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Thinking and Wondering Out Loud About a Big Tesla Transformer

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jpsmith123

Wed May 17 2017, 03:57AM

Registered Member #1321 Joined: Sat Feb 16 2008, 03:22AM
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I'm referring to the Tesla transformer shown in fig 5, on page 5 of this paper:

From what I can see, the primary winding consists of four copper straps, each one apparently connected to a capacitor by way of its own spark gap switch. And the capacitors in the primary circuit can apparently be charged up to 100 kv, although in the text it looks like their limit is 90 kv.

The oil-insulated conical secondary has 80 turns of 3mm diameter copper wire. (I assume that they're using such big wire to try to minimize the e-field between secondary turns because of the high primary voltage).

According to some rough calculations I did, it seems to me that this transformer should have a step-up ratio of somewhere between 40 and 50; say (850 uH/400 nH)^0.5 = 46 or something like that.

And from the dimensions of the transformer, it seems quite possible to me that the transformer could produce 5 MV or so without breakdown (assuming the oil has a breakdown strength of 75 kv/mm or so in pulsed duty).

Anyway, when I look at the last paragraph on page 12, I infer that a 68 kv primary charging voltage gave a 2 MV output (apparently as measured at the pulse forming line (after the laser triggered spark gap) with a capacitive sensor.

The output (Vo) of 2 MV with a charging voltage of 68 kv seems too low, IMO. It seems to me it should be in the range of 2.7 to 3.4 MV.

So here are my questions: (1) I assume that the significantly-lower-than-expected Vo is due to stray inductance in the primary circuit. Does that seem plausible? And (2) assuming a high enough primary charging voltage could be applied, does this transformer look like it could handle 5MV?

Proud Mary

Wed May 17 2017, 09:00AM

Registered Member #543 Joined: Tue Feb 20 2007, 04:26PM
Location: UK
Posts: 4992

jpsmith123 wrote ...

The oil-insulated conical secondary has 80 turns of 3mm diameter copper wire. (I assume that they're using such big wire to try to minimize the e-field between secondary turns because of the high primary voltage).

Perhaps this is to

(a) keep the Q as high as possible

(b) make the time constant as short as possible to reduce the amount of shaping that must be done by the pulse forming line to form the nanosecond pulses required.

jpsmith123

Wed May 17 2017, 05:53PM

Registered Member #1321 Joined: Sat Feb 16 2008, 03:22AM
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Posts: 843

One of these days I'm going to try to simulate that transformer, which will hopefully shed some light on it. (I'm leaning toward building something similar to it for my demountable X-ray tube project).

Does it seem to you like that transformer design is quite conservative regarding to primary to secondary clearance? It seems to me that the conical secondary coil has more of a taper than may be necessary for the voltage they're working with (considering the relatively short pulses and the dielectric strength of dry, high quality transformer oil under pulsed conditions).

I see that the conical helix type secondary design is popular with the pulsed power group at Loughborough universisty, and I have seen it also in some research papers from India and China.

One variation that I have been wondering about (when dealing with high primary voltages and fast pulses) but haven't seen exemplified anywhere is a design where the winding pitch of the secondary coil would vary in relation to the distance from the primary. IOW, as the secondary winding tapers radially inward away from the primary, the volts/turn would be decreasing, so why not increase turns/length as volts/turn decreases? It seems to me this would increase the output voltage for a given winding length secondary (with a slight decrease in fo). Or for the same number of turns, the secondary winding length could be shorter, with less capacitance to ground and higher fo.
Does this seem plausible?

Proud Mary

Wed May 17 2017, 10:31PM

Registered Member #543 Joined: Tue Feb 20 2007, 04:26PM
Location: UK
Posts: 4992

This Russian paper (below) says that the reasons for using a conical coil is to increase the coupling coefficient and reduce the overall dimensions of the device. It also says the coil is massive to increase its heat capacity and reduce its resistance so it can run longer before having to switch it off to prevent over-heating.

The authors also give a bit of practical information about the pulse sharpening gas switches etc.

