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Old 26th January 2011, 05:45 PM   #1
Join Date: Oct 2010
Default SMPS Transformer Primary Turns Calculations


I found this formula helpful to any one who build SMPS.

It will calculate Turns for SMPS Transformer.

Primary And Secondary, look carefully before you enter values, cos it confuse.

* however, its as is as I found!

Good Luck
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Old 15th February 2011, 08:05 PM   #2
KlaRa54 is offline KlaRa54  Germany
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look here,
Dimensionierung von Schaltnetzteilen
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Old 15th February 2011, 08:11 PM   #3
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I also wish to design a transformer.
In my case, a toroidal will be used.
The input current is sinusoidal and the transformer will step up it 3x higher than primary voltage.
Kindly share if you know how to design it.
It's designed for 10kHz application.
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Old 10th January 2012, 08:01 PM   #4
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this formula is good for toroidal cores?
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Old 11th January 2012, 08:59 AM   #5
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OP's spreadsheet is worse than mine.

that said, it will work for toroids, just enter the core sizes that pertain to the proper dimensions. but the only useful math you'll get is the turns count.
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Old 12th January 2012, 04:39 PM   #6
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oops, your formula lookx complex also
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Old 14th January 2012, 07:00 PM   #7
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N = Vrms / (4.44 * F * B_max * A_e)

Easy to remember because 4.44 might be familiar from books on transformers, and if you keep track of the units, you can remember:

Vrms in volts
F in 1/sec
therefore, V / (4.44 * F) == Phi_max, peak flux

B_max in tesla == flux/area per turn (uV.s/mm^2.t are handy engineering units)

therefore, Phi_max / B_max = mm^2.t

Finally, divide by A_e of whatever core you're looking at to find number of turns. Alternately, if you want the area for a given number of turns, divide by turns instead to get A_e. This is handy when you need a large current and can only get a single turn foil winding to handle it.

1/4.44 comes from: 1/4 because the magnetic flux goes from zero at the voltage peak, up to its maximum value at the voltage zero crossing, hence only a quarter of the wave needs to be considered; 4/pi ~= 1.11 comes from the integral of the sine wave (this also shows up in choke-input rectifiers, because the average value of a full-wave rectified sine is pi/4 times the input peak); and sqrt(2) comes from the RMS to peak conversion for the sine wave.

For square waves, the factor is NOT 4.44, but 4.0 even, and the voltage is simply the applied squarewave voltage (Vrms = Vpk for a true square wave, so it doesn't matter). This applies most directly for forward converters at maximum duty cycle.

This also applies to half wave converters (forward/flyback) in CCM, with double the turns, because the flux only goes one way.

For more detail and complete transformer formulas, try this:
For any given core geometry, you can develop a rough formula relating a proportional dimension (like overall size) to an overall property (like core product, mm^4) to calculate, in one step, what minimum size core is required for a particular voltage and current capacity.

Inductors can be calculated in the same way, with the additional feature of gap length, which is calculated from desired inductance (in transformer design, the core's permeability is assumed high enough that the resulting inductance is not a concern for the user, i.e. load current is higher than magnetizing current).

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