

Chokes: I don't recommend the use of chokes any more!
As Terry said: When the main gap shorts, the cap to ground and the series choke will ring just like the primary circuit. You are shorting the filter caps out through the inductor. This ring may be just as bad as the primary circuit ring. Thus "I" would use resistors instead of chokes so there will not be any ringing. You may want to check the following especially the last two. rcfilter.html, pricir.html, NSTFilt.jpg, Filter.jpg.

RF with small amplitude is "shorted to ground" by the bypass caps (not more than 0.5-1nF per side, they act like snubbers). If you have no other caps at hand, you can use two small salt water bottle caps.
The damping resistors help to damp any parasitic oscillations between the bypass caps and the other components.
The safety gap on the transformer outputs protects against any very high spikes that get through the RCR-filter. The gap is set to be just wide enough to prevent arcing when full output voltage is present but no TC in operation (disconnected tank circuit). With a center tapped xfmr, the safety gap and bypass caps are arranged symmetrically to the centertap which is connected to the RF-ground. As you should shut down the power immediately when the safety gap barks, it don't has to be a very robust one. Just use two screws against a metal plate (same as for the capacitor safety gap).
As a last safety element (though not depicted in the schematic above) one might add some surge supressors, socalled MOVs (from "Metall Oxide Semiconductor"). Use a chain of them to achieve the (peak!) voltage of your xfmr (slightly more of cause). If you'll get an overvoltage condition, a nice flaming and smoking MOV will tell you - much cheaper than a new xfmr...

To be effective, there have to be many losses in this filter circuit. Wattless losses in the bypass caps (P=2*Pi*f*C*U²) decrease the usable amount of current as well as resistive losses in the damping resistors (R=P_loss/I²). Of course, the damping resistance has to be high to be effective. Therefore, the filter board has to be designed new for every different power level. I myself go for 1% to 10% losses in the filter. This way, I never had a failure in my xfmrs. The best way is to test the filter board with a function generator hooked up to the filter output and an oscilloscope hooked up to the filter input. It is important to connect the HV-xfmr also in this test! If there should be any resonance peak, one should redesign the filter board.

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Main system spark gap

The first element of the tank circuit is the main system spark gap. It is located in parallel between the two high voltage feed lines coming from the filter board. This spark gap has to be very robust as it has to handle several hundreds of amperes at a voltage of tens of kilovolts. Luckily, the phase angle is about 90° and the duty cycle is very low (below 0.2% in case of my 4"-system), but there ARE significant losses (HEAT) in the arc. It is the element with the biggest (unwanted) losses in a well designed TC. The purpose of the gap is to act as a very fast switch for high voltage and high power. It has to open the circuit after the energy stored in the cap has moved into the primary coil and has taken up by the secondary. If it would still conduct after that "first primary notch", the energy would be transferred back into the tank circuit where a significant portion will be wasted as heat in the spark gap. To help in cooling (and therefore quenching), a static gap is usually splitted into several (usually 5 to 10) narrower gaps.

A very effective gap consists of some large diameter copper pipes about (1 to) 3 inches long, lined up in parallel with a small gap (< 0.018"-0.025") in between. This is a so called 'static gap'. At the funet-archives one can find a very neat version of this gap invented by Richard Hull and published by Richard Quick. Here the copper pipes are mounted in a circle on the inside of a PVC pipe. It is called the 'cylinder static gap'. The copper tubes are bolted in place. A fan is needed on high power Tesla coils to prevent the copper tubes from getting hot and to remove the ions. A box or muffin fan works fine. Click here to go to the separate page I made about this type of gap.

By mounting the copper tubes flat side by side and placing the thing on top of a box with a vacuum blower inside, the air can be sucked through the gaps into the box. This is a so called 'vacuum gap' (one of my countless projects for the future). The air helps cooling and removes the ions. A vacuum fan with a variac speed control works even better because the fan speed can be adjusted for best spark output of the coil. It works better than the cylinder static gap and is recommanded for power levels above 1 or 2kW.

"Often people notice that the wider the (static) gaps the longer the arcs. So they keep making them wider, and wider, and POW!!... Most people find it is better to have a little shorter arcs for years than longer arcs for 10 seconds..." (Terry Fritz)

A very neat thing is the 'rotary gap'. It is used in series with one or two static gaps usually and is a must for high power xfmrs (usually without buildt-in current limiting) in the multi-kW range. A rotary has a set of rotating electrodes and some fixed ones. The disk with the electrodes spins either asynchronous or synchronous to the line frequency (ASRSG = asynchronous rotary spark gap, SRSG = synchronous rotary spark gap). With a synchronous rotary gap, most power can be transferred (but it is the complicated one to built). An ASRSG should NOT be used with neons, because it stresses them so much that they will fail. A few people use the syncronous rotary gap successfully together with neons, I never tried this. Perhaps it will be a good idea to make a DC-system with a variable speed rotary gap. I'll make a rotary gap in the future, here you can see the first steps. For a given cap size, higher BPS results in longer sparks. Higher break rates can deliver more power (read fatter sparks). Also the ionisation at the top of the secondary coil will be increased. This leads to longer sparks. If a bigger cap can be used together with an SRSG 100(120)BPS is best.

