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A Question About Turns^2 and AL...

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Patrick

Thu Dec 15 2011, 06:17AM

Registered Member #2431 Joined: Tue Oct 13 2009, 09:47PM
Location: Chico, CA. USA
Posts: 5639

Ok i know from personal experience that HV transformers with large turn ratios can have very large inductances on the secondary side. I still have 2 HEI iggy coils that have 33 and 25 Henries (though they both have air gaps in the two EE cores, so the H value might differ due to the air gap.) anyway,i know there can be huge Inuductances in ferrite and steel core transformers.

my questions are:

First, if my Al value is 7500 on the datasheet, and i have N = 600 turns, then N^2 x 7500nH = 2.7H is this right?

Second, if i have a few pico farads of capacity across the 2.7 H secondary, does this mean i get some really slow RC time constant, at the secondary. Or the pico farad value reflected back to the primary via secondary turns squared?

Third, i presume flybacks have equally large inductances, and im sure they have capaciteces all over, yet they respond at the 10kHz to 40kHz banwidth, right?

Mattski

Thu Dec 15 2011, 07:33AM

Registered Member #1792 Joined: Fri Oct 31 2008, 08:12PM
Location: University of California
Posts: 527

Patrick wrote ...

First, if my Al value is 7500 on the datasheet, and i have N = 600 turns, then N^2 x 7500nH = 2.7H is this right?

Yep, that's correct. I don't have any practical experience with transformer design but with an inductance this high I'd check to make sure that the current you put through it doesn't saturate the core. Given the Al I'm guessing it's ferrite, which usually makes use of an air gap for flyback circuit transformers to limit the flux, which will also change the Al.

Patrick wrote ...

Second, if i have a few pico farads of capacity across the 2.7 H secondary, does this mean i get some really slow RC time constant, at the secondary. Or the pico farad value reflected back to the primary via secondary turns squared?

Often a transformer model is treated as an ideal transformer with a "magnetizing" inductance in parallel with the primary. The load can be reflected across the ideal transformer as usual, and the magnetizing inductance models the self-inductance of the transformer. It only goes in parallel with one of the windings, and if you pick the primary side winding then presumably the inductance is much lower than your secondary. In principal you can also pick the secondary as the place to model the magnetizing inductance, but the circuit would still work the same because even though the inductance is larger the voltage driving it is increased by the turns ratio. A more complete model for a transformer will also include leakage inductances: inductances in series with each winding. A pancake-style winding would have a lot more flux leaking out and hence more leakage inductance.

Under certain conditions the magnetizing inductance can be ignored as most of input current is flowing into the load rather than magnetizing the core. For a flyback topology magnetizing inductance must be modeled to understand what's going on.

Patrick wrote ...

Third, i presume flybacks have equally large inductances, and im sure they have capaciteces all over, yet they respond at the 10kHz to 40kHz banwidth, right?

Somehow they muddle through :)

Patrick

Thu Dec 15 2011, 07:44AM

Registered Member #2431 Joined: Tue Oct 13 2009, 09:47PM
Location: Chico, CA. USA
Posts: 5639

Mattski wrote ...

Patrick wrote ...

First, if my Al value is 7500 on the datasheet, and i have N = 600 turns, then N^2 x 7500nH = 2.7H is this right?

Well, its a planar core, ferrite, at 100kHz, 2300 Guass, doesnt seem to saturate if the current is low in the secondary, by
Amp-turns. Also it comes out to 11 volts per turn. When i power up the first prototype this weekend i expect it to be quite hot, so it will be in circulating oil.

crap, i was really hoping to avoid the need for an airgap, as energy storage is something i try to avoid in my transformers.

Transformers are a series of comprimises, and always a PITA.

Mattski wrote ...

Somehow they muddle through :)

This isnt the answer i was hoping for.
Im crying on the inside, now

Steve Conner

Thu Dec 15 2011, 10:09AM

Registered Member #30 Joined: Fri Feb 03 2006, 10:52AM
Location: Glasgow, Scotland
Posts: 6706

The magnetizing inductance is the wrong one to be worrying about. It's pretty much irrelevant in a forward converter, as long as it is fairly large compared to the load impedance.

And in a forward converter, no amount of load current will "saturate the core". The core doesn't see the magnetic field due to load current, because the primary amp-turns are cancelled out by the secondary ones. Only an excess of volt-seconds (too high a drive voltage at too low a frequency) or DC current in a winding will saturate it.

The leakage inductance is the bad one. The resonant frequency (or time constant if you prefer?) of the leakage inductance with the secondary self-capacitance is what causes trouble in HV transformers. It makes the transformer look like a 2nd order low-pass filter, and the cutoff frequency of this filter had better be above your operating frequency if you want it to work.

Of course you can drive the transformer right at its resonant frequency and get a huge output voltage from resonant rise, like a Tesla coil. But then you have to pay attention to loaded Q and so on.

