Why does flux walking in a magnetic core occur?

[mercurial]

I'm finding it a bit difficult to grasp the concept of flux walking in a magnetic core.

I'm not sure how flux walking occurs but I was thinking of the BH curve of a material and its shown in the image below.

What I was thinking is at start the Flux starts at point 0 at this point lets say we give a square wave voltage pulse to a coil wound around the core.
As the current in the coil (wound around the core) increases the flux moves towards saturation at point 1 now as long as the pulse is high the core would stay at this point correct?.
Now let's say the pulse voltage starts dropping to 0 at this point the flux also would continue to drop till point 2 and stay there when the current drops to 0 (due to hysteresis of the core).
I think from now on for subsequent voltage pulses the flux should move from 2 to 1 and back to 2 so I'm not sure how flux walking would occur since the operating point is moving from 2 to 1 and back to 2?

[MarkT]

From what I read flux walking is just having unwanted DC component in the voltage across the inductor, nothing to do with the magnetics per se.

[mercurial]

From what I read flux walking is just having unwanted DC component in the voltage across the inductor, nothing to do with the magnetics per se.

Wouldn't the dc component manifest as a small offset on the bh curve, why would the dc cause the flux to saturate?

[T3sl4co1l]

From what I read flux walking is just having unwanted DC component in the voltage across the inductor, nothing to do with the magnetics per se.

This.  It's another peculiar phrasing that, while not out-and-out wrong, is highly misleading as to the effect and mechanism, yet which persists, being repeated time and again without critical consideration.  It is a meme, reproducing freely and stably in a system of idea-passing, without being policed for its quasi-technical payload, that should invite rational scrutiny, but instead is smuggled through potential censors time and time again.

The other big one in magnetism being "collapse of the magnetic field"; no, you're just switching the coil to a high-impedance state, EMF goes up (constrained by terminal capacitance or other impedance), and discharge is relatively rapid (higher V <--> higher dI/dt).  "Collapse" implies something entirely catastrophic, no doubt in part leading newbies to put oversized diodes in more places than is necessary, or indeed wise.  (I'm always amused to see a 1N4007, rated 30A peak and probably breaking down around 1600V, applied to a 5V 100 ohm relay coil; not that it hurts anything, and not that it costs much -- it's probably one of the cheapest diodes out there -- but the juxtaposition of a small-signal driver transistor like BC847, with a rectifier diode like 1N4007, is just that: amusing.  On the more serious side, I've seen newbies propose SMPS circuits with diodes shorting the primary; those precipitate a rather faster realization. )

From what I read flux walking is just having unwanted DC component in the voltage across the inductor, nothing to do with the magnetics per se.

Wouldn't the dc component manifest as a small offset on the bh curve, why would the dc cause the flux to saturate?

It does.  But permeability is high, so it doesn't take much magnetization (A/m) to saturate.  A typical ferrite-core transformer say of 200W scale, saturates in a couple to tens of At.

When DC can be relieved, such as with a coupling capacitor, it's fine, and so you have many half-bridge applications that do this.  When it can't, as in a push-pull converter, the inverter's fixed DC offset (determined by comparative timing of the two switches) is applied directly to the low-resistance primary, and currents can be quite high, comparable to reflected load current for example.

This feels different enough to the... Idunno, the less technical or in-depth, the more casual or informal? mind, that it seems to deserve its own term.  Or perhaps the phrase originated with some author looking for a catchier title than "DC offset", and other authors found it similarly catchy enough to include, despite its shortcomings.  Whatever the case, we're stuck with it, it isn't going away from historical references any time soon, and the best I can do in a post-"flux walking" world, is to hopefully innoculate readers against it, by explaining it, stopping to perform that critical analysis that's so often left without.

Besides balanced timing (which you can only do so well before design variance is dominated by gate driver and MOSFET parameters), reducing duty cycle is a viable strategy: leaving the inverter open-circuit for a fraction of the cycle, effectively gives it a higher average drive impedance over the cycle.  Mechanically what's happening is, the rising or falling edges are faster or slower depending on current at that phase, therefore there is some current-to-flux squishiness.  This is further compromised in CCM, where load current clamps secondary voltage to zero during off-cycles, unless (secondary-referred) magnetization current exceeds load current (at which point you're probably running the transformer very close to or banging into saturation already?).  In DCM, the transformer is allowed to be open-circuit (free ringdown) for a fraction of the cycle and therefore flux is always reset (give or take how much ringdown occurs, but if it's not banging into the supply rails, it's going to be a tiny fraction of load current).

Two-switch forward, or one-switch with reset winding and catch diode, ensures reset by limiting duty cycle below 50%.  With equal switch-on and reset voltages, this is exactly BCM; in practice, switch and diode voltage drops will take in less flux during the on-time and (potentially) deliver more flux during off-time, so there is guaranteed margin, even if the duty isn't limited to exactly 50%, but say 52 or 55% or something, might still be perfectly fine.

