SMPS transformer power capability

[Elerion]

I know about the area-product and the Kg criteria, for selecting the core size.
There're also some nice tables, given by Ferroxcube and others, that tells us that a ETD-29 can handle 20-50 W.

For a 45 W design, using area-product formulas recomended by OnSemi, Fairchild,... I get a core requirement of about 0.15 cm^4.
Using Kg formula, requirment is 0.026 cm^5.

ETD-29's area-product is 1.08 cm^4, and Kg is 0.052 cm^5.
Kg is double of that required, and area-product is ten times larger.
It just doesn't make sense to me.
(I'm using 150 mT working flux, and 100 kHz, for Vi=24, Vo=16@3A.)

Now, what if we derive some simple relation?
We know that energy stored in an inductor = 0.5*L*I^2

Using relation: L = N*phi/I = N*Ac*B/I

E = 0.5*N*Ac*B*I

Using relation: H*MPL = N*I, subtitute for N

E = 0.5*B*Ac*H*MPL

Using relation: B = mu*H

E = 0.5*B^2*Ac*MPL/mu

Now, power is energy divided by time, so we can multiply by frequency divided by duty cycle.

P = (f/D)*0.5*B^2*Ac*MPL/mu

Do we agree up to this point?
I get 5 W, far less than the expected.
Ac = 0.761 cm^2
MPL = 7.2 cm
mu = 2000 * pi * 1e-7
D = 0.5

Any comments?

 

[Elvee]

I didn't check everything in detail, but if your calculation apply to a FB topology, shoudn't you use µeff instead of µi?

After all, you are going to gap your core?

 

[Elerion]

Yes, a FB needs gap, and using µeff will, indeed, increase the result.

This leads to another question... would the reasoning based on stored energy work in case of forward converter too?


Searching, I found a similar discussion on this thread:
How to calculate maximum power output of a ferrite core?


They do not specifically talk about flyback topology, but the maximum power of a ferrite.

 

[Elvee]

This leads to another question... would the reasoning based on stored energy work in case of forward converter too?

You could certainly do it via stored energy, but it would require extensive calculations, ending with massive simplifications if you made no errors.

It is simpler to use the simplifications from the start: regarding the core, the number of turns n required not to exceed a given induction B is n=Von*Ton/(B*Ae) for a single forward topology, assuming the core is fully demagnetized at the start of Ton.
For a double forward (push-pull), this becomes n=Von*Ton/2(B*Ae) or n=Vs/4(B*F*Ae) for steady-state conditions.

If you combine these formula with the copper capability of the core, you can derive the power