Restoring a Rogowski coil calibrator

[klugesmith]

This is to complete an unfinished thread from 4hv in 2010, about some DIY Rogowski coils and the beginnings of a calibrator.
https://4hv.org/e107_plugins/forum/forum_viewtopic.php?id=82880

Among boxes of stuff, I found some coils and the main part of original calibrator.
Originally powered by a 9 volt battery, it generated 40 amp oscillatory pulses, with similar shape and timing as can crusher pulses.
It's a simple LCR circuit where:
 C = 51.9 uF (as measured), about the same as my 22 KV Aerovox capacitor.
 L is an actual can crusher coil, roughly 2 uH if I recall correctly.
 Switch is a MOSFET, FDD8586 (now obsolete) with Rds on the order of 5 mΩ.
The loop has no intentional extra R. Total R and L can both be computed from measured frequency and damping. Then, from initial capacitor voltage, we can figure the peak current and initial di/dt value.

The main unit has a cable with 3 wires: charging power, gate drive, and common.
Not found was old solderless breadboard with 9V battery connector, 1500 ohm charging resistor, and 555 timer circuit for gate drive.
For check-out,  I substituted an existing breadboard circuit with a manual SPDT switch and debouncer.  Its 74HC00 gate IC limits voltage to 6 V, so peak current is about 26 A.  Each toggle from low to high produces one LCR discharge pulse. 
This was tested with both kinds of Rogowski coil. 

Got a phone picture of scope screen; measurement and analysis are a job for another day.
Yellow is capacitor voltage.   Blue and white are voltages from two different Rogowski coils.

The scope and simulation both show a detail mentioned at end of old 4hv thread.
Rogowski coil (RC) output is proportional to di/dt, which matches the voltage on ideal inductor.
Its phase noticably leads the capacitor voltage, by an angle that's larger when damping resistance is greater.
That means that at the end of initial step, when Q1 is fully On, the coil signal is beyond "top dead center" and is already sloping down.  That makes it tricky to use first high point in measurement of damping and/or period.

Next round here will be to measure the amplitudes, frequency, and damping.  Then solve for model parameters: L, R, and Rogowski coil sensotivity factors.   IIRC, the latter are expected to be about 32 nH and 39 nH based on geometric formulas given in the old 4hv report.

[klugesmith]

Here's the schematic/sim file from previous post.   I think it will open in LTSPICE if extension is changed from .txt back to .asc.  A report of success or failure would be welcome!  rlc_disch2.txt

Without Rogowski coils, I got some discharge waveforms before & after putting a can in the coil.
Also got waveforms from scope into a spreadsheet (which is not required for measuring amplitudes and frequency).

For these pictures the scope trigger is on Q1 gate instead of vC, so we can see proper time relation between Vc curves.  The spreadsheet plot includes an intermediate can position, with a small increase in frequency and damping.

Here the 52 uF capacitor was initially at 6.2 V, for energy of 1 mJ.
With 52 uF high voltage capacitor and suitable switch, we could turn the knob up to 6.2 kV.
Discharge should have exactly the same shape and timing, except 1000 times more current and 1 million times more energy.
Not counting minor increase in R from metal heating during the pulse, and major change in can geometry (it would end up in two pieces).

It will be interesting to match the can-presence effect in simulation model.  Have any can-crushing or coin-shrinking or disk-launching hobbyists worked on that?  We can lower the hurdle by ignoring changes in conductor geometry during the pulse.

[davekni]

I think it will open in LTSPICE if extension is changed from .txt back to .asc.  A report of success or failure would be welcome!  * rlc_disch2.txt

Yes, opens in LTSpice.  To simulate, needs a path to ground from one side or the other of L1.  Spice doesn't allow completely floating sets of nodes.  With that tweak, simulates fine.

[klugesmith]

Good point Dave. It's a mystery why it works in my version of ltspicevii. I had overlooked that rule when I disconnected L1 from GND before original post,  to make a point. When I'm at computer, will investigate using .op directive, and also try disconnecting L1 from the E element (which is just for plot scaling convenience) to see if that breaks it.

[davekni]

It's a mystery why it works in my version of ltspicevii.