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Cap

The capacitor is the second critical element. Critical because it is really punished by the oscillations of the Tesla tank circuit. The tank current can easily reach a value of 500 amperes (Î=sqr(^2.Ec/_Lp)). The RF produces intense stress on the dielectric of the cap. The voltage can rise above the peak voltage of the xfmr due to resonance with 50(60)Hz line frequency. For limiting the cap voltage, a second safety gap (as described under the filter paragraph) is usually set directly across its terminals. This cap safety gap always should have a current limiting resistor in series with a resistance equal to the impedance of the tank circuit!
Professional caps for Tesla coil circuits usually cost hundreds of US$ depending on the capacitance value. Therefore, most coilers produced their own caps - before the MMC was re-invented and optimized in 1999. But lets start where beginners usually start: the cheap and easiest way is to make a couple of salt water caps. They are nothing else than glass bottles filled with salt water and wrapped with aluminium foil on the outside. But these glass caps are lossy. The best cap (nearly no losses) is built with LDPE-foil as the dielectric. But if you try to build one on your own, the thing has to be operated under oil to prevent corona discharge which will easily melt the LDPE otherwise. So it will get messy, bulky and needs lots of work. Better use some small commercial buildt PP-caps instead and arrange them in series/parallel to achieve the desired voltage, capacitance and current rating - this approach is the best you can do today and is called MMC (MultiMiniCap).
The cap has to be matched to the xfmr what means it has to have roughly the same reactance as the output impedance (mostly inductive) of the xfmr is for maximum power transfer:

Z=U_o/I_s=¹/_{(2^.pi^.f^.C)}

This formula gives the matched capacitance value. The U_o is the open circuit output voltage of the xfmr, the I_s is the short circuit current of it, f is the line frequency. This generates a line frequency resonant circuit between the xfmr and the cap for optimum power transfer. Make C about 120% (up to 160%) of the optimum value for static gaps and up to 240% for syncronous rotary spark gaps (SRSGs). This approach to use a large cap is called "LTR" which means larger than resonance, it avoids resonant voltage rise and give best performance.
A description how I built my caps and some important safety hints can be found on my cap page.

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Primary

The primary coil is usually built out of flexible copper tubing (from the hardware store, diameter ¹/₄" -³/₈"). This is a very good conductor for RF currents. The shape of the coil can either be a helical spiral (constant diameter) or a flat spiral or a hybrid coil in the form of a conical section (often called 'saucer shaped'). The last one is the preferred one for medium sized coils due to the efficient energy transfer into the secondary (excellent field shape and no danger of arc-overs). A typical primary has about a dozen or more windings.
Above the coil, there is usually a 'strike protection ring'. This is an open (!) ring of wire about 2 inches above the last turn of the primary. It is connected to the RF-gnd. The strike protection ring attracts every downward strike from the secondary and prevents the primary from being hit. The supports of this ring have to be insulators! The minimum distance to the primary coil has to be determined by experiment. This is because when the primary is tapped somewhere in the middle, it acts like an autotransformer and can generate very high voltage (way above the HV-xfmr rating) in the last turns. The inner turn of the primary should be at the same height as the lowest turn of the secondary coil. Distance between the primary turns should be about 3/8" (so you can tap it with your desired clamp).
You can calculate the inductance of the saucer shaped primary with these formulas:

L=sqr((L_v^.sin(a))²+(L_h^.cos(a))²)

with

L_v=W_n^2.n²/(9^.W_n+10^.h_n)

(vertical component of the inductance, Wheeler equation)

L_h=W_n^2.n²/(8^.W_n+11^.w_n)

(horizontal component of the inductance)

a is the angle of the coil: tan(a)=h/w,
h is the height of the coil,
W_n is the average radius (W=R+¹/₂^.w)
at the tap point,
w is the "width" at the tap point,
n is the number of tapped turns,
h_n is the height up to the tap point,
w_n is the "width" to the tap point.

h_n , w_n and W in inches, L in microhenries.

