Pulse tests of current transformer - clearly shows instantaneous rate current change!

[Al (astral highway)]

With permission from mods, I've split this from another thread.

I wound a current transformer, (CT) and needed to do some tests on its behaviour with medium and large currents. Without these tests, I wouldn't be able to calibrate the CT and I would risk destroying some expensive silicon - IGBTs.

So these results mean a lot to me.

Specifically, I needed to visualise the derivative - di/dt - the instantaneous rate of current change - not the RMS - but not using a calculator. I realised that theoretical calculations couldn't really take me anywhere reliable.

So I'm delighted to share these results. Since the induced voltage across the inductor is the derivative of the current through the inductor, the burden resistor and current transformer can directly trigger a scope to display the precise moment in time of interest - that is, the derivative.

Current transformer is 60 turns Litz wire (1.3mm) wound on an 8700nH toroid from Epcos.


The rig was a 3200uF, 400V- rated pulse capacitor, (EPCOS, B43415-S9328-A3 type).

It was charge to 28V (for my safety, keeping it low) and then switched into a giant inductor of around 2.6uH

(6 turns, spaced. Diameter 4cm, length, 5.5 cm) I calculate the ESR of the circuit (DC, not including complex impedances in the resonant circuit) to be around 0.053R. The cap obviously has to be pulse rated and sees a large potential difference for pulses of <250uS.

In one-shot, 'single' trigger mode, the scope reads a maximum voltage of minus 3.36V.

This corresponds to a peak of minus 200A.[/I]

Analysis:

1) The first waveform is irregular, not quite sinusoidal. I wonder if this irregularity is explained by the fact that the switch isn't ideal.

It's me, manually connecting a wire to the inductor from the charged capacitor (safe, as very low voltage.) The current is large enough to partially fuse the copper passing through the CT, in a 1.5mm^2 conductor, at the point of contact (basically, the soldered joint on the cap lead outs).

As I say, I wanted a quick and dirty test rather than getting involved with the complexities of power semiconductors at this stage. Calibrating the main feedback mechanism for any future tests is the first priority.

2) There is then a delay of slightly more than one period, 250uS.

3) There is then the peak pulse of around 250uS, sign is minus 200A, showing a magnetic field collapsing in an inductor. Unlike the first pulse, where I made contact to complete the circuit, this is the first of two resonant pulses. The fall time is incredibly pronounced. The -ve going part of the waveform is like a sawtooth but the rising edge is not.

The set up is like a pulse-forming (delay) network but with only one unit instead of repeated units.

4)then a pulse of around 120uS, same sign. The capacitor is completely discharged in the initial 'ragged' switch of 220uS, plus the two, resonant events totalling 370uS.

With permission from mods, I've split this from another thread.

I wound a current transformer, (CT) and needed to do some tests on its behaviour with medium and large currents. Without these tests, I wouldn't be able to calibrate the CT and I would risk destroying some expensive silicon - IGBTs.

So these results mean a lot to me.

Specifically, I needed to visualise the derivative - di/dt - the instantaneous rate of current change - not the RMS - but not using a calculator. I realised that theoretical calculations couldn't really take me anywhere reliable.

So I'm delighted to share these results. Since the induced voltage across the inductor is the derivative of the current through the inductor, the burden resistor and current transformer can directly trigger a scope to display the precise moment in time of interest - that is, the derivative.

Current transformer is 60 turns Litz wire (1.3mm) wound on an 8700nH toroid from Epcos.


The rig was a 3200uF, 400V- rated pulse capacitor, (EPCOS, B43415-S9328-A3 type).

It was charge to 28V (for my safety, keeping it low) and then switched into a giant inductor of around 2.6uH

(6 turns, spaced. Diameter 4cm, length, 5.5 cm) I calculate the ESR of the circuit (DC, not including complex impedances in the resonant circuit) to be around 0.053R. The cap obviously has to be pulse rated and sees a large potential difference for pulses of <250uS.