LTSpice has an option to automatically add a small parallel conductance to inductors to speed up simulation.  Perhaps other SPICE variants have options to automatically add small conductance to ground on floating nodes.

[klugesmith]

You nailed it, Dave.  In LTspiceXVII under .OPTIONS, I found gfloat with default value of 1e-12.   
Setting .OPTIONS gfloat 0
brought a fatal error message saying "This circuit has floating nodes".
Correctable by adding an explicit DC path, even 1e12 ohm resistor, between L1 and another node.

In other news, I got the alpha and omega of first spreadsheeted Vc waveform. https://en.wikipedia.org/wiki/RLC_circuit
Damped omega is 91600 (14.58 kHz) and alpha is 7400.   Q is 6.21, zeta is 0.081, undamped omega is 91900 (14.63 kHz).
Consistent with C = 51.9 uF, L = 2.28 uH, R = 33.7 mΩ.
A next step is to get the di/dt values and Rogowski coil M values analytically.
And maybe experiment with different Q1 gate voltages, to see change in damping as Rds changes.

[klugesmith]

Before sending any PCB Rogowski coils to friends, I wanted to check the matching of 5 specimens that have been cut out from their original big heavy disks. They are from at least two different fab lots.   

Didn't get to Rogowski coil sensitivity (mutual inductance), where we expect very close matching.

DC resistance ranges from about 0.9 to 1.2 ohms.  Might be attributed to variation in etch widths, copper foil thickness, and plating thickness in vias (which represent around 40% of the path length).

I was surprised to see self-inductance range from about 2.7 to 2.9 uH, in initial quick-and-dirty test. Any ideas how that could vary so much?
Measurement used another artifact from same old box:  a breadboarded oscillator copied from "PIC  based LC meter" by AADE (the late Neil Heckt).  Who needs a PIC when a frequency counter and spreadsheet calculator are at hand?   In this case, fixed capacitor is labeled 0.1 uF and fixed series inductor is labeled 51 uH.


Coils aren't going to be mailed until next week.   I want time to properly enlarge the central holes from 4 mm to 25 mm, using same old hole saw which I found in a tool drawer.

[davekni]

Any ideas how that could vary so much?

First thought would be ECB thickness.  Trace width would have some effect too.

[klugesmith]

First thought would be ECB thickness.  Trace width would have some effect too.

Agreed.  Original fab drawing for this 32 layer board calls out 0.250 +/- 0.010 inches (+/- 4%).
I have the 5 sawed specimens assigned to 3 fab lots based on differences in coloration, mainly the contrast in ground plane gap. More on that later.

Rogowski winding is right-hand helix on layers Top (red) and 30, then left-hand helix on layers 3 and Bottom (blue).

Enlargement of the 1/8" central holes is waiting for a drill jig.   As a former machinist, maybe I am being too picky. Don't trust the self-centering of hole saw pilot drill (3/16") going into the circuit board on a drill press. Fab has 0.125" holes 'cause that drill size was needed for mechanical kit in main circuit board. 

Don't want to miss the opportunity to measure self-inductance and mutual inductance before and after the hole saw removes a stack of ground plane disks on layers 2,4,6,8,10,12,14-19,21,23,25,27,29,and 31.  Does anyone agree or disagree with my prediction that its effect should be negligible? I don't see how any current is induced in the disks, except by variation in magnetic field parallel to axis of the holes.  There won't be any B in that direction from primary wire or from Rogowski winding.

[davekni]

Does anyone agree or disagree with my prediction that its effect should be negligible?

I'm not thinking of any reason for change either.

[klugesmith]

Thanks for your concurring opinion, Dave.   
Today I didn't cut any material, but took inventory of all the boards at hand. Mostly made in 2010, a scrap cutout from middle of a 52-cm round board.   Individually marked 1 through 13.   There are 4 or 5 fab lots:
Boards 1 and 3 are visually a matched pair.
Board 2 has same soldermask finish but different visual contrast at the ground plane gap. Perhaps the pre-lamination stackup is different (core outside or prepreg outside).  IIRC, one board from first fab lot was rejected, and vendor made a replacement.
Boards 4, 5, and 6 have a different soldermask luster, perhaps dry film instead of liquid, and the outline router made a plunge cut well inside the scrap part.
Boards 7 through 11 don't have that plunge cut, and are in individual bags with vendor stickers.
Boards 12 and 13 look like 7-11 but are shrink wrapped for some reason.

