Transformer Design for a Series Resonant Converter

Question

I am determining the Area-Product of the core required for a transformer to be used within a series resonant converter. The specifications are as follows:

• Switching frequency = 400 kHz
• Primary current = sine wave with a peak value of 500 mA
• Power output = 1 W

These are my calculations:

• I decided to use a core made out of N49 (since many such cores are already available)
• From the data given on this website, I have determined the saturation flux density of the ferrite core as: 0.04 T (approx.)
• The winding factor is considered to be 0.2
• Since we are dealing with 400 kHz, I decided to use a Litz wire with a 44 AWG strand size which has a bare Copper diameter of approximately 0.051 mm
• Since the RMS value of the primary current is 0.353 A, I decided to use a Litz wire with 18 such strands. This may be too much, but it is fine for my initial design (the overall conductor area now comes out to be 0.0368 \$mm^2\$).
• I calculated the current density of this conductor as follows: \$J = \frac{0.353}{0.0368} = 9.59 A/mm^2\$
• The Area-Product of the transformer is given by: \$A_cA_w = \frac{VI}{2\; f_{sw}\; B_m\; k_w\; J} \$ This gives a value of \$\frac{1}{2 \times 400000 \times 0.04 \times 10^{-6} \times 0.2 \times 9.59} \$ = \$ 16.293\; mm^4\$

Is my area-product calculation correct based on the specifications? Is the saturation flux density value as well as the current density, correct? Also, will there be any issue due to more number of strands (more than the required value) within the wire?

Answer 1

The calculation appears fine. The values put into it require more thought though.

Saturation flux density is 400mT or more, see datasheet: SIFERRIT material N49 | TDK. Peak flux density may come down, particularly as frequency goes up, due to core loss. For a small transformer like this, and with efficiency unstated, I might be fine running it at 0.1-0.2T.

Likewise I wouldn't worry about litz, at such low current. I would probably reach for 28AWG myself.

If you need particularly low loss (maybe this is more of a signal than power application, I mean, done with a little power, but point being, the purpose is more finesse than raw output), that would be fine, and probably stranding of 36AWG or finer would suffice. (Since you don't mention application, I'm free to suggest either direction.)

Note that V*I in the relation is apparent power, not real power. Since you say it's resonant, you must define the resonant energy* as well.

And to achieve target flux density, you need so-and-so turns, and to achieve target inductance, you need so-and-so inductivity, which is to say, air gap of the core, or effective permeability in any case. And fringing flux around the airgap will put more pressure on the choice of litz (which, the above values will still be fine for, unless the required Q factor is EXTREMELY high, say upper hundreds or more).

*Reactive power is energy, in the same way that torque is N.m and work is N.m but the directions are different. Essentially the (phase) direction is different, so S has units of VA but represents energy instead of power. To get the (peak or circulating) reactive energy, divide by angular frequency. This is true, at the fundamental at least; of course you'll need to use Parseval's theorem for the general (all frequencies) case.