# Current Density: Whether to calculate or use thumb rule in designing the ferrite core transformer

I am referring the book Transformer and Inductor Design Handbook[4E] by Colonel Wm.T.McLyman.
In which he has emphasised to calculate the current density, rather than using the thumb rule value of 3-6 Amps per millimetres squared.
Here is my design file .

• Problem is Frequency is low as well as my secondary current is also very low, such low that, skin effect wire area is coming to be far more than the wire area coming from calculated current density.
• Another problem is window Utilization Factor is not coming to in and around 0.29 within the designed ferrite core[ETD39].
My understanding:
• If i keep the current density calculated value , i have to use bigger core, to bring down K_u = 0.29.
• If i use thumb rule and use current density a higher value , i can fit even in smaller core like [ETD29].
• Temperature rise is way too little [1.4110]. I don't know if smaller core will increase it.
What should i do?

What should i do?

You'll see that there's no exact way actually, when it comes to practice. The way given in your textbook might be a general way providing safer solutions with big margins. I don't know. But what matters is whether the design requirements and targets are met or not.

You can go for either the proposed way for a guaranteed/safer solution, or your "thumb rule". At the end of the day, if

• Size requirements,
• Electrical requirements,
• Temperature rise requirements,
• Isolation requirements,
• Core and copper loss requirements,

and other (if any) requirements are met then no one cares which way you went for.

Here's what I personally follow in my designs:

Start with manufacturers' core selection tables based on power level, frequency and topology. If can't find a suitable core then go for area-product approach. If size is a limitation factor then consider increasing the switching frequency. But increasing the frequency brings another problems, and also it's not easy and possible to find a core material for every frequency range. So a compromise between something and something... For wire selection, start with 420A/cm² and take the skin effect into account depending on the RMS and DC current levels. Select the wires and see if the windings will fit in bobbin. Finally, get (or prepare) a few gold samples for the transformer and perform the initial tests.