Dc losses in an ideal transformer

[Avizor]

I have a doubt about wire losses in transformers. In the magnetic design cookbook of Texas Instruments, copper losses are estimated with Rac and Rdc in a flyback converter (https://www.ti.com/lit/ml/slup127/slup127.pdf page 12), and I agree with this method because a flyback transformer isn't a true transformer, it's coupled inductors, so they have a dc level.

In a true transformer there's no dc component, but in the cookbook (https://www.ti.com/lit/ml/slup126/slup126.pdf page 11) they still consider dc losses.

How can an ideal transformer have a dc current? Considering it's a real transformer with a sinusoidal waveform, a dc level would saturate the transformer.

In my opinion, the copper losses should be:

Pdc = Rdc*Idc² , with Idc = 0, then Pdc = 0
Pac = Rac * Iac² , with Rac = AC/DC ratio * Rdc, and Iac = Irms of the sinusoidal waveform

I can't find any clear info about this, can anyone help? Thanks!

 

[godfreyl]

In a true transformer there's no dc component,......

That's quite a wild assumption.
A transformer is a transformer whatever current happens to be flowing in it's primary or secondary, and it doesn't suddenly turn into "not a true transformer" whenever there happens to be some DC current involved.

In fact transformers quite often do have DC current flowing through them, by design or otherwise.

How can an ideal transformer have a dc current?

I guess there's no such thing as an "ideal" transformer in the real world, but here's a couple of examples of why real transformers may have DC current:

• Consider a single-ended class A amplifier with a transformer coupled output. For it to work, the DC current through the transformer's primary winding must be at least as great as the peak AC current.
  
  This arrangement is common in RF circuits, and also applies to single-ended valve audio amps (although they're not very popular anymore).
  
  
• Consider mains power transformers. In theory, mains voltage is a sine wave, usually either 115V @ 60HZ or 230V @ 50 HZ, with no DC component. In practice (especially near industrial areas), it's not a very good sine wave and there is often a small DC voltage imposed on the AC.
  
  Because the winding resistance is low, especially for high power transformers, even one or two volts of DC can cause significant DC current to flow in the primary winding.

......a dc level would saturate the transformer.

Yes, this can be a real problem with power transformers, (especially toroids for some reason that escapes me - something to do with tighter coupling and/or lower winding resistance compared to EI cores, IIRC :-?).

Typical symptoms are audible humming from the transformer, but only occasionally or at certain times of day, when there is a heavy unsymmetrical current load on the mains somewhere nearby.

 

[Avizor]

Thanks for your reply godfreyl.

When I talk about "real" vs "ideal" transformer I'm taking about the theorical calculations, where a common approach is consider the transformer ideal. The common and simple way to avoid the problems you point is oversize.

If we follow the papers of TI (the bible of transformers in my opinion), to estimate the DC losses, we'd have to calculate Idc as the medium value of a semiperiod of the sinusoidal waveform, and this doens't make any sense.

I found a paper where it seems the author thinks this way too: https://thayer.dartmouth.edu/inductor/papers/litzj.pdf page 2 eq. 1

 

[godfreyl]

...but in the cookbook (https://www.ti.com/lit/ml/slup126/slup126.pdf page 11) they still consider dc losses.

That reference is discussing a forward converter (SMPS).

If we follow the papers of TI.... we'd have to calculate Idc as the medium value of a semiperiod of the sinusoidal waveform, and this doens't make any sense.

There is no sinusoidal waveform. It's a PWM square wave. Do you have a simulation that can show you the voltage and current waveforms in a circuit like that? That may help you understand what's going on.

 

[mtwieg]

Ideal transformers cannot produce an EMF at DC, but they can surely conduct DC currents. There's nothing about the nature of a transformer that prohibits this. The only bounds on transformer behavior is that the net magnetic flux is bounded and continuous.

 

[emontllo]

The document you mention talks about power transformers for various converters that do have DC currents. For instance, the forward converter typically needs a core desaturation circuit!

If we assume a perfect sinusoidal waveform with no DC component there will be no "DC power loses", Pcopper = R * I(AC)RMS.
The document makes a difference between "DC resistance" and "AC resistance" is because the skin effect, at 50 Hz to 60 Hz, skin effect will be negligible.

 

[Orson Cart]

Yes, this can be a real problem with power transformers, (especially toroids for some reason that escapes me - something to do with tighter coupling and/or lower winding resistance compared to EI cores, IIRC ).

Because toroids have a closed mag path with no gap and high u, it takes fewer ampere-turns per m of mag path length to get them to saturation - other core structures with gaps (e.g. double E, ETD series) suffer from this to a slightly lesser degree.

Designers often use the "DC" resistance of a winding as a starting point for a transformer design, multiplying by the RMS current in the winding to get an estimate of the copper losses in the tx - usually losses are higher due to current crowding in the wires (skin effect & proximity effect) at AC frequencies typically used.

A flyback has (mathematically) net DC in the pri and sec windings - but the volt seconds applied are balanced to reset the flux every cycle.

Again it is common to calc the true RMS in each winding and use the DC res to estimate losses as a starting point.