Tim

[mag_therm]

I don't recall the term "walking" in the old days, but it was a problem.
Adding blocking capacitors to MW inverters was costly and used a lot of enclosure volume.
We used lower quality cores, I recall specifying motor grade lams instead of GOSS in 50 Hz inverters
We used airgaps. I even recall addition of a delay pot after the D flop on one side to null of the offset!
It might be one reason the push pull inverters went mostly obsolete.
One way to avoid the problem is to use a half bridge with split capacitors.- Another is  asymmetrical core excursions as used these days.

[David Hess]

We used airgaps. I even recall addition of a delay pot after the D flop on one side to null of the offset!
It might be one reason the push pull inverters went mostly obsolete.

The Tektronix push-pull designs always seem to have reliability problems.  In some cases I think they tried to keep the flux balanced by selecting matched transistors, or at least avoiding mismatched pairs.

[coppercone2]

I think collapse is a fine word to describe a whole bunch of things getting shifted at once after standing upright.

This is a term that is used by plenty of professors, literature, etc.

Inductor Politics??

I literally heard at least 50 professionals use that term in real life. No one is trying to change it.

[mag_therm]

Hi David, Yes, the Tek 465/466' scopes of early '70s  had a p-p 12V to 120 V option, but I never saw one.

I was des eng in mainly p-p from 1973 but it was going out of fashion after about 1976 I recall.
I did not work on that topology from then  until I retired, when I revisited.
With present day components, I think p-p is feasible (and maybe competitive)  up to 30 kW or so.

I have built a Solar/Battery model power supply for the ham radio station.
It has (3) p-p ferrite DC converters each of about 300W rating.
They are running 24/7 .
Apart from the DC core saturation, the snubbering was a problem, made worse if the core "hung up" on one side.
I ("hobby machinist only") have made metal flux control parts for the transformers based on FEM for the above mentioned p-p converters.
That seems to have improved the leakage, side to side imbalnce and reduced the snubber losses.

However the efficiency is not as high as I see claimed for present day topologies.
The main converter here is a boost connection from 24V solar panels to 36V battery bank.
I have data logger on it , today it ran in full sun range 270 ~ 320 W at 77% efficiency.

Regards

[David Hess]

Hi David, Yes, the Tek 465/466' scopes of early '70s  had a p-p 12V to 120 V option, but I never saw one.

I was thinking of the off-line inverter in the 22xx series of oscilloscopes.  Later models changed the off-line regulator to produce a current output instead of a voltage output to drive the inverter, which I assume solved the problem because those power supplies never seem to mysteriously fail.

[mag_therm]

Hi David,
Thanks, I will try to find the info about that 22 series inverter when I have time.
Today found  inverter for the Tek 466 scope in the service manual.
It was Option 7, built in to the 'scope . Input  12 or 24 V , it provided  400Hz to windings on the 'scope's main power 120V 60 Hz transformer.
It had a small saturating transformer giving feedback to the bases.

And Hooley Dooley! it has the "balance" pot that I mentioned above on one side to handle the "flux walking"
(that until Mercurial's thread I called "core hung up on one side" )

I wonder how many of these had transistors cooked by the balance drifting off.

[ejeffrey]

From what I read flux walking is just having unwanted DC component in the voltage across the inductor, nothing to do with the magnetics per se.

Wouldn't the dc component manifest as a small offset on the bh curve, why would the dc cause the flux to saturate?

Imagine if you apply, starting at time t=0 a small DC offset to the primary winding.  The current will initially rise slowly due to the inductance, but since it is DC, it will eventually be limited only by resistance.  If the resistance is low enough, the core will eventually saturate because V*T becomes infinite.

Now take that DC and superimpose an ideal balanced large AC voltage.  The AC will cause the desired flux curve, but each cycle will return to a slightly different location becauae of the steady ramp from the DC offset.  Hence "walking."

[mercurial]

From what I read flux walking is just having unwanted DC component in the voltage across the inductor, nothing to do with the magnetics per se.

Wouldn't the dc component manifest as a small offset on the bh curve, why would the dc cause the flux to saturate?

Imagine if you apply, starting at time t=0 a small DC offset to the primary winding.  The current will initially rise slowly due to the inductance, but since it is DC, it will eventually be limited only by resistance.  If the resistance is low enough, the core will eventually saturate because V*T becomes infinite.

Now take that DC and superimpose an ideal balanced large AC voltage.  The AC will cause the desired flux curve, but each cycle will return to a slightly different location becauae of the steady ramp from the DC offset.  Hence "walking."

Ok so let's say the primary resistance is 1ohm and the dc voltage given is 0.1V which gives a current of 100mA, Lets say turns of primary are 100. So that makes it 10AT.
So wouldn't the dc voltage act as a fixed magnetization that's provided to the primary. I mean 10AT of magnetization, but I didn't get why the 10AT should saturate the core?. Assuming that the core here saturates at say 100AT.

[ejeffrey]

Well what if the DCR is 100 mohm?  Or what if the DC offset is 1 V?

