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Leakage inductance of ferrite transformers

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Dr. Slack

Fri Jun 09 2017, 04:18PM

Registered Member #72 Joined: Thu Feb 09 2006, 08:29AM
Location: UK St. Albans
Posts: 1659

I'm amusing myself doing a paper design of an alternative SSTC, the OfflineFerriteTransformerMagnifierTC, and need some help estimating leakage inductance.

Pre-ramble
The basic thinking goes that in an SSTC, the magnetising current of the primary is very high. That's mitigated in a DRSSTC by supplying the mag current from an MMC. An alternative way to reduce the mag current would be to put a ferrite core in the 'transformer' formed by the primary and the bottom of the secondary, and split the secondary so we have a real transformer, and a magnifier inductor. With intermittent operation, I don't see any reason why a ferrite transformer can't have the nuts thrashed off it, just as one does with bricks, as long as the duty cycle and hence heating is kept low. My outline figures to explore are sort of 300kHz, 100kW peak through an N97 ETD 59/31/22. Can it run at 300kHz? That's why I need to estimate the leakage L and stray C to see what it would resonate at. If the figures come out grossly stupid, then I won't have to buy anything to test.

The self-C is fairly straightforward. As for the leakage inductance, after some googling, I found

, which gives some fairly straightforward (looking) equations, and I'm trying to use 17-2. The first problem is there's a term (MLT) which is not referenced in the paper anywhere. I'm guessing it means mean length turn, which seems to be backed up by searching for that+transformer. The second issue is that I'm getting a huge (seems to me) answer of 45uH secondary referred leakage. Does this sound reasonable for this sort of transformer? I'm using b1=0.2cm (pri thickness) c=0.1cm (interwinding insulation), b2=0.7cm (sec thickness), a=4cm (winding width), MLT=10cm (I hope it would be cm to be consistent with the other parameters, but can't tell), and N=60 turn secondary (that's 60 turns for 10kV).

Can anyone help me with real ballpark figures for real transformers, and any better backed up formulae for estimating leakage inductance?

hen918

Fri Jun 09 2017, 05:01PM

Registered Member #11591 Joined: Wed Mar 20 2013, 08:20PM
Location: UK
Posts: 556

Have you got / heard of / used the software (freeware I think) called ExcellentIT ?
It's designed to be used as tool for designing SMPSs, but it would be really useful for your application, giving you ballpark figures for everything (apart from leakage inductance, I think it assumes the transformers are perfect).

I've attached it in a zip, it's a standalone executable.
]excellentit7100.zip[/file]

Dr. Slack

Fri Jun 09 2017, 06:41PM

Registered Member #72 Joined: Thu Feb 09 2006, 08:29AM
Location: UK St. Albans
Posts: 1659

Thanks hen, I appreciate the thought. I've had a little look. It seems a bit sniffy about core dissipation, doesn't seem to like the frequency/flux choices I try to make. I can calculate everything manually except leakage inductance, and it won't do that for me either, so it's of very limited use.

FWIW, with the 45uH estimate I'm questioning, I get a 3.5MHz SRF, so it appears there's a lot of scope to be fairly wrong, and still have a transformer that's usable at 300kHz.

Dr. Slack

Fri Jun 09 2017, 07:27PM

Registered Member #72 Joined: Thu Feb 09 2006, 08:29AM
Location: UK St. Albans
Posts: 1659

johnf

Fri Jun 09 2017, 07:58PM

Registered Member #230 Joined: Tue Feb 21 2006, 08:01PM
Location: Gracefield lower Hutt
Posts: 284

Dr slack
from my experience leakage inductance is all about winding topography and also to some extent turns ratio. So a one to one transformer with layered windings it is possible to get to 99.98 coupling which if the inductance was 100uH when the other winding was shorted the new inductance would be 99.98uH or a leakage inductance of 20nH.
As you leave the 1:1 scenario the coupling gets worse also any barrier layers add very quickly to the leakage inductance.
Many years ago I worked for a modem manufacturer where we did all sorts of modems and the hardest jobs were line powered ISDN units that had to support POTS as well so 70VDC on the line supplied through a 1000 ohm resistor (max line resistance) switching supply was to have many 3.3 5 volt windings all isolated from each other, line side, subscriber side electronics and to support POTS we had a 50 and 200 volt supplies for the the line bias and ring amplifier respectfully.
the tiny transformer was too complex and the leakage inductance was reflected as snubber dissipation so we could not meet the line length objective of 1000 ohms(fallng short to 760 ohms). In a stroke of brilliance I removed the 200 volt winding and stole some of the 50 volt winding to power a quadrupler to get the 200 volt rail. The reduction in leakage inductance was massive so much so that we got to 1450 ohms line resistance with the modem still operating.
Your 300kHz might lead to significantly increased core loss.
I was lucky to have an inductance bridge that I could program the output frequency on. 10Hz to 10MHz so exact measurements on the actual transformer at its operating freq were doable

Sulaiman

Fri Jun 09 2017, 08:01PM

Registered Member #162 Joined: Mon Feb 13 2006, 10:25AM
Location: United Kingdom
Posts: 3140

When I've made ETD transformers (only a few times)
I have been happy to achieve <1% leakage inductance
e.g. 1 mH inductance with 10 uH leakage inductance is acceptable to me.
Even the pressure keeping the two cores together makes a difference,
so I Imagine that designing for a given leakage inductance will require some kind of shims.

Dr. Slack

Sat Jun 10 2017, 06:42AM

Registered Member #72 Joined: Thu Feb 09 2006, 08:29AM
Location: UK St. Albans
Posts: 1659

I've always assumed that with a 'very high' permeability core, one can get coupling 'very close' to unity, reaching one at infinite permeability. I'm beginning to realise that the absolute minimum leakage inductance stays constant, and is a function of the non-core space around the windings.

Is it the case that the leakage inductance for a given winding is (very loosely) bounded above by what would be the inductance of that winding with no core present? As the core is fitted, and as interleaved windings encroach on the free space around a winding, that reduces the volume of space in which we can store energy that's not linked with the other windings, so reduces the non-linking (leakage) inductance?

It seems that in a high voltage transformer that requires much free space around the secondary for insulation, that dooms us to a significant leakage inductance from that volume alone?

Uspring

Fri Jun 16 2017, 10:39AM

Registered Member #3988 Joined: Thu Jul 07 2011, 03:25PM
Location:
Posts: 711

Getting the coupling close to unity by adding a ferrite and reducing the leakage inductance to zero isn't quite the same. Leakage inductance can be calculated by

L = Lwinding * (1-k*k)

Adding a ferrite can get you a higher k, but at the same time Lwinding will increase, so the leakage inductance might stay non zero even at infinite permeability.

Intuitively, you get a k=1, when the field produced by a current solely in one coil can be matched exactly by a current solely in the other coil. An exact match being the same field in every point of space. In the less ideal situation, where there are regions in which the fields are e.g. opposite in direction, coupling can be increased by putting ferrites only there, where the fields are parallel. A ferrite in all of space won't change coupling.

In a high voltage situation, the coils have to be separated, which implies, that the fields, that currents in either coil produce, won't match everywhere. That implies less coupling and more leakage inductance.

Formally, insights can be derived from the equation of energy content in the field, i.e. the B^2 volume integral and comparing it to the energy content from the coupled transformer equation utilizing primary, secondary and mutual inductance and currents.

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