# Passing both DC and pulses through a toroid?

#### neazoi

Hi,
Suppose I have a toroidal core and I wind one turn of wire through it, as my primary.
My secondary is also one turn through this core.
For the next description assume no core saturation at any point.

Now, suppose I pass DC 5v through the primary wire from the left to the right (this is just a representation to indicate the DC polarity to you). Nothing will be output on the secondary as a transformer will not work at DC.

Now suppose I wind a second primary with 1 turn at the same phase as the first primary.

Question one:
If I feed a 5V rising edge to this second primary at the same direction of that of the DC, will this rising edge present at the secondary? Will this be 5v or 10v at the secondary?

Question two: If I feed a 5V rising edge to this second primary at the reverse direction of that of the DC, will this rising edge present at the secondary and at what voltage?

Ignore falling edges of the pulses in the previous questions.

#### asdf44

An ideal transformer does work with DC.

A real life transformer can't transmit DC because the core eventually saturates (primary inductance isn't infinite therefore magnetizing current increases until the core saturates).

In your example if we assume no saturation then it will transmit your 5V DC.

In real life it will also transmit a pulse if the DC input ramps from 0-5V fast enough (this is how pulse transformers work).

In both your questions it comes down to this: If the core is saturated it won't transmit anything and it should be saturated if DC has been applied. If it isn't saturated then it will be transmitting 5V DC to the 'second primary' and the secondary (there is no distinction between those two). And therefore you can't drive any other winding with your pulses without it effectively causing a short.

neazoi

### neazoi

points: 2

#### neazoi

An ideal transformer does work with DC.

A real life transformer can't transmit DC because the core eventually saturates (primary inductance isn't infinite therefore magnetizing current increases until the core saturates).

In your example if we assume no saturation then it will transmit your 5V DC.

In real life it will also transmit a pulse if the DC input ramps from 0-5V fast enough (this is how pulse transformers work).

In both your questions it comes down to this: If the core is saturated it won't transmit anything and it should be saturated if DC has been applied. If it isn't saturated then it will be transmitting 5V DC to the 'second primary' and the secondary (there is no distinction between those two). And therefore you can't drive any other winding with your pulses without it effectively causing a short.
Thanks a lot!
Please help me understand the thing with my second question, if the DC is in one direction in one primary winding (assumming no saturation) and if my 0-5V edge is at the opposite direction (in the other primary) to that of the DC, will the DC pose a force to cancel out the pulse at the secondary?

This would happen if you feed the two primaries with rising edges in opposite direction, but I want to see if this will happen with an "edge" and an opposite DC applied, if you know what I mean.

#### asdf44

Again: If the transformer isn't saturated then the simplest model is to consider all wingdings as tied together. If you apply 5V to one then 5V comes out all the others. You can't then apply 0V to any other winding without effectively causing a short to ground.

Similarly you wouldn't want to apply opposing pulses for the same reason. It's effectively a short (of course limited by parasitics in a real life).

neazoi

### neazoi

points: 2

#### KlausST

##### Super Moderator
Staff member
Hi,

I agree with asdf44.

* applying DC
* non saturating
* no output

If you apply DC... then there will be output.
(So far this is true for ideal transformers)
In real world it is "saturation" that degrades the output signal.
Without saturation .... there still will be an output signal.

Klaus

neazoi

### neazoi

points: 2

#### Easy peasy

for a very large toroid; the first single turn with 5V applied will have its current ramping up at 5/Lpr amps per sec, the flux in the core will ramp in proportion to the current, any sec single turn will have 5V on its o/p.

The sec single turn primary with the 0-5V rising edge; firstly this turn will have the 5V on it from the other pri wdg, so your driving ckt will need to over come this, i.e 5 ->10V rising edge - as a 0-5V rising edge will achieve nothing - except draw current if it is a perfect volt source ( at 0v it is shorting the Tx, and it is still shorting the Tx until it rises to 5V whereupon it is in balance with the other 5V drive source) - if it is a volt source with a perfect diode - then is will achieve nothing - but a 5 -> 10V rising edge will push current, now on the single turn sec might expect to see 5V -> 10V at the same rate as the pri rising edge. However if the first 5V drive is a perfect volt source it will sink all the current from the rising 5->10V source - the load currents will be infinite and it will be a mess.

