Stefan's Tesla-Pages

Technological background, part#3
(or 'how to produce your own indoor lightning')


Efficiency of the whole system (diagrams)  

Setup and tuning (tips for beginners)

output voltage

interturn voltage (and breakdown)

Efficiency of the whole system

The most often heard term in Tesla coiling concerning efficiency is "watts per foot spark length". But that is not the best thing to describe a system because of the following reasons:

From the above, you see that the spark length, one can achieve with a given high voltage xfmr, is not easy to estimate. But it is still the first and most important question asked by most of the beginners. In the beginning of my coiling times, I've collected many data points of many different systems of many coilers (mostly from the Tesla-related email lists, see the link-section).

In the first of the following pictures, you can see the traditional way of measurement: the 'length' (not consistently measured!) of an output spark or arc is compared with the input power of the whole system ('wallplug power'). But nobody knows if this will be the real power (measured in WATTS) or if there is a significant reactive part (VOLT-AMPERES) also in some cases. This is a very inaccurate comparison, but gives a rule of thumb what one can expect from a certain xfmr. Most of the data points are within a small band of factor 2 (half time up to two times) from the 'fit' line. (Click on the image for a better resolution.)

As said, the length of the arcs and sparks is dependent on the brake rate. To get some information on this important parameter in coiling (think of rotary spark gaps), I performed some tests with my 2"-system. The cap value was 5.7nF, all data points were achieved with the same configuration (tuning). For low breakrates, I used my new HVDC-source (my second fly back circuit). This source has no centertap of course, so I disconnected the centertap connections from the filter circuit. The ground connection of the source was connected to the safety ground, and to the RF ground on the other side of the filter circuit. The thin spark was not very bright and only barely visible, so I decided to measure the length in 'horizontally attached arc length mode' to get the max. length each arc achieved. Surprisingly, at frequencies up to about 7Hz, no dependence of the BPS was detectable. When I switched to my 10kVAC-source (with centertap), the first 'smooth' run when turning the knob on the variac indicates probably 100BPS (at 180W input power, the 'matched' value). When I turned the variac further up, the break rate rised (at least theoretically - I had no scope available at this time to verify this). I got the following diagram, where I added the measurements with my 4"-system done in August '97.

The last picture shows the relation between the applied voltage (line frequency), radius of curvature and the distance between the electrodes (data from several different books as well as own measurements). As said, this picture is for line frequency (50Hz), our Tesla coils work from 50kHz up to 5MHz! So please don't apply this data to your coil, because high frequency Tesla discharges can jump several times this distances, depending on many other factors (bps etc.). I placed this diagram here because it shows the relation between the radius of curvature and the voltage. (Click on the image for a better resolution.)

It is very difficult to measure the output voltage of a Tesla coil directly. There is an interesting thread on the TSSP and TCML mailing list in late summer 2004.which will perhaps clarify something in the near future. From the point of energy, there can be no more energy in the total capacitance of the secondary than previously had been in the primary cap. This equation gives an upper limit for the maximum voltage Ûsek produced by a certain coil. A bigger toroid leads to less voltage but more (pulse) current available. Experience has shown, that in most cases a bigger toroid means fatter and longer sparks because the spark grows also through current. So a 'cool' coil is perhaps not always the coil with the highest output voltage. Look at the section below on this page for calculating the maximum output voltage.

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Setup and tuning (general tips for beginners)

When you set your system up for firing please be aware of the following things (read this section completely before applying power!):
Tuning means to bring the secondary coil (with its top load) in resonance with the tank circuit. Under the assumption that our calculations are not to bad, one should achieve resonance by finding the right tap point on the primary coil (if not, one has to change the top capacitance of the secondary or the capacitance of the tank circuit). This is usually done by tapping at the expected point minus one turn (this is for stray inductance in the tank circuit wiring). The following section is mainly based on a text from Mike Hammer I found in my early coiling days somwhere in the web, spiced with my own experience:
If you find the best tune point is with very few primary turns then your primary cap is too large. Adding a larger toroid to your secondary will lower its resonant frequency and allow you to tap in more primary turns also. If you get tuned all the way out to your last primary turn and you still haven't found the resonant point, then your primary cap may be too small or your toroid too large.
A system in proper tune should not break down the safety gap often. The safety gap once set properly should not be too active.
If your safety gap is firing continuously then you may be out of tune or you may be running too wide a main gap. Try closing down your main gap slightly and retuning for best output.
The only thing I would like to add to that is you should always work towards having as many primary turns tapped in as possible. Higher primary inductances improve gap operation. One thing you can do to allow for more primary turns include adding a larger toroid to the secondary. This will give several benefits. The lower resonant frequency will allow for more primary turns and the larger capacitance represented by the toroid will give longer hotter sparks. Plus lower frequencies give longer sparks due to the lowering of several loss factors like corona loss and loss due to skin effect.
Last safety hint:
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.

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How to calculate the output voltage?
My way to do this is via energy preservation. But this of course only gives a maximum value.
The formula is:
Eprim * (1-loss) = (Eself + Etop)
(1-loss)*[ 1/2 * Cp * Ûp2 ] = [( Eself ) + (1/2 * Ctop * Ûtop2 )] (1)

If I remember right, Terry says that about 1/4th (loss=0.25) of the energy you pump into the system will not make its way to the secondary, I have to verify this or at least have to find his posting on the TCML again. Until then, I will write this as a variable factor.

Problem is how much energy (Eself) will be stored (='lost') in the selfcapacitance of the coil. To calculate this, we have to take into account the nonlinear voltage rise along the coil length and the nonlinear selfcapacitance along the coil length (and perhaps a phase angle?).

I think the worst case is an effective self capacitance (as calculated via the Medhurst formula) and a linear voltage distribution (which seems to be a good approximation for coils with a not to small toroid, Terry performed some measurements on this for the TSSP, see also the exact math on the TSSP website), so we can say that the maximum energy 'lost' in the self capacitance is:
Eself = 1/2 * Cself * (Ûtop/2)2 (2)

When we combine formula (1) and (2), we get
(1-loss) * [1/2*Cpp2 ] = [ 1/2*Cself*(Ûtop/2)2 ] + [1/2*Ctoptop2 ]
and therefore
(1-loss) * Cp * Ûp2 = [ (1/4*Cself + Ctop) * Ûtop2 ]

which gives finally
Ûtop = Ûp * sqrt {[ Cp * (1-loss) ] / (1/4*Cself + Ctop) }    
(have to check if the data used for 2"new, 4"new and 10" is still valid)
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I guess the major problem is a short between two secondary windings approx. 1/3rd up of the lower end of the coil (as happened to a coiling friend twice when I visited him). The voltage rise is a bit higher here (lets call the factor "a" here, it depends on the size of the toroid, in Terry's measurements it is about 1.12) because of the slightly nonlinear voltage distribution along the coil.
This would give you a voltage between two turns of
dÛmax=a*Ûtop/N (4)

where N ist the total number of turns.
From my memory (which is degrading from day to day :'-(  ) I would say that most wires in the 0.5-2mm range are rated 2-3kV (single enameled, up to 7kV for triple enameled). As you have two insulations between two turns, the insulation should be good for at least 4kV interturn voltage. But better check the insulation via its data sheet or an destructive test (shunted xfmr, variac, two twisted wires) and derate by factor 3 for RF (your test will be only 50Hz!) and factor 1.5 for safety reasons (totally factor ~4). Perhaps you can perform the test with RF in a small tank circuit, that would give more reliable results. The rough estimation gives a permissable dÛmax of approx. 1kV, so I'm right in the ballpark with my coils. 
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