In one-shot, 'single' trigger mode, the scope reads a maximum voltage of minus 3.36V.

This corresponds to a peak of minus 200A.[/I]

Analysis:

1) The first waveform is irregular, not quite sinusoidal. I wonder if this irregularity is explained by the fact that the switch isn't ideal.

It's me, manually connecting a wire to the inductor from the charged capacitor (safe, as very low voltage.) The current is large enough to partially fuse the copper passing through the CT, in a 1.5mm^2 conductor, at the point of contact (basically, the soldered joint on the cap lead outs).

As I say, I wanted a quick and dirty test rather than getting involved with the complexities of power semiconductors at this stage. Calibrating the main feedback mechanism for any future tests is the first priority.

2) There is then a delay of slightly more than one period, 250uS.

3) There is then the peak pulse of around 250uS, sign is minus 200A, showing a magnetic field collapsing in an inductor. Unlike the first pulse, where I made contact to complete the circuit, this is the first of two resonant pulses. The fall time is incredibly pronounced. In fact, the -200A event takes place within 101uS, as shown on the scope display.

The -ve going part of the waveform is like a sawtooth but the rising edge is not.

The set up is like a pulse-forming (delay) network but with only one unit instead of repeated units.

4)then a pulse of around 120uS, same sign. The capacitor is completely discharged in the initial 'ragged' switch of 220uS, plus the two, resonant events totalling 370uS.


Conclusion: my new current transformer is fine at very high peak currents: (200A). (I'd already tested it at 5.5A with 230KHz pulses, too.)

This means I can continue with the next bit of test equipment, which will use a semiconductor switch instead of my ragged version.

I wonder if anyone with magnetics insight can comment on the slightly unfamiliar waveforms in the resonant periods?

[Radio1950]

Hi there,

Its not quite the same but for what it is worth ...

We used to monitor the cathode current pulse of a 2.2 Megawatt ATC search radar with a ferrite curent transformer.
The pulsewidth was 2.5uS, PRF 400 ppS, and current was 24 Amps approx.
The cathode voltage was about 24KV.
The pulse was monitored on a Tektronix 545B CRO. It was a while ago!
The pulse was square with a risetime adjusted to about 50nS, so as to keep the dV/dt from being too fast, and thereby giving magnetron arcing.
The falltime and pulse droop was also monitored, but I wont bore you with why.

I give you the above details only for perhaps some comparison.

I am not quite sure what you are trying to achieve as a final result, but maybe you would be better using a square wave pulse generator for tests, with specified rise and fall times, and with defined source impedance.
Some AF generators have square wave abilities.

Our radar current transformers were designed to be terminated in 50 ohms.
Can I suggest you try the same, as your results seem "differentiated", but then again you are using effectively a charged capacitor as the source.
Try 470 ohms then lower, until you see the expected pulse.

Also be aware that the bandwith of your CRO vertical amp has to be factored into any rise time observations.

Dont know if any of that helps.

Good luck.

[Al (astral highway)]

Originally Posted by Radio1950

We used to monitor the cathode current pulse of a 2.2 Megawatt ATC search radar with a ferrite curent transformer.
The pulsewidth was 2.5uS, PRF 400 ppS, and current was 24 Amps approx.

...That's 9 million, six hundred thousand Amps per second! (Although of course, the point of my post is precisely to show the instantaneous behaviour). Thanks for posting that: I find it fascinating to hear from people who are or were doing this for real, at the sharp end.

... pulse was square with a risetime adjusted to about 50nS, so as to keep the dV/dt from being too fast, and thereby giving magnetron arcing.

I can see how that overvoltage condition could happen with such fast di/dt. Did you use a conventional pulse forming network / transmission line/ for the delay?

The falltime and pulse droop was also monitored, but I wont bore you with why.

Actually, I'm really interested in this so you have no danger of boring me. Please could you say more?