A 390 V square wave as you might find in a power factor corrected offline converter doesn't need much duty cycle error to have a 1 VDC offset.  Higher frequency converters usually have lower DC resistance and are more succeptable to duty cycle mismatch.

If the intended AC signal has excursions of 90 AT, an additional 10 AT is enough to start saturation.

[mercurial]

Well what if the DCR is 100 mohm?  Or what if the DC offset is 1 V?

A 390 V square wave as you might find in a power factor corrected offline converter doesn't need much duty cycle error to have a 1 VDC offset.  Higher frequency converters usually have lower DC resistance and are more succeptable to duty cycle mismatch.

If the intended AC signal has excursions of 90 AT, an additional 10 AT is enough to start saturation.

I probably get what you say. However its the ramp part that i find counterintuitive, does the core ramp into saturation cycle by cycle is what I cannot grasp completely, i guess it does it cycle by cycle that's where the term flux walking comes from.
So coming back to it why does a small dc offset cause the flux to walk into saturation.
I see that you also used the term "ramp".

Now take that DC and superimpose an ideal balanced large AC voltage.  The AC will cause the desired flux curve, but each cycle will return to a slightly different location becauae of the steady ramp from the DC offset.  Hence "walking."

could you please expand on this?

[MrAl]

I'm finding it a bit difficult to grasp the concept of flux walking in a magnetic core.

I'm not sure how flux walking occurs but I was thinking of the BH curve of a material and its shown in the image below.

What I was thinking is at start the Flux starts at point 0 at this point lets say we give a square wave voltage pulse to a coil wound around the core.
As the current in the coil (wound around the core) increases the flux moves towards saturation at point 1 now as long as the pulse is high the core would stay at this point correct?.
Now let's say the pulse voltage starts dropping to 0 at this point the flux also would continue to drop till point 2 and stay there when the current drops to 0 (due to hysteresis of the core).
I think from now on for subsequent voltage pulses the flux should move from 2 to 1 and back to 2 so I'm not sure how flux walking would occur since the operating point is moving from 2 to 1 and back to 2?

Hello,

In summary, the main cause is an asymmetrical pulse train, and the main effect is the flux builds up over time, and the main result is an average DC current in the coil, which causes the core to eventually saturate or at least cause the converter to become a lot less efficient.  Also note that to visualize this better most BH curve plots will not help because they only show the effect of one pulse, while the upper curve will keep ratcheting up with multiple pulses.

The metal core of a transformer is magnetically active.  As you energize the primary winding and then remove the power source, the core goes through what we call an "Hysteresis Loop".  Well, they call it that for a good reason. The phenomenon of hysteresis is when the value of a physical property lags behind changes in the effect causing it.  Here that means that the flux does not return to zero just because the current that caused it was turned off.  With repeated on and off cycles, that means that the magnetization could build up over time.  That's what we call "walking".  The flux increases with each 'on' pulse, and that means that if it keeps up it could reach the point where most of the magnetic domains have been flipped into mutual alignment, and that means there are no more left to flip.  That in turn means there is no more "back EMF" to counter the applied voltage, meaning the coil becomes mostly a pure resistance.  Because copper is a good conductor, it will cause a much higher than normal current to flow in the primary. That causes the drive transistors to blow out.

To understand the idea a little better, we can imagine charging a capacitor through a resistor with a voltage pulse with a certain duty cycle.  The first pulse causes the capacitor to charge a little which means it attains some voltage level.  When the pulse goes low though, the capacitor does not immediately discharge to zero volts, it retains some of that voltage.  In magnetics, this would be called "retentivity".  It retains some of that voltage because it does not have time to discharge all the way yet.  When the next pulse starts, the voltage again starts to rise.  This time though it did not start from 0 volts, it started from the voltage level that was left over after the first pulse.  If after the first pulse the retained voltage was 1 volt, after the second pulse the voltage may be 1.9 volts.  As the third pulse comes, the voltage may then climb to 2.5 volts, and this process continues and the voltage keeps rising.  After some time, it is possible that the voltage reaches the voltage rating of the capacitor.  At that point the capacitor would burn out.

So, understanding the "walk" is simply understanding how inductances or capacitances charge with drive pulses and how the flux or voltage builds up over time when not given enough time to discharge.  In magnetics however, there is often a negative drive pulse to counter the positive drive pulse, and that "resets" the flux to zero.  That means that the next pulses do not cause the flux to keep increasing, and thus the design works out well.

Back in my days in the power control industry, we were faced with this problem several times.  After a little research into this phenomenon and some careful measurements, it was determined that the main reason for the flux walk was because of an asymmetrical pulse shape.  If the pulse does not go negative by as much as it went positive, the core never resets.  This gives rise to an average DC current that flows through the primary, and that can cause saturation.  If if it does not rise high enough for saturation though it may go undetected.  That causes the whole thing to become less efficient, and that can be almost as bad in a converter especially these days when energy consumption is a high priority in many designs.  Another side issue is that the flux may walk up and down, which can cause a lot of audible noise.  We had some clients complain about that too, and that required audio insulation around the converters in some cases.  Anyway, the solution I was able to find was simply to monitor the pulse train with a circuit that could integrate the pulses getting to the primary and use that as a secondary feedback to the main controller.  The integration measures the amount of DC offset over time. If the offset goes up, the controller will modify either the negative or positive pulse width in order to get equal negative and positive pulse widths.  The result is that the flux can only walk up to a certain small level before it goes back down due to the feedback mechanism.

