Transformer's core size

[andre_luis]

Andre, what are the units for Ae? Square millimeters or square inches? Or square centimeters?

well-minded, it is in square centimeters.

 

[julian403]

well-minded, it is in square centimeters.

From where that formula came? How do you get to it?

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FvM you said

based on Bmax of about 1.2T and 90 percent core fill factor. Double number of turns for audio output transformers (25 Hz lower cut-off frequency).

Why did you use 1.2[T]? this is almost the max, bacause B saturation is on 1.5[T]. Do you means that's better to get almots the saturation field.?

 

[FvM]

Why did you use 1.2[T]? this is almost the max, because B saturation is on 1.5[T]. Do you means that's better to get almost the saturation field?

Tradeoff core losses against transformer size. Engineering is more than reading theoretical numbers and equations from a physics text book. Pushing Bpeak too high promotes also inrush currents during power switch-on. Transient volt-time product is up to double the periodical peak value.

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well-minded, it is in square centimeters.

Really? I see e.g. A = 10 cm² for a 150 VA transformer. With the 1/10,000 factor, it rather looks like m².

 

[andre_luis]

Really? I see e.g. A = 10 cm² for a 150 VA transformer. With the 1/10,000 factor, it rather looks like m².

I have to admit that at this moment I cannot detect the correct unit factor for the above formula, but I've used this for a design I made and it matched exactly with the cross sectional area of most commercial transformers.

Now by a reverse engineering based on my last design ( putting it in S.I. base unit ):

• A ≅ 6cm x 6cm ≅ ( 0.06 x 0.06 ) m² ≅ 0.0036 m²
• P = 1KVA = 1,000W

We have:

\[1,000 = \frac{\left ( 0.06\, \, \, x\, \, 0.06 \right )^{2}\, \, x\, \, \left ( K \right )^{2}}{\left ( 1.2 \right )^{2}}\]

And K is ~10,000, so you're right, the above formula is defined for meters and watts.

 

[julian403]

I have to admit that at this moment I cannot detect the correct unit factor for the above formula, but I've used this for a design I made and it matched exactly with the cross sectional area of most commercial transformers

Well that's what i means. Maybe we are using something we do not know where it came from. I want to know what I'm doing.

 

[andre_luis]

Maybe we are using something we do not know where it came from.

The core heating is the factor that limits the power rating of a transofrmer, and if you want to determine this by some kind of calculation ( estimate, rather ) you should at least have in hands the BxH curve to know the expected amount of losses within the core. In practice we just assume an effective B_sat for which temperature rises acceptably.

 

[FvM]

I want to know what I'm doing.

Then read electrical engineering text books dealing with transformer design and datasheet specifications giving core loss versus B.

 

[andre_luis]

In particular, take a look on how the EMF Equation was derived.

 

[c_mitra]

you should at least have in hands the BxH curve to know the expected amount of losses within the core. In practice we just assume an effective B_sat for which temperature rises acceptably.

Core loss per cycle due to hysteresis is proportional to the area of the hysteresis loop; hence power lost will be proportional to the area of the hysteresis loop and frequency (Steinmetz theorem)

 

[andre_luis]

Core loss per cycle due to hysteresis is proportional to the area of the hysteresis loop; hence power lost will be proportional to the area of the hysteresis loop and frequency (Steinmetz theorem)

Although the hysteresis loop would be the formal way to estimate the core losses on transformer, for the specific case discussed on this thread ( assumed pure 60Hz, Silicon steel lamination ), considering that there is no much variation on the magnetic properties of these materials, a simple formula/chart is the suited method for selecting the core size. We should also keep in mind that the bigger the core, the reduced ability to dissipate generated heat ( "Area/Volume" increases in a ratio smaller than '1' ).

I've used this formula for a design I made and it matched exactly with the cross sectional area of most commercial transformers.

Just a remark on that statement: Equipment which operate with reduced autonomy, such as UPS with limited capacity of the battery bank, some ones are manufactured with smaller transformers than we would expect for the rated load. Manufacturers take advantage of the fact that for a limited time, the core heat profile over time during battery discharge will not reach a critical temperature, and thus saving in material cost ( for power equipments, sometimes the core represents the more expensive part of the BOM ). Therefore, sometimes we cannot infer the transformer capacity of some equipament just by its size, as we usually do.

 

[julian403]

I was watching ferrita materials like this: https://www.ferroxcube.com/FerroxcubeCorporateReception/datasheet/3f3.pdf

Whats Pv parameter? It's the max power per volumen for the transformer?

 

[FvM]

Pv is specifying the core losses. Look at figure 6.

 

[julian403]

So, Pv determines the core size?

 

[FvM]

Let's say core losses determine the useable B for a given frequency which in turn sets the minimal core size for a specific transformer power.