Totally unsuitable wire used for SMPS transformer (skin depth)?

[treez]

Hello,
Do you believe that the 60W flyback SMPS transformer on page 21 of AN3089 (see below) has been wound with massively over-expensive multi strand wire?

The primary has been wound with turns of 30 x 0.1mm wire, and the secondary with 90 x 0.1mm turns.

This is far too expensive, and pointless, because the skin depth of copper at 85KHz is 223um.

So why have they used such totally unsuitable, overly expensive wire?

Also its worth remembering that this is a quasi resonant flyback, and the primary and secondary currents are trains of triangles, which have an overall DC level. Obviously the DC level is not in any way impeded by the skin effect.

AN3089:
https://www.st.com/st-web-ui/static...tion_note/CD00252755.pdf?s_searchtype=keyword

 

[D.A.(Tony)Stewart]

I's not just the skin depth losses they are trying to mitigate but 90 turns reduces the inductance to 1.1%

The Q at resonance has a big effect on efficiency , I would expect as well as raising the f helps to reduce conduction losses.

But perhaps more important is that it is not a true resonant SMPS but rather a flyback with hiccup mode and skips on firstvalley signal of ZCD. So timing is important to this chip's performance.

I don't know the cost of the transformer, but I imagine it to be <$3 in very high volume.

 

[FvM]

If you review manufacturer catalogs, you find 0.1 mm wire diameter as a standard suggested for 50 - 100 kHz operation frequency.

And 0.1 mm is also widely available, even if you come to the conclusion that 0.2 mm wire could be used. In so far I don't see a point of "totally unsuitable".

 

[Vbase]

Also small diameter wire fills the space with more copper, less resistance, less heat.

 

[treez]

Thanks, but do you agree that the DC component of the flyback primary and secondary waveforms does not suffer from the skin effect, it is only the AC component which suffers this?

Incidentally, the power.com PI Expert software does the same spec of flyback in CCM, with 32 turns of 2 x 0.45mm ECW for primary, and 6 turns of 4 x 0.45mm TIW for the secondary. This sounds far cheaper than that 30*0.1mm wire, even of you are saying that 30x0.1mm wire is common....I cant find 30x0.1mm anywhere on the web, and definitely not 90x0.1mm wire.

 

[FvM]

Obviously, skin effect losses apply to the AC current components. To derive it exactly, you'll determine the RMS value of each harmonic component.

Use whatever is easily available at your site. I presume 4x0.45 isn't available as ready-made litz wire, so you have to strand it yourself.

 

[D.A.(Tony)Stewart]

It is true that the minimum total loss design for proximity effects, skin effect and dc resistance may not be the minimum cost.

But cost has a huge variable with advantage to major transformer factories close to sources. Fill factor can be improved even more with square Litz wire perhaps even more scarce than Hen's Teeth "off shore".


Side note.
I once used a supplier in TW to get a quote on 10K units/day for resonant HV sweep regulator for a Lexmark laser printer 2nd source. I met the cost requirements but they did not accept my bid.
Magnetic costs come down in price significantly in volume.

 

[treez]

Obviously, skin effect losses apply to the AC current components. To derive it exactly, you'll determine the RMS value of each harmonic component.

Well, at worst case minimum vin, the flyback SMPS has average input current of 1.21 Amps, and an RMS input current of 1.9 Amps......therefore, as you can see, a very significant proportion of the primary current here is DC component, to which no skin effect applies. -It just gets into perspective how 30 x 0.1mm strands appears excessive.

As you know, the total AC component of the primary current is SQRT(1.9^2 - 1.21^2) = 1.46 Amps.

So as you can see, its not the full 1.9Amps of rms current that suffers the skin effect

 

[Vbase]

I's not just the skin depth losses they are trying to mitigate but 90 turns reduces the inductance to 1.1%

Tony please correct me if I'm wrong.
When you put 2 leads running in parallel with a distance between them you get half the inductance of one lead. It is common practice in RF.
When you wind 2 wires on a bobbin you get the same inductance as with one wire.
I know it from experience only and I don't know the theory.

 

[treez]

I think I need to double up on the turns..........but I wonder how this is going to effect leakage, with the windings being overall fatter....not only that, but theres a limit to the number of ECW wires that one can terminate to a single former pin......you can use two pins, and connect them on the pcb, but that must definitely worsen leakage.

 

[Orson Cart]

0.1mm will work well at 85kHz, 0.45mm not so well, you will use more copper and get the same heat in the wire, and more leakage inductance..., there is no continuous DC in your windings to which skin effect would not apply. All the power is via pulses, with the fundamental at 85kHz, hence low diameter wire is needed. If you sandwich the sec around the primary (or vice-versa) you can then use slightly bigger wire....

p.s. the skin depth tells you what distance into the wire the current density falls to 37% of that at the surface.

 

[treez]

there is no continuous DC in your windings to which skin effect would not apply.

Thanks, but as you know, a ccm flyback primary current is a train of trapezoids, which can be described as a constant DC level, with some AC components, the skin effect will surely not apply to the DC level?

 

[Orson Cart]

sorry your logic is flawed, work out the AC rms current, square this x the AC resistance = losses in watts, there is no proper DC that skin effect would not apply to...

 

[treez]

a train of trapezoids as in a flyback primary current does definitely have a DC component, and surely no skin effect will apply to this component.

I don't disagree with your IAC RMS ^2 * R though

 

[Orson Cart]

Mathematically you can average the pulse train to give an average DC level, this bears no relation to the RMS current (AC) flowing, as it could be peaky or not so peaky, depending on the operating point, also by direct observation there is no real "DC" flowing...

 

[treez]

sorry I disagree, there is a dc component to which no skin effect applies. I agree with you that the skin effect applies to all the ac components.
if the same waveform were somehow adjusted to have no dc level , then the loss due to skin effect would be much worse, as it would apply to the entire waveform.

 

[FvM]

if the same waveform were somehow adjusted to have no dc level

How do you "adjust a waveform"? For a given converter design, there's a fixed relation between DC and AC component.

I don't understand what the DC discussion is all about. Skin effect applies to AC current. Full stop.

You'll determine the frequency and respective level of AC components and determine AC losses.

 

[Orson Cart]

FvM, for a flyback as the input volts vary the pulse width changes, giving a different ac component for the same dc out...

treez, you seem to be implying you can subtract your "DC" component from the ac to arrive at ac losses, not really so in this case as there is no true net DC flowing.., there is no I^2R for some unspecified dc to add to the ac i^2 R losses. Its all ac.

 

[FvM]

FvM, for a flyback as the input volts vary the pulse width changes, giving a different ac component for the same dc out...

Obviously. But you'll hardly "adjust" the flyback current waveform to "have no dc level". Isn't it?

 

[treez]

treez, you seem to be implying you can subtract your "DC" component from the ac to arrive at ac losses

....I definitely don't mean that.

I believe we agree there is a DC component. I don't believe you mean that when you say "its all AC".....there is a DC component, and I believe we agree on this, after all its a train of unipolar trapezoids.
I think FvM's post of a few back says it like it is.

But you'll hardly "adjust" the flyback current waveform to "have no dc level". Isn't it?

I understand, I was speaking figuratively, to express a certain point.