I am not quite sure what you are trying to achieve as a final result, but maybe you would be better using a square wave pulse generator for tests, with specified rise and fall times, and with defined source impedance.

The toroidal current transformer is the main current feedback loop in my next iteration of a solid state Tesla coil. The reason I wanted to put such a high current pulse through it was to see if the core would saturate. The size of the pulse was the key thing for this test, read below.

I chose a core of 8700nH Al, 45mm OD, 25mm ID, 20mm H - a cross-sectional area of 200 square mm. The test shows that it is fine - the waveform doesn't have to be a sawtooth, but the sharp falling edge is a good sign.

I'm still intrigued by the waveform of the resonant pulses. The falling component/sawtooth/ clearly is the differential - that's the information I wanted. But I wonder that the hybrid form of it, sawtooth for the falling component, and then a virtual sine-wave rising component, is explained by the magnetics in a complex way that I don't fully understand? I sense it's because there is a DC component in the pulse, too.

This was the second of two tests. The first test was a pulse of just 5.5A, at the design frequency of around 230Khz, and, as you say, from a square wave source with a class B follower stage to give it a bit of oomph. The result is pleasing.

The output of the CT goes to overcurrent detection circuitry that I am still tweaking. The voltage from the burden resistor will be full-wave rectified and filtered. It will then drive logic that will shut down the whole drive in less than two RF periods (5uS) to protect an expensive IGBT. The calibration of this part of the circuit is the most critical to the overall design. Without it, I'm shooting in the dark. Next step is to calibrate the voltage output from the op-amp...

Our radar current transformers were designed to be terminated in 50 ohms.
Can I suggest you try the same, as your results seem "differentiated", but then again you are using effectively a charged capacitor as the source.
Try 470 ohms then lower, until you see the expected pulse.

Hello, yes, I know I can't use an ideal voltage source in my home set up, not one that will produce such huge pulses. The 1.1R termination/ burden resistor was the conclusion of various tests with higher burdens, and seems easiest to work with - I want low voltages out of the CT.

Also be aware that the bandwith of your CRO vertical amp has to be factored into any rise time observations.

Can you say more? mine isn't really a lab grade model, just 100MHz bandwidth, and even my two scope probes yield different results under the same conditions. But that's what I have to work with, and even if it takes a bit more effort, I'm sure I can do what it takes.

Thanks again for posting - that sounds like a fascinating career indeed!

Mods: I just noticed that I posted the whole OP twice - apologies for the oversight.

[Radio Wrangler]

My transmitters have about a 60ns risetime of RF voltage into the load and run about 15A during their pulse If the current was linear, that would be 250 mega-amps/ second. A carefully chosen LDMOS device is all it takes.

The gate drive's fun, though, and that risetime is deliberately controlled so the TX spectrum meets a specified template.

David

[Al (astral highway)]

Hey David,

Yes, quite a ‘flux-capacitor’ charger there! You mention the gate drive, is it unconventional? I’d be interested to know more...

[GrimJosef]

Originally Posted by Radio Wrangler

My transmitters have about a 60ns risetime of RF voltage into the load and run about 15A during their pulse If the current was linear, that would be 250 mega-amps/ second. A carefully chosen LDMOS device is all it takes.

The electron beam I worked with here https://cpb-us-e1.wpmucdn.com/blogs....QE-2e5m2jl.pdf rose from zero to 80kA in 10ns, so 8 tera-amps/second. That took a very low inductance spark-gap switch followed by a tapered transmission line 'transformer'. Actually the harder job was switching the pulse off just as cleanly, without either a long tail or significant voltage reversal.

Getting back to the OP's issues, it gets progressively more difficult to build trustworthy voltage and current monitors as dI/dt and/or dV/dt get large. A tiny bit of stray capacitance or mutual inductance can couple EM noise from the main experiment into the monitors and it can be very hard indeed to work out what's real signal and what's just unwanted leakage. We were definitely in the regime where it was at least as hard to design the monitors as it was to generate the pulses in the first place.

