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I am working on making a simple step-down transformer whose input will be 220V and output will be 12 V. The formula I have seen for calculating the turns per volt being calculated by the following formula: enter image description here

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I want to ask how to choose the value of the flux density. Some people say the flux density depends on the frequency and the emf as shown in the formula:

enter image description here

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Some say that it depends on the core material. I am confused regarding the selection of the core flux density value. Does that mean that for a single frequency we will have various flux density values depending upon the material. As the frequency changes then the flux density value also changes?? Kindly guide me

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I want to ask how to choose the value of the flux density.

Having paid good money for core material, we generally want to operate it as efficiently as we can. So we need to know what the limiting flux density is, and operate close to that.

There are two materials we generally meet, iron for low frequency mains transformers, and ferrite for high frequency switch mode power supplies.

Iron is easy. When operating at mains frequencies, only the Bmax matters, the losses are so low that it doesn't really get hot from hysteresis. The Bmax is fairly consistent for iron in the 1.5 T o 2.0 T region. Cheaper materials will have lower losses and higher Bmax. If you don't know what you've got, aim for 1.5 T max and you should be fairly safe. Cores that you can buy intended for mains use are only useable for mains frequencies, their laminations are not thin enough to manage eddy current losses for higher frequencies.

Ferrites have a Bmax, but their hysteresis losses are sufficient that when operating above a few 10s of kHz, core heating (proportional to frequency and flux squared) will limit the maximum flux useable. You will therefore see designs for ferrite transformers with maximum fluxes from 400 mT (for low frequency designs) down to sub 100 mT to cope with heating. Ferrite transformer design has more variables and tradeoffs than iron transformer design.

Once you've chosen a maximum operating flux and a frequency, then use the formula to get turns per volt. Make sure you use consistent units for the formula.

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