Just for reference, to understand saturation with respect to the current level, it is best to think of it in terms of the instantaneous current rather than an AC or DC current.  As the current rises, the increase in flux could eventually reach the maximum level that the core can handle without becoming inactive.  Once it becomes inactive, it can no longer react with a back EMF and so it becomes almost like a short circuit.

[ejeffrey]

Now take that DC and superimpose an ideal balanced large AC voltage.  The AC will cause the desired flux curve, but each cycle will return to a slightly different location becauae of the steady ramp from the DC offset.  Hence "walking."

could you please expand on this?
[/quote]

It's literally just adding the two flux waveforms, one caused by the DC offset and one caused by the AC component.  You can always take a waveform and rewrite it as the sum of a DC term and an AC term.  The AC signal is periodic (returns to the same starting point each cycle) while the DC term accumulates over time.  The DC offset is much less than the AC amplitude, so it's a small offset per cycle.  But if it's never cancelled it accumulates over many cycles until it causes saturation.

[MrAl]

It's literally just adding the two flux waveforms, one caused by the DC offset and one caused by the AC component.  You can always take a waveform and rewrite it as the sum of a DC term and an AC term.  The AC signal is periodic (returns to the same starting point each cycle) while the DC term accumulates over time.  The DC offset is much less than the AC amplitude, so it's a small offset per cycle.  But if it's never cancelled it accumulates over many cycles until it causes saturation.

Now take that DC and superimpose an ideal balanced large AC voltage.  The AC will cause the desired flux curve, but each cycle will return to a slightly different location becauae of the steady ramp from the DC offset.  Hence "walking."

could you please expand on this?

Hi,

The DC does not accumulate, the FLUX accumulates.  You can keep the DC constant (actually the average DC) and see the flux walk higher and higher.  The word we use "walk" is really a ratcheting action where after each pulse the flux ends up being higher.
If the flux went up to 10 with the first pulse with an average DC=1 then the flux may go up to 20 with the second pulse while there is still an average DC of 1.  For the third pulse the flux may go up to 30 still with an average DC of 1.

You may want to note that if you integrate the DC drive pulses you get a constant value after some time for a constant duty cycle.

Once the core begins to saturate, THEN we may see an increase in the average DC if the converter does not blow out first.

[MrAl]

Here are some plots that show how the core flux can increase over time with multiple pulses.

First there is a plot with perfectly symmetrical pulses.  The duty cycle is 50 percent and the plus and minus voltages are the same.  The flux stays at zero.

Second, there is a plot with a change in the high time pulse width while keeping the voltages the same.  The high time is longer than the low time so the flux ratchets up.

Third, there is a plot with a change in the minus voltage.  The new minus voltage is chosen to again balance the flux in the core.  The high pulse width is longer than the low pulse width, but the low voltage is made even lower so that it compensates for the shorter low pulse with.  This again balances the flux in the core.

There are a lot of possibilities here only three cases are shown in the attachment.  The idea is that the volts times the seconds must be equal and opposite for both high pulse times and for low pulse times.  This is often just referred to as the "volt seconds".

In the first plot, we have +10 volt seconds and -10 volt seconds and this balances out so the flux does not walk up or down.
In the second plot, we have +15 volt seconds for the high pulse time but only -5 volt seconds for the low pulse times.  This is an imbalance in drive so the flux walks up.
In the third plot, we have +15 volt seconds and -15 volt seconds so the flux stays at zero.

[T3sl4co1l]

As said, perfectly decomposable into "DC" (transient, exponential) and periodic (square/triangle) components.

That's a linear RL load, I assume--?  The above can be proven analytically from the differential equation, without much effort (granted we're talking diff eq to begin with, lol).

I suppose, purely in the sense that, when dI/dt is positive or negative (read: ignoring by how much), and after each cycle of alternation, I is higher each time, it could be said to "walk" -- but it isn't much of a walk, if, after a while, it shuffles down to a crawl, right?  Nor is it much of a "ratchet" (a mechanism with equal-spaced teeth to hold force/torque against).  Pedantic perhaps -- but it shows the discrepancy between hand-waved descriptors and real behavior.

On the other hand, I suppose a real example might look more meaningful: with a saturating transformer, the per-cycle deltaI can be fairly constant (along just the initial slope of that exponential), until it hits saturation and inverter current explodes.