One very useful approach is to build two monitors based on as widely different principles as possible e.g. one voltage monitor based on a 'simple' resistive divider and another one based on a D-dot probe plus fast integrator, both looking at the same pulse. If they agree with one another then that's a huge confidence boost. If they don't then the details of the differences can very quickly point up what might be going wrong.

Cheers,

GJ

[Radio1950]

Hi again,
One of my mates just corrected me.
Cathode current pulse being monitored was a bit over 100Amps.
I am getting my PSR radars mixed up!

[Radio Wrangler]

Nothing exotic in the gate driver, it's just that it can afford to be very inefficient because this transmitter is only on for less than 1% of time. Crude is the word, but very effective for its job.

David

[Argus25]

Al,

I think the remarks in post 6 are very wise about measuring the current in two ways. With the transformer method there will always be differentiation and loss of the DC component, you may want that, but if you sensed the current across a very low value resistor, you can do what you like with the signal then.

It is important that the sense resistor has a zero temperature coefficient and can handle the current. One way is to use a number of pieces of thick (>1.5mm)Constantan wire in parallel and less than 10mm long. I have used this wire in current sense applications up to 50A, but it could easily be made to sense many hundreds of amps with the right number of wires. It is super easy to solder to, unlike nichrome. There are many pre-made current sense resistors available too.

Then the voltage across can be sensed with a differential OP amp to get rid of any common mode noise. One handy circuit , if the sense resistor is on the high side, is to ground reference the output by using the voltage developed across the resistor to unbalance a current mirror. There are also IC's available from LT that do essentially this as high side current detectors.

Once you have the current monitored this way you can process the signal and easily differentiate it if you required it in that form.

I cannot attach a link easily on the device I'm typing on, but if you wanted to look at some current detectors using op amps and unbalanced current mirrors and some Constantan wire (these were for a 25A application) have a hunt around on www.worldphaco.com for an article called Historical Dynamo regulators or something like that, and there are some example circuits in there.

...also if you use this method, you can scale the resistor up and check the function/frequency response and noise immunity of your circuitry at much lower currents.

Hugo

[Al (astral highway)]

Originally Posted by GrimJosef

The electron beam I worked with...rose from zero to 80kA in 10ns, so 8 tera-amps/second. That took a very low inductance spark-gap switch followed by a tapered transmission line 'transformer'. Actually the harder job was switching the pulse off just as cleanly, without either a long tail or significant voltage reversal.

Hey GJ, that is a fascinating experience, no doubt, in your career history. Are you one of the co--authors of that paper? (I don't of course know your identity in real life!). The figures you refer to up there in that para are astronomical and I can only imagine what collosal voltage resulted from such di/dt.

One very useful approach is to build two monitors based on as widely different principles as possible e.g. one voltage monitor based on a 'simple' resistive divider and another one based on a D-dot probe plus fast integrator, both looking at the same pulse. If they agree with one another then that's a huge confidence boost. If they don't then the details of the differences can very quickly point up what might be going wrong.

Very interesting and rigorous approach. And yet, on the face of it, I have the problem that I can't stick a 'scope probe across a simple resistive divider (for the comparison purposes you describe) beyond this test stage as that (resistive divider) will ultimately be connected directly to the mains... it will just trigger my RCD and MCB instantly. I'm reluctant to lift the safety earth from my 'scope, although perhaps this isn't such a bad idea. The case is double insulated (plastic) and as long as I'm very methodical and think through every step, it may be justified.

A D-dot probe looks like a very specialist and I'm guessing, costly bit of kit! I'll dig out a bit more on the principles. I hadn't heard about it until you mentioned it.

