Rogowski transformer query

Not if there's no ferromagnetic core in the toroid, it isn't. The coupling coefficient in that geometry wil be way less than 1.

With no core, there's a strong tendency for the contributions of the inner and outer sides of the toroid to cancel each other.

Cheers

Phil Hobbs

OK, point taken, thanks.

So, not a Rogowski coil, but a long 1000 turn solenoid wound on some flexible (or hinged) core material up to the end and back so the two connecting wires are at the same end.

Bend it into a circle to form a toroid around a single wire and you have a transformer with a 1000:1 turns ratio. What if you bend it into two turns of a circle with a single wire through it? Or three? Does it matter, as far as first-order effects are concerned?

Cheers

It certainly has a 1000:1 turns ratio. But it doesn't act much like a

If the core material is not magnetic, then there is not much coupling from the turns on the end to the single turn (presumed) in the middle.

Is there some reason not to use a ferrite? George H.

No, I'll use ferrite, I had thought I could use air, but I was wrong.

What of the question about how the number of wraps of the solenoid would affect the turns ratio?

Cheers

OK, pretend I have a flexible ferrite core. What difference is there between bending my solenoid into a ring (toroid) and passing a wire through as opposed to bending my solenoid into a double (or triple) ring and passing a wire through?

I think none, to a first order, but need a sanity check.

Cheers

Clive,

The result is correct, but the reasoning is not quite right. The output voltage of a Rogowski coil is not a direct function of turns ratio. Instead, the output is proportional to the total number of turns in each major loop around the current-carrying wire, the area of each turn, and the di/dt of the central conductor.

So, if your Rogowski coil has a total of N turns, a single loop of N turns around the central wire develops the same output voltage as two loops, where each loop has N/2 turns.

Bert

A true Rogowski coil does not use ferromagnetic core materials. These materials will create saturation problems for very high peak currents for pulsed power measurements. Air-core Rogowski coils provide virtually linear response, even for currents in the meg-ampere range. Adding ferromagnetic material would simply degrade accuracy and limit dynamic range.

Bert

this experiment is easy enough to do with a pieces of string.

straighten the loop out into a single loop and count how many passes the main wire makes through it.

You need a continuous path in ferrite, so either you need to take 2 turns of the high-current wire through a normal annular toroid, or you need the core to be like a figure-8 except with a full twist instead of a half-twist between loops. ;)

With an air-core toroid, the signal will depend somewhat on the exact position of the high current wire inside the coil, so if you make the loops really symmetrical it should work fine. You have to have an even number of twists in the loop though, or the two will cancel out instead of adding.

Cheers

Phil Hobbs

Given that it's understood to be, not just any transformer, but a Rogowski transformer, with all the support hardware needed to use it, yes.

Yeah. Doesn't matter where wire goes, in the along-the-circle (toroidal) direction. Only poloidal direction (turns around the round support) matters.

Definition:

Because the directions are orthogonal, and the field obeys superposition, we can separate the total field into poloidal (i.e., the torus-shaped field you get from a single turn loop, or a short solenoid) and toroidal (field that goes into the core, if it's a regular cored toroid, or that does the Rogowski thing otherwise) components.

When we do this, then the winding (the part making a helix around the form) has some positive amount of poloidal field, because it makes a loop. If we have the end return through the center, then the segment making the non-coiled return path makes the same loop, but in the opposite direction, so its field is negative, and equal. The total is now zero.

Now, having said all that definition: what do you mean? Do you mean to have two layers of 500 each, so the winding goes down, then comes back over the first layer (progressive wind, I think)?

If you keep going around the loop (which you can do on a closed toroid, but not an open and flexible Rogowski), the poloidal field adds up, rather than canceling.

Tim

The series resistance of the Rogowski coil wire kinda dominates the output current. For meter applications that's not a killer, but for power, you'd want superconductors.

You're right, the number of turns and the shared flux over the area of those turns matters, but not the stacking. If stretching the Rogowski coil changed the cross sectioinal area, that WOULD have an effect.

Doesn't help if there's no coupling.

Cheers

Phil Hobbs

Coupling is overrated; to transfer power, ANY coupling works, and if the primary side doesn't have resistive losses, the coupling constant doesn't contribute to inefficiency. Economics of superconducting machines are amusingly different from copper-and-iron ones.

Now take a very very long, 2-layer Rogowski coil ...and wind it into a torus-shape rather than ring-shape.

Doesn't that only detect the RF e-field of a vibrating PZT rod threaded through the donut hole?

Heh.

ALso:

But Q can only do so much.

You don't have any room for manufacturing variation, you need very high Q capacitors as well (ideally, vacuum dielectric!), and you have very little bandwidth: which means tolerance in mains frequency, ability to measure fluctuations or distortion, and sure, even startup time.

The superconducting resonators used in LINACs have Q factors in the 10^9 range, at 100s of MHz. That's better than quartz crystals, and a human-scale time constant (~seconds)!

Transformers become very interesting, though. You want suitable interleaving of primary and secondary, to minimize proximity effect, maximizing current capacity (because critical field). Meanwhile, flux still dominates overall size.

It's probably not so convenient to dump the iron core just yet (even despite core loss); but given enough turns, and maybe a PFC capacitor, that's still an option.

Heh, funny, a PFC capacitor would be bigger than using iron core...

Tim

So, a ring of incandescent filament?

Sounds like one of those setups for magnetic vector potentials. :) See: Aharonov-Bohm effect.

Tim

Thanks, all, this discussion has clarified a few things for me, very helpful.

Cheers