Put another way: the winding resistance will generally be quite low compared to magnetizing inductance, and saturation relatively close at hand (design Bpk might be 10-80% of Bsat, depending on Fsw, acceptable losses, etc.), so that not much imbalance needs to accumulate before saturation ensues (and saturation will be relatively hard and quick, because mu_eff will be fairly high in a power transformer).

Put still otherwise: a linear system might not be a good illustration, specifically because it can be decomposed as above; a nonlinear system however, while it admits the same decomposition before saturation, superposition is violated afterwards.  (Within whatever approximation margin counts for "before" vs. "after".)  The significance of this change is enough, and its occurrence in practice, to demand a signifier to represent it.  Thus a meme is born; but as with many signifiers, the literal meaning of it is only loosely connected to its new meaning, and confusion ensues among those who haven't yet been initiated into that meaning.  Which happens often, as the purpose of the signifier is to represent the thing without having to say what it is, and just explaining the thing would take longer by way of having to explain the phrase plus what it's talking about in the first place.

I guess the complaint comes down to this: if you object to phrases like "defund police" for facial / literal reasons ("defund... and then what?"), you should object to "flux walking" for the same reason ("walking...where? ...does it have legs now?").

(To be clear, the context of this post is mainly philosophical.  I've already commented on the electronics, or physics, of this subject, and I'm not trying to reiterate that; nor has anything particularly contradictory been written since.  What's new, I suppose, is I hadn't noted the above similarity explicitly before, which I guess is interesting enough to post?  Perhaps others will find some insight in the philosophical or linguistic or thought-process given above.)

(I don't particularly care if you [the reader] use the term ["flux walking"], just realize it means something, not what is "written on the tin", and is really just a mimetic substitute for "DC imbalance", which is perfectly descriptive of what's happening, but I guess just too banal for the memes.  Hence the former term continues to persist.)

Tim

[mercurial]

Thanks to all for the amazing replies especially MrAl, ejeffrey, T3sl4co1l to name a few.
It was a highly enlightening experience reading thru all your essays, I really appreciate the time you'll put in to answer the question.

Some questions still bug me though.

1. Does the flux accumulate over time primarily due to "hysteresis" property of the core or are there any other factors contributing to it?
2. Could a simple drive circuit to a coil wound on the core cause ratcheting of flux.
3. Does that mean that it is mandatory to always drive a transformer with a bipolar drive?

[Andy Chee]

1. Does the flux accumulate over time primarily due to "hysteresis" property of the core or are there any other factors contributing to it?

The hysteresis property is not really a factor, but the permeability property is a major one.

2. Could a simple drive circuit to a coil wound on the core cause ratcheting of flux.

Potentially yes.

3. Does that mean that it is mandatory to always drive a transformer with a bipolar drive?

No. 

Single-switch flyback, two-switch flyback, single-switch forward, and two-switch forward converters, are all unipolar.  They are all limited to 50% duty cycle maximum, in order to allow the core to reset during the other 50%.  Or if driven with low duty cycle 10%, the remaining 90% is plenty of time to allow the core to reset.  If you go beyond 50% duty cycle, the core will not properly reset, resulting in eventual core saturation.

Bipolar drive permits high duty cycle beyond 50% (and commensurately higher power conversion), because the core is reset via polarity reversal.  But unbalanced drive waveforms will eventually lead to core saturation as well, for example 90% in one direction and 91% in the other.

[jonpaul]

Bonjour, bravo for the question.

As a power electronics designer since 70s, I have not hear this term "flux walk" , Iit is commonly called  core saturation.

Any ferrous material  has a non linear  a B-H (flux vs exitation) relation.    near linear at low flux  and  a flux  limit at very high exitation.

Core losses due to heysterysis etc are also changng nonlinear with H.

For a perfect AC exitation, zero DC omponent, the cycle by cycle peak B is not changinbg.

In case a DC bias exists in exitation, eg now quite 50% DC in puch pull/bridge, the DC then causes a sucessive creeping cycle by cycle of the B in one dirsction.

As the B increases cycel by cleyc the magnetizing current increases as incermental L decreaes. See the B-H curves by core manufactureses, Arnold, Mag Mtls , Thomas for lams and tapewound iron, TDK, EPCOS, Siemens, etcv for ferrite.

Suggest you read a classic text on static electromagneti devices like Hunt and Stein, to lear about the reasons for ferrous material nonlinearities.

We never had these ussus: in 1970s various  DC cancelling FB were used to even the V-S area plus/minus applies.

We avoid push pull, centertapped transformers.

If some DC is present use an airgap in the core.

Most modern topologies use a series  cap to remove change of DB bias.

Bon chance,

Jon

[MrAl]

As said, perfectly decomposable into "DC" (transient, exponential) and periodic (square/triangle) components.

That's a linear RL load, I assume--?  The above can be proven analytically from the differential equation, without much effort (granted we're talking diff eq to begin with, lol).