You can get a rough idea of leakage inductance by measuring the primary inductance with the secondary shorted out.

Of course you calculated all of this before even buying any materials.

Dr. Dark Current

Thu Dec 15 2011, 12:50PM

Registered Member #152 Joined: Sun Feb 12 2006, 03:36PM
Location: Czech Rep.
Posts: 3384

I'll add to this, be aware that driving a HV transformer with a square wave will result in voltage spikes on the secondary winding, possibly up to 2-3 times the designed peak output voltage.

Patrick

Thu Dec 15 2011, 04:01PM

Registered Member #2431 Joined: Tue Oct 13 2009, 09:47PM
Location: Chico, CA. USA
Posts: 5639

wrote ...

The leakage inductance is the bad one. The resonant frequency (or time constant if you prefer?) of the leakage inductance with the secondary self-capacitance is what causes trouble in HV transformers. It makes the transformer look like a 2nd order low-pass filter, and the cutoff frequency of this filter had better be above your operating frequency if you want it to work.

This is exactly what i need to know ! Ill post a ideal transformer with non-ideal paths here shortly. letme know what you all think. Ill try to see how bad my 2nd order low-pass numbers look!

wrote ...

Of course you calculated all of this before even buying any materials.

Of course i did! (no, not really) every time i make a small change here or there all the math changes dam it.

Steve, Im ussing a PP-CT for the first prototype, and ill be using a half bridge for the final design. None of the forward converter topologies, they cuase to many "issues".

MArko?

wrote ...

I'll add to this, be aware that driving a HV transformer with a square wave will result in voltage spikes on the secondary winding, possibly up to 2-3 times the designed peak output voltage.

Yes i relise this and my core-to-secondary and secondary-to-primary insulation will be quite hefty, multiple layers of mylar. Also ill be using Radhoo's method (#3) for HV coil winding.

Steve Conner

Thu Dec 15 2011, 04:52PM

Registered Member #30 Joined: Fri Feb 03 2006, 10:52AM
Location: Glasgow, Scotland
Posts: 6706

wrote ...

Steve, Im ussing a PP-CT for the first prototype, and ill be using a half bridge for the final design. None of the forward converter topologies, they cuase to many "issues".

Anything that isn't a flyback converter is a forward converter.

Sorry for hitting "Moderator Edit" instead of "Reply With Quote" btw!

Patrick

Thu Dec 15 2011, 08:43PM

Registered Member #2431 Joined: Tue Oct 13 2009, 09:47PM
Location: Chico, CA. USA
Posts: 5639

Steve Conner wrote ...

Anything that isn't a flyback converter is a forward converter.

no prob on the mod edit,

didnt relise that! flyback, forward its all a blur to me.... look here->

As for steves comment on the second order low-pass filter i was reviewing the math here:

and found this pic....

The steepness of slope on the upper limit of the pass-band is twice that of normal, -40dB.
i presume resonance is right within the f sub c gap, with Q considered?

im also researching how to model a real transformer, using sources like this ->

and the TI unitrode PDF's.

More sources:

transformer math and circuits.

transformer stuff.

And our own 4HV.wiki!

im trying to figure out these pics from the above sources:

Wolfram

Fri Dec 16 2011, 10:58AM

Registered Member #33 Joined: Sat Feb 04 2006, 01:31PM
Location: Norway
Posts: 971

That model doesn't take the reflected secondary capacitance in account. The secondary capacitance is not usually significant in low voltage transformers, so it's not usually considered in transformer modelling for low voltage power supplies. It can be very significant in high voltage transformers though, as the capacitance as seen from the primary is equal to the secondary capacitance times the number of turns squared.

The frequency response is going to look something like this

, ignore the values on the X and Y scale values, I used arbitrary component values. This is just a simple approximation of a HV transformer in the form of a 2nd order LC low pass filter with the inductance being the leakage inductance and the capacitance being the reflected secondary capacitance. There are other parasitics too in a real transformer, but these are mainly the ones determining your max frequency. The most "peaky" curve (highest Q factor) represents a low load case, and the flattest curve represents a heavily loaded case.

Also, on your question about flybacks, most modern DC flybacks are so-called diode-split transformers. This means that the secondary is wound in separate sections with diodes between each section. The diodes effectively isolate the secondary sections from each other AC-wise, so you don't get the huge reflected secondary capacitance of a typical high step-up ratio HV transformer.

Patrick

Fri Dec 16 2011, 08:48PM

Registered Member #2431 Joined: Tue Oct 13 2009, 09:47PM
Location: Chico, CA. USA
Posts: 5639

Last night i was trying to figure out these simulations.

And using my derivation, for a LV primary and HV secondary, i get the reflected capacitence.
(Ns/Np for step up, Np/Ns for step down)

C sub p, eff = effective capacitience reflected to primary.
C sub s, act = actual capacitience present on secondary.

Is this what you mean Anders M? is "case B" a good example or not?

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