## Tesla Coil Grounding

The grounding (or not) of a Tesla Coil is a topic that receives perennial interest on the Tesla Coil Mailing List (http://www.pupman.com/). I suspect that it's largely because there are lots of different opinions, and lots of widely differing practical experience. Radio Frequency (RF) signals play a big role, and any time you start getting up in to the RF area, mechanical details can start to have large effects, because of parasitic inductance and capacitance. In this page, I work through some typical situations, do the analysis, and hopefully, provide information to let you figure out for yourself what an effective strategy will be. As with all things RF and HV related, there is a large amount of "art" in what you do, so use this information as a guide, not as an absolute dictum. "your mileage may vary"

There are two basic kinds of grounds of concern in Tesla Coiling. One is the safety ground, which reduces the chance of inadvertent shocks, or burning down the building. The other, which is more important from a "performance" standpoint is the RF ground, or, more properly, the RF return. The secondary of a tesla coil is an LC resonant circuit, where the C is the capacitance of the topload against "ground", or, more generally, the surroundings. In elementary physics, equations for the capacitance of an object (typically a sphere) in free space are derived, but in the TC world, they don't have much relevance, since there is always something near by (if only the primary of the coil) which will dominate the capacitance, and the corresponding RF path.

### Parasitic Capacitance

In most electronic circuits, parasitic capacitance is an evil thing, mostly because it is unpredictable and tough to model. However, one parasitic capacitance is what we depend on to make a TC work: the capacitance of the top load to the other end of the secondary inductor.

In some TC designs, the bottom end of the secondary is connected to the primary in some way. This makes the entire primary winding act as the "other plate" for the topload. The real problem is that now your secondary is connected directly to the HV in the primary, and if some low impedance path (like an ionized gas path) should occur from top load to you or something important, you wind up connected directly to the HV. Bad news all around.

One possible solution is to connect with a capacitor to the primary. The capacitor needs to hold off the full primary voltage (and then some), and needs to be low impedance at the working frequency (i.e. 100 kHz), but high impedance at power line frequency (i.e. 60 or 50 Hz). How low? A few tens of ohms should be ok. At 100 kHz, 1.6 uF is 1 ohm, so if you allow 100 ohms in that circuit, you'd need .016 uF (16 nF). That's comparable, though, to the size of the primary tank capacitor, and will be just as expensive, etc.

There is also a parasitic capacitor from the topload (and secondary coil) to the primary. The other parts of this circuit are through the tank cap, the spark gap, and the power transformer. If significant power flows here, you might wind up with transformer failures. The usual Pi circuit RFI filter would provide a nice low impedance path for the RF instead of going through the transformer secondary.

### Why you want the counterpoise (and the secondary) connected to the safety ground

Safety, of course. More seriously, if you don't connect the counterpoise to something close to "operator ground", then it can float up to whatever it wants to. Consider the equivalent circuit illustrated here, where the counterpoise is isolated from "real ground". There are three capacitors to consider: 1) The top load to counterpoise capacitance: This is the one that makes the TC actually work; 2) The top load to surroundings and 3) The counterpoise to surroundings.

### Why you don't want RF going through the safety ground

Running a signficant RF current through the safety ground is sort of a bad idea. While the inductance is low, and the wavelength is long, there can be significant induced voltages which can wreak havoc on equipment (like your VCR) that happens to be on the circuit. Most consumer equipment is designed to deal with RF voltages in the microvolts or millivolts range, and even 10 volts is a big problem. In a really bad case, the ground wires might serve as a conductor to something with a sharp edge, from which sparks will emerge, potentially causing fires, shocks, and all around problems.

The other objection is philosophical: Nothing should be designed to put current into the safety ground. It's supposed to just sit there until a fault occurs. If nothing intentionally puts current on the safety ground, then it can truly serve as a "reference", and any current that does appear indicates a fault.

### Safety Grounds - How to avoid killing yourself or burning down the house

When electricians talk about grounds, the "safety ground" is what they are talking about. Also called the "green wire" ground, it is what is connected to the "third pin" on a standard 110VAC receptacle.

### RF Grounds - The myth of needing a low inductance, really short "ground strap"

There are numerous recommendations that your ground connection should be a short, low inductance, wide strap (not braided), etc. I'm not sure that this is warranted. Low resistance, certainly, but low inductance? Short? In part, these concerns come from the fact that Tesla Coils are "radio frequency", albeit at a pretty low frequency, and the fact that the ARRL "Radio Amateur's Handbook" is a standard and useful reference. The ARRL handbook goes into great detail on grounding, low inductance, wide straps, etc., all of which are important to the radio amateur (typically running at 7 or 14 MHz), but not necessarily for a Tesla coil running at 100 kHz.

