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Re: 8 kHz Tesla Coil

Original poster: "Barton B. Anderson" <bartb@xxxxxxxxxxxxxxxx>

Hi Gerry, Malcolm,

I've considered what you said and also Malcolms reply to you. I think you are right and I must retract my comments regarding losses as per sD. As the frequency decreases, sD increases which means a larger portion of the wire determined by the frequency is available to carry current, but this doesn't infer the wire size itself needs to increase. As the wire reaches full density, sD is no longer valid (sD tends towards zero because sD is at full density). Losses due to skin effect is not appropriate if the depth is larger than the wire diameter. This is the part I wasn't getting. However, thermal losses due making available too much current is still valid.

The effective resistance with the addition of sD at resonance becomes:

Re = Rac + Rdc = Rdc(1+(r/(2sD)) if sD is < wd
else Re = 2Rdc

In your case given,
Rdc = 61 ohms
Rac = 61(1+(.011/(2*.009)) = 98 ohms
Re = 61 + 98 = 159 ohms or 1.2 watts

Note, as long as sD is smaller than the wire, sD is valid. Your 23 awg is larger than sD, thus current density is not 100%. There is a small portion in the center of the conductor, which as you stated, is wasted copper. Thus, I expect Re to be slightly more than 2Rdc, which it is by 37 ohms.

We should also state that we are not considering adjacent wire proximity affects (and these are parallel currents thus causing attraction introducing eddy currents). I have to imagine these as little voltage drops along the length of the winding, unevenly distributed. These would certainly be worse in closewound coils. But, that's a different subject.

I will have to rethink the sD portion in this area following discussion. It really should show "minimum wire size recommended" and a resultant Re and Rac would be helpful and meaningful. Proximity losses would certainly be worthy of inclusion if I can dial that out correctly. There is certainly plenty of papers on the subject.

Take care,
Bart


Tesla list wrote:

Original poster: "Gerry  Reynolds" <gerryreynolds@xxxxxxxxxxxxx>

Hi Bart,

I agree with most of what you say. The one possible exception are the RF losses. For purposes of exploring the ramifications of a 8KHz coil, I explore this with less than a full effort.

Since I dont have a complete design for a huge 8KHz coil (and I really dont want to invest too much time in it), I use my 8x36 coil as an example. It uses a 15Kx120ma power source and a synchronous gap with 55nf Cp. Ip_peak is 700 amps (with a 8x32 toroid and tapped at 12 turns). Lp=70uh and Ls=80mh. If I use the energy equations and assume no loss from primary to secondary, then Is_peak=Ip_peak * sqrt(Lp/Ls) or about 21amps. The energy transfer time is 50us and I run at 120bps. If I assume that Is_peak does not decay and stays constant for the full 50us then I calculate the Is_rms=0.707*Is_peak*(50us*120bps) or about 90ma. Since my coil is 61 ohms DC, the power loss in the windings is about 1/2 watt. However, as you rightfully mention, the skin depth for my operating frequency is 9 mils and I use 23 awg with a radius of about 11 mils. So my wire accomodates only a little more than one skin depth. Therefore, the current density at the center is about 1/e or 40% of the current density at the surface. The AC resistance will therefore be larger and I will guess that the 61 ohms is no more than 120 ohms at resonance. Even with the larger effective resistance, the power loss in the coil would be 1 watt. I've tried to make my simplifying assumptions to error on the high side so the actual power loss should be less.

If the skin depth is very large compared to the wire size, it seems like the resistance approaches the DC resistance (current density in the center is about the same as at the surface). If the wire size is very large compared to the skin depth, most of the current flows on the surface and the resistance of the wire become inversely proportional to the wire diameter instead wire cross sectional area.
In other words, a wire with too large of a diameter is a waste of copper.

Please comment if I made any significant error or I'm missing something.

Gerry R.


Original poster: "Barton B. Anderson" <bartb@xxxxxxxxxxxxxxxx>

Hi Gerry,

Everything moves to 6780 turns using #30, but nothing is gained. It's still very high loss. As you continue to increase coil size, the wire size will grow for what it takes to get to 8 kHz. Eventually you'll end up at a typical coil except it will be exceptionally large. Knowing the sD is 29 mils at 8 kHz, it's easier just to select a suitable wire size (6 x sD for closewound coils) and we end up at about #5 ideally (I was conservative with #8 previously). However, since #5 is "HUGE" for the purpose, we would likely tradeoff a little RF heat for a smaller wire size, maybe even only #12 (which is 3 x sD).

So, say we do that:
To get to 8 kHz with a single layer coil, we have to increase inductance starting with the 16x80 coil. It all works itself out geometrically from there. We end up with a huge coil - once again - and the top load should grow proportionally (otherwise, the coil gets even larger). In any case, you end up at 44x220 at 2534 turns and proportionally huge topload.

Granted, it's smaller than the last, but it's the sacrifice of losses to get it down in size. It would likely work just fine for whatever someone wanted to do with it. I do note that as RF losses come into an acceptable range, the turns get lower and lower.

Get rid of the RF losses and then we can get the coil size down. The only way to that is to increase the frequency. Consider that at 8kHz sD is .029", 800 is .092", 80 Hz is .29", and the infamous 8 Hz coil is a staggering .92". So, the bigger the coil, the lower the frequency, and if RF losses are not considered at the design stage, it will just be big, hot, and inefficient. Of course, going the opposite direction (high freq, smaller, etc..) the power handling goes down, so we end up at the typical size range we all build now.

The single layer approach is certainly limited no matter what you do. The multilayer of course has it's own stress to deal with.

Take care,
Bart

Tesla list wrote:

Original poster: "Gerry  Reynolds" <gerryreynolds@xxxxxxxxxxxxx>

Maybe next step is to try a 16x80 inch secondary with the 24x80 toroid and see what guage wire is needed to get 8 KHz. If high voltage is the result of such a coil, more height than 30 inches will be required.

Gerry R.

Original poster: "Barton B. Anderson" <bartb@xxxxxxxxxxxxxxxx>

Hi Bill,

Tesla list wrote:

Original poster: William Beaty <billb@xxxxxxxxxx>

On Fri, 16 Sep 2005, Tesla list wrote:

Large resistance per inch of secondary, so lower Q than normal, less
resonant rise, and broader band output.   But are these values
UNREASONABLY low?


I guess that depends on what you want to do with the coil. If it's just to produce sparks, probably not a problem. Other tid bits have changed, but I'm a firm believer that any obstical can be overcome. For some other purpose, who knows. I can tell you however, Javatc thought this coil needed at least 8 awg wire on the secondary. That is from skin depth formulae, so there is quite a bit of loss in a coil down to 40 awg. Kind of intersting regardless.

Take care,
Bart



>
> Take care,
> Bart
>
> Tesla list wrote:
>
> >Original poster: Ed Phillips <evp@xxxxxxxxxxx>
> >
> >Here's the design of an 8 kHz TC I whipped up last night:
> >
> >Diameter: 8 inches, height: 30 inches
> >
> >101,182 turns of #40 SF wire
> >
> >Wire length 21,327 feet, weight 0.66 pounds, DC resistance 2237 2 > >ohms
> >
> >Inductance 4.1896 henries
> >
> >Self-capacitance 14.5 uuFd
> >
> >Resonant frequency unloaded 20.4 kHz
> >
> >Toroid top load 72" OD, 24" tubing, capacitance ~79.2 uuFd
> >
> >Resonant frequency loaded = 8.04 kHz
> >
> > Who wants to build it?
> >
> >Ed
> >
> >
> >
> >
> >
>
>
>

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