I suppose, purely in the sense that, when dI/dt is positive or negative (read: ignoring by how much), and after each cycle of alternation, I is higher each time, it could be said to "walk" -- but it isn't much of a walk, if, after a while, it shuffles down to a crawl, right?  Nor is it much of a "ratchet" (a mechanism with equal-spaced teeth to hold force/torque against).  Pedantic perhaps -- but it shows the discrepancy between hand-waved descriptors and real behavior.

On the other hand, I suppose a real example might look more meaningful: with a saturating transformer, the per-cycle deltaI can be fairly constant (along just the initial slope of that exponential), until it hits saturation and inverter current explodes.

Put another way: the winding resistance will generally be quite low compared to magnetizing inductance, and saturation relatively close at hand (design Bpk might be 10-80% of Bsat, depending on Fsw, acceptable losses, etc.), so that not much imbalance needs to accumulate before saturation ensues (and saturation will be relatively hard and quick, because mu_eff will be fairly high in a power transformer).

Put still otherwise: a linear system might not be a good illustration, specifically because it can be decomposed as above; a nonlinear system however, while it admits the same decomposition before saturation, superposition is violated afterwards.  (Within whatever approximation margin counts for "before" vs. "after".)  The significance of this change is enough, and its occurrence in practice, to demand a signifier to represent it.  Thus a meme is born; but as with many signifiers, the literal meaning of it is only loosely connected to its new meaning, and confusion ensues among those who haven't yet been initiated into that meaning.  Which happens often, as the purpose of the signifier is to represent the thing without having to say what it is, and just explaining the thing would take longer by way of having to explain the phrase plus what it's talking about in the first place.

I guess the complaint comes down to this: if you object to phrases like "defund police" for facial / literal reasons ("defund... and then what?"), you should object to "flux walking" for the same reason ("walking...where? ...does it have legs now?").

(To be clear, the context of this post is mainly philosophical.  I've already commented on the electronics, or physics, of this subject, and I'm not trying to reiterate that; nor has anything particularly contradictory been written since.  What's new, I suppose, is I hadn't noted the above similarity explicitly before, which I guess is interesting enough to post?  Perhaps others will find some insight in the philosophical or linguistic or thought-process given above.)

(I don't particularly care if you [the reader] use the term ["flux walking"], just realize it means something, not what is "written on the tin", and is really just a mimetic substitute for "DC imbalance", which is perfectly descriptive of what's happening, but I guess just too banal for the memes.  Hence the former term continues to persist.)

Tim

Hi there,

Well if you want to be perfectly 'real' then we have a ways to go yet.
First of all, the flux ratcheting does not have to be the same for each step just to call it ratcheting.  But more exactly, the ratcheting tends to get worse and worse with bigger and bigger steps because the permeability starts to decrease with each step.  That would make the more realistic picture look like a plot that is curving up rather than leveling out.  The leveling out part would only come if the core did not get too saturated, and there was sufficient resistance to limit the amount it was able to go up.

This is kind of like everything else ... if we want to understand it we have to start with simpler explanations, then if the interest is still there we go with a more in-depth analysis.

I have some other plots around that show the path on the BH curve as the flux ratchets up.  You can see the curve that encloses the origin get wider and wider and if there is an asymmetrical drive the whole thing works its way up with an offset too so it's not symmetrical about the origin anymore.
I'll see if i can find them.

[MrAl]

Thanks to all for the amazing replies especially MrAl, ejeffrey, T3sl4co1l to name a few.
It was a highly enlightening experience reading thru all your essays, I really appreciate the time you'll put in to answer the question.

Some questions still bug me though.

1. Does the flux accumulate over time primarily due to "hysteresis" property of the core or are there any other factors contributing to it?
2. Could a simple drive circuit to a coil wound on the core cause ratcheting of flux.
3. Does that mean that it is mandatory to always drive a transformer with a bipolar drive?

Hi,

The hysteresis property means the core flux does not decrease even when the current goes to zero.
With an asymmetrical drive, the flux is higher in one direction than the other and that can cause the metal to be saturated in that one direction.  As it gets higher and higher the permeability decreases and that decreases the inductance, and that causes more current to flow during each cycle.  With more current each cycle the condition becomes worse.  If the permeability did not change this would not happen as in an air core inductor.

If you could see the current during the time when it just starts to go into saturation it would be starting to go up sharply and then it starts to look like a spike. As the core becomes more and more saturated, it starts to look more and more like a short circuit which of course draws more current from the power source until something blows out.

Theory has advanced but it's still useful to think of the core as being made up of tiny domains where each domain acts like a tiny magnet.  These magnets start out all randomly oriented.  As current is applied, the magnets start to align with each other.  This also creates a back EMF that counters the applied voltage, and that is the basis for the inductance.  Since there is only so much bulk to any one core, there are only so many magnets.  Once they become all aligned there are no more left to rotate and create a back EMF, so now the core behaves almost like there is nothing there.
We may still see a small inductance but because it becomes so much lower than the target design, the voltage pulses encounter an almost pure resistance that is very low and so we see a huge increase in current.