In practice the source impedance of the drivers and the res of the windings determines what will happen - along with the coupling - which we have assumed K=1 up till now.

If you try and apply this 2nd 0-5V rising edge in the opp direction you are effectively applying another source in series - effectively a large short circuit - the load currents will be infinite ( in practice limited by Source and Tx Z's ) the first source would have the higher current as it started earlier and has Imag.

neazoi

### neazoi

points: 2

#### neazoi

Hi,
If you apply DC... then there will be output.
(So far this is true for ideal transformers)
In real world it is "saturation" that degrades the output signal.
Without saturation .... there still will be an output signal.

Klaus
So a big transformer core that is saturated less easily, would allow DC to pass from the primary to the secondary?
That's really new to me, if I understand this ok!

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If you try and apply this 2nd 0-5V rising edge in the opp direction you are effectively applying another source in series - effectively a large short circuit - the load currents will be infinite ( in practice limited by Source and Tx Z's ) the first source would have the higher current as it started earlier and has Imag.
If I understand this ok, then there will be no change on that case because DC will dominate?
I am talking about the time where the rising edge is applied, because afterwards there will only be DC in the core.

#### KlausST

##### Super Moderator
Staff member
Hi,

So a big transformer core that is saturated less easily, would allow DC to pass from the primary to the secondary?
That's really new to me, if I understand this ok!
YES, but only theoretically with an infinite big core.
NO, for real transformers.

The bigger the core, the lower the frequency you may pass from primary to secondary.
But low frequency does not mean DC. DC is "infinitely low".

Klaus

#### asdf44

Here is my overview of transformers in general that might help. Online resources are actually quite poor in my opinion at covering some of this.

Voltage on winding-> [Magnetizing Current]'
[Magnetizing Current]' -> Flux'
Flux' -> Voltage on other windings

Obviously the voltage<->Flux' relationship is proportional to turns.

The applied voltage ends up creating a [Magnetizing current]' and Flux' that equals a rate sufficient to cancel out that applied voltage. Secondary current then induces primary current by cancelling that flux, forcing primary current to increase until a new equilibrium is reached.

A transformer with DC applied will have a steadily increasing magnetizing current and therefore flux. You can predict the current and flux by keeping track of the applied volt-seconds and all cores will eventually saturate at a specific values of volt-seconds/flux/magnetizing current.

A 'big core' for the purpose of passing DC would be able to handle lots of volt-seconds and this is easily figured out by checking the voltage and frequency rating. A 50hz/250Vrms transformer must handle the volt seconds contained in each half of a 50hz/100Vrms sin wave. A 50hz/1kv transformer must handle 10X as many volt seconds.

You could then back-calculate how long such a transformer can pass DC by taking the volt seconds and diving by your applied DC volts. The 1kv transformer could handle 1/1000th the voltage (1Vrms) for 1000X the time (0.05hz or 20 seconds).

Kajunbee

### Kajunbee

points: 2

#### KlausST

##### Super Moderator
Staff member
Hi,

You could then back-calculate how long such a transformer can pass DC by taking
I know what you mean.

Just to be more exact:
* DC means infinite time.
* If time is finite ... better talk about a "pulse"

And even such a pulse needs to be a "single" pulse... at least when one assume that the voltage after the pulse is 0V.
The magnetism will be kept and a second pulse will almost immediate lead to saturation.

And even if one makes the input high impedance .. causing a high voltage pulse when the magnetic field collapses. Dangerously high!!... then still there is remanence making a second pulse to cause saturation within a shorter time than the first pulse.

Klaus

Kajunbee

### Kajunbee

points: 2

#### crutschow

If you apply an ideal DC voltage source, that source has zero impedance, so any pulse applied at a different winding will be absorbed by the source, since it's effectively an AC short.

If you want to apply DC to the winding then you should use a current source, which has infinite impedance and won't affect the pulses.

