Back EMF cancelation question with multiple coils wound on the same core

[artis]

While thinking about back EMF I stumbled upon a curious question.
We know that whenever a coil/conductor that passes current is switched OFF and the current is stopped it never stops immediately but instead has a type of "inertia" where the magnetic field created by the current as it passed now diminishes but since that takes time, the field now creates it's own current in the coil/conductor and this in the absence of a conductive path can create a high transient voltage.

So I am linking this high transient voltage in the absence of a conductive path to the changing (decreasing) magnetic field within the coil, after the coil current path has been broken.
But what if the magnetic field doesn't change after the current path is broken?
Is there still a back EMF then?

I have attached a drawing to provide an example for such a situation. There are 3 coils, each coil passes some AC or DC current to the same extent as any other coil. They are all in parallel so to speak, but only 2 of them are conducting at any moment.
When the next coil gets switched ON, simultaneously the last coil is switched OFF. (just assume a perfect transition)
All coils share the same core.
Doesn't this mean that with only 2 of the 3 coils ON at any moment , the flux through the core is the same and stays the same even during coil switching? Because as the next coil is switched ON, the previous switches OFF.
So given the coils share the same core, if a coil switches OFF but the total flux of the core that the coil shares is kept non changing , is there any back EMF inductive voltage induced within the coil that switched OFF?

 

[Baluncore]

Doesn't this mean that with only 2 of the 3 coils ON at any moment , the flux through the core is the same and stays the same even during coil switching? Because as the next coil is switched ON, the previous switches OFF.

You are correct.
If the flux does not change, then there is no voltage induced in the coil.
So long as the total amp*turns of the coils remains constant, the magnetic flux does not change.
To maintain a steady current in an inductor, requires that there be zero voltage across the inductor; v = L * di/dt .

A short-circuited inductor, will retain the initial magnetic flux, until the series resistive losses in the inductor, have consumed the magnetic energy.
That will take forever, as the current exponentially decays.
di/dt = v/L; where v is the voltage dropped by the series resistance.

All coils cannot share 100% of the same core. There will be some small leakage inductance that passes through the air. That will still generate a small voltage kick across the switch while switching between coils. It is that negative voltage kick, that stops the arc of current across the opening switch contacts.

 

[artis]

You are correct.
If the flux does not change, then there is no voltage induced in the coil.
So long as the total amp*turns of the coils remains constant, the magnetic flux does not change.
To maintain a steady current in an inductor, requires that there be zero voltage across the inductor; v = L * di/dt .

A short-circuited inductor, will retain the initial magnetic flux, until the series resistive losses in the inductor, have consumed the magnetic energy.
That will take forever, as the current exponentially decays.
di/dt = v/L; where v is the voltage dropped by the series resistance.

All coils cannot share 100% of the same core. There will be some small leakage inductance that passes through the air. That will still generate a small voltage kick across the switch while switching between coils. It is that negative voltage kick, that stops the arc of current across the opening switch contacts.

Ok , I get it, so as I thought, with all coils being equal and identical parameter wise there should be no inductive voltage in the ideal case and some small in the practical due to, as you said, leakage inductance etc.

So if I drive the coil switching with a 50/50 duty cycle where the moment of one coil switching off while the next turns on almost overlaps I would approach a situation where the back EMF would be as minimal as possible.
Using semiconductors I think it is possible to time the switching taking into account the individual coil inductance value to get to a point where the next coil can be switched ON before any significant back EMF has developed across the inductor that was switched OFF.Just out of curiosity, let's assume I delay the switching timing and now I switch one coil OFF and allow for a significant back EMF spike to form , before that voltage spike can dissipate itself, what would happen to it if I immediately switched the next coil ON?
The core flux would now be restored back to previous value, but the field that "collapsed" already created the voltage as it transformed it's energy into potential, does the restoring of the flux through the core and coil in question now cancels that created potential without it being dissipated through an arc or some other means of back EMF transient dissipation?

 

[Baluncore]

Just out of curiosity, let's assume I delay the switching timing and now I switch one coil OFF and allow for a significant back EMF spike to form , before that voltage spike can dissipate itself, what would happen to it if I immediately switched the next coil ON?

If a back EMF appears, then the breakdown voltage decides; di/dt = v/L.
Consider what would happen if you short-circuited a disconnected winding before open-circuiting another winding that had current, but zero voltage.

 

[artis]

If a back EMF appears, then the breakdown voltage decides; di/dt = v/L.
Consider what would happen if you short-circuited a disconnected winding before open-circuiting another winding that had current, but zero voltage.

Hmm, are you hinting that the collapsing field from one coil that is Switched OFF would instead dissipate itself as current through an adjacent coil that is shorted. And the original coil that was switched OFF having no induced voltage spike because of it?

 

[Baluncore]

I am not hinting at anything in particular.
I am just expanding on your curiosity and trying to tie it down.

 

[artis]

I am not hinting at anything in particular.
I am just expanding on your curiosity and trying to tie it down.

Ok but what is the answer then?
Now that I think of it , having multiple coils share the same core in theory should result in very little (no?) back EMF within any individual coil when it is switched OFF because the decreasing field as a time varying field can dissipate it's energy through any adjacent coil sharing the same core. Am I right?

 

[Baluncore]

You assume that the coils each have energy associated with them, but that energy is mainly associated with the magnetic field of the common core. That core field must be supported by the sum of the amp⋅turns of all the coils.

What happens will depend on what you mean by "turn off", and the sequence in which you transfer the field support current. If you short-circuit an available coil, then open-circuit another that is carrying a current, then the supporting current will be transferred from the opened-coil to the shorted-coil and there will be no spike of back EMF.

Now, how would it be different if you analysed it as a transformer, rather than as a DC electromagnet?

 

[artis]

Now, how would it be different if you analysed it as a transformer, rather than as a DC electromagnet?

Actually I thought of it as a transformer too. I imagine that all my 3 coils pass the same AC current through them that is shared in parallel between 3 equal coils on the same core.
Now based on my reasoning , given the current passes in the same direction in every coil at every instant and AC can be treated as DC if looking at a "moment by moment" time frame , then suddenly disconnecting one coil will produce a similar result as if the current in the coils was DC. The other coils that stay ON will have a current boost proportional to the field change due to the coil that was switched OFF.

So for example if the current was AC, then switching one of the 3 coils OFF would produce a slight voltage/current increase that is in phase with the driving AC, or so I think.
Meanwhile switching a coil ON when it was OFF before would result in a slight "dip" in the sine because now extra current needs to be added to build up a larger flux in the core.

But lastly if you always have just one coil ON while the previous is switched OFF and the next turned ON simultaneously then assuming perfect timing there should be no change because the collapsing field from the previous coil would be used up by the coil that is switched ON.

 

[TonyStewart]

There will always be BEMF when turning off any coil as well as mutual coupling of EMF between coils.

The rate of change for dI/dt is not simply dI/dt=ΔV/L as there is a series resistance that limits current in each state (off/off) so the time constants of Tau=L/R will occur unless some over-voltage clamp is used for turn-off and for turn-on there is a current limit from DCR and RdsOn.

Since there is no motion in this model , unlike a 3phase BLDC motor, it will behave like the locked-rotor condition so some method of current limiting is necessary.

 

[artis]

There will always be BEMF when turning off any coil as well as mutual coupling of EMF between coils.

exactly and that is why I believe @Baluncore said that in a common core scenario turning OFF one coil will instead put the back EMF discharge energy through the adjacent coils that are ON and can pass current, so the coil that was switched OFF never develops a transient voltage spike across it