SMPS Design Transformer Core Selection

I'm trying to construct an SMPS power supply with 230VAC at 50 Hz input and 5.6V/2.5A output. Here is the schematic:

The design was optimized with EE19 core selected and I am expected to optimize the power supply with EE16 core to save space on board. The problem is that, as PI expert simulation indicates, maximum flux density limit exceeded.

1) What points should I take into account to solve this problem?

2) Is there any recommended book, or resource to understand the theory better?

I've just worked on PS unit; so, I really appreciate any comments whether it is related to my problem, or not.

Thanks

• What core gap does the transformer have? – Andy aka Jan 12 '15 at 9:20
• It is ungapped EE core. @Andyaka – cryptokovski Jan 12 '15 at 9:51
• Does the PI expert allow you to add a gap to the core - this will reduce peak flux density at the expense of more winding turns. – Andy aka Jan 12 '15 at 9:53

Any core without a gap will have its maximum value of permeability. Adding a small gap can significantly reduce the permeability of the gapped-core and this reduces peak flux density significantly for the same number of turns and current flowing.

It's all contained in this formula, B = $H\cdot\mu$

where B is flux density, H is magnetic field strength and mu is the actual magnetic permeability of the core (or core with gap).

H is the ampere-turns of the excitation coil (primary) divided by distance around the core. If you add a gap that reduces B by 2 then, you should add turns back-on to restore the inductance of the primary. The beauty is that inductance is related to turns squared so if B halves (due to the gap) then you need to increase turns by 1.414 to restore the inductance.

But, this increases H by 1.414 so the halved value of B increases by 1.414 to 70.7% of where it was originally.

So now you have a transformer with a gap that has exactly the same inductance as before but only 70.7% of the peak flux density (at the expense of more turns). If you can fit the extra turns on and reducing B to 70% is acceptable then you have a simple solution.

Of course you'll now have bigger copper losses and you might be fighting a battle that cannot be cheaply won. Keeping the turns as low as you can is a big help - having no more turns than necessary is the trick.

• By increasing C2 capacitor significantly (82uF) solves the problem; but, with much higher ripple current and ESR value. Is it appropriate to make such a change? In addition to, PI warns me that EE16 core is too small for the specified output power(14W). Why is it so? – cryptokovski Jan 12 '15 at 12:55
• You can increase C2 sure but it may become physically too large for your job. EE16 may be too small because to keep the flux low (when gapping the core), the required number of turns on primary and secondary may become too large and to fit them may require smaller diameter wires and hence copper losses increase too much. – Andy aka Jan 12 '15 at 12:59
• Is air gap solution too complex considering I'm not experienced with transformer design? Using already optimized EE19 core makes more sense to me after all your explanation. – cryptokovski Jan 12 '15 at 13:57
• You may also want to increase the switching frequency in an attempt to find a solution. But that increases other losses and may mean you have to change the IC, add external MOSFETs and so on... It all adds up to ... there's probably a very good reason why the original EE19 core was chosen. – Brian Drummond Jan 12 '15 at 14:14
• On one hand you have a requirement to use EE16 and, on the other hand you have your confidence level about applying an air gap. Add to this is the real dilemma of whether a gapped EE16 will ever work and you have a decision to make. Luckily, I don't have to make this decision!!! – Andy aka Jan 12 '15 at 14:15