#### asdf44

Not to disagree but to add: my preference is to understand AC as DC that just happens to eventually change polarity sometime in the future.

It all depends on frame of reference really. DC is only DC over a small enough timeframe (since no DC is actually infinite). And AC is only AC over a sufficiently long timeframe (to a 100Khz SMPS transformer 50hz might as well be DC).

So I don't mind calling a known finite pulse DC. At any instant all signals are DC in my view.

#### c_mitra

So a big transformer core that is saturated less easily, would allow DC to pass from the primary to the secondary?
The question is framed badly (sorry!).

To make the first current truly DC, you must ramp it up infinitely slowly. The output will be ZERO.

Next you apply a 5V pulse via the other winding; the output pulse will be another 5V pulse.

With the DC const current, you have shifted the operating point. If the operating point is far from saturation, you will see no significant effect.

The steps in the experiment should be:

1. Take a toroid core.
2. Slip a wire (1 turn, for example) around it.
3. Connect a 100mA const curr source with this winding.
4. Slip another wire (preferably a twisted pair) and form the primary; make also secondary.
5. Perform your experiment with the 5V pulse.

#### Easy peasy

Not to disagree but to add: my preference is to understand AC as DC that just happens to eventually change polarity sometime in the future.

It all depends on frame of reference really. DC is only DC over a small enough timeframe (since no DC is actually infinite). And AC is only AC over a sufficiently long time frame (to a 100Khz SMPS transformer 50hz might as well be DC).

So I don't mind calling a known finite pulse DC. At any instant all signals are DC in my view.
interestingly - this appears not to be the case in power electronics when applied to losses in magnetics (and wires) - you would think the DC period(s) in a 50kHz square wave pulse would be just that - DC periods between impulse changes - but the losses go up with freq more than in proportion with the edge losses - a mathematics approach gives us the Fourier series of the square wave and tells us that things are changing at the fundamental + odd order overtones - and this is bourne out in the behaviour of materials over freq every time - somewhat at odds with logic but apparently true ...

#### c_mitra

and this is bourne out in the behaviour of materials over freq every time - somewhat at odds with logic but apparently true ...
I do not understand why you think that "somewhat at odds with logic"

Sine and cosine functions form basis sets (in Fourier analysis) and edges in the square waves are singularities.

But I am amused to see the comment that " At any instant all signals are DC in my view"; nothing can be further from the truth.

The values of a function and all the derivates at a given instant specifies the function completely for all times.

But the edges of the square waves are really messy to deal.

#### Easy peasy

it is at odds with logic, because, a piece of wire or magnetic core, cannot "know" when next in time a signal is going to reverse .... so how long after a pulse edge does the material consider itself to be in a DC state...? there appears to be something of an LC time constant in the material where the current density ( or mag field density ) spreads out at a finite speed after a pulse edge - the lower the freq the nearer to DC steady state it gets before the next reversal - giving rise to higher losses at higher frequencies ...

For a proper sine wave fundamental, the current or mag filed is always changing hence the AC effect is always there - in this respect sine waves are a special case - one can say that a square wave is the composite of fundamental and odd harmonics - but one cannot ignore the actual real application of square wave when the time to the next reversal is unknown ....

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" At any instant all signals are DC in my view"
looks to be ASDF44's view, not your view ...

#### asdf44

Yes that’s exactly how I’d think of it too.

I don’t understand there to be any time constant in the core or core losses. An inductor saturates at a given current, time doesn’t enter the equation. And I believe core losses are linear with frequency all else being equal - there is a fixed loss for moving the BV curve a certain distance, regardless of time. Agree?

Skin effect I’ll have to think more about.

#### Easy peasy

has nothing to do with saturation - look up dimensional resonance - of course there is a time constant for propagation of B and J - the limit being the speed of light - EM waves are slower in mag materials ....

#### asdf44

Yes I understand. I'm jumping to an instance where such a time constant might be observed: saturation. We can agree the speed of light isn't an issue here I hope.

Do you agree that core hysteresis losses are linear with frequency? I.E. that there is a fixed loss for moving the field (magnetizing current) a fixed distance in the core regardless of time? Because I think that's true.