[Al (astral highway)]

Originally Posted by Argus25

I think the remarks in post 6 are very wise about measuring the current in two ways. With the transformer method there will always be differentiation and loss of the DC component, you may want that, but if you sensed the current across a very low value resistor, you can do what you like with the signal then.

Hey Hugo,

Thanks for affirming what GJ advises up there. It's great to have such clear advice from two experts.

I think it's important for me to distinguish the stages of this project.

1) Development,trialling and calibration of adequate test equipment and along with that, calibration of magnetic components that are necessarily home-made. These are current transformers that will have a key feedback function, and the main gate transformer. I can't use commercial products for either, or don't want to.

2) Future stage when I'm directly measuring what's happening in a circuit directly connected to the mains - not isolated as this test was.

But I haven't reached this stage yet. There will be more tests along the lines of the pulse test I posted yesterday, but with successively higher voltages - nothing too scary, but first 50V and then 80v, isolated.

I can, at this stage, use a current sense resistor as you describe. The constantan wire idea of yours is great. I had got stuck with nichrome, but of course rejected it because of its inductive properties. I was, however, aware of sub-ohmic current sense resistors of substantial pulse capacity.

3) Building the prototype. But there's no hurry. Some of the components I'm already working on, and some are complete, but putting it all together isn't going to happen until I can exactly quantify everything I need to.

I am intrigued by the role of hysteresis in the magnetics I'm using (the home made CT's as well as my gate transformer, which is still under test, too.) It appears to be quite a complex subject, however.

[Argus25]

There are always more options for current detectors too. Another method I have used is to get a small iron toroidal core, split the ring with a junior saw and file the slot out a little to slip in a Hall device. Then the current can pass through 1 turn or more and the magnetic field in the ring passes through the faces of the Hall device.

I found with this method though and the type of toroid and Hall device (there is one version of this detector in the article I mentioned) the frequency response was limited to about 20kHz. That is actually good in some ways as it is self immune to RF and other interference etc and it provides electrical isolation from the circuit being monitored, but it is probably far too slow for your application, but still it is a good method for detecting average DC without the heat losses of a current sense resistor.

[GrimJosef]

Yes Al, I'm Graeme Joseph Hirst - my forum name comes from the first two of my real names which the Russian embassy's visa dept once converted, via Cyrillic and back, to GrimJosef and then stamped that in my passport. My wife still thinks it's funny.

The electron-beam diode in the paper was about an 8ohm load at 80kA so there was about 650kV across it. If I remember rightly our primary Marx generator ran at 1.6MV which was rung up in voltage into an under-matched pulse-forming line and then transformed back down again by the tapered line after the output switch.

D-dot probes are most useful when you have access to relatively 'stiff' electric fields in the dielectric between the high voltage conductor you're interested in and the return current (often ground) plane. They're actually simple beasts - just a small isolated patch in the return current plane which acts as a capacitative sensor to the high voltage conductor. I think there are, or at least used to be, people who would sell them to you but since we were usually designing all of the rest of the kit we normally just built our own. If we needed a high-speed passive integrator though then we would typically buy that as they are hard to design if you haven't had a good deal of experience (by this stage signal voltages will be relatively small and stray effects can become very important).

EDIT: I should add that the cross-checking between two different techniques may be made easier if you can rely upon the probes' linearity. Something as basic as a stray capacitance in a simple dielectric, for example, can often be very linear. So you can calibrate it at low voltage using another sensor which you absolutely trust but which you know can't be used at high voltage. Since the first sensor is linear the calibration at low voltage will be just as valid at high voltage.

Cheers,

GJ

[Al (astral highway)]

Originally Posted by Argus25

I found with this method though and the type of toroid and Hall device (there is one version of this detector in the article I mentioned) the frequency response was limited to about 20kHz. That is actually good in some ways as it is self immune to RF and other interference etc and it provides electrical isolation from the circuit being monitored, but it is probably far too slow for your application,

Hi Hugo,

The Hall device is a great idea of yours. Following your post, I've found a chip that will be sound up to 80KHz, surprisingly, which is still low for my purposes but still has value.