Make at least two additional turns, experience has shown that you'll need them for bigger top loads! The angle a should be around 30° to 0° for medium or high power coils. Make the connections in the tank circuit short! At the tap point, the primary should not be wider than the secondary is tall. The inner turn should have a distance of 1"-2" to the secondary. Try to achieve a tap point of 4-20 turns for the two extrema C_t=¹/₂^.C_self up to 4^.C_self and primary cap size from 120%-30% of the matched one (C_t=toroid capacitance and C_self=self capacitance of the secondary coil, see below for more information on these parameters). This way you can change components very flexible if you're upgrading your system (and you WILL upgrade your system someday...). Of course this is only true 'till you start swapping your static gap against an ASRSG or SRSG...

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Secondary

Some words about safety at first:
The secondary coil output voltage is less dangerous than the primary circuit although it can be deadly under the right (wrong) circumstances. In our effort to increase the strength and length of the output streamers from our coils we are pumping more current into those streamers. The use of large toroids and high power make the streamers just that much more dangerous. Many Tesla coil schematics show the base of the secondary coil attached to the primary coil. This is WRONG! In this configuration, lethal 50/60 Hz line current is superposed to the output of your secondary. Under no circumstances the secondary coil should be connected to or come into contact with any primary component. The secondary should be connected to a suitable RF ground instead.
The sparks and arcs will produce a good amount of ozone. Ozone is classified as a health hazard at quite low concentrations. If you can smell it the concentration is already well above safe limits. The smell is a slightly sweet bleach type odor. You may also notice some stronger biting odors. These are caused by various oxides of nitrogen. These are even more noxious than ozone. These gases are produced in great quantity by our spark gap and secondary output. They are a fact of life with high voltage and should be dealt with. Provide some form of airflow to the outside if you coil indoors. Open a window for fresh air. If all else fails limit run times and remove yourself to fresher air. A good idea is to blow the exhaust of the vacuum gap out into the garden.
The high power streamers from our coils can set objects on fire. Be aware of what objects are getting struck by the output streamers. Remove any flammables from the vicinity of the coil. Keep a fire extinguisher in the coiling room at all times. Make sure you get the type that is safe for use on electrical fires.
Tesla coils are noisy devices. Small coils are just loud. Larger coils are absolutely deafening. It's a good idea to wear some sort of hearing protection (like ear muffs meant for use on a pistol range) while running your coil indoors.
More sarety hints can be found on my safety page, be sure to read them!

The secondary is a single layer coil wound on an insulating form (plastic pipe, preferrable PP) with capped ends (sealed). The secondaries range from tiny ones about 1" in diameter (d) and about 5" or 6" long, to monsters that are over 12 feet long (look at my link section to find images of such a 40kW monster coil made by Greg Leyh). These are extremes though. The most common sizes that I've seen are 4 or 6 inches in diameter, and about 4 times as long. The rule of thumb for secondary coils is 3:1 minimum and 5:1 maximum diameter to length ratio.
Choose the length of the coil with the expected spark length in mind: h should be about 0.3-2 times the expected spark length. Before the TCML spreads the knowledge in a lightning fast way, I collected the data of many coils and generated a chart which can be found here. A new formula developed by John Freau even incorporates the BPS besides the wallplug power:
spark length = 5.8 * sqrt (power input) / 4th root ( BPS)
The coil is usually wound with enameled magnet wire. Select the wire gauge that around 1700 turns fit on the desired winding length (this is new, the old wisdom was 1000 turns). 26 gauge up to 18 gauge is common, e.g. AWG22 (0.63mm dia) on 8" coils. If the high voltage xfmr only puts out 'low' voltage (<10kV), then the therefore required big tank cap lowers the resonance frequency of the tank circuit to much. So it will be a good idea to go for more secondary turns by using a smaller wire diameter. The secondary has to be closewound for maximum inductance. The voltage distribution is nearly linear if a toroid of sufficient size is used (for detailed info read more about this in Terry Fritz' paper and on the TeslacoilSecondarySimulationProject-pages of Paul Nicholson at http://www.abelian.demon.co.uk/tssp/), so there is no(!) need for spacewinding the lower part of the secondary.

(Schematic image
courtesy Brent Turner)

The secondary coil itself has inductance and self capacitance. You can calculate the self capacitance C_self of the secondary coil with the Medhurst formula:

C_self = K^.d^*

with d^*=diameter in cm (!!!), C_self in pF and K from the table below:

^h/_d
5
4.5 4 3.5 3 2.5 2 1.5 1

K .81 .77 .72 .67 .61 .56 .5 .47 .46

or you can use the fit formula (valid only for 1 < h/d < 5):

K = .585 - .25442^.h/_d+ .15563^.(^h/_d)²- .02777^.(^h/_d)³+ .00172^.(^h/_d)⁴

You can calculate the inductance L of the secondary coil with the Wheeler equation:

L = R^2.n²/(9^.R+10^.h)

R is the coil radius (=0.5^.d),
h is the winding length,
n is the number of turns.
R and h in inches, L in microhenry.