In this section, we'll cover Inductance (i.e. the reactance of a long wire at RF can be quite high), Skin Effect (AC resistance is greater than DC resistance), and Transmission Line/Standing Wave effects (resonant ground wires).

#### Inductance

Let's look at some typical numbers. A single wire has an inductance of around 1 microhenry per meter (rough approximation: it's lower for larger diameters, and adjacent current carrying wires can change it significantly). Say we have that big 10 kVA distribution transformer (pole pig) powered coil, running at 50 kHz. We've got a 10 meter long run to the "ground point"(about which, more later). What's the inductance, and more important, the impedance at 50 kHz of that wire.

L = 10 meters * 1 microhenry/meter = 1E-5 Henry (10 microhenries)

omega = 2 * pi * f = 6.28 * 50E3 = 3.14E5

X = omega L = 3.14 ohms

A big 3 ohms: At an RF current of 10 Amps (which is pretty significant, 10kVA at 500 kV is only 0.2 Amp RMS), the voltage is going to be a few tens of volts. By the way, that 3 ohms is reactive, and so is NOT a loss factor.

One also has to be careful about using RMS numbers in these calculations, because the typical disruptive (spark gap) coil is basically pulsed with a fairly low duty cycle. If the loaded Q is 10 (optimistic), at 50 kHz, most of the pulse is over within 200 microseconds (10 cycles). There is a long delay (8-10 milliseconds) before the next pulse (at 100-120 breaks per second), so the duty cycle is probably less than 5%. That 10 kVA average power corresponds to 200 kVA peak power. However, since I assumed 10 Amps (50 times the average...), the conclusions are still relevant.

So, inductance is NOT a factor, at least for big coils. If your coil is running at 500 kHz, it gets a bit worse (30 ohms), but a higher frequency coil is likely to be operating at lower power and be physically smaller, so the currents will be lower.

#### Skin Effect

What about skin effect and resistive losses? Here it gets a bit trickier. It's well known that RF currents flow only on the surface of a conductor (they get "squeezed out of the middle by the magnetic fields). Again, let's work some numbers. Assume a #10 AWG wire (5 sq mm: roughly 2.5 mm diameter (0.1")) and the same 50 kHz and 10 meter run.

From the handy tables in the Electronic Engineer's Handbook (3rd edition, page 17-13), at 0.1 MHz (the lowest frequency in the table): The largest permissible wire diameter for a resistance error of 1% (i.e. Rac/Rdc = 1.01), is 14 mils (0.014 inch, 0.36 mm) in diameter. For a 10% error, the largest size is 25 mils (0.63 mm). This IS significant. 14 mils is pretty small. But, let's continue, because the DC resistance of a AWG10 wire is pretty small, so even a 100% increase in resistance probably isn't a big factor.

For that AWG 10 wire, using Circular 74 (page 300), for 50 kHz, we calculate

x = 2.395 * 2.5 (equation 209) = approx 6

And then look up the Rac/Rdc ratio on page 309 which comes out to 2.394. This means that that #10 wire will have 2.4 times the resistance as we would think from the copper wire tables. But, is this significant? AWG 10 wire is roughly 1 ohm per 1000 ft, and we've got about 33 feet (10 meters), so the DC resistance is 0.033 ohms. Factor in the skin effect, and the AC resistance at 50 kHz is about 0.08 ohms. I suspect that the connectors will have more resistance than this.

It looks like we don't need to worry about using copper strap or litz wire.

Another reference (http://www.signalintegrity.com/news/skineffect.htm) provides a handy equation:

Rac per unit length = (2.61E-7*sqrt(f))/(pi * D)

D is diameter in same units as length. This equation breaks down at DC (obviously, because Rac isn't zero at DC, is it...)

#### Standing Waves/Transmission Line effects

Tesla coils do use RF after all, and "RF in the Shack" because of a long ground wire is a traditional problem in amateur radio: I used to have problems with that tingle in your lips when hitting the PTT on 40 meters. However, a quick calculation shows this probably isn't an issue for Tesla coiling. These effects come about when the ground wire is some odd multiple of a quarter wavelength at the frequency of interest. On 40 meters, a quarter wavelength is 10 meters (of course!), and a ground wire 30 feet long isn't all that out of the question, particularly if you are on the second floor.

However, at 100-500 kHz, common frequencies for small to medium sized coils, the wavelength is 600-3000 meters, so a quarter wavelength is 150-750 meters. Somehow, I suspect that you're unlikely to have a ground wire on your TC that is that long, and the higher odd multiples are even less likely.

Copyright 2001, Jim Lux / tcground.htm / 9 Oct 2001 / Back to HV Home / Back to home page / Mail to Jim