I am reminded of your paper on ignition systems for cars and rocket motors and may adapt a circuit based on those principles, but using a SIDAC as the power device.

I also have a gas discharge tube in my collection, so if I measure the pulse in its E-field, once I have a circuit put together, I should get interesting results

[Al (astral highway)]

Originally Posted by GrimJosef

The electron-beam diode in the paper was about an 8ohm load at 80kA so there was about 650kV across it. If I remember rightly our primary Marx generator ran at 1.6MV which was rung up in voltage into an under-matched pulse-forming line and then transformed back down again by the tapered line after the output switch.

That's a whole lotta Joules!

Hi Graeme, it's great to have your input: you obviously couldn't have higher credentials for commenting in this field of expertise. The paper is obviously for peers working in this domain, so I won't try to decode it!

EDIT: I should add that the cross-checking between two different techniques may be made easier if you can rely upon the probes' linearity. Something as basic as a stray capacitance in a simple dielectric, for example, can often be very linear. So you can calibrate it at low voltage using another sensor which you absolutely trust but which you know can't be used at high voltage. Since the first sensor is linear the calibration at low voltage will be just as valid at high voltage.

This is a great methodology and one that I will follow. Cheers!
It sounds as if the cross-check sensor could be as simple as a current sense resistor, although my previous comments on lifting the 'scope ground apply.

I also have the Hall effect sensor circuit to put into action, once the 'chip arrives.

[kalee20]

Originally Posted by astral highway

The rig was a 3200uF, 400V- rated pulse capacitor, (EPCOS, B43415-S9328-A3 type).

It was charge to 28V (for my safety, keeping it low) and then switched into a giant inductor of around 2.6uH

(6 turns, spaced. Diameter 4cm, length, 5.5 cm) I calculate the ESR of the circuit (DC, not including complex impedances in the resonant circuit) to be around 0.053R

My calculations then indicate a resonant frequency of 1.744kHz (so not high), and a characteristic impedance of 28.5mΩ. This is very low – if your capacitor ESR is 53mΩ then it will dominate and the resonance will be damped out of existence, so you won’t see any ringing. But with a circuit resistance as low as this, it won’t be very well defined and all bets are off if you wanted an accurate current to characterise your CT.

You also should consider the insertion loss of the CT. If you have 1 ohm burden (?) and 60 turns, then reflected resistance = 1Ω / 3600² = 0.28mΩ (which is rather negligible in comparison with the other resistances, luckily).

Time constant of 3200μF and 0.053Ω is approx. 170μsec. This does tie up with your ‘scope trace in the first post of this thread.

Originally Posted by GrimJosef

One very useful approach is to build two monitors based on as widely different principles as possible... If they agree with one another then that's a huge confidence boost. If they don't then the details of the differences can very quickly point up what might be going wrong.

Absolutely! It’s what I was getting at here in one of the earlier threads (but GJ has spelled it out much better):

Originally Posted by kalee20

What would be helpful is some photos of scope traces - both of what you get across your burden resistor, and what you get across your 3.3 ohm load. These of course should look the same shape, just scaled differently.

So the 3.3Ω load in the original thread doubles as a sense resistor, and it also has the CT with its burden providing an (isolated) replica of the output current. If you can superimpose the two traces (twiddling the variable volts/cm sensitivity control)) then you can be confident in your CT.

[Argus25]

Al,

One thing you could get into the swing of with your scope & toroidal cores/transformers is to start to get familiar with using the scope in X-Y mode. In this mode the X axis and the Y axis are driven by separate signals to deflect the beam (You have probably done this already for Lissajous figures).