Finally you can calculate the natural frequency of the bare secondary coil with this formula:

f = 1/[2^.pi^.sqr(L^.C_self)]

With top capacitance C_t, the frequency of the secondary drops down to approximately

f = 1/{2^.pi^.sqr[L^.(C_t+C_self)]}

(From the schematic above, you can see that the total capacity of the coil is not C_t+C_self, but the term is a good approximation at least for the frequency.)

If you want to build a piece of art, read this text from Richard Quick on how to build the perfect secondary (highly recommended though it is a bit outdated!).

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RF-ground

The RF-ground applied to the bottom of the secondary has to be very conductive for RF currents because it has to deliver the huge currents that are converted into the beautiful power arcs we all love. (Look at my experiences with the 4"-system for an description of an always to small RF ground.)

The RF-gnd is a very important component of Tesla coils, so I decided to make a separate page on this (READ it!).

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Top capacitance

On the top of the secondary there is the discharge electrode. It is usually in the shape of a sphere or toroid, with the toroid being the preferred shape. A toroid is like a donut with a web across the hole in the middle. It is electrically connected to the secondary coil and is physically connected to the form that the secondary is wound on. A big radius of curvature (read smooth surface) prevents breakout until a certain voltage is reached. The capacitance C_t of the toroid can then deliver high peak currents for powerful discharges. The bigger the top capacitance, the fatter and longer the sparks. Use at least C_t = C_self (rule of thumb is C_t = 1 up to 4 times C_self or go by dimension and make the D about h/2 (big TC, h = length of the secondary) or up to D = h (small TC) and d ~ D/3 (small TC) down to D/6 (big TC)). When mounting the toroid about the half coil diameter above the coil, the capacitance is approximately:

C_t=(1.28-^d/_D)^.sqr[2^.pi^.d^.(D-d)]

C_t is in pF, D is the outside diameter and d the cross section (cord diameter) of the toroid in inches. For better shielding, its a good trick to mount a large toroid above a smaller one (try and error :-). A toroid can be made from nearly everything: corrugated plastic pipe, aluminium vent ducting or something else wrapped around a circular disk. Use hot glue and self adhesive aluminium plumbers tape to stick the thing together and make the surface conductive. (Tip: plastic is not as fragile as alu vent duct or styropor. You can also use some layers of any standard tape for smoothing the surface before you apply the plumbers tape.)
Here are some texts on how to build a toroid from scratch.

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How to calculate a TC "from bottom up"

When I begin to design a Tesla coil system, my goal is to achieve a certain spark length. That means, I have to get my hands on the right xfmr which can deliver the needed power. The next step is to build an efficient(!) secondary coil which will deliver and withstand the spark length I desire. In the old times of coiling, most of the secondaries were buildt on a long thin coil form (1:10) with about 2000-3000 turns. Later, all people buildt their coils after the rules Richard Quick posted on the web: an aspect ratio of 1:3 up to 1:4 with only 500-1000 turns. Today, common wisdom is an aspect ratio of 1:4 to 1:5 and the optimum number of turns seems to be about 1600 (read more about this on the TCML in 2000/2001). This is a compromise between the losses in the secondary and the losses in the gap. The smaller the primary inductance, the higher the primary current and the higher the losses in the gap. OK, let's begin our calculation:

1600 turns
ratio 1:5
The winding length of the secondary? I go for 50-30% of the expexted arc length because then it would look "cool" _and_ will survive ;-)
How long the arcs will be? That depends on the power input (usually your given xfmr) and the BPS according to the empirical formula developed by John Freau::
spark length = 5.8 * sqrt (power input) / 4th root (BPS).
Width and cord diameter of the toroid? Well, anything that looks good ;-)) Usually I try main diameter = winding length of the secondary, cord diameter as thick as possible (its a matter of $$$ and available space).

The above steps defined the freuquency of the secondary and therefore the frequency of the primary circuit, too.

We already defined the input power and BPS (when calculating the spark length), now we have to pin down the primary voltage (which is usually fixed because you only will have one xfmr at the beginning of your new hobby). As a rule of thumb one can say that the higher the voltage the better. Optimum will be around 10-15kV. Below 10kV the gap losses will be to high, above 15kV you will get LOTS of problems with corona and arc-overs (and considering the current in the primary circuit, something WILL die from an arc-over).
Primary capacitace: go for an LTR cap (Larger Than Resonance cap), this is about 120-160% of the resonant value (at 50/60Hz) when using a static gap.
Ok, the only thing still missing is the inductance of the primary coil, here you have to take the value which results from the frequency equation fp=fs.

For all those calculations, you can use the very good computer programs, some can be found on the web site of my coiling friend Kurt Schraner.

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