The plots I had shown previously show what happens when the core does not saturate completely as there is some external limit that holds the current down.  In an actual core the plot would curve upward rather than level off and that's the more typical case because there is often very little to limit the current except for an active current limit mechanism.  An active current limit mechanism will prevent the converter from blowing out.

[#3]
The main idea is that the core has to be reset.  This means getting the flux back to zero.  There are other ways to do this, but in something like a push pull circuit it is usually done with a symmetrical drive.

[mercurial]

We never had these ussus: in 1970s various  DC cancelling FB were used to even the V-S area plus/minus applies.

We avoid push pull, centertapped transformers.

If some DC is present use an airgap in the core.

Most modern topologies use a series  cap to remove change of DB bias.

1. Why center tapped transformers to be avoided? Don't center tapped also reverse the flux in the core?
2. What is wrong with push-pull why that needs to be avoided?
3. What is the V-S area.

[MrAl]

1. Does the flux accumulate over time primarily due to "hysteresis" property of the core or are there any other factors contributing to it?

The hysteresis property is not really a factor, but the permeability property is a major one.

2. Could a simple drive circuit to a coil wound on the core cause ratcheting of flux.

Potentially yes.

3. Does that mean that it is mandatory to always drive a transformer with a bipolar drive?

No. 

Single-switch flyback, two-switch flyback, single-switch forward, and two-switch forward converters, are all unipolar.  They are all limited to 50% duty cycle maximum, in order to allow the core to reset during the other 50%.  Or if driven with low duty cycle 10%, the remaining 90% is plenty of time to allow the core to reset.  If you go beyond 50% duty cycle, the core will not properly reset, resulting in eventual core saturation.

Bipolar drive permits high duty cycle beyond 50% (and commensurately higher power conversion), because the core is reset via polarity reversal.  But unbalanced drive waveforms will eventually lead to core saturation as well, for example 90% in one direction and 91% in the other.

Hi,

I am not sure if you could say that bipolar drive permits duty cycles above 50 percent when the core is reset via polarity reversal.  That's because in that case we would need a 50 percent one polarity and 50 percent the other polarity, or at least each half cycle would have to have the same pulse width.

It's hard to pin this down in simple terms though because even that isn't really the end of the story.  For example, we could have one pulse that is 25 percent V+ and 75 percent V-, which is asymmetrical, but then the next pulse that is 75 percent V+ and 25 percent V-.  The first and second pulses are asymmetrical, but together they balance out the core.  This is as long as the initial inductance is high enough to accept that without saturating after the first pulse.  This is the case with pure sine synthesized converters where there is a long train of varying pulse widths of the positive polarity followed by a long train of pulses of the negative polarity (or similar).  After the second train of pulses the core is back to the original state.

[mercurial]

Here are some plots that show how the core flux can increase over time with multiple pulses.

What software was used to create those plots, is it a magnetic simulator of some sort?

[MrAl]

Bonjour, bravo for the question.

As a power electronics designer since 70s, I have not hear this term "flux walk" , Iit is commonly called  core saturation.

Any ferrous material  has a non linear  a B-H (flux vs exitation) relation.    near linear at low flux  and  a flux  limit at very high exitation.

Core losses due to heysterysis etc are also changng nonlinear with H.

For a perfect AC exitation, zero DC omponent, the cycle by cycle peak B is not changinbg.

In case a DC bias exists in exitation, eg now quite 50% DC in puch pull/bridge, the DC then causes a sucessive creeping cycle by cycle of the B in one dirsction.

As the B increases cycel by cleyc the magnetizing current increases as incermental L decreaes. See the B-H curves by core manufactureses, Arnold, Mag Mtls , Thomas for lams and tapewound iron, TDK, EPCOS, Siemens, etcv for ferrite.

Suggest you read a classic text on static electromagneti devices like Hunt and Stein, to lear about the reasons for ferrous material nonlinearities.

We never had these ussus: in 1970s various  DC cancelling FB were used to even the V-S area plus/minus applies.

We avoid push pull, centertapped transformers.

If some DC is present use an airgap in the core.

Most modern topologies use a series  cap to remove change of DB bias.

Bon chance,

Jon

Hi,

Very surprised to hear you have never heard of the term "flux walk" maybe it is just a US thing.
All the engineers I have ever met that worked with power converters knew of this term, but that was in the US mostly.

As you probably know, the air gap allows some DC mainly because it lowers the permeability which then requires more wire turns.  The net effect is it takes more offset to saturate the core.
It's also interesting that the air gap permeability is so low compared to the base core metal permeability that it can be very short and still affect the entire construction significantly.

[MrAl]

Here are some plots that show how the core flux can increase over time with multiple pulses.

What software was used to create those plots, is it a magnetic simulator of some sort?

Hi,

I created those plots with a circuit simulator like the LT Spice simulator which you can download for free.
I wanted to show the essence of what happens while staying away from the more complicated operation, but I have other plots that show a more complete picture which I will try to find now.

The second picture shows the BH curve when the flux is imbalanced and saturating on the positive part while not quite on the negative part.

