> As regards air gaps: My understanding is that they reduce the magnetic 
> permeability and thus the inductance (while increasing Isat?). As such, I 
> figure that for off-the-shelf parts that that should already be factored in 
> to the specs, air gap or no?

Yes, but hopefully the specs will also show if the transformer core is gapped.  
Transformers for SET amplifiers and flyback mode power supplies, generally are, 
mains transformers and Royer converter transformers generally aren't.

> If I am winding my own, and I have separable cores, then I should definitely 
> include that though?

If you're planning on using them in flyback mode, yes.  The gap shouldn't be 
big, a fraction of a millimeter.  E core transformers often have the outer arms 
full length and the center one slightly short to create the gap.

> 
> When used in flyback power supplies, I assume that the output voltage still 
> follows the winding ratio but that the input voltage is actually that of the 
> back-emf induced by the field collapsing in the input coil? Is there 
> something else happening?

Something else is indeed happening (as Greg mentions).  The output voltage 
actually depends on the duty cycle as well as the winding ratio.  This is why 
some of our nixie supplies are twitchy: in order to get a large voltage ratio, 
the duty cycle becomes somewhat extreme.  As Greg also points out, you need to 
arrange the timing, voltage, inductance, and saturation so that you've put as 
much energy as you can into the magnetic field.  Even more importantly, you 
need to remove all that energy too.

Remember, you can get a couple hundred volts from an ordinary buzzer running on 
a 1.5V cell.  That's just one coil.

> What happens if the two coils wrap around cores of different permeability?

If they're different cores, I don't see how they can be magnetically coupled 
properly.

> Also need to keep an eye on the isolation voltage - a few I looked at had 
> very low isolation voltages, I assume that would not end well for my purposes?

Yeah, that can be important, one of those many transformer specifications you 
have to check when working with high voltages.

> That LPR6235 is a perfect example of a transformer I couldn't find! After you 
> pointed it outAnd yes I tried to order samples, but they rumbled that I 
> wasn't going to go into production and said it wasn't their policy to send 
> samples out to people like me (I paraphrase, I am not trying to imply that 
> they were nasty about it or anything). Understandable, but a little 
> disappointing. I guess I'll just have to try and buy one from somewhere!

They're not expensive.  I didn't look up that one, but the FA2786-BL is four 
bucks apiece in quantity one (cheaper if you buy 400 at a time).

Then again, I don't buy a lot of CCFL transformers, as I keep finding nice CCFL 
inverters from surplus vendors for a buck apiece.  I can't buy the transformers 
alone that cheaply, and these include the driving circuitry, output coupling 
capacitors, and printed circuit board.  One common model even has a handy notch 
in the trace that joins the LV and HV sides, so I can easily cut it to separate 
them (I really would rather not have the ground return for my HV through the 
switching transistor in my regulator).

- John

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