Can anyone think of a reason to keep the center hole small, except for automatic centering of the primary conductor?

[klugesmith]

The calibrator in OP, with some updates, served to compare the sensitivity of all 13 RCB's and the hand-wound coil, shown as #14. Story and pictures to follow. Vertical scale is Rogowski voltage (measured between first minimum and second maximum) with respect to average of 13.

Getting absolute values, e.g. 32 nanohenries, will take more analysis because of the amplitude decay and phase shifts from damping.  We might avoid that using a continuous wave current source, as from a Mazzilli oscillator, but at similar currents and frequencies it would consume lots of power and wires would get hot.  The pulsed calibrator could still run for hours with a 9V battery.

To gain some insight, I adjusted model to get much more damping (zeta = 0.20, Q = 2.5) and a damped frequency of 12.5 kHz. Now each quarter cycle is 20 microseconds.  Here are simulated waveforms: red for current, green for voltage on ideal C, and blue for voltage on ideal L.  Rogowski coil outputs are proportional to the last one.

Look at timing on the 0V, 0A line.  Inductor voltage leads and capacitor voltage trails the quarter-cycle times.   Current peaks come ahead of the quarter-cycle points, and Rogowski voltage peaks come ahead by twice as much.    Anybody got an analytic solution already?

[klugesmith]

Perhaps I was too quick to dismiss CW reference current sources, where it's much easier to figure peak values of i and di/dt.
A year or two ago I reported experiments with LC tanks driven with benchtop signal generator (as opposed to "power sourcing inverter").
https://highvoltageforum.net/index.php?topic=2299.msg16805#msg16805
The di/dt levels were similar to those in pulsed calibrator, at roughly 10 times higher frequency.
As a practical calibrator, we'd need to address the stability and repeatability of frequency and amplitude. Including inductance of a wire loop that can be connected through middle of a big round Rogowski coil board.

[klugesmith]

Bit of progress on the analytical front, looking at that model with exaggerated damping.  At instants when current is zero, including immediately after switch closure, VC (voltage on ideal capacitor) is at a peak, and VL (voltage on ideal inductor) is equal to VC.  Rogowski voltage is smaller than VL by the same ratio as Rogowski mutual inductance is smaller than tank L.

But can we really measure VC waveform? How much of the damping is from inside the capacitor?   Waveform in OP has damping that matches R of 33 mΩ, but there's only about 10 mΩ in the coil wire and supposedly 5 mΩ in MOSFET.  Let's check the phase shift between apparent VC and Rogowski voltage; see how it matches the phase shift in RLC model that matches observed damping.  (Note: with real world Q being higher than 6, phase shift questions affect the bottom line by only a small percentage. Perhaps similar to percentage error in measurement of C value, which is fundamental to our determination of R and L.)

Now for mechanical things.  Spot checking board thickness over soldermask showed variations between 0.234" (#13, in low sensitivity group) and 0.257" (#7, with anomalously high sensitivity for its supposed batch).  #2 seems to be an outlyer, with low sensitivity although similar in thickness to #3.
It's hard to systematically measure the whole lot, because on boards that are full disks we can only reach the periphery.   It's systematically thinner because all metal in 18 nominal ounces of ground planes has been etched away.   With care we might use the caliper's "tail probe" to measure thickness at central small hole, after removing burr from drilling out to 3/16".

Finally, after hole sawing #7 and #13, I saw exposed ground plane metal on inside of hole. Turns out the " 7/8 inch, 22mm " hole saw has become smaller with each cut.  Hole diameters so far are 23.07, 22.85, 22.55, 22.44, and 22.33 mm.  In the board's Gerber file, central ground plane disk diameter is about 22.86 mm.

[klugesmith]

Today I made one straight saw cut on the five RCB's that were still round.  Picture attached below.
That enables uniform caliper access for thickness measurements close to the coil section.

RCB thickness ranges from 0.233 to 0.264 inches, with average of 0.248. Chart attached below.  That's over soldermask in a place with no outside copper. I should take measurements over the vias and soldermask-covered outer layer wires in coil section.

A couple weeks ago (before July 25 post), the calibrator got some improvements.  Old can crusher coil was replaced with a more compact air-core inductor, moving in the direction of Brooks coil proportions.  AWG14 magnet wire, 15 turns in 3 layers using a flux felt pen as a temporary former.  There are a couple of short wires with round pin and socket connectors to pass through the Rogowski coils under test.

Oscillation frequency came down to 11.6 kHz, implying that L went up to 3.6 uH. Q is still about 6. I think the coil DC resistance went from about 9 to 11 mΩ, and total loop ESR (figured from observed damping) went from 34 to 45 mΩ.

The new saw cuts in RCB will allow the calibrator to be mechanically more compact.  I want a horizontal surface on which to rest Rogowski coils, with a vertical wire for the reference current pulses.   Need to consider the whole reference current path, including placement of the inductor and its stray field.

Now let's consider the capacitive coupling of voltage from reference pulse conductor to the Rogowski coil.  It's got the same proportion, with respect to signal of interest, as that from kilovolts in the kilojoule pulses to be measured with the RC.  Be nice if we don't need to add electrostatic shielding.

So where in the test pulser loop should we put the Device Under Test?  Suppose we continue to say "ground" node includes the MOSFET source and one end of capacitor.   With DUT between C and L, as in tests so far, it sees full oscillatory capacitor voltage but no sharp steps.   Between L and switch, there would be one fast voltage step with flat levels before and after.  Between C and switch ( one or the other being "ground") there would be no significant voltage on the test current conductor.  Where in real kilojoule pulse apparatus can Rogowski coil reasonably be placed?

[klugesmith]

Been measuring inductors between 1 uH and 100 uH using a fancy HP 4285A (75 kHz to 30 MHz), and a notorious LC-100A (around 600 kHz) just acquired new for $20.  That deserves its own thread at highvoltageforum.   

Also made a DIY circuit board microsection from the hole saw plug of a RCB shown in August 1 post above.
We get to see how things were torn up by the hole saw, including at the ridge where top and bottom saw kerfs met. The round plug was sawed along a diameter and potted in Devcon 5-Minute Epoxy, using a disposable coffee-creamer cup as a cylinder mold.


I'd pre-tested this two part resin from 10 year old bottles, practically empty after this exercise.  Part B was exceptionally viscous but the stuff seemed to cure properly. On same test date, I found that JB-Weld in squeeze tubes I'd started in 2005 was still good.   Yay for long shelf life.   One product to beware of is RTV silicone caulk. Sometimes, in tubes started a year ago, it squeezes out and spreads normally but never cures.

After removing the mold, surface of interest was lapped against sandpaper resting on a flat surface.   The finest I could find is what they call 500 grit in USA.  What are popular metric sandpaper sizes?   It was plenty fine to reveal the 18 layers of 1-ounce-copper ground planes, but professional microsections are much more finely polished.

[edit] This is a response to Alan's response below.  Sandpaper seeking was limited to 5 minutes in my garage this morning, where the traditional shelf is practically blocked by a rolling shelf unit full of wife's stuff.  I know there's super fine sandpaper and crocus cloth somewhere in that room, but it's probably easier to buy new stuff.

[edit edit] It's the first time I remember mixing 2-part epoxy by weight instead of volume.  Put mixing cup on a digital scale and hit the zero button.   Then squeezed in the thicker (slower than molasses) resin. When I stopped, the scale indicated 5.2 grams. Then squirted the thinner resin on top of that, taking only a few seconds, easy to stop at indicated total of 10.4 g.

[alan sailer]

I was surprised when I found very fine sandpaper in an auto parts store. It is used for paint polishing.
They went down to 3000 grit.

When I was still at work I got a few sheets of even finer stuff. Some of it felt less rough than a sheet
of printer paper...

Cheers.