[mercurial]

Hi MrAl

For someone who worked in the power electronics industry for so many years it would be interesting to hear how did you really measure core saturation did you only use current as your eyes into the magnetics.
Did you use any special tools to measure the magnetic field while the transformer was operating?

[T3sl4co1l]

Single-switch flyback, two-switch flyback, single-switch forward, and two-switch forward converters, are all unipolar.  They are all limited to 50% duty cycle maximum, in order to allow the core to reset during the other 50%.  Or if driven with low duty cycle 10%, the remaining 90% is plenty of time to allow the core to reset.  If you go beyond 50% duty cycle, the core will not properly reset, resulting in eventual core saturation.

Bipolar drive permits high duty cycle beyond 50% (and commensurately higher power conversion), because the core is reset via polarity reversal.  But unbalanced drive waveforms will eventually lead to core saturation as well, for example 90% in one direction and 91% in the other.

Single-switch flyback, and forward if using RCD clamp snubber for reset, can go higher than 50%.  Or conversely, conditions exist where unwanted DC imbalance occurs below 50%.  Forward, as long as magnetizing inductance DCM or BCM is maintained, full reset is achieved (e.g. using a RCD clamp snubber for reset).  Flyback can simply be operated in CCM with no consequence, as long as the control is suitable (it often isn't, e.g. peak current mode control requires high ripple fraction).  In that case, the limit is not 50% unilaterally, but depends on the voltage ratio in CCM, D = Vo / (Vi + Vo).

Similarly, the subharmonic oscillation threshold that is often erroneously repeated in appnotes, is precisely the same threshold: it's simply to say current is continuous, regardless the voltage ratio.  You do most of your design calculations at 50% duty, so it's not far in practice, but it is strictly wrong to claim a fixed 50% for all cases as appnotes inevitably do.

Incidentally, this means the intentional opposite of "flux walking" is simply CCM.  That is, precisely the same phenomena, but actually intended.  It's just total unbalanced DC bias current in the core.

Ah, yes-- not to mention that's another reason I object to the term -- it implies some ignorance of the system, some agency of it, unconstrained by the designer, that it can just wander off on its own for reasons inexplicable.  As a designer, I find this wholly antithetical.

Tim

[MrAl]

Hi MrAl

For someone who worked in the power electronics industry for so many years it would be interesting to hear how did you really measure core saturation did you only use current as your eyes into the magnetics.
Did you use any special tools to measure the magnetic field while the transformer was operating?

Hi,

I did design work and also some troubleshooting when needed so I had theoretical as well as hands on experience in that field.  What I liked best was trying to come up with new ways to make power converters, especially the synthesized sine type converters.

The main way to find out if the core is going to saturate is to bring the power to the converter up slowly, which meant bringing the DC buss voltage up little by little often with the control circuitry powered with a separate power source so it would operate normally even with a low DC buss voltage.
As the voltage pulses to the transformer get higher and higher, if the core starts to enter into saturation, the current goes from a regular up and down sawtooth to a sawtooth where near the end of the pulse it rises up sharply.  That tells you right there, and if you raise the voltage higher the current at the end rises up more and more so you see the spike go up even higher and sharper.  Going too high at that time will blow the bridge transistors.
In some designs we used current sensors to sense transistor currents so we could provide feedback to prevent them from blowing out.  That came later though.

The field of the transformer core is almost all confined within the core so the only measurements I ever did was with a hall effect device inside the gap.  This ends up being like a hall effect current probe used with oscilloscopes and DC current clamp on meters.  I don't remember much about the measurements though because this was more of a curiosity than a regular test technique.

Now that you mention it, the best way to test a core like in an inductor made for say a buck converter is to test it in a buck converter.  The actual buck converter provides the normal operating conditions so it's like a full test.  Testing it any other way is much harder to do because you have to provide all the operating conditions the buck converter would see anyway, such as the average DC current which is an important factor in a buck converter.

[jonpaul]

Mercurial:

>>1. Why center tapped transformers to be avoided?
Wdg is More expensive and takes more space for taps. Single P and single S always preffered in mfg, prod.

 >>Don't center tapped also reverse the flux in the core?
V-S  depends on the drive symmetry, switch saturation, switch recovery, and drive pulse symmetytr.

2. >>What is wrong with push-pull why that needs to be avoided?
see above.

3. >>What is the V-S area. (VOLT*Seconds) Voltage applied integrated over the time = Area integrated .

Enjoy,

Jon

[jonpaul]

>> how did you really measure core saturation 
Did you use any special tools to measure the magnetic field while the transformer was operating?

1. Change in magnetizing current with applied exitation voltage.

2. Wdg a few turns search coil on core leg, use   X-Y scope to see B-H curve.

https://phys.libretexts.org/Bookshelves/Electricity_and_Magnetism/Book%3A_Applications_of_Maxwells_Equations_(Cochran_and_Heinrich)/06%3A_Ferromagnetism/6.02%3A_B-H_Curves

Jon