But it's great for plotting the Hysteresis or B-H curves of magnetic materials, All that you need is a function generator or AC source (sometimes an amplifier) and a current sense resistor on the primary, the voltage across the resistor drives the X amplifier. Then a simple OP amp integrator on the secondary to drive the scope's Y amplifier. (The integration is required because the induced voltage is proportional to the rate of change of flux, so to get back to the flux and therefore flux density B, an integration is required)

Then you could test any cores you plan to use too, especially if they were ones of unknown properties that are often unlabelled as typically many toroid cores are. And it's lots of fun to see the hysteresis loops. I came across a transformer used as the inverter driver transformer in the 12V DC/DC converter psu option from a Tek 464 scope that has an astonishing almost perfectly rectangular B-H curve, it's like that so it saturates suddenly.

If you search B-H curve measurements on google images there are example circuits.

Hugo.

[Radio Wrangler]

In any field, once you start pushing things towards extremes, certainty becomes hard to get. One risk is of people getting desirable results due to measurement problems and being happy with the result. You have to teach young engineers/scientists to be more suspicious of 'good' results, at least until they've got corroboration measured by an unrelated technique.

In my field we're often looking for things like intermodulation products down towards noise floor levels, wanting to verify that they are below a specified limit. Not seeing a component at the expected frequency is a very good result and is what you get when the device under test is only experiencing low stress levels. You wind up the stress to the required level and check that any component seen is below the spec limit. Nothing visible is a great result, but it could also be achieved by forgetting to switch on the output af any of several signal generators or power supplies. Good practice is to wind up the stresses above the normal test values until non-linearity produces a visible intermod product, just to prove that the test is working. The formal documents for certification tests just give a simple process with no self-checking and so small mistakes can easily produce false passes. It's a general problem with specs which are single-sided. Corroboration with a different measurement process is always an important confidence booster.

David

[Al (astral highway)]

Originally Posted by Argus25

One thing you could get into the swing of with your scope & toroidal cores/transformers is to start to get familiar with using the scope in X-Y mode. In this mode the X axis and the Y axis are driven by separate signals to deflect the beam (You have probably done this already for Lissajous figures).

Hi Hugo, yes, I have indeed done it with Lissajous figures - there was an excellent article in a 1960's Practical Wireless, incredibly informative on how to drive an analogue 'scope to display various of these. You've reminded me to dig it out in case it's of interest to others.

But it's great for plotting the Hysteresis or B-H curves of magnetic materials, All that you need is a function generator or AC source (sometimes an amplifier) and a current sense resistor on the primary, the voltage across the resistor drives the X amplifier. Then a simple OP amp integrator on the secondary to drive the scope's Y amplifier. (The integration is required because the induced voltage is proportional to the rate of change of flux, so to get back to the flux and therefore flux density B, an integration is required)

Now that's something I hadn't thought of. It's an excellent idea, thank you; I do follow your reasoning and explanation. Neat!

...it's lots of fun to see the hysteresis loops. I came across a transformer used as the inverter driver transformer in the 12V DC/DC converter psu option from a Tek 464 scope that has an astonishing almost perfectly rectangular B-H curve, it's like that so it saturates suddenly.

If you search B-H curve measurements on google images there are example circuits.

Again, yes, it would be both instructive and helpful for me to visualise hysteresis loops. All of this is a lot more of a handrail than doing endless theoretical calculations, I realise, which may or may not be anything close to reality.

The problem of having cores with indistinctive properties (based on their external appearance and even provenance) is quite a headache. This looks like a good remedy!

[Al (astral highway)]

Hugo: afterthought !

If I were working out the relevant integral for the op-amp’s Vout on a calculator , I would work with the actual value of C in its feedback loop. It wouldn’t matter so much what it was, only that I used its exact value.

But if the op amp is doing the integration for me on the Y input of the scope, how can the circuit of the feedback looop be, as it were, tolerant of any value of C in the op-amp’s feedback loop? Even if the input waveform were perfectly regular, it would matter. And with an irregularly irregular waveform, then what ??