I'd never have expected to see a multigap rotary spark gap Tesla transformer in a 2014 design, but that's the Russians for you; - a funky machine, I bet it fires off like the clappers.

jpsmith123

Mon Jun 05 2017, 05:33AM

Registered Member #1321 Joined: Sat Feb 16 2008, 03:22AM
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I found another Tesla transformer that uses big wire in the secondary (link below). It's described in somebody's thesis from Loughborough University.

I didn't look over the paper very carefully yet, but the author mentions something about Q and field stress between turns, IIRC.

Also I could be wrong, but as I'm glancing at Tesla transformer designs such as this one, it seems to me that many of them are not optimal; that is, the output voltage and the energy transfer efficiency are lower than they could be.

Dr. Slack

Mon Jun 05 2017, 05:56AM

Registered Member #72 Joined: Thu Feb 09 2006, 08:29AM
Location: UK St. Albans
Posts: 1659

It's a Tesla-like transformer, but not as we know it (Jim).

The ones we build transfer all of the primary energy to the secondary over several oscillation cycles, neglecting Q and spark losses. If it had to operate in a single pulse, it would not do very well. It uses the fact that several cycles are available to mitigate the low coupling. The output voltage is defined by the energy transferred to the topload capacitor.

A conventional transformer couples primary with secondary closely, can operate in a single pulse, and produces an output voltage defined by the the turns ratio.

This transformer is somewhere between the two. As it has to produce a single short output pulse, it cannot use multi-cycle energy transfer. As the output voltage is very high, it cannot use close coupling. Its output voltage is lower than would be expected for the turns ratio because the coupling is low, it's defined instead by the mutual inductance. If you do the mutual inductance sums for the actual coil geometry (one of the TC calculators may be general enough to handle that geometry) then you'll probably find better agreement.

jpsmith123

Mon Jun 05 2017, 01:23PM

Registered Member #1321 Joined: Sat Feb 16 2008, 03:22AM
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Exactly Dr. Slack.

The Tesla transformers designed as tools for scientific research and for industrial purposes, such as the ones described in the papers I've linked to, seem to generally employ a coupling factor of 0.6 or greater.

This is apparently because the designers frequently want to charge a low impedance pulse forming line, and they want that to happen quickly, so as to get fast multi-channel switching in the output spark gap. I think secondary and/or alternate goals are to minimize both the size of the transformer and the time period that insulators are subjected to HV stress.

I am studying these transformer designs and preparing to build my own version.

When I compare different transformers built by different groups, I see what I believe are sub-optimal designs, and that's what I'm trying to understand.

For example, from fig. 3.19 on page 77 of the thesis paper, it looks like the spark gap is breaking at about 280 to 290 kv, and from his simulation, it looks like the maximum negative voltage swing would be about 320 kv or something like that (with 24.5 kv on the primary capacitors).

Yet when I look at the transformer parameters on page 44, it seems to me he should be getting close to 500 kv with a well designed system or at least 400+ kv.

Going back to the numbers on page 77, it looks like his tuning is off a little bit, the (effective) coupling coefficient is a little shy of 0.6, and the primary resistance of 0.047 ohms seems a little on the high side. Apparently his copper sheet primary is only 100 um thick (page 36), which seems way too thin for the 600 J pulse energy it has to handle, IMO.

Maybe later I'll try to simulate it to see how much of a performance improvement might be gained by tweaking this design.

Edit: This system could be improved if the stray inductance in the primary circuit could be reduced, IMO.

Proud Mary

Mon Jun 05 2017, 02:12PM

Registered Member #543 Joined: Tue Feb 20 2007, 04:26PM
Location: UK
Posts: 4992

Over the years I've seen quite a number of designs for HV generators published in the scienttific literature that looked as though they could have done a lot better until one realises that these circuits were usually designed to fulfil a specific function - delivering nanosecond pulses to an experiment which was the object of the paper, for example - and so long as they deliver said pulses to the experiment in a repeatable, safe, reliable, and economic manner then they are good enough.

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