Transformer Flux Density

Hi,
I have been trying to figure out how the inductance factor (physically, proportional to the core gap distance) has an effect on the flux density of a transformer in operation as per faradays law:

B = (Vin x 10^8) / (4.44 x freq x Ae x Np)

Ae is core area, and Np is primary turn number. This calculation is for a sine wave.

The inductance factor (Al ill call it) is not in this equation, but I know that if I were to gap the core (which changes Al), that would change the flux density. The BH curve would get streched out and id loose efficiency but I'd be able to avoid saturation in certian cases. So, I know that B changes if I change Al, but Al is not in the equation. Can anyone shed some light on this for me...I know its in there somewhere, I just cant see it...
-Mike

I just had a thought... could it be that its just H that changes, not B, when the Al is changed? That would explain the diagonal streching of the hysteresis loop...
meh...i guess im still confused about the change...I guess the "knee" of the curve would somehow have to be at a higher B value now due to the stretching of the curve?
-Mike

You need turns squared in that denominator.

And, there is a stacking factor if using anything but a C core. Stackin for 29 ga EI is usually taken as 0.9, so that 4.44 gets aproxied down to 4.

Also, you need area in cm^2

I have some jpg's I snapped of a transformer book, good info, I will dredge up the relevant pages as soon as the boss quits breathing down my neck while I'm trying to roll the bones.

Here are some different versions of the B max formula, some are for the core cross area in inches, some for cm, 16 hz used for f, division done on denominator, etc.:

You can use 4 hz for super fidelity designing. Or 12. Everybody has their own criteria.



You could use the last formula to make some cool design charts, like take all your favorite cores, plug in their areas, then build a chart of that core vs turns.

Then, when ever you start a new design, you just take your flux from the operating level, and you can look it up.

cj

OK, here is about a meg of gap stuff.
Knock yourself out.
McLyman is an easier read than Grossner.
Don't get too hung up on the more obscure formulas and stuff, just try to grab the basics. In real life, xfmr engineers do more experimenting than calculating.



Sorry about the quality, but hey, it's cheap!
Print it out so you can read it.

http://vacuumbrain.com/The_Lab/TA/Transformer_Design/Air_Gap

[quote author="CJ"]McLyman is an easier read than Grossner.
[/quote]

CJ, is McLyman about your favorite?

If I were going to a desert island, it would be Grossner.
McLyman is great, more like a Jr College book, Grossner would be more up to your level, I believe. Takes up less space also. McLyman's books are huge and expensive, Grossner is small, a bit harder to see, but cheap and packed.



This is another good book, hard to find books just on xfmr steel, but here it is.
Only problem is, what are you gonna do? Specify an anealing tempeture for your next batch of lams?
But still, good for selection of core steel.



And if you want to impress your xfmr friends, have a copy of this on the coffee table, becuase thats about all it's good for.
Very complete.
You can find out how many months it takes to pickle paper in copper sulfate and have it come out as fish paper.
This book is a thick 2000 pager, or so it seems.

Thanks. The two last ones I didn't even know of. Grossner I've seen and yet somehow don't think I have---but it might still be in a box in storage. I have one by Flanagan, HB of Transformer Design & Applications, 2nd ed. 1993 ISBN 0070212910 that seems fairly decent.

CJ, thanks for all that material. I am just now getting a chance to look at it... I'll probably end up buying a McLyman or Grossner book at some point as well.
-Mike

when are you gonna wind me a present!

well, when I come home you should show me how :grin:

A second question I have about the Bmax equation: The 4.44 is not really well explained anywhere I've looked (perhaps I've not looked hard enough).

What variables have an effect on that number?

I know that waveshape has an influence on that number, and CJ mentioned that stacking factor also influences it. What other factors have an influence?

Also, are any of the files you put up from the Grossner book? I found one book entitled "The Magnetic Circuit", as the first 10 or so pages seem to be from that, but it was not written by Grossner. I'm just trying to get an idea of what I'm going to get out of each book (Mclyman, Grossner) before I spend my money on something...perhaps I'm just spoiled by Pressman